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CONSTRUCTING SUBJECT MATTER IN HIGH SCHOOL PHYSICS:
AN ETHNOGRAPHIC STUDY OF THREE
EXPERIENCED PHYSICS TEACHERS

presented by

Armando Contreras

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CONSTRUCTING SUBJECT MATTER IN HIGH SCHOOL PHYSICS:
AN ETHNOGRAPHIC STUDY OF THREE
EXPERIENCED PHYSICS TEACHERS

BY

Armando Contreras

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Teacher Education

1987

 

Copyright by
ARMANDO CONTRERAS

1987

ABSTRACT
CONSTRUCTING SUBJECT MATTER IN HIGH SCHOOL PHYSICS:

AN ETHNOGRAPHIC STUDY OF THREE
EXPERIENCED PHYSICS TEACHERS

BY

Armando Contreras

The purpose of this study was to examine the way in
which experienced high school physics teachers construct
subject matter in their daily interaction with students.
The goal of the study was to derive detailed accounts of how
teachers enact similar instructional units and topics as
they strive to communicate the information content imbedded
in them.

Data were gathered over a period of six consecutive
months of a school year using ethnograhic techniques:
participant observation, videotaping, document gathering and
teacher interviews. The study of the coherence of the three
teachers' discourses in an instructional unit on dynamics,
showed that experienced, qualified physics teachers differ-
entially construct subject matter by breaking the unit into
topics that may or may not be logically connected. Also,
analysis of the coherence of a common single topic, such as
Newton's Second Law, revealed that the teachers enacted a
series of logical successive steps that had different

antecedents and eventual usages throughout the discourse.

Armando Contreras

In addition to structural patterns in the way information
content was temporally and logically organized, there were
variations in the way teachers sequentially organized the
physical materials used in teaching the content.

The study has implications for practice and research on
preservice and inservice education and student learning.
Its main contribution to the language of teaching and
learning lies in the introduction of the notions of topic
and coherence, two constructs borrowed from discourse
analysis, as an alternative to interpreting subject matter
enactment. A second contribution is an extensive corpus of
datum in videotape formats that can eventually be used for
further' analysis and. teacher' practiceu In this sense,
inservice physics teachers can reflect upon their own
discourse when organizing subject matter, and in doing so,
make the changes they consider appropriate for students'
understanding. Also, perspective physics teachers, and
science teachers in general, can benefit from the strategies
used by more experienced teachers to organize similar
organic units and topics. The findings also direct
attention to the issue that a large cohort of high school
students are learning differently organized bodies of
knowledge under a common rubric. This suggestion has some
implications for those concerned with the assessment of the

knowledge students are constructing out of schooling.

ACKNOWLEDGEMENTS

The completion of the dissertation has been possible
thanks to the contribution of many individuals and insti-
tutions who throughout the entire process provided me with
the necessary support to successfully achieve this goal.

I would like to thank my Ph.D. program adviser,
dissertation director and friend, James Gallagher, for his
continuous support and ability to patiently listen and
actively engage in the generation of new ideas in science
education. It thank "Jim" for allowing me to work closely
with him, as a research assistant, in the IRT-Secondary
School Science Program from which the guiding questions of
this study emerged.

I would also like to thank my friend Frederick Erickson,
member of my guidance committee, from whom I learned the
foundations of ethnographic research. His contribution to
my work is clearly manifested throughout the entire body of
this dissertation. Thanks also to the other two members of
my guidance committee for their assistance and encouragement
along the way.

Christopher Clark continuously helped me to dialectically

reflect upon the data and the guiding questions as a way to

gain insight on how teachers ‘construct subject matter.
Edward Smith was an active and careful reader of my
manuscript and was always ready to ask provoking questions
that added to my understanding of the issues being raised.

My closest family also contributed to this final product.
Discussions with my wife Consuelo enlightened my own work by
providing’ me ‘with "daily life" experiences connected. to
research. My six year old daughter Indra constantly kept
asking questions about "deadlines" and "papers." She wished
to have more "time to play" and "learn to write."

I appreciate the help of the participant teachers of this
study denoted as Mr. Simon, Mr. Ellis and. Mr. Howard.
Because of the need to protect their right to privacy, I
cannot cite their real names and those of their schools and
students. To them my deepest appreciation for letting a
stranger study their teaching. Their contribution and daily
cooperation for more than six months made possible the
writing of the histories narrated in this study. To these
friends of mine, I dedicate this study.

My thanks to my typists and editors, JoAnn Lewis and
Linda Carroll for their prompt and effective work.

Finally, my appreciation goes to the Universidad Los
Andes (Venezuela), the institution that gave me the

financial support to attend Michigan State University.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . .
LIST OF FIGURES. . . . . . .
NOTES ON STYLISTIC CONVENSTIONS USED

CHAPTER ONE INTRODUCTION .
The Problem . . . . . .
The Research Questions.
Research Design . . . .
Purpose of the Study. . .
The Importance of the Study
Assumptions . . . . . . . .
Overview of the Dissertation

CHAPTER TWO INSTRUCTIONAL SEQUENCING OF

SUBJECT MATTER. . . . .
Introduction. . . . . . . . . .

IN THE TEXT

SCHOOL

Sequencing Instruction: An Educational

Psychological View. . . . . . .

Micro-Sequencing Versus Macro-Sequencing.

Micro-Sequencing . . . . .
Macro-Sequencing . . . . .
The Spiral Curriculum

Progressive Differentiation

Hierarchical Sequencing
Synthesizing Strategies

Networking . . .
Mapping. . . . .
Concept Mapping.
Summary. . . . . . . . . .

Sequencing as a Teacher Construct
Ethnography of Communication

Constructivist Perspective of Teaching .

A Constructivist Perspective of

Instructional Sequencing .
Discourse Analysis. .

The Topic of Discourse

Topic Boundaries .

The Notion of Texture,

and Coherence. .

vii

o 80 o o o

ohesion

xii
xiii

18
18

22
23
23
24
24
24
25
25
26
26
26
27
28
28
31

34
39
4O
42

43

TABLE OF CONTENTS, CONT'D.

Characterization and
Discourse Coherence.

Types of

Events in a Discourse. . . . . . .
Classroom Discourse and Academic

Content . . . . . . . . .

CHAPTER THREE THE CONDUCT OF THE INQUIRY: A GUIDE
TO STUDY SUBJECT MATTER (CONTENT-

KNOWLEDGE) IN PHYSICS CLAS
Introduction. . . . . . . . . . . .
Background of the Study . . . . .
Research Questions. . . . . . . .
Research Plan . . . . . . . . . .

Participant Observation. . .

Videotaping of Classroom Events

Interviews with Teachers . .
Analysis. . . . . . . . . . . .
Discourse Analysis and Selection of
The Corpus of Datum . . . . . . . .

CHAPTER FOUR CONTEXT FOR SUBJECT MATTER
AND SEQUENCING . . . . .
Introduction. . . . . . . . . .
The Schools and the Classrooms.
School 1 (Classroom 200) .
School 2 (Classroom 100)
School 3 (Classroom 150)

The Teachers. . . . . . . . .
Mr. Simon (Room 200) . . . . .

Mr. Ellis (Room 100) . . . . .

Mr. Howard (Room 150). . . . .

The Textbooks . . . . . . . . . . .
The Harvard Project Physics. .

The Physical Science Study Committee

Teachers' Planning. . . . . . . . .
Teacher's Conceptions of Planning .
Mr. Simon's Planning . . . . .
Mr. Ellis' Planning. . .
Mr. Howard's Planning. .
Summary . . . . . . . . . . .

viii

SROOMS.

pisodes

0 we 0 o o o o o

ORGANIZATION

’U
o 0 me o o 0
U)
o o o o o o no a o o

46
49

51

54
54
55
55
58
59
61
64
65
68
70

72
72
72
72
75
78
81
81
83
85
86
87
89
9O
91
92
93
94
97

TABLE OF CONTENTS, CONT'D.

CHAPTER FIVE SEQUENCING SUBJECT MATTER IN HIGH
SCHOOL PHYSICS . . . . . . . . . . . .
Introduction. . . . . . . . . . . . . . . . . .
PART I
Constructing a Macro-Sequence on Dynamics . .
Story-Lines on Dynamics. . . . . . . . .
Mr. Simon's Story-Line on Dynamics . . .
Interpretation of Mr. Simon's Story-Line
Mr. Ellis' Story-Line on Dynamics. . . .
‘Interpretation of Mr. Ellis' Story-Line.
Mr. Howard's Story-Line on Dynamics. . .
Interpretation of Mr. Howard's Story-Line .
Summary and Conclusions on the Theme
"Dynamics as Taught by Teachers . . . . . .
The Nature of the Global Coherence . .
The Nature of the Information
Content and Environment. . . . . . . .

PART II
Constructing a Micro-Sequence on Newton's
second Law 0 O O O O O O O O O O O O O O O O O 0

Mr. Simon's Discourse on Newton's Second
Law . . . . . . . . . . . . . . . . . . . .
Discussion of Mr. Simon's Micro-Sequence
on Newton's Second Law. . . . . . . . . . .
Mr. Ellis' Discourse on Newton's Second Law
Discussion of Mr. Ellis' Micro-Sequence
on Newton's Second Law. . . . . . . . . . .
Mr. Howard's Discourse on Newton's Law. . .
Discussion of Mr. Howard's Micro-Sequence
on Newton's Second Law. . . . . . . . . . .
A Comparative Analysis on Newton's Second
Law as Taught by Teachers . . . . . . . . .
Connecting Newton's Second Law to
Previous Topics. . . . . . . . . . . .
Topic "Closing" or Termination . . . .
The Structure of the Information
Content. . . . . . . . . . . . . . . .
Information Content and Environment. .
Results and Conclusions on Newton's
Second Law. . . . . . . . . . . . . . . . .

ix

98
98

100
100
101
120
124
152
155
198

181
182

193

198

201

210
214

227
230

241

243

244
246

248
252

257

TABLE OF CONTENTS, CONT'D.

CHAPTER SIX OVERVIEW, CONCLUSIONS AND IMPLICATIONS

FOR PRACTICE AND RESEARCH. . . .
Overview . . . . . . . . . . . . . . . .
Conclusions. . . . . . . . . . . . . . .
Implications for Educational Research and
Practice: Preservice, Inservice Teacher
Education and Student Learning . . . . .

Preservice Teacher Education.
Inservice Teacher Education .
Student Learning. . . . . . .
Implications for Further Research.

APPENDIX A MR. SIMON'S "UNIT PLAN" ON DYNAMICS .
APPENDIX B MR. SIMON'S WORKSHEET ON NEWTON'S LAWS.
APPENDIX C MR. ELLIS' UNIT PLANNING ON DYNAMICS. .
APPENDIX D MR. ELLIS' EXPERIMENT SHEET ON NEWTON'S
SECOND LAW. . . . . . . . . . . . . .
APPENDIX E GRAPH OF VELOCITY VERSUS TIME: "GALILEO
COASTING" . . . . . . . . . . . . . . .
APPENDIX F GRAPH OF VELOCITY VERSUS TIME: ONE AND
TWO BRICKS PULLED BY A RUBBER BAND. . .
APPENDIX G GRAPH OF ACCELERATION VERSUS FORCE
(MASS CONSTANT) . . . . . . . . .
APPENDIX H GRAPH OF ACCELERATION VERSUS INERTIAL
MASS (FORCE CONSTANT) . . . . . . . . .
APPENDIX I GRAPH or PERIOD VERSUS INERTIAL MASS .
APPENDIX J THE FLASH PHOTOGRAPHS: FORCE AND
ACCELERATION. . . . . . . . . . .
APPENDIX K MR. SIMON'S WORKSHEET ON NEWTON'S
SECOND LAW EXPERIMENT . . . . . .
APPENDIX L HANDOUT 32: NET FORCE AND ACCELERATION
APPENDIX M TRANSCRIPTION CONVENTIONS . . . . . . .
BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . .

266
266
269

276
277
280
281
283
287
289
292
293
294
295
296

297
298

299
301
303
307

308

LIST OF TABLES

ab e Page
5.1 Topics Delivered by Individual Teachers

on the Theme Dynamics . . . . . . . . . . . . 183
5.2 Mr. Simon's Enacted Topics and Physical

materials 0 O O O O O O O O O O O O O O O 0 O 194
5.3 Mr. Ellis' Enacted Topics and Physical

materials 0 O O O O O O I O I O O I O O O O O 194
5.4 Mr. Howard's Enacted Topics and Physical

materials 0 I O O O O O O O I O O O O O O O O 195
5.5 Mr. Simon's Discourse Segment on Newton's

Second Law. . . . . . . . . . . . . . . . . . 203
5.6 Mr. Ellis' Discourse on Newton's Second

law 0 O I O O O O O O O O O O O O O I O O O 0 215

5.7 Mr. Howard's Discourse on Newton's Second
Iaw O O O O O O I O O O O O O O O O I O O O O 232

xi

LIST OF FIGURES

The two dimensions of events in a discourse
Floor map Of classroom 200. . . . . . . . .
Floor map of classroom 150. . . . . . . . .
Floor map Of classroom 100. . . . . . . . .

Chronology Of major topics and activities
in Mr. Simon's sequence on dynamics . . . .

Mr. Simon's macro-sequences on dynamics . .

Chronology Of major topics developed in
Mr. Ellis' macro-sequence on dynamics . . .

Mr. Ellis' macro-sequence on dynamics . . .

Chronogram Of major topics and activities
in Mr. Howard's macro-sequence on dynamics.

Mr. Howard's macro-sequence . . . . . . . .

Temporal representation Of Mr. Simon's
micro-sequence on Newton's Second Law . . .

Temporal representation Of Mr. Ellis'
micro-sequence on Newton's Second Law . . .

Temporal representation of Mr. Howard's
micro-sequence on Newton's Second Law . . .

Micro-sequence structures on Newton's
Second Law compared . . . . . . . . . . . .

xii

77

79

102

121

125

153

156

179

212

229

243

250

NOTES ON STYLISTIC CONVENTIONS
USED IN THE TEXT

This study is an ethnographic research to learn about
how experienced teachers organize subject matter. To gather
the data and make the proper references with respect to this
question, the researcher established a close and personal
relationship with teachers and students. Because of this,
the necessary steps have been taken to protect anonymity of
those involved. Pseudonyms have been used throughout this
study, to protect the privacy Of students and teachers.

Throughout the body of this dissertation, quotation
marks (" ") have been used to indicate the exact words of the
speaker. If the quotation was longer than five lines, it was
typed in the block format. These quotations are generally
followed by a notation indicating the source and the date;
for example, fieldnotes, September 22, 1986 means the
quotation was "pulled out" from the fieldnote set taken on
September 22, 1986. In the case of long discourse segments
from videotape transcripts, the source is generally iden-
tified at the beginning of the transcript, using the
following items: teacher's name, topic, time frame and date.
(Details of specific notations used in the transcripts are
given in Appendix K.) There are a few places in study where
it was necessary to paraphrase what the speaker was saying.

In those cases, the single quotes (' ') was used instead.

xiii

CHAPTER ONE

INTRODUCTION

The purpose of this introductory chapter is to provide
the reader with a general overview of the study. It pro-
vides a brief description of the nature of the problem,
followed by a description Of the questions addressed, and a
summary Of the research methodology. Also, the assumptions
made in the study are given as well as a summary. The

chapter ends with an overview of the dissertation itself.

W

As the title of this study suggests, teachers in their
daily interaction with students, books and other instruc-
tional materials, enact subject matter as they select the
"academic work" (Doyle, 1983) students are expected to do.
Through these instructional processes, students acquire
information, and learn the skills necessary to assimilate
such information.

The purpose of this study was to research the nature of
teacher interaction in order to describe how school subject
matter is enacted in real time. The study Of the subject
matter (i.e., what is taught and how it is taught) is a

common concern among policy makers (Bybee, Carlson &

McCormick, 1984; National. Research. Council, 1985; Holmes
Group, 1986), and educational researchers (Doyle, 1983:
Erickson, 1982; Buchmann, 1983) for it has profound
consequences on what students are learning: the fundamental
reason for schooling. Buchmann (1983) highlighted the
importance of subject :matter' when. she ,pointed out that
"content knowledge is a logical precondition for the
activities Of teaching; without it, teacher activities such
as asking questions or planning lessons hang altogether in
the air" (p. 23).

One aspect Of concern with respect to school subject
matter is how it is organized and accomplished. in the
classroom (Doyle, 1983). A second concern is learning how
to construct and enact subject matter for meaning (Doyle,
1986). Researchers agree that these topics have been
neglected in contemporary empirical studies on research on
teaching and learning -- specifically, in research studies
that focus on the nature of teacher interactions (Cazden,
1986; Erickson, 1986b). Teacher interaction can be seen as
having twO major functions (Lemke, 1982b: Erickson, 1982a).
The first major function is to produce and maintain the
social roles that are appropriate and expected from the
participants in a Classroom setting such as asking
questions, lecturing, working in groups, etc. (Mehan, 1979;

Florio, 1978). A second function is to construct the

content of the subject by tying together different pieces
of knowledge as organic units in the form Of themes or
topics (Lemke, 1981a: Stubbs, 1981). In a recent review on
classroom discourse, Cazden (1986) indicated that studies
pertaining to the nature Of the relationship between class-
room social structure and the school academic content are
still rare. Generally, studies of classroom discourse have
focused on the social structure of the class and. have
ignored the subject matter content being communicated in the
discourse. Erickson (1982) acknowledged that subject matter
has been neglected in his research when he pointed out that,
in his Observation of arithmetic classes,

There were descriptions of social relations that

were partly constituted by subject matter (by its

logic of sequencing) and by the cues present that

pointed to the sequential steps in task comple-

tion, yet my notes contained no mention of the

actual subject matter content. What appeared in

the notes were data about turn-taking patterns in

conversations, the exercise of social control by

the teacher, cultural patterns in the children's

speech and nonverbal behavior. There was rela-

tively little reference to what the teacher and

the students were talking about and taking turns

at or to the instructional aims toward which

social control was being exercised. (p. 157)

Erickson's assertion has a parallel within research
traditions that focus on the measurement Of teachers'
characteristics and instructional program effectiveness. As
Doyle (1983) argued, school subject matter has been

neglected in contemporary research at the expense of studies

on topics such as amount of praise, the frequency and types

of questions, time spent lecturing, ways of providing feed-
back and reinforcement, student perceptions and behaviors
and cognitive Operations.

A second set of concerns is how different teachers
enacted and organized subject matter across different
disciplines and within a single discipline. As early as
1973, Shulman and. Tamir' pointed out that sequencing of
subject matter had been a "disappointing variable" in
science education research due to the limited way in which
that variable had been "experimentally manipulated." These
authors hypothesized the existence Of four different ways in
which one could look at content organization and sequencing
in a particular discipline: (a) the order in which the
elements of instruction are presented within a single
lesson; (b) the order in which lessons are sequenced within
an instructional unit: (c) the order in which units are
sequenced within an instructional term; and (d) the order in
which instructional programs are sequenced and/or correlated
across a multi-year curriculum. Shulman and Tamir (1973)
pointed out that most empirical studies were of the first
type, i.e., the study of single lessons, while the other
three remained relatively "innocent of empirical trammeling"
in spite of their importance for curriculum planning and
development. More recently, in a review Of research from

the Institute for Research on Teaching, Porter and Brophy

(1987) reinforced a similar assertion when they pointed out
that:

Research tends to look at teaching in small

segments, typically concentrating only on

particular lessons taught within one subject
matter area. Mbre attention needs to be focused

on larger units of instruction and on what is

required to teach effectively all day, every day,

year after year. (p. 23)

The study Of subject matter knowledge through time and
across different disciplines and teachers, as well as within
specific disciplines, can provide us with multiple ways Of
teaching a topic or set of topics (Shulman, 1986).

This leads us to the third major concern: the teaching
of school disciplines, such as physics, which have a
"logical grammar" (in Hirst's sense) that need to be
respected when the discipline is enacted. As Hirst (1974)
stated, "this logical grammar involves an order of terms
such. that the 'meaning Of certain terms presupposes the
meaning Of others" (p. 129). For example, the meanings Of
"acceleration" and "momentum" presuppose the meaning of
"velocity." In this case, as Hirst (1974) argued, "the
teaching Of the subject must of course respect these
elements of logical order" (p. 129). What the above
discussion suggests is that teachers can approximately
construct different logical sequences and strategies to

teach subject matter as long as they adhere to the logical

grammar imbedded in it.

The study of the enactment content organization and
sequencing in school physics (the focus of this study) is a
topic that has not been fully explored in contemporary
research on teaching as inferred from recent reviews of
literature in the natural sciences (White & Turner, 1986;
Gallagher, 1987). Research on science teaching, instead,
has focused on issues dealing with preinstructional
strategies (e.g., use of advanced organizers), interaction
and control in the classroom and the role of questions
(e.g., questioning skills, wait time, etc.). The problem of
what is actually' taught in school physics becomes more
critical in the content of high school physics1 since it is
here that most students encounter, for the first time in
their lives, the "logical grammar" (Hirst, 1974) Of physics
knowledge. Thus, what they learn here and how they are
taught may have profound consequences on their future
academic life.

TO sum up, there is a need to study classroom
interactions in order to learn about how high school physics
teachers enact subject matter; and communicate the

information content imbedded in the instructional events.

 

1High school physics is usually regarded as one Of the
most difficult subjects by students. According to Pallrand
and Lindenfeld (1985), only 3 percent Of the high school
population (in U.S.A.) is exposed to this discipline.

The Research Questions

The research questions that guided this study revolved
around one very broad question: How do experienced physics
teachers organize subject matter? Out of this question,
three sets‘ Of more specific questions emerged as the
research study proceeded. According to Erickson (1986a) ,
research questions can be "reconstructed in response to
changes in the fieldworker's perceptions and understanding
Of events and their organization" (Erickson, 1986a:121)
while in the process of conducting the research. In this
sense, in trying to understand and interpret how subject
matter was enacted by experienced teachers, several issues
initially emerged.

The first one was the study of classroom interaction
and discourse sequencing. As Stubbs (1981) indicated:

By studying discourse sequencing, one can study in
empirical detail how teachers select bits of
knowledge to present to pupils; how to break up
topics and order their presentation; how these
discrete items Of knowledge are linked: how
distinct topics are introduced and terminated; how
pupils' responses to questions are evaluated: how
pupils are made to reformulate their contribu-
tions; how bits of knowledge are pieced and
allowed to emerge when the teachers consider it
appropriate. I cannot see how such topics could
be studied, other than in an ad hoc way, by
looking at isolated utterance by or features Of
language. But by studying the overall structure
Of the teacher-pupil interaction as a discourse
system, these topics are inevitably studied. (p.
128)

Stubbs' insightful statements, undoubtedLy brought up
important methodological strategies concerning the method Of
studying structure Of subject matter by researching
teacher's discourse sequencing and, specifically, the nature
Of the discourse coherence within topics and across topics.
The second issue that emerged, which also shaped the nature
of the guiding questions, dealt with the proper "inter-
pretive framework" (Erickson, 1986a) to explain the nature
Of the subject matter being enacted in those events.
Erickson (1982) proposed a constructivist view Of subject
matter organization, according to 'which, there are four
aspects that define the academic task structure in a lesson:
(a) the logic Of subject matter sequencing: (b) the
information content Of the various sequential steps; (c) the
"meta-content" cues toward steps and strategies for com-
pleting the task: and (d) the physical materials through
which tasks are manifested and accomplished.

Drawing from knowledge on discourse analysis (as
suggested by Stubbs, 1981) , from Erickson's constructivist
view Of subject matter, as well as from the researcher's
understanding of the events under' study (i.e., physics,
classroom interactions), the set of research questions was

eventually established as follows:

1. What is the nature of the coherence (global)2 Of
the subject matter information content in the unit
on dynamics as taught by three high school physics
teachers?

2. What is the nature of the coherence (local)3 of
the information content delivered in a single
topic (a part Of the unit on dynamics) as taught
by three high school students physics teachers?

3. What is the nature Of the enacted task environment

through which topics are delivered?

Research Design

The study of teacher interaction to make inferences
about subject matter organization required the use Of
ethnographic techniques for data collection and analysis.
For six consecutive months, the researcher attended three
high school physics classrooms. Each classroom was visited
daily. Several strategies were used to gather information
on subject matter organization in high school physics. They
included: participant Observation, interviews with
teachers, document gathering, and videotaping.

During six months Of "participant observation"
(Spradley, 1980), this researcher described, via fieldnotes,

the nature of the classroom interactions in the three

 

2I3The notions Of global and local coherence have been
adopted from Van Dijk (1985) and Agar and Hobbs (1985).

10

participating physics classrooms. During the initial phases
of the research, emphasis was placed on the social structure
of the class -- getting to know what role teachers and
students played and how these roles were exercised. Also,
emphasis was made on the description of the physical
environment (classroom, physics equipment, textbooks, etc.)
in which interactions took place. As the research progres—
sed, the fieldnotes focused. more on 'the subject. matter
content and specifically on how teachers planned for it, and
eventually enacted the relationships between different
topics. Special attention was paid to events such as:
lecturing, laboratory activities, classroom demonstrations,
homework and reading activities. Early analysis of these
fieldnotes already indicated that there were variations in
the way physics teachers structure similar topics.

Teachers were interviewed frequently -- formally and
informally. Informal interviews yielded relevant inform-
ation dealing with issues such as planning for the next day
(i.e., what is tomorrow's topic and how will it be han-
dled?), difficulties encountered by teachers in teaching a
particular lesson or sequence of lessons and teachers'
perceptions Of students' understanding. These interviews,
most of which took place during class breaks, proved to be
very helpful in the comprehension Of unclear statements made

in the fieldnotes which needed further clarification. More

11

formal interviews were conducted in order to gather
information about the teachers' perceptions on planning for
teaching and subject matter, as well as on the actual
enactment of these plans. These formal interviews focused
on the topic being selected for further analysis (i.e.,
dynamics). They took place several days after each
individual teacher had formally concluded with the target
unit Of analysis.

Apart from the fieldnotes and interviews, the
researcher also gathered information about subject matter
sequencing through classroom documents. Most documents used
by students were carefully filed and noted accordingly in
fieldnotes. Documents included such items as quizzes,
worksheets, laboratory reports, handouts, assignments and
textbooks. These curriculum materials are important tools
in science classes as they influence the nature of the
scientific explanation during teacher-student verbal
interaction (Roth, Anderson and Smith, 1986) . Though not
all Of these documents were considered as part of the final
analysis in this study, some Of them proved to be key
elements in the description Of how physics teachers convey
information to students. It was noticed that laboratory
reports, handouts and worksheets contained important clues
and strategies used by teachers in the process of

structuring such information.

12

The fourth source of information on which these studies
relied was videotapes. After properly "negotiating entry"
(Erickson, 1986a) with teachers, it was possible to video-
tape most of the events that surrounded the teaching Of an
instructional unit on dynamics as taught by the three
participating teachers. The transcripts from this video-
taping’ gave detailed accounts as to 'what. teachers (and
students) said with respect to specific topics imbedded in
the teaching of dynamics (see Chapter Three for more
details).

The above-mentioned data gathering process yielded an
enormous amount of information for analysis. A decision was
made to analyze the physics unit on dynamics. The decision
was ‘based on the importance Of such a theme in the high
school curriculum3 and the extent to which it is taught.
The entire unit on dynamics was videotaped in each of the
physics classrooms. The study Of how teachers organized
the theme on dynamics was carried out through a discourse
analysis conducted at two levels: first, at a macro-level
to see how different topics fit together; and second, at a
micro-level to see how the elements of a single topic are

coherently connected.

 

3All high school physics books include this theme (see
Pfeiffenberger & Wheeler, 1984).

13

Purpose Of the Study

The main purpose Of this study was to learn about how
experienced physics teachers structure subject matter in
their daily classroom interaction. To achieve this purpose,
the following specific objectives were considered:

1. To describe, via "story-lines" (Erickson, 1982)

how a selected group Of experienced physics
teachers link the different topics included in a
unit Of instruction.

2. To describe how teachers' discourses on a common
topic compare in terms of the information content
being delivered.

3. To describe the nature of the environment through
which topics are actually delivered by teachers.

4. To interpret the findings Of the study, including
an assessment of the implications these findings
have for further research and staff development.

Descriptions and interpretations Of this nature are
important when it comes to inform decision makers about
teaching practices as they naturally occur in classrooms
(Zumwalt, 1986). Zumwalt argued for the need to inform the
deliberation Of teachers, and to encourage similar inquiry
from them. As has been suggested by several researchers
(Erickson, 1986b; Shulman, 1986; Clark, 1987), ethnographic

descriptions of cflassroom events can be appropriately used

14

as a means for staff development and for the improvement of
the teaching profession by having teachers reflect upon

their own practices or their peers' practices.

The Importance of the Study

This study was conducted to generate knowledge which
might prove useful to practicing teachers, prospective
teachers, policy makers and educational researchers. The
study describes a history of events (Erickson, 1982) on how
three experienced teachers sequentially organized the
subject matter imbedded in a unit of dynamics. Each
account represents a separate case study that may be used
independently by interested parties to study the strengths
as well as the weaknesses of the subject matter organization
as enacted by the participating teachers.

In addition, the study aims at contributing to the
research literature of subject matter sequencing from the
teachers' perspective. The study's main contribution to the
literature lies especially in the development of a
methodology to describe how practicing teachers actually
construct subject.:matter' in.‘their' day-to-day' interaction
with students and classroom materials such as books, lab

equipment, etc.

15

Assumptions

Several major assumptions are made throughout this
study. These assumptions reflect the nature of the inter-
pretive framework of the study as well as the nature Of the
methodology being employed. The first major assumption is
that the teachers investigated have some knowledge they
share and that this knowledge has important consequences for
how their actions are interpreted (Magoon, 1977). This
knowledge (school knowledge) is "purposive" (Magoon, 1977)
and as such it possesses some degree of organization and
complexity. A second major assumption is that the knowledge
enacted in classrooms is context specific. In this sense,
"What people are doing and where and when they are doing it"
(Erickson & Schultz, 1981) changes from moment to moment and
from place to place. This leads us into the third assump-
tion: the primary concern Of interpretive-ethnographic
research is particularizability rather than generaliz-
ability. "One discovers universals as manifested concretely
and specifically, not in abstraction and generality"
(Erickson, 1986a:180). In this sense, the study focuses on
particular cases (e.g., three experienced teachers teaching
a "unit on dynamics," or even more specifically "Newton's
second law") so as to generate knowledge on the nature Of

the enactment Of subject matter in high school physics.

16

Overview Of the Dissertation

This dissertation contains six major sections. Chapter
One provides an introduction Of the basic study problem and
the research questions. Chapter Two contains a review Of
literature related to the theme Of the study. The first part
Of Chapter Two describes some Of the most common sequencing
strategies (macro-sequencing and micro-sequencing) derived
from the work Of contemporary educational psychologists such
as Ausubel, Bruner and Gagne, etc. The second part Of Chap-
ter Two introduces a "constructivist" notion of sequencing
derived from theoretical constructs in discourse analysis
and ethnography Of communication.

Chapter Three presents an account Of how the study was
accomplished. It includes a background of the study, the
initial and final research questions and the research
methodology including data collection techniques and
analysis.

Chapter Four describes the nature Of the context in
which the present study was conducted. This chapter
describes the classrooms ‘where the actions of the case
histories took. place, the teachers, the ‘textbooks Ibeing
used, as well as a description of the teachers' conceptions
Of planning. This also includes a brief discussion of how
the three participant teachers planned the unit on dynamics

on which this study eventually focused its analysis.

17

The next section, Chapter Five, addresses the main
questions Of the study. The chapter is divided into two
interrelated parts. The first part introduces a macro-
analysis of each one Of the teacher's discourses on
dynamics. The data are presented in the form of "story-
lines" which detail information on how teachers sequentially
enacted the theme of dynamics through their interaction with
the immediate environment. Both the nature of the
information content as well as the environment are compared.
A similar study is done through a micro-analysis Of the
teachers' discourse on Newton's second law.

In Chapter Six, the dissertation concludes with a
discussion Of implications of the study for further research

and for practice.

CTLXPTER.TVWO

HWSURLKHHINQAL.SECNflENCTNCiCH:
SCHOOL SUBJECT MATTER

Introduction

The purpose Of this chapter is two-fold: first, it
Offers a review Of instructional sequencing from a psycho-
logical theory viewpoint; and, second, it presents an
alternative view which asserts that instructional sequencing
is socially constructed by teachers and students in their
everyday classroom instruction.

Sequencing Instruction:
An Educational Psychology View

HOW’ academic work is organized. and. accomplished in
elementary and secondary classrooms has been an area of
relatively new concern in educational research (Doyle,
1983), as it has a direct influence on what students are
actually learning. The students' academic work is deter-
mined by the type Of academic tools imbedded in the everyday
classroom school context, the way information (facts, con-
cepts and principles) is organized, and by the type of
Operations needed to achieve the goals demanded by the tasks
(Doyle, 1983, 1986). This section focuses primarily on the
second aspect (i.e., how information is organized by
teachers for learning to take place). Specifically, it

18

19

deals with the order in which content presentation is
organized (sequenced), the kind of content relationships,
and the way content relationships are taught.

The review follows the same line of reasoning as that
developed. by Van Patten et a1. (1986) with respect to
classroom content sequencing and synthesizing. In a recent
review of literature, the authors focused on two fundamental
questions: (a) how should. the instructional events be
sequenced over time, and (b) how should the interrelation-
ships among different ideas and concepts be taught (syn-
thesis). The bottom line of these two questions is that
knowledge Of instructional strategies for sequencing and
synthesizing can help teachers to properly break the subject
matter into small pieces, teach them accordingly and
eventually pull them together according to the nature of
their relationship (Van Patten et al., 1986).

Instructional strategies for sequencing (and
synthesizing) deal with two questions: What is to be
sequenced and how is it to be sequenced? (Van Patten et al.,
1986) . With respect to the first question, these authors
pointed out the existence of two different views. One view
argues in favor of factor sequencing the response and
performance Of the learner, and. that. relevant. concepts,
principles and procedures should be appropriately organized

into the sequence in order to attend to students' responses.

20

The second view indicated that content should be sequenced
and. that learners' responses should. be included in the
sequence to assure a mastery of the content under study.

With respect to the second question: How are content
or response to be sequenced?, there are different ways to
organize the elements of an instructional sequence. Hirst
(1974), for example, identified three principles: logical,
psychological and historical. Tyler (1950) indicated the
existence Of four organizing rules, logical, psychological,
chronological and part to whole. Thomas (1963) recognized
five rules for organizing instructional sequences: known
to unknown, simple to complex, concrete to abstract,
Observation to reasoning and whole to detailed.

Posner and Strike (1976) proposed a scheme to
specifically organize subject matter content. The scheme
identified five types of principles that can. be either
empirically or logically based. These authors described the
set of principles as follows:

1. World-related principles (based on space, time and
physical attributes) that yield world-related
sequences in which, "there is consistency among
the ordering Of content . . . and relationships
between phenomena as they exist or occur in the

world" (Posner & Strike, 1976).

21

Concept-related principles based on class
relations, propositional relations, sophistication
level and logical prerequisites. These principles
determine concept related sequences that reflect
the organization Of the conceptual world. Exam-
ples of these instructional sequences are found in
curricula that focus on "the structure and the
discipline" such as PSSC physics, BSCS biology,
etc. (Posner & Strike, 1976).

Inquiry-related principles that focus on how
propositions and concepts come about. The
instructional sequence derived from these prin-
ciples are based on the "nature Of the process of
generating, discovering, or verifying knowledge"
(Posner & Strike, 1976).

Learning-related principles are based on how
students learn as a function of pre-requisites,
familiarity, difficulty, interest, inter-
realization, and development. These principles
result in learning-related content sequences that
draw primarily from knowledge about the psychology
of learning. The work of Gagne (1977) and Ausubel
(1964), as applied to curriculum development and

planning, falls into this category.

22

5. Utilization-related principles that focus on how
the learner utilizes the content once he has
learned it. The instructional sequences that
result from these principles generally deal with
three possible contacts: social, personal and
career. SO, the content is organized according to
the "personal needs" Of the learner (Posner &
Strike, 1976).

It is important to stress that Posner and Strike (1976)
do not advocate the idea that only one type of principle is
useful to create instructional sequences, rather, they
indicate that highly sophisticated sequences can result when

combining different sets Of principles.

Micro-Sequencing Versus Macro-Sequencing

Two types of instructional strategies have been
identified to guide teachers and curriculum designers in the
sequencing Of classroom content: micro-strategies and
macro-strategies (Reigeluth & Merrill, 1979). Macro-
strategies are used to organize skills and knowledge into
lessons, and to structure content ideas. Micro-strategies,
on the other hand, are used to teach individual ideas and to
structure the teaching Of individual facts, concepts, prin-
ciples and procedures (Van Patten et al., 1986). Basically,
micro-strategies differ from macro-strategies in the sense

that the former deals with a wider range of concepts and

23

ideas while micro-strategies are related to the teaching of
one concept or idea at a time. In what follows, these two

ideas are explained in more detail.

Micro-Segpencing

Merrill et a1. (1979) pointed out that the "grist" of
instruction is composed of two main elements: generalities
and instances. A generality is a definition or rule whereas
an instance is a particular example Of that rule. These
authors suggested that generality and instances can be pre-
sented to the students in two ways: expository (e.g., here
is an example of . . .) or inquisitory (e.g., is this an
example of . .. .). The combination of these two forms Of
presentation gives rise to four different "primary presen-
tation forms for microsequencing: (a) generality in an
expository form, (b) generality in an inquisitory form, (c)
instance in an expository form and (d) instance in a
requisitory form" (Van Patten et al., 1986).

Merrill et a1. (1979) also suggested a sequence of
events to teach simple topics or general rules. First,
present the generality or rule; second, introduce example;
and third, give more practice (feedback). Van Patten et al.
(1986) identified other principles commonly used for the
selection and sequencing of instances in instruction. These
authors argued that a micro-sequence can be organized as

follows: (a) matching examples versus non-examples, (b)

24

selecting successive divergent examples, and (c) selecting

examples according to their degree Of difficulty.

Macro—Sggpepcing

There is a variety of theoretical prescriptions for
sequencing a set of concepts, generalities and rules. Some
of these instructional strategies include: (a) the spiral
curriculum (Bruner, (1960), (b) progressive differentiation
and. advance. organizers (Ausubel, 1968), (c) Ihierarchical
sequences (Gagne, 1977), (d) elaboration (Reigeluth & Stein,
1983), (d) backward chaining (Gilbert, 1962), (e) snowball
(Landa, 1974), etc. The first. three have been widely
implemented by curriculum designers and will be briefly

discussed below.

The Spiral Curricula

Bruner (1960) suggested that a specific concept can be
taught to students in a gradual manner, according to their
intellectual development. The fundamental ideas of a dis-
cipline, according to Bruner, can be structured and taught
at each school grade level but with an increasing level Of

difficulty (in a spiral format) as the school grade goes up.

Prpgressive Differentiation

Ausubel's (1968) major assumption was that learners
"subsume" detailed and specific information under more

general and inclusive types Of information. He suggested a

25

general to detailed top-down sequence in which the more
general and inclusive ideas (advanced organizers) are
presented first to the learner, followed by more specific
related ideas which are "anchored" to the advanced
organizers and which they themselves act as organizers to

the material to come.

flierazchical Segpencing

Gagne's (1968) theories that content can be broken into
components which then can be taught in a hierarchical manner
following "part to whole" or "simple to complex" are

organizing principles.

Sypthesizing Strategies

Synthesis is considered to be a macro-sequencing
instructional strategy rather than a micro-strategy. It
indicates the way content relationship should be taught (Van
Patten et al., 1986). The idea of synthesis, in this sense,
is related to what is commonly referred to as the content or
structure Of the discipline. As Bruner stated, "grasping
the structure Of a subject is understanding it in a way that
it presents many other things to be related to it meaning-
fully (Bruner, 1960, p. 7). The structure Of a subject (or
synthesis) indicates how concepts are logically related. It
is considered to be an efficient tool for learning as well

as an important aspect of the content of the discipline in

26

its own right (Schwab, 1962). Several strategies have been
proposed in the literature to synthesize the concepts,
procedures, and principles of a discipline. Some Of the
most well-known strategies include: networking, mapping and
concept mapping.

Marking

Networking has been suggested as an instructional
strategy to effectively teach content relationships.
Network models have been suggested by Rumelhart, Lindsay and
Norman (1972), and Bobrow and Winograd (1977), among others.
The basic idea is that a network can identify the most
important ideas in a text and describe the interrelation-
ships among ideas in the form of a diagram using nodes (for
concepts) and links (for relationships) (Van Patten et al.,
1986).

HAPPEN:

The idea of mapping (a text) was suggested by Hanf
(1971). This is a technique for organizing the structure of
a text in which the main task consists of having the reader
(teacher or student) first searCh for the main idea Of the
text, then locate the secondary ideas and connect them
accordingly to the main idea.

22W

The idea of concept mapping is widely used by current

researchers in science education. This idea is theoretical-

27

ly based on Ausubel's notion of learning (Novak & Gowin,
1982: Moreira, 1979). A concept map can be defined as a
two-dimensional diagram representing the conceptual
structure of a unit (or topic) of subject matter. It shows
a "top to bottom" fashion in different elements (concepts,
principles and examples, etc.) of the synthesis. The
different elements are logically linked by lines. This
strategy is usually used to identify students' conception as

well as students' learning of relationships among concepts.

Summapy -— Segpencing Instruction

The preceding review describes some Of the main ideas
concerned with strategies for sequencing and synthesizing
subject matter. Researchers seem to agree that the role of
sequencing needs to be further explored and that new models
need to be developed and tested (Van Patten et al., 1986).
One of the major Obstacles for effective research on sequen-
cing is the lack of a precise and consistent terminology
among researchers. Several models have been proposed by
specialists in the field. Of' educational psychology, but
little empirical research has been carried out as to how
curriculum designers and teachers actually sequence and
synthesize a unit Of instruction.

The previous account shows a normative approach towards
research on sequencing and synthesizing. It indicates how

instructional sequencing "should be" conducted and carried

28

Out, instead of how that strategy is actually enacted in
real life. The purpose Of the following discussion is to
present a theoretical framework that will be used to
conceptualize how an instructional sequence is constructed

by the participants in a classroom setting.

Sequencing as a Teacher Construct

This section. Offers an alternative view towards
conceptualizing instructional sequencing. This conceptual-
ization draws on theoretical constructs from linguistics
(discourse analysis), and ethnography Of communication. The
model derived from ‘these disciplines and its analytical
methods suggests that an instructional sequence is socially
constructed as teachers and students interact and as they
engage in daily classroom practices dealing with academic
content. The model proposed follows a constructivist
perspective as opposed to a psychological one. First, we
will focus on a constructivist view of teaching; and second,
we will discuss a constructivist view of instructional
sequencing based on the work Of Kelly (1955), Yorke (1987)

and Erickson (1982).

Ethnography pf Communicahiop

Consistent with a constructivist view of the world are
the methods and assumptions of ethnography Of communication.

This research tradition derives from work in sociolinguis-

29

tic, verbal and nonverbal communication, anthropology and
sociology (Erickson & Mohatt, 1982; Erickson & Wilson,
1982).

The use of ethnographic methods in the field of
educational research has steadily been increasing as a major
paradigm (Spindler, 1982) . An ethnographer "strives to
define Objects according to the conceptual system Of the
people he studies" (Frake, 1961:192). An ethnographer
discerns how people construct their world Of experience from
the way they talk about and interact with it. Ethnography
is the work of describing a culture (Spradley, 1980). Its
aim is to understand people's ways of life from their own
point of view. As Malinowski (1961) said, "the goal Of
ethnography is to grasp the native's point of view, his
relationship to life, to realize his vision of his world"
(p. 25).

Ethnographers are mainly concerned with three
fundamental aspects of human experience: what people do
(cultural behavior), what people know (cultural knowledge),
and the things people make and use (cultural artifacts)
(Spradley, 1980).

Ethnography Of communication specifically developed out
Of an interest in face-to-face interaction as to understand
how these "micro" processes are related to broader cultural

and social issues (Erickson & Mohatt, 1982; Jacob, 1987).

30

Jacob (1987) summarized the major assumption of ethnography

of communication as follows:

1. Culture is central to understanding human
behavior.
2. Context influences the patterns and rules Of

interpersonal interaction.

3. The social structure and outcomes of institutional
process are derived, in part, from the process of
face-to-face interaction.

4. Detailed study of interactional pattern says much
about the culture Of a group under study.

Focusing on "particular central scenes within key
institutional settings" (Erickson & Mohatt, 1982:137),
ethnographers of communication are fundamentally concerned
about two issues: (a) understanding the rules of social
interaction for various cultural groups, and (b) determining
how "outcomes" are produced through social interaction.

In describing social interactions as well as outcomes,
ethnographers fundamentally base their work on a phenom-
enological approach (Magoon, 1977; Yorke, 1987) as to
construct knowledge-based human experience derived from the
researcher's participation and Observation in the social
scene. In this sense, phenomenology is the basis Of ethno-
graphic research. As Bogdan and Taylor (1975) stated, "the

phenomenologist view human behavior -- what people say and

31

do -- as a product of how people interact with their world .
. . the phenomenologist attempts to see things from the
person's point of view" (p. 14). The person's point of view
is a research construct within the phenomenological
approach. Phenomenologists suggest that in order to Obtain
valid inferences from a phenomena, it is important to keep
in mind the following considerations or rules (Ihde, 1979):

1. Attend to the phenomena of experience as they
appear (p. 34).

2. Describe, don't explain the phenomena (p. 34).
This rule prevents the researcher from judging the
phenomena prematurely from his/her point of view.

3. Horizontalize or equalize all immediate phenomena
(p. 36).

4. Seek out structural or invariant features of the
phenomena (p. 39).

Repeated patterns (characteristic of empirical science) are
significant and must be actively probed.

Phenomenologists also recommend that it is necessary to

retain the informants' own words because they provide
important insights into how they describe and define their

world from their own perspective (Dodge & Bogdan, 1974).

Copstppctivist Perspective of Teaphing

Constructivism in educational research is nothing new,

and it has been brought to life with the upcoming of ethno-

32

graphic research and the need to account for explanations of
"thick descriptions" that result from this type of research
perspective (Magoon, 1977) . A constructivist perspective
holds the chief assumptions that the "subjects" being
studied must be considered knowing Objects, and that the
knowledge they possess has important consequences with
regard to how actions and behaviors are interpreted (Magoon,
1977). A second major assumption is that the subjects must
construct knowledge purposely (i.e., aimed at a specific
end). In this sense, they have control over how they carry
out this construction process. A third major assumption is
that the human species has a highly developed capacity for
organizing and constructing complex knowledge on its own
(Magoon, 1977). The idea that individuals in their soci-
eties do precisely what individual scientists and scientific
communities carry out too (i.e., invent, organize and
produce knowledge) which deserves to be studied by social
and behavioral scientists. Constructivist perspectives that
focus on how individuals in their societies construct
knowledge, come from different fields Of inquiry such as
anthropology (Geertz, 1973), psychology (Heider, 1958;
Kelly, 1955), and sociology (Schultz, 1970). Recent ethno-
graphics of classroom studies rely on these perspectives for
interpretation (Green & Harker, 1982). They focus specifi-

cally on the acts Of construction as they occur in schools.

33

In this sense, researchers may, for example, describe how a
"problem student" becomes such a "problem" (Erickson et al.,
1985); or how motivation is "negotiated" by the participants
of a classroom setting (Sivan, 1986).

A constructivist view of teaching assumes that
knowledge is the product Of social interaction in which the
knower (teacher or student) acts upon the subject (dis-
cipline) to organize the world and make sense of it
(Kitchener, 1986). Drawing from Piaget's notion of con-
structivism, Kitchener (1986) derived three constructivist
formulations as to how knowledge is acquired (e.g., teacher,
student).

1. Constructivism is the view that reality itself is
constructed by the epistemic subject (e.g., the
teacher, the student).

2. Constructivism is the view that the subject
constructs the epistemic Object (e.g.,
discipline).

3. Constructivism is the view that the subject
constructs the cognitive schema, categories,
concepts and structures necessary for knowledge.

In this sense, teaching is an interactive process
between the conception Of the world (epistemic Object), the
conception Of the person as knower (epistemic subject), and

a conception of the act of knowing (epistemic relation).

34

Teachers, then, can act over the discipline and organize it
accordingly so as to communicate the necessary information
'so that students also construct their view of the disci—
pline. In doing so, teachers are selective of the type Of
information needed to construct the epistemic subject (or
discipline). This perspective Of teaching is consistent
with Kelly's constructivist position that people usually
construe their world by selecting the pertinent from the
insignificant, by coding and selecting the proper inform-
ation, and by anticipating events (Frake, 1962). In this
construction process, people define alternative courses of

action and make decisions among them (Frake, 1962).

A Constructivist Perspective of
Instructional Segpencing

Constructivist perspectives are now common in
educational research, particularly in studies that rely on
ethnographic approaches (Magoon, 1977). Studies of class-
room interaction Or "micro-ethnography" (Erickson, 1986a)
are consistent with constructivist assumptions. In a review
of ethnographic research on classroom face-to-face inter-
actions, Green and Harker (1982) pointed out the existence
Of a set Of constructivist "premises" as follows:

1. Conversations are rule-governed, constructed

entities.

35

Messages in conversation (verbal and nonverbal)
can be transmitted in more than one channel of
communication which can be Operating at the same
time. These messages may have different purposes.
The context in which converSations take place is
not a given entity but it is constructed as part
Of the conversational process.

The context contributes to the interpretation of
meaning in the classroom.

"Contextualizing cues" are the means by which a
speaker (teacher) signals and the listener
(student) interprets the semantic content. This
content (or behavior) may be related to what
precedes or follows.

The products of conversational processes are a
series Of meanings which are socially and
semantically context dependent.

Lessons are not. preset entities, but. they’ are
constructed by teachers and students to achieve
instructional goals. In this sense, "classroom
conversations" are not scripts to be followed
rotely by teachers and students (Green & Harker,
1982). This situation allows for "breaches" in
the cohesion of the lesson as conversation

develops.

36

With these premises in mind, it should be noted that an
instructional sequence is a teacher construct which is
developed as teachers (the epistemic subject) interact with
students and classroom materials as to enact the necessary
actions (and events) that. will result in the epistemic
Object (knowledge of subject matter) that students
eventually will learn. They may choose lecturing, lab
activities, seat work, etc. as some of the actions to be
undertaken in the classroom. The analytical model that
follows draws from two constructivist perspectives on
teaching and learning which complement each other. In the
first instance, Erickson (1982) arguing in favor Of a
(constructivist) natural history Of learning, pointed out
that in their daily interaction, teachers and students enact
in academic task environments with a structure determined by
four constitutive aspects:

1. The subject matter information content.

2. The logic of subject matter sequencing.

3. The meta-content cues toward task completion

strategies and steps.

4. The physical materials through which tasks are

manifested and completed.

Erickson (1982) pointed out that the first two aspects
constitute the "underlying learning task structure" Of the

subject matter. The last two aspects represent the "enacted

37

learning task environment" or "the physical stuff" through
which academic tasks are accomplished.

The above four aspects are interrelated to the social
task environment which is also characterized by four
different aspects.

1. The social gatekeeping of access to people and

other information sources during the lesson.

2. The allocation of communicative rights and
Obligations among the various interactional
partners in the event.

3. The sequencing and timing of successive functional
slots in the interaction.

4. The simultaneous real-time actions of all those
engaged in the interaction (Erickson, 1982).

The present study will focus specifically on the first
aspect, academic task structure, keeping the second aspect
in the background (i.e., the social task structure).
Researchers seem to agree that a substantial number of
studies have been conducted on issues related to the social
task structure at the expense of the academic task structure
(Erickson, 1982; Cazden, 1986: Stubbs, 1981).

The second constructivist perspective is derived from
Yorke's (1987) work on teacher thinking. Yorke, drawing
from Kelly's (1955) personal constructivist theory, argued

that Classroom events can be constructed in retrospective if

38

the researcher is to adopt an approach that is informed by
phenomonology of the philosophy Of history. In this sense,
a. teacher's construct system. can Ibe explored. via three
possible avenues:

1. The protagonist's verbalization concerning the

event(s) Of interest.

2. The protagonist's behaviors (actions) during that

verbalization.

3. The researcher's direct observation of the

event(s).

Yorke's approach towards curriculum construction
(methodologically) supports (or complements) the study of
"subject matter task structure." This suggests that the
logic of subject matter, the information content, the meta
cues used to accomplish tasks, as well as the usage Of
physical equipment, can be fully studied in retrospect by
developing a "natural history" (Erickson, 1982) based on the
participants' verbalization and actions as well as on the
researcher's interpretations of these actions. As it is
clear, a researcher needs to rely on a "metalanguage" to
interpret those verbalizations and actions. The section
that follows will focus on a discussion Of discourse
analysis as a means to develop the metalanguage needed to

construct and interpret an instructional sequence.

39

on se 1 s's

In order to properly describe and analyze participants'
actions and verbalizations as to construct a history line Of
how events are constructed in real life, researchers fre-
quently rely on constructs drawn from discourse analysis.
The discussion that follows will focus on discourse anal-
ysis, with an emphasis on classroom discourse. The language
Of discourse is described as an analytical frame to inter-
pret how a teacher's discourse leads to the construction of
an instructional sequence.

A discourse can be defined as a socially constructed
phenomena (Gardner, 1985) that occurs in the context Of a
"speech event" (Hymes, 1962) . A discourse can have two
major functions: transactional (i.e., to express content)
and interactional (i.e., to express social relationships and
personal attitudes) (Brown & Yule, 1983). In either case,
it can be produced in both spoken and written format. Both
types of discourses are structurally different in terms of
cues, phrases, environment, connectors, etc.

As pointed out before, a discourse is a contextualized
social phenomena that depends on the circumstance in which
it happens to take place. Hymes (1962, 1964) specified
several features of that context which may be relevant to
the identification and characterization of a type of speech

situation. He focused on the role of the addressee and the

40

addressor, or the listener and the speaker. A third feature
of that context is the topic, or what is being talked about;
the setting, which indicates where the event takes place:
the channel Of communication between participants (sig-
naling, writing, language): the code being used (e.g.,
English); the message form (e.g., debate, lecture, letter,
etc.): and, finally, the event that is taking place. FOr

example, in a physics classroom, the following features may

be seen:
Addressor: physics teacher
Addressee: students
Topic: "Newton's second law"
Channel: speech
Code: English

Message form: conversation

Event: physics demonstration

Lewis (1972) discussed a different list of features to
define the discourse context, which somehow overlap with
Hyme's categories. Lewis' features include, "possible
world," time, place, speaker, audience, indicated Object,
previous discourse, and assignment.

O 'c O 's urs
Every discourse has a topic (Givon, 1983): and it is up

to the discourse analyst to judge when the topic begins and

when it ends. The notion of topic is fundamental in the

41

representation Of the content Of a discourse. In this
sense, a discourse can be fragmented using "topic boun-
daries" which show where a fragment begins and where it ends
(Brown & Yule, 1983). The topic may just be a sentence or a
sequence Of sentences. Brown and Yule (1983) suggested the
term "topic framework" as a more comprehensive term for
"what is being talked about in a discourse." The topic
framework consists of elements devisable from the physical
context and from ‘the discourse domain of any discourse
fragment. This is similar to Venneman's notion Of "presup-
position pool" which contains information from general
knowledge Of the context as from the discourse itself
(Venneman, 1977). This would include participants and
verbal and nonverbal cues.

Related to the definition Of topic is the notion Of
"speaking topically." This term refers to the situation
when a discourse participant is making a contribution that
fits into the most recent elements of the topic framework
(Brown & Yule, 1983). In this case the speaker's discourse
is said to be "relevant." The term relevance in the anal-
ysis Of conversations is derived from the conversational
maxims proposed by Grice (1975). According to Grice, when
there is a general agreement Of cooperation between con-
versation participants, then each speaker is supposed to

comply (inexplicitly) with a series Of conventions. These

42

conventions are telling the truth (maxim of quality),
telling the listener all he needs to know and no more (maxim
of quantity), saying things that are relevant (maxim Of
~relation), and using speech clearly and unambiguously (maxim
of manner) (Kreckel, 1982).
O n 'e

Important concepts in discourse content representation
are the notions of topic shift and boundary markers. They
are related to how the speaker structures what he is talking
about (topic). Topic shift is the boundary between two
different topics (Schank, 1977: Maynard, 1980). It can also
represent the boundary between two paragraphs. The point to
be made here is that a topic shift represents a way of
"partitioning a discourse" (Grimes, 1975:109). This par-
tition can be related to a change in time, theme or context
(Brown & Yule, 1983). In the case Of verbal discourses,
linguists refer to boundaries called "paratones" which mark
the boundaries between continuous paragraphs.

Generally speaking, topic shifts can be of two types:
a termination or a break (Jefferson, 1972). In a termin-
ation, the topic is shifted from one area to another, and
the first area is never picked up again in the development
of the discourse subject matter. A break occurs when there
is a topic shift and later another topic shift brings the

discussion talk to the previous topic. If a topic is not

43

talked about again, linguists refers to this phenomenon as

"persistence decay" (Givon, 1983).

The NOtions Of Textupe, Cohesion
ghg Qohepence

Three important concepts related to large chuncks of
language are the notions of texture, cohesion and coherence.
The three terms are commonly employed when referring to the
"well-formedness" in a thematic development of a discourse,
theme or topic. Here, the term thematic development indi-
cates the process by which sentences, paragraphs, episodes,
and discourse itself, are organized around the central topic
or subject of discourse (Brown 8 Yule, 1983). The theme or
central topic can be developed in an array of several
constitutive topics (or subtopics). These topics may or may
not be arranged sequentially in time (Brown 8 Yule, 1983).

In the process development Of a theme, a text is being
produced. Several authors are concerned with the principles
that bind the constitutive elements Of a discourse together
tO makeqit a text (Halliday 8 Hasan, 1976; de Beugrande,
1980: Givon, 1983). Halliday and Hasan, one Of the most
widely cited references in discourse cohesion, argue that it
is the nature of the cohesive relationships ‘within and
between the sentences Of the discourse that give "texture"
to a particular text. The texture is provided by a set of
relationships that can be categorized under the headings Of

reference, substitution, ellipses and lexical relationships.

44

The reference relationships, in particular, are of funda-
mental importance tO the study Of the coherence (logical
connection) Of a discourse or text. The reference relations
"instead of being interpreted semantically in ‘their' own
right . . . make reference to something else for their
interpretation" (Halliday 8 Hasan, 1976). When their
interpretation lies outside the text, in the context Of
situation, the relation is called "exophoric" (it does not
play a part in textual elaboration). The expression "look
at that" would be an example Of that relation (Brown 8 Yule,
1983). When the interpretation of the relation lies within
the discourse or text itself, then we talk about endophoric
relation. Halliday and Hasan (1976) identify two types Of
endophoric relations: (a) anaphoric relations that look
back in the discourse for their interpretation, and (b)
cataphoric relations that look forward in the text for their
interpretations.

Related to the concept Of cohesion is the notion Of
coherence of a discourse (Givon, 1983: Hobbs, 1979; Brown 8
Yule, 1983). Coherence refers to the well-formedness Of a
discourse and how the elements of a discourse are connected
together (Brown 8 YUle, 1983; Hobbs, 1979). It is related
to how the different topics Of a discourse or text are put
together by the speaker(s). The coherence of a discourse is

not located in the linguistic properties Of the discourse

45

sequence itself, as is the case of cohesion (Carrell, 1982),
but it is located in the interpretation of the speaker's
intended meaning in producing a discourse (Brown 8 Yule,
1983) . This process of interpretation may involve three
aspects: (a) the communicative function of the discourse:
(b) the general social-cultural knowledge (of the discourse
analyst and hearer): and (c) the inferences made out of the
discourse (Brown 8 Yule, 1983). In relation to the first
aspect above, it is argued that utterances in a discourse
must be interpreted as actions of different types and that
the coherence (or incoherence) Of a discourse lies in the
relationship between the actions performed with these
utterances (labov, 1972). Secondly, using knowledge about
the world also contributes to the interpretation of a
speaker's discourse in a way that it may seem coherent to
the listener. This knowledge about the world can be looked
upon as background material in the form of "scripts" (Schank
8 Anderson, 1977); scenarios (Sanford 8 Garrod, 1981):
schemata (Anderson, 1977): mental models (Johnson-Laird,
1980), and frames (Minsky, 1975). The listener's world of
knowledge is a substantial key element in the interpretation
and understanding Of a discourse and its coherence.

The third aspect mentioned above with respect to the
process of interpreting a speaker's intended meaning is that

Of determining the inferences the reader needs to make to

46

arrive. at. a coherent and logical interpretation of the
discourse. In this sense, an inference can be defined as
the connections people make when striving to read and
interpret a discourse.

a '0 d es

Qispoupse Coherence

Coherence in conversational discourse can be
characterized by a set of relations that connect (logically)
the different pieces (utterances, episodes, paragraphs,
etc.) Of a discourse together. Its interpretation lies in
the context of the discourse and not necessarily in the
linguistic format of the discourse itself. Hobbs (1983)
summarizes the different views on coherence as follows:

1. A discourse is coherent if it exhibits a
structural relationship between its various
segments and topics Of the segments.

2. A second view is that a discourse is coherent if
the utterances it yields are seen as actions to
achieve some goals. Coherence then can be infer-
red from the speaker's actions and its place in
the overall discourse. This view is particularly
shared by Labov and Fashell (1977).

3. A third view of coherence is the one suggested by

Chafe (1979). According to Chafe, the coherence

47

of a discourse reflects the structure of content
in memory.

In Hobb's view, for a discourse to be coherent, four
requirements are needed: (a) the message must be conveyed;
(b) the message must be related to the goal of the dis-
course; (c) what is new and unpredictable in the message
must be related to what the listener already knows: and (d)
the speaker must guide the listener inference processes
towards the full intended meaning of the message (Hobbs,
1983). In order to fulfill these four requirements, there
is a set of fOur corresponding coherent relations that the
speaker needs to keep in mind.

1. Strong temporal relations. These refer to what
happened first and what caused what in the
discourse sequence.

2. Evaluation relations. These relations derive from
the set of goals that speakers and hearers have.
Hence, the need to evaluate and judge the
discourse's effectiveness as it is enacted.

3. Linkage relations. The speaker needs to provide
the proper linkage between what the actual message
is about and what happened before. This linkage
is achieved by making explicit background inform-

ation and by explaining the new information.

48

4. Expansion relations. These types of relations
refer to discourse statements that account for how
the speaker moves between specific and general
statements. This process can be achieved by
contrasting, generalization, exemplification. and
parallel methods.

In the speaker's discourse, the coherence can be either
local (one segment of the discourse) or global (the entire
theme of the discourse) (Van Dijck, 1985: Agar 8 Hobbs,
1985). A speaker relies on local coherence strategies when
he assumes that each new clause or sentence (or action) is
being linked to the previous information. Apart from local
coherence relations, the speaker also employs global
coherence strategies to make the theme of the discourse
understandable to the listener. In doing so, the speaker
makes use of strategies to properly connect the different
topics (or subtopics) that make up the entire discourse.
Van Dijk (1985) referred to these "global theme" strategies
as macro-rules or rules to sequence and construct semantic
macro-structures. Examples of these macro-rules are: using
implicit knowledge the hearer may have on the topic of the
discourse: relying on information from previous texts:
pointing at title and headings: using thematical sentences
and key words (e.g., signalling what the passage is);

referring the listener to the structure of the discourse

49

passage; or telling him about the schematic structure Of the
discourse itself (Van Dijk, 1985).

Events in a hiscourse

Both macro-sequence (several subtopics or social
themes) and micro-sequence (one topic) are made up of events
that may or may not be logically connected. Different parts
Of the discourse communicate different kinds of information.
Depending on the nature of the information, the discourse
analyst is looking for, the discourse can be "partitioned"
(Grimes, 1975) in events which can have two dimensions, one
is "tight versus loose" and the other is "temporal versus

logical" (see Figure 2.1).

 

 

Temporal Logical
Tight TT LT

 

 

 

 

Figure 2.1. The two dimensions Of events in a discourse.

The result Of this 2x2 matrix is four different types
of sequences in which discourse events can be classified:
(a) "temporally tight sequence" in which the actions of the
discourse overlap in time; (b) "temporally loose sequence"
in which the next action begins sometime after the previous
event ends; (c) "logically tight sequence" where the next

action of events is a direct consequence of the event that

50

happened before; and (d) "logically loose sequence" in which
"earlier actions have effects which persist and are factors
in what takes place later, but without direct connection"
(Grimes, 1975:233-234).

In the study Of text and narrative content, linguists
focus on two important text relationships that describe how
events. become related" The first. relationship (already
mentioned) is given the name of linkage. This is an ana-
phoric relationship that is employed when language events
are linked to preceding events by repeating them or making
reference to them, 'The second relationship to connect
discourse events is given the name of "chaining," catha-
phoric relation (Grimes, 1975). This relation refers to the
prediction of some of the content that the following event
will contain. If the second event is to be about a dif-
ferent subject, then a "topic shift" has occurred (Brown 8
Yule, 1983). Otherwise, "topic decay" occurs (Tannen,
1984). Both chaining and linkage systems may coexist in a
discourse in a situation in which an event in a sequence of
events may be chained forward to the next event and at the
same time may be linked backward to the preceding event

(Grimes, 1975).

51

Qiesspopm Discpugse end Academic gohtent

Teachers and students devote a great deal of time in
classroom communicating and talking. Teachers, in parti-
cular, have to lecture, inform, explain, define terms, post
questions, correct students' answers, request, etc., while
they engage in their daily work (Stubbs, 1983). Much of the
talk is characterized by having one speaker, the teacher, in
control of the topic or events in which classroom partici-
pants take part. Teachers decide on where to start a topic,
where to stop, what should be in it, how it should be
organized for a coherent discourse, and how topic related
events need to be properly sequenced.

Traditional research on classroom discourse has not
primarily focused on the cognitive aspect Of the discourse
itself but on the social structure imbedded in the classroom
discourse (Cazden, 1986). In this sense, the way teachers
enact subject matter through their daily interactions with
students is a research topic largely ignored by discourse
analysts. Cazden summarized the research on classroom
social structure under the following headings:

1. Events and their participating structure.

2. Features Of teacher-talk register.

3. Cultural differences and differential treatment.

4. Interaction among peers.

5. Talk on the unofficial peer culture.

52

6. Classroom discourse and learning.

Inspite of the wide variety of research on topics being
studied, researchers acknowledge that the issue Of academic
content is Often ignored in descriptive-ethnographic
research (Erickson, 1982; Cazden, 1986; Stubbs, 1983).
Erickson (1982) and Stubbs (1983) stressed the need to look
at the organization Of classroom content as a way to shed
light on what and how knowledge is transmitted by teachers.
Stubbs (1981) has stressed the need to empirically study
clasroom discourse as a way to describe how different "bits"
Of‘ knowledge are structured. by 'teachers in their daily
interaction with students.

The analysis Of teacher-student interactions as a
discourse system can yield important educational insights as
tO how educational knowledge is socially defined, selected
and made available to students (Stubbs, 1981). A similar
argument. was raised. by Doyle (1983:159) who called for
explicit attention to "how academic work is organized and
accomplished in classrooms. . ."

As far as discourse analysis Of science classroom
content is concerned, research is scarce. The research on
how single topics are formulated in science classrooms
(Heyman, 1986) and how the content of single science lessons
is developed in its relation to the social structure of the

classroom (Lemke, 1982a) are worth mentioning.

53

With the above discussion in mind, a discussion Of the
methodological issues involved in the study Of classroom
content will be presented in the next chapter. Specifi-
cally, Chapter Three describes an ethnographic study that
focused on the nature Of the construction Of an instruc-
tional sequence as enacted by three high school physics

teachers.

CTLXPTERLTIHKEEZ

TIES(XJNTKKCT(DF'THTEHWQLHRJE14(3LHEE31I)
STUDY SUBJECT MATTER (CONTENT-KNOWLEDGE)
IN PHYSICS CLASSROOMS

Introduetioh

This chapter is organized into five sections. The
first section gives the background Of the study. Next, the
research. questions that. guided the. study' are jpresented.
Third, a description Of the methodological approach is
described. The method of analysis used to reach the
findings is outlined. And finally, the main corpus of datum

is briefly outlined.

Background of the Spudy

In the 1984-86 academic years, a research study of
secondary school science was carried out at the Institute
for Research on Teaching at Michigan State University. The
study was ethnographic and its main purpose was to focus on
the question: "What is the nature of the interaction among
secondary school teachers, school administrators, and how do
these interactions influence the character Of the science
program?" (Gallagher, 1985, 1986). In trying to answer

this question as well as other questions generated by the

54

55

nature of the research, the research team (Of which the
writer was a member), relied on ethnographic techniques such
as participant observation, interviews and videotaping.
Each member visited a school site once or twice a week
during the data gathering phase of the project. Discussion
among team members was held regularly to generate assertions
and design strategies to confirm or disconfirm those asser-
tions. Although the main purpose Of the project was to
study the nature Of interaction among science teachers, very
early on the project, the issue of what was taught in the
science classrooms began to emerge as an important element
in the teachers' daily discourse. Questions such as, What
is the topic Of the instructional sequence in Mr. X's class?
How does Mr. X structure his class?, and the like were
constantly asked. These questions were not really addressed
fully as the project came to an end in June 1986. However,
the project coordinator and this writer thought these ques-
tions were pertinent and should be pursued by a graduate

student.

Research Questions

The nature of the content of instruction as enacted in
physics classrooms was the topic of this study. In partic-
ular, the study initially focused on what was taught in
physics classrooms and how it differed among different

physics teachers. Since teachers usually act as gatekeepers

56

of what is taught in their classrooms, it was assumed that
there were variations on how to organize the subject matter
of a lesson or unit and what to include in each one of these
entities.
The original main questions addressed by the proposed
study were stated as follows:
1. What is the content of instruction for a single
curriculum unit as taught by physics teachers?
2. What is the logical development of the flow of
information between teacher and student?
3. What is the "story line" or "sequence of connected
actions" (Erickson, 1986b) as a unit of

instruction is developed.

a. How is this "story line" constructed by
participants?
b . What are the boundaries between phases Of

events (Erickson, 1986b) as the "story line"
is developed? (In a physics class, examples
of these events can be lectures, demon-
strations, laboratories, films, etc.)

4. How do physics sequences vary among different
teachers dealing with different textbooks and
equipment?

After re-entry of the schools again (August, 1986), the

author realized the questions were too broad and general to

57

be studied. This situation led me to focus on a topic
taught by the participant teachers. It was decided to
particularize the research questions to look at what was
taught in a unit on dynamics. Also, the nature Of ethno-
graphic research drove the researcher tO redefine my
questions as the research was carried out. According to
Erickson (1986a), ethnographic research questions can go
through a process of reconstruction in "response to changes
in the field worker's perceptions and understanding of
events and their organizations during the time spent in the
field" (1986:121). In effect, "the understanding Of events
and their organizations" in physics classrooms in light Of
analytical constructivist framework and its method Of
inquiry, led the researcher to redefine the researCh ques-
tions in the following terms:

1. What is the nature Of the coherence (global) Of
the subject matter information content in a unit
on dynamics as taught by high school physics
teachers?

a. ‘What topics are included in such an
instructional unit?

b. How are the different topics sequentially
taught through time?

2. What is the nature Of the coherence (local) Of the

information content delivered in a single topic

58

(on dynamics) as taught by high school physics
teachers?
a. How is the topic connected to other topics
within the unit?
b. How is the topic introduced and terminated?
c. What are the enacted logical steps as the
topic is constructed?
3. What is the nature of the enacted task environment
through which the topics are delivered?
With this set of questions in mind, the next step is to
describe the research plan undertaken while the study was

carried out.

Research Plan

The nature of the questions and the need to focus on
specific understandings of content-knowledge construction
required the use of an "interpretive research" (Erickson,
1986a) approach to gather data for the study. An inter-
pretive research seeks to understand how "local meanings"
and actions are constructed from the actor's points Of view
and how those meanings and actions compare (Erickson,
1986a). Answers to questions revolving around the foregoing
issue are needed in educational research because of:

1. The need to make explicit the "invisibility of

everyday life."

59

2. The need for specific understanding through
documentation of concrete details Of practice.

3. The need to consider "the local meanings" that
events have for participants in them.

4. The need for comparative understanding of
different social settings.

5. The need for comparative understanding beyond the
immediate circumstances of the trial setting
(Erickson, 1986a:111-121).

It is the purpose of this study to make explicit what
is taught in physics classrooms in terms Of content-
knowledge as well as how that knowledge is organized and how
such organization compares across three different teachers.
To shed light on these questions, the researcher relied on
extensive. participant Observation, videotapes, interviews

and document gathering.

Bagpicipant Qbsepyation
Two months before the end Of the 1985-86 school year,

the researcher "negotiated entry" (Spradley, 1983) with
three high school teachers to learn how they actually
sequenced the content-knowledge in their daily interaction
with students. Weekly visits were made to each teacher and
field notes were carefully recorded. At the beginning Of
the 1986-87 school year, the researcher continued his

observations from August 1986 through March 1987. During

60

this time, the Observations were done on a daily basis in
two classrooms and on a weekly basis in the third one.
There was a practical reason for this: the third teacher
had begun his course with a unit on light and waves, and
there was no plan to focus on such a unit. However, inten-
sive Observation of the third teacher began in January 1986
as he started a unit on kinematics. From mid-March until
the close of the school year (mid-June), the researcher
maintained contact. with. the three teachers by' means of
periodic visits. This was done to clarify unclear state-
ments in the field notes, and also to sustain the friendship
already established between the researcher and the teachers.

Overall, 200 classroom Observations were made from
August 1986 through June 1987. Observations focused
primarily on the teacher's activities and its relation to
the information being delivered to students. Students'
activities and interactions were also recorded as they were
relevant to the guiding questions of the study. During the
Observation phase, iieldhotes were carefully taken and
relevant documents (worksheets, lab sheets, quizzes, etc.)
were collected. These documents proved to be helpful tools
during the process Of re-writing and analyzing field notes.
Over 2,000 hand-written pages were gathered during the

participant Observation phase of the study.

61

The nature of the research questions forced the
researcher to focus on classroom events dealing with the
organization and sequencing of content-knowledge, as Opposed
to issues dealing with the social structure of the classroom
or students' learning which were kept in the background.
This situation led the researcher to pay specific attention
to the content of the teacher's discourse as well as the
actions undertaken by participants as they were motivated by
such discourse. In this sense, classroom events were
described through the teachers' verbal statements and meta-
cues that indicated the beginning and end of events. The
descriptions were also constructed in terms of elapsed time
between perceived events and changes in context (from lec-
ture to lab, from lab to seat work, etc.).

Each Observation was immediately followed by a write-
up process in which field notes were carefully elaborated
and substantiated with memos that helped to clarify and
explain the field notes and the research guiding questions.
Occasionally, field notes had to be rewritten as a conse-
quence of new information gathered from teachers, students,

or from more recent Observations.

V' eota n O Classroom e ts
With the purpose Of focusing on specific details Of
classroom activities as related to content organization and

sequencing, a whole unit of instruction was videotaped for

62

each of the three teachers. Classroom ‘videotaping is
another important technique to gather ethnographic data.
This technique was suggested by Erickson (1986a) as a way of
reducing the bias of "premature typification" (jumping to
early conclusions) and the bias "toward emphasis on analysis
Of recurrent events at the expense Of analysis of rare
events" (p. 144). This approach of relying on machine
recording' as a ‘means Of“ gathering data in interpretive
research is Often referred to as "microethnography"
(Erickson, 1975), "constitutive ethnography" (Mehan, 1979)
and "sociolinguistic microanalysis" (Gumperz, 1982: see
Erickson, 1986a). Erickson (1986a) anticipated three
advantages of tape recording over participant Observation:
1. "Capacity for completeness Of analysis" (p. 145).
Tapes can be revisited and analyzed as many times
as required by the researcher or analyst.
2. "Potential to reduce the dependence of the
Observer on primitive analytic typification" (p.
145). In this sense, a tape recording gives the
researcher an Opportunity for further deli-
beration, thus avoiding faulty inferences,
particularly at the early stages Of the inquiry
process.
3. Tapes "reduce the dependence Of the Observer on

frequently occurring events as the best sources Of

63

data" (p. 145). In this sense, classroom video-
tapes provide the analyst with an opportunity to
learn about "rare events" not accessible or
visible through field notes.

However, Erickson (1986a) cautioned researchers about
the limitations of this strategy:

1. When reviewing a tape, the researcher can only

interact with it vicariously.

2. A tape itself lacks contextual information.

Both limitations can be ameliorated by the use of field
notes.

The method of videotaping was particularly useful in
the description of the events that took place as the three
participant teachers dealt with a unit on dynamics. (In
all, 25 hours Of videotaping were conducted.) Soon after
the proper negotiation with each individual teacher, the
researcher brought a videotape camera into the classroom in
order to familiarize the students with the camera. It was
previously agreed that the focusing would primarily be on
the teacher and not on individual students. The portable
video camera used for the occasion was placed at the rear of
the classroom, on a tripod, overlooking the teacher and the
whole class. The camera was permanently held in the locked-
On position (Erickson 8 Wilson, 1982) in order to record

transitions between classroom events. Though the wide angle

64

shot was generally used, on several occasions it was conven-
ient to zoom in on specific details that were considered to
be important in 'the process Of inquiry. Specifically,
close-up shots were appropriately directed toward the board
whenever an equation or statement happened to be written
there. Also, close-up shots were aimed at the teachers
explaining a demonstration, giving lab instructions, or
drawing diagrams on the board or any other place. In all,
the researcher made 25 videotapes.

During the recording Of the videotape, the researcher
simultaneously took notes Of the timing between events as
well as other relevant information not captured. by the
videotape. These types Of field notes were helpful in
calibrating the tape transcripts (Lemke, 1982a). As these
field notes were taken, the researcher focused primarily on
Off-camera events such as students working in the back-
ground, Or the visual cues and dietic references (Lemke,
1982a) which were thought to be of relevance in the process
of inquiry. Videotapes were transcribed and correlated with

field notes gathered from the videotaped lessons.

ihtegyiews with Teachezs

Periodic informal interviews were held with teachers in
order to gain insights into the hunches and inferences made
by the researcher with respect to the organization Of the

content—knowledge being delivered on a daily basis. These

65

conversations usually took place during class breaks,
recesses, after school or during planning hours. The
conversations served several purposes: (a) to clarify memos
and questions left unanswered on previous field notes, (b)
to find out about the next day's topic or activity (useful
information during the videotaping phase), and (c) to keep
record Of the teacher's perception Of "connectedness" across
different topics. In addition to informal daily interviews,
the three participant teachers were formally interviewed
after they had completed the unit on dynamics. Two leading
questions were formulated during this occasion: (a) Why did
the sequence (on dynamics) come to be the way it did? and
(b) How did you plan to teach such a unit? In addition to
these two guiding questions, additional information was
requested on the teacher's professional experience, overall
content coverage (during the school year) , perception Of
students, classroom environment, etc. These interviews were

audiotaped and the transcripts included in the data corpus.

a sis
The data that forms the central core of Chapter Five of
this study was Obtained through a method which required two
levels of analysis. At this point, it is important to note
that in the case of interpretive research, documentary mate-

rials such as field notes, videotape transcripts, documents,

66

etc. are sources Of information from which data can be
constructed (Erickson, 1986a).

The first level of analysis was based on Yorke's
methodology to reconstruct classroom events (Yorke, 1987).
He proposes three possible avenues of exploration: the
protagonist's verbalization concerning the event(s); his or
her behavior during that verbalization; and the researcher's
direct Observation of the events (Yorke, 1987). For the
purpose of this study, this categorical system was modified
as follows:

1. Participant's verbalization.

-- What was being said by whom during the
event(s).

2. Participant actions.

-- What participants (teacher and students) were
doing while the event(s) were taking place:
e.g., what was written on the board, how
students were taking notes, etc.

3. Researcher's interpretation:

-- What the researcher thought was taking place
with respect to the development Of the topic
or theme. Specifically, the researcher's
interpretation. was based on. the ‘meta-cues
being employed as the topic was constructed.

These meta-cues were considered to be: topic

67

shift, linkaging, chaining, elaborating,
restating, closing, Opening, etc.

The above three categories, verbalizations, actions and
interpretations, form the basis for a three-column coding
system used to interpret the videotape transcripts described
above.

The second level of analysis dealt with the structure
of the text (transcript) to be analyzed. Since the purpose
of the study was to learn about the nature of the coherence
in the content-knowledge delivered by physics teachers, it
was assumed beforehand that the ‘teacher's. discourse and
activities revolved around a structured topic. To get a
sense Of how different pieces of the teacher's discourse
baout a specific theme (dynamics) are bound together, a
segmentation of the discourse was made. The major criteria
followed in this process was that of identifying major topic
shifts during the discourse. A similar approach was
implemented by Agar and Hobbs (1985) and Lemke (1982a).
Agar and Hobbs (1985) first macro-analyzed a whole text Of
an interview to put together a life history of a heroin
addict who became a burglar. They then microanalyzed one
segment of the history which dealt with the burglar's
arrest.

A similar analysis was one employed by Lemke (1982a) in

a study Of the way teachers develop their science lessons.

68

Lemke (1982a) carried out a segmentation analysis based on
major topic shifts during the teacher's discourse. This
process consisted of reviewing a few lessons several times
and noting topic shifts, verbal statements or other features
that can be used as boundary markers within a lesson or
unit.

A preliminary analysis Of field notes and videotapes
showed that in naturally occurring events, boundaries are
fuzzy events difficult to trace within a lesson or set of
related lessons. Videotape transcripts, however, are more
precise for locating the moment in time when a teacher has
shifted to a new topic or theme. These shiftings usually
emerged in the form of statements like the following.
"Let's get started with this (new) topic." "Yesterday, we
talked about . . . today, we will refer to. . . ." "Today,
we are ready to talk about a new subject." "Let me tell you
about. . . . " On many occasions, topics were not announced
at the beginning of a discourse stretch but at the close of
it. This was the case in which topic-related demonstrations
or tales were introduced before formally verbalizing what

the conversation was about.

piscou se Anal sis and Selection O es
Preliminary analysis of field notes and videotape
transcripts clearly indicated that definitions made in

physics classes were highly content-dependent (Lemke,

69

1982a), i.e., the way meanings were constructed by different
teachers varied across settings. Teachers use different
sequencing strategies when they teach a topic or a series of
related topics. The physics content talked about in similar
units showed variations in terms Of the topics, the order in
which the topics were arranged and the strategies
implemented to teach these topics.

Analysis Of classroom discourse of more than 200
classroom observations and the videotapes would have been a
very time consuming activity. Instead, a "funneling"
approach was implemented to draw on a more narrow scope Of
information from a larger pool. In this sense, it was
decided to focus on the theme "dynamics" (as traditionally
defined by physicists). It is important to point out here
that several themes were studied during the Observation
phase including areas such as kinematics, waves, momentum,
energy, Optics and the solar system. However, one Of the
reasons for selecting the unit on dynamics was the fact that
it was possible to videotape most Of the teaching episodes
that evolved around that theme.

A careful analysis of the episodes led the researcher
to learn how the different pieces Of the discourse were put
together, giving an understanding Of the nature Of the
coherence of the whole unit. In addition to this macro-

analysis of the whole unit, a micro—analysis of one segment

70

(topic) was also conducted. In this case, a decision was
made to micro-analyze how the three participant teachers
dealt with Newton's Second Law of Thermodynamics (an
episode) and how this topic is connected to the other topics

considered in the unit as a whole.

The Coppus of hatum

The following is a list Of the videotapes which formed
the basis Of the analysis of the present study. Although 25
videotapes Of 50 minutes each were made, only 20 of them are
mentioned below as they form the major data source from
which conclusions and findings were derived. (The remaining
five tapes correspond to Mr. Howard's teaching the last five
lessons of a Kinematics unit.) The videotape topics and
activities are described under the corresponding teacher's

name (M. Simon, Mr. Ellis and Mr. Howard).1

Mr. Simon

1. Tape 1: The Principle of Inertia (demonstrations).
2. Tape 2: Newton's Laws.

3. Tape 3: Experiment on Newton's Second Law.

W
1. Tape 1: Newton's First Law.

2. Tape 2: Newton's Second Law (friction).

 

1Note: Each one of the participant teachers will be
described in the next chapter.

3. Tape
4. Tape
5. Tape
6. Tape
7. Tape
Mr . flower-d
1. Tape
2. Tape
3. Tape
4. Tape
5. Tape
6. Tape
7. Tape
8. Tape
9. Tape
10. Tape

3:

10:

71

Newton's Second Law (demonstrations).
Weight and Mass.

Weight, Free Fall, and Terminal Velocity.
Newton's Second Law Experiment.

Newton's Third Law.

Experiment: "What

(Experiment 20).

Procedures on the
Forces DO To Motion"

Conducting Experiment 20 (PSSC).

a) Data Analysis on Experiment 20.

b) Introducing Experiment 21: How Force
and Mass Affect Acceleration.

Data Analysis of Experiment 21.

Conclusion Of Experiment 21.

"Wrap Up" Of Experiment 21.

Introducing Experiment 21: Inertial
Versus Gravitational Mass.

Conducting Experiment 22.

a) Conclusion of Experiment 22.

b) Solving' "HDL's" (Home, Demonstration

and Laboratory) Problems.

Solving "HDL's" Problems.

CHAPTER FOUR

CONTEXT FOR SUBJECT MATTER
ORGANIZATION AND SEQUENCING

Introductioh

The purpose of this section is to present a profile of
the participant teachers in this study. First, the school
and the classroom are described in detail. Second, an
overview of each teacher is given. This is followed by a
summary of the textbooks used by each teacher: and, fourth,

a description of each teacher's plan for a single unit.

The Schoole and the Classrooms
The schools used in this study are located in the mid-
Michigan area close to the state capital. They house
students from the 9th up to 12th grades. Each school is
under the administration of different school districts with

different policies.

School 1 (Room 200)

This school is located in an extremely mixed neighbor-
hood shared by blacks, hispanics, orientals and caucasians.
A large, well-known car manufacturer and middle-class houses
are adjacent to the school. The school's population is

about 1,400: and it has been steady for a few years. The

72

73

building dates from 1928, with three floors and indoor and
outdoor sport facilities.

Room 200 (fictional number), where the actions
described in this study took place, was located on the
second floor at the end of a large corridor with student
lockers on both sides. During breaks, the corridor was
usually an area of intense social activity. A small hall-
way, framed by bulletin boards, led to room 200. These
bulletin boards were frequently used by the teacher to post
science articles and posters that served to attract students
to physics.

The classroom itself was semicircular (see Figure 4.1)
with eight glass windows overlooking the school's main
entrance and the students' main parking lot. The room was
equipped for teaching high school physics to sophomores,
juniors and seniors. There was space and facilities for at
least 35 students. The room's seating structure was
arranged in three large rows facing the teacher's desk.
This structure was frequently changed to accommodate labor-
atory demonstrations or to prevent students from "cheating"
during test periods.

The lab tables were mobile and were located in the
curved section of the room, close to the windows. Behind
each lab desk and attached to the walls were the gas, water

and electricity outlets.

74

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75

There were three blackboards located at different spots
throughout the room. There were also two small bulletin
boards on both sides of the blackboard close to the
teacher's desk. These boards were frequently used for
posting students' grades, cartoons and teacher's memos. In
one of the classroom's corners there were twO shelves used
by the teacher to store handouts, worksheets and other
classroom written materials. Close to the teacher's desk
were the doors that led to the storage room and to a lecture
room. The first room was used to store lab equipment and
important documents such as quizzes, tests, etc. The
lecture room was not part Of the physics laboratory. Due to
the lack of space, it was used to teach social science
classes. Still, the physics teacher constantly needed to

get through it because that room led to the physics library.

School 2 (Room 100)

The second school used in this study was located in a
small community Of about 40,000 people. It was close to a
major state university and some local government offices.
The school was attended mainly by caucasian students. The
school was a one-level building erected in 1963 with a
capacity for 1,300 students.

Room 100, where the Observations took place, was the
school physics laboratory with a seating capacity of 25

students (see Figure 4.2 for details). A large corridor

76

with lockers on both sides led to room 100. The room had no
windows. A fire exit led outside to the school playground.
The room was rectangular in shape; and it was equipped with
an overhead projector, bookshelves (displaying high school
physics textbooks) and physics equipment stored on shelves
located around the room. There were 12 fixed lab tables
properly equipped with gas, electricity and water facil-
ities. The ceiling of the room was fixed with metallic
hooks used frequently by the teacher to carry out classroom
demonstrations.

The blackboard covered a large portion Of the front
wall. Its frame was used to display the most common metric
prefixes, and their numerical values, used in physics such
as centi, nano, mili, micro, etc. Above the board was a
permanent display which listed the more fundamental equa-
tions developed throughout the course. Alongside the board,
there was a large bulletin board frequently used by the
teacher to display cartoons, papers, posters, etc. allegoric
to the physics unit being developed at that time. The
teacher of room 100 always made sure the material displayed
on the bulletin board was there before the referred unit got
started.

The teacher's desk was located in front of the class.

It was Often used in conjunction with a large demonstration

I

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77

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 4.2:

Floor map of classroom 100.

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78

table to conduct class experiments. Before these
demonstrations were actually carried out, the teacher made
sure the equipment to be used was below the table. This way
he did not waste time in between events, particularly on
those occasions in which he wanted to sustain student

interest in the concept being dealt with.

8 ho 3 oom 50

The third school used in the study was located in a
white rural middle class neighborhood, 15 miles away from a
major state university. The high school was closely
associated with frame houses and a middle school. The one-
level school building was about 20 years old and was well-
equipped. with indoor and outdoor sport facilities. It
'accomidated from 700 to 800 high school students.

Room. 150 (fictional number), where ‘the. observations
were carried out, was located halfway down a corridor that
led to other classrooms and school facilities. The room had
a fire exit leading to the schoolgrounds outside; and there
were no windows. The room was rectangular with a seating
capacity of 30 students. Figure 4.3 shows the relative
position of tables, teacher's desk, and lab facilities.

Room 150 was equipped with basic Physical Science Study
Committee (PSSC) apparatus, which was stored in a contiguous

room. This ajoining room was also used as the teacher's

79

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Figure 4.3: Floor map of classroom 150.

80

office, and it housed some bookshelves with a few, rarely
used books. Some cabinets contained microscopes which were
never used in physics lessons. The room was also used by
the physics teacher to teach a course in zoology for
freshmen students.

As one entered the room, the first thing that attracted
one's attention was a black and white poster of Albert
Einstein stating something to the effect that, "It is not
hair that counts, but the ideas." Alongside Einstein's
poster, there was an old periodic table of the elements. 0n
the front side of this wall, an old metric rule and a
bulletin board were hooked to the wall.

The blackboard was multi-purpose in nature with
facilities for film projection and other teaching appli-
cations. On one side of it, there was a pendulum (2 meters
long) used for classroom demonstrations. On the opposite
side, there was a metal hook used by the teacher to hang
objects such as scales, springs, etc. Very close to this
side of the board, hanging on the wall, there was a poster
of Alice in Wonderlan . This poster was used in the past to
teach students about graphing complex relations between
physical variables. Later, the teacher preferred to use the
story of Gulliver's Travels.

The physics equipment was stored in the teacher's

office, which was also used to keep the filing cabinets and

81

some bookshelves. These shelves had several editions of the

PSSC series as well as some zoology textbooks.

ID§_I§QQDQE§

The purpose of this section is to introduce the reader
to the main characters of the study. Up to this point, they
have been described only as "he," or "the teacher." Mr,
Simon (Room 200), Mr. Ellis (Room 100) and Mr. Howard (Room
150) (not their' real names) were the three participant
teachers in the study. They were experienced high school
physics teachers1 who expressed (at the researcher's request
in late June 1985) their willingness to let the researcher
learn about their teaching, and especially about the nature

of the physics content being enacted through their teaching.

Mr. Simon (Room 200)

Mr. Simon was in his early 605. He had been teaching
at the same school for 29 years, and at the time of the
study, he was acting as the science department chairman. He
held a master's degree in physics and had been active in
professional organizations in his own state (he is a past

president of the State Association of Physics Teachers). He

 

1In a 1983 survey, a typical high school science
teacher in Michigan was a male, with about 16.5 years of
experience, and holding a master's degree (see Hirsch,
1984). In this study, two of the participant teachers held
master's degrees in physics and physics education, and the

average years of experience was about 22.

82

was responsible for the teaching of seven physics courses
offered at the school. This responsibility was shared by
another physics teacher who was in charge of three of the
courses.

Mr. Simon had been teaching the Harvard physics course
since its creation in the early 19608. His name appears in
the "consulting committee" as one of the high school physics
teachers who helped to put the course together. He had the
philosophy that the course "Physics for Everybody," which
was one of his major concerns, was a means of motivating
students to take physics (35 percent of the graduating popu-
lation at his school takes physics). In the early stages of
implementation of the Harvard physics course, Mr. Simon was
heavily engaged in the design and construction of the
necessary equipment to run the course.

Mr. Simon was an eager reader of such professional
journals as The Physics Teachers, American .Journal of
Physics and Scientific American. In addition to this, he
was also knowledgeable about most high school physics text-
books available on the market. His experiences as a physics
teacher were not only the result of teaching physics, per
se, but also of his involvement in other related activities.
During the data gathering phase of this study, he was acting
as the school district coordinator of museum science

activities. For this, he was later given a national award.

83

Apart from his interest in physics teaching (as shown
in our daily informal conversation), Mr. Simon was a
football fan. On this matter, he was a strong supporter of
the school football team, so that during the football
season, football was the subject of Mr. Simon's discourse at
the end of class on Friday, and at the beginning of class on
Monday. During this conversation, they talked about
predicting scores, players, fan behavior, results, etc.

It should be noted that Mr. Simon was an excellent
discussant on issues dealing with his personal views about
his classes and the school as a whole. Through his actions,
this researcher "became native" up to the point of assisting
(on many occasions) his students on classroom physics tasks
and participating openly in everyday social conversation

inside and outside the classroom.

Mr. ll's

Mr. Ellis was in his late 505. He had been teaching
physics at the school for 20 years since he graduated from
college. He held a master's degree in science education
from the university located in the vicinity. He was the
coordinator of six physics courses offered at his school,
where 20 percent of the graduating class took at least one
course in physics. He was assisted by another physics
teacher who was responsible for two of these courses. In

addition to the four courses in introductory physics, Mr.

84

Ellis was also responsible for teaching an advanced physics
course offered to seniors.

Mr. Ellis was an active member of the State Association
of Physics Teachers and was a regular reader of such peri-
odicals as The American Journal of Physics, Psychology Today
and The Smithsonian. From these journals and other sources,
he constantly extracted his papers, cartoons and posters
which he eventually used to enrich the bulletin board with
materials related to the topic of the physics unit being
developed.

Mr. Ellis had been teaching physics with the Harvard
physics course since 1967, when he became familiar with the
course materials. The year before he had taught the PSSC
course. Through the years, he prepared a "package" for each
one of the Harvard physics courses. The package contained a
number of items such as unit objectives, exemplary tests,
lab instructions, problems sets (assignments) and readings.

During my role as a participant observer in Mr.Ellis'
classroom, I learned that Mr. Ellis was a rather reserved
person. who rarely' openly' gave his opinion on something
unless he was asked. However, it should be mentioned that
as I was about to leave the school, our discussions of
school physics and related issues were more open than at the
initial stages of the study. He was very concerned with

"what his students were getting" in his classroom which he

85

claimed to be "one of the best physics classrooms around."
In. our after' class conversations, he :made reference to
Piaget's psychology and the need to teach students to reason
before they go to college.

Apart from his duties as a physics teacher, Mr. Ellis

worked as a baseball coach for the school.

Mr. oward Room 150

The third character of this study was Mr. Howard, an
experienced teacher who was in his late 505. Mr. Howard had
been teaching physics at the school for 29 years. He
graduated about 31 years ago as a geologist-engineer and
eventually became involved in physics teaching after being
offered the opportunity to participate in the initial trials
of the PSSC implementation as a nationwide physics course.
He was in charge of four physics courses for seniors and a
zoology course for freshmen. .About 15 percent of the
graduating school population took physics at his school. He
had also taught chemistry and mathematics, in addition to
physics.

Mr. Howard had been teaching the PSSC course for 29
years. Apart from teaching physics and zoology, he was the
coordinator of the school media center, and assisted
students and teachers from the university located nearby.
In addition to his role as a physics teacher, Mr. Howard was

engaged in non-school related activities. He was one of the

86

co-owners of a small oil-rig company that operates in the
region. In this company, his main function was to work as a
"dowser" as a means to search for oil and gas. In the late
phases of this study, this researcher learned. that. Mr.
Howard was a strong believer in transcendental meditation,
and that during summer vacations, he offered courses on this
subject to parents, teachers and other interested people.
Mr. Howard was very open in our conversations on high
school physics and related topics. His main concern was to
have students "learn the vocabulary to talk physics." He
was also very open to having his classes videotaped or
audiotaped, without objecting to the researcher's purposes

and means.

The extbooks

Textbooks play an essential role in the nature of the
academic context enacted in schools. The purpose of this
section is to give the reader a broad description of the
textbooks being used in each one of the classrooms studied.
Both, Mr. Simon and Mr. Ellis relied on The Haryarg Ezgject
Ehygiggz or just project physics as it was frequently

called. Mr. Howard, on the other hand, advocated the use of

 

2Published. by Holt, Rinehart. & ‘Winston, New ‘York,
1981, under the direction of F. Watson, G. Holton and F.J.
Rutherford.

87

the Physical Science Study Committee3 (PSSC) . Both text-
books were widely used in high school physics courses across

the U.S.A. (see Pallrand & Lindenfield, 1985).

The ngyard Project Physigs
The harvard Project Physics was one of the new science

programs of the 60s. It was designed with three major
goals: (a) to teach physics from a humanistic perspective,
(b) to attract students to introductory physics and (c) to
find out more about the factors that influence the learning
of science (see The Harvard Project Ehysics, Preface). The
project directors spelled out the project aims as follows:

1. To help students increase their knowledge of the
physical world by concentrating on ideas that
characterize physics as a science at its best,
rather than concentrating on isolated bits of
information.

2. To help students see physics as the wonderfully
many-sided human activity that it really is. This
meant presenting the subject in historical and
cultural perspectives, and showing that the ideas
of physics have a tradition as well as ways of

evolutionary adaptation and change.

 

3Published by D.C. Heath & Company, Lexington, Mass.,
1976: and edited by V. Haben-Schain, J.B. Cross, J.H. Dodge
and J.A. Walter.

88

3. To increase the opportunity for each student to
have immediately rewarding experiences in science
even while gaining the knowledge and skill that
will be useful in the long run.

4. To make it possible for instructors to adapt the
course to the wide range of interests and
abilities of their students.

5. To take into account the importance of the
instructor in the educational process, and the
vast spectrum of teaching situations that prevail
(The Harvard Project Physics, Preface, 1981).

To achieve the above goals and aims, the authors
proposed a one-year course subdivided into six big units as
follows:

1. Concepts of Motion4

2. Motion in the Heavens

3. The Triumph of Mechanics

4. Light and Electromagnetism

5. Models of the Atom

6. The Nucleus

 

4This research study focused primarily on Chapter 3 of
this unit, which is entitled "The Birth of Dynamics:
Newton Explains Motion."

89

The Physich Science §thdy Committee (PSSC)

The PSSC physics course is one of the oldest "new"
science programs of the 605. It is a college-bound course
whose aim is to present physics "not as a mere body of facts
but basically as a continuing process by which men seek to
understand the nature of the physical world" (Haber-Schain
et al., 1976, Preface). The textbook is divided into 27
chapters which can be categorized under four main sections
or themes:

1. Optics and Waves (7 chapters)

2. The Study of Motion (10 chapters)5

3. Electric and Magnetic Properties (6 chapters)

4. The Atom (4 chapters)

In contrasting the characteristics of the PSSC physics
course with traditional physics courses, Marshall and
Burkman (1966) stated that:

1. The course covers less topical material than is
usually presented in high school physics while
penetrating more deeply into selected areas which
contribute most heavily to an understanding of the
universe.

2. Physical models are developed and used as they are

by scientists in attempting to explain phenomena.

 

5The data reported here, as far as this textbook is
concerned, focused on the third chapter entitled "Newton's
Law of Motion."

90

3. Physics is treated as a unified, interconnected
story, and as a human activity "set within our
society and carried on as part of the historical
development of mankind."

4. Less emphasis is placed on technological appli-
cations of physics and more on an understanding of
fundamental principles.

5. The laboratory is integrated more closely with the
rest of the course than is customary.

6. The materials provided for the students and the
teachers make a more complete kit of materials for
learning than have been available in any course
previously (Marshall & Burkman, 1966:28).

Aims, goals, characteristics and content of the

textbooks are key elements that determine how teachers enact

the school academic content (Clark & Elmore, 1981).

Tghcheg's Plghhihg
Teacher planning is a teacher's construct that has a
powerful influence on how academic contact is organized and
enacted in real life (Clark & Yinger, 1989b: Smith &
Sandelsach, 1979; Clark & Petersen, 1986). Clark and Yinger
(1979) identified at least eight different types of planning
as carried out by teachers: weekly, daily, unit, long

range, short range, yearly and term planning. Unit planning

91

is reported to be the most common approach followed by
teachers.

-According to Clark and Yinger (1979), there are three

clusters of reasons as to why they carry out planning:

1. Planning to meet immediate personnel needs (e.g.,
to reduce uncertainty and anxiety and to find a
sense of direction, confidence and security).

2. Planning as a means to the end of instruction
(e.g., to learn the material, to collect and
organize materials, and to organize time and
activity flow).

3. Planning to serve a direct function during
instruction (e.g., to organize students, to get
activity started, to aid memory and to provide a
framework for instruction and evaluation). (Clark
& Yinger, 1979, cited in Clark & Peterson, 1986:

261-262.)

Teachers' Conceptions of Elhnhihg

Analysis of field notes, interviews and documents from
the three classrooms observed, clearly indicated that plan-
ning was an important element of how the academic content
transpired in these settings. Basically, the type of
planning was by unit of instruction or chapter of the book.
This type of planning was conducted just before the chapter

got underway. Daily planning was also visible during so

92

called planning periods. During these sessions, teachers,
for example, decided what to include in the lesson, what
problems to solve, what demonstrations should be conducted

and what equipment to use, etc.

Mg. Simon's Planning

Mr. Simon's conception of planning is portrayed in the
following excerpts from an interview:

Planning is done by chapters from the project
physics textbook . . . and that usually takes a
week and a half . . . so we are biting off a chunk
of about that time size . . . and from there we go
to the objectives . . . and maybe this is the key
thing that we try to figure out. What is reason-
able to teach. the students about this?’ ‘What
skills we expect students to display?

Our planning includes a time line for this
material, and it also includes the objectives to
clarify our thinking about ‘what it is 'we are
teaching.

In planning, there are several parameters that we
consider, variety of activities . .. . and avail-
ability of equipment. Activities are varied as to
motivate students. They include: reading,
problems to solve, lecturing, experiments. The
equipment determines the type and variety of
demonstration and experiments that can be carried
out in class, either in a group or by individual
students.

Daily planning is carefully done through

worksheets which the activities . . . lectures . .

. labs. They also indicate where they (the

activities) start and what assumptions we would be

making. (Interview, December 12, 1986)

Examples of a unit plan and a daily plan are given in
Appendices A and B. The first one shows how the chapter on

dynamics was planned for. It includes days, topics,

93

objectives and assignments. Appendix B shows the worksheet
that was distributed to students on the day Newton's laws

were taught by Mr. Simon.

Mr. ElTis' Planning

Like Mr. Simon, Mr. Ellis also plans his teaching by
textbook. chapters which. were blocked out in. topics and
activities. The following excerpts from an interview help
to shed light on the above assertion. To the question of
how planning was conducted, Mr. Ellis answered as follows:

The basic part of planning comes from the textbook

(project physics). You either follow it in that

order, or try to amplify it by giving examples . .

. which are not in the textbook.

When planning for a unit (or chapter), I look at

the materials . . . textbook . . . equipment. I

block (the topics) out on the assignment sheet.

Some (blocks) take two or three days to complete.

When jplanning’ a chapter, I start out. with an

overall picture of what the chapter is about . . .

how much time should we spend, and then I

subdivide it. (Interview, December 12, 1986)

According to Mr. Ellis, the planning of a unit
includes: (a) searching for the appropriate demonstrations
to explain concepts, (b) arranging the bulletin board and
(c) preparing readings from the textbook and the package.
This process has become easier over the years as the
information pool has increased as a result of Mr. Ellis'

interest in searching for problems, questions, posters, etc.

relative to the units he teaches in his physics course.

94

Appendix C shows unit planning carried out by Mr. Ellis
as he was about to start teaching the unit on dynamics.
Text refers to the project physics textbook (1976 edition)
and H0 stands for handout in the package. This package, as
mentioned before, contained a series of handouts that
indicated the objectives of the unit, problems to solve,

experiments to be conducted and a sample test.

ML, Howgrd's Planning

Contrary to Mr. Ellis and Mr. Simon, Mr. Howard did not
rely much on written planning in order to guide the
organization of the academic contact. However, daily
observations of his classes clearly indicated the existence
of an underlying operational planning that was made
explicitly to students at the start of a textbook chapter.
Subsequent activities were somehow rooted in that initial
planning.

The following excerpts from an interview' with Mr.
Howard explain the above assertion. To the question, "What
kind of planning do you do in your physics class?" Mr.
Howard responded:

Well, most of it is in my head. Okay, I got to

know my kids pretty close . . . so my planning
will attempt to set up the experiments so that my
kids can do it . . . and if the data they are

going to get will be viable. That's my initial
step . . . get the graph done . . . interpret the
graph . .. . and find out what kind of conclusion
we can draw.

95

Planning derives from my experience with students

over the years. I first try to find out what they

know . . . and how badly those ideas are

"entrenched" on them. (Interview, February 24,

1987)

In subsequent excerpts of the interview, ZMr. Simon
indicated that his 29 years of experience with the PSSC
allowed him to conduct his teaching "relying on his head"
and not on "written notes" though he usually "scribbles a
few things . . . mostly on a weekly basis." This type of
written plan "never works out."

Mr. Howard's conception of planning was very much
consistent with what actually happens in his classroom
during the teaching of a unit on the topic of that unit.
For example, as he was about to start teaching the chapter
on dynamics, and after he introduced the nature of what the
chapter was about, Mr. Howard wrote out on the board the
purpose and procedures of experiment 20 as follows:

Experiment 20

Purpose: to determine how a force affects the velocity
of a body.

rocedure :

1. Practice giving a cart a run and then hook a timer
and run a recording tape for a v-t graph.

2. One tock is four time intervals of ticks.
3. Make a record of a push and let the cart coast.

4. Run two trials: 1. A cart and one brick.
2. A cart and two bricks.

96

5. Plot v-t graph of each type on a sheet of graph
paper.
(Field notes, February 4, 1987)

The above procedures somehow illustrate the subsequent
activities in the three days that followed until the
procedures for Experiment 21 were spelled out in a similar
fashion. During these three days, Mr. Howard made sure that
students get the graphs to him so that he could interpret
them on the blackboard and find out what kind of conclusions
can be drawn. Generally, once these conclusions were drawn,
the next step was to apply them in the solution of numerical
type of problems.

The teachers' conceptions of planning seem to fall
into two categories. The first type of planning was ex-
hibited by Mr. Ellis and Mr. Simon, who carried out a
written unit plan that was carefully segmented in topics.
The second category was represented by Mr. Howard, who, when
teaching a unit of instruction, relied less on written plans
and more on his experience and the knowledge of his
students. Mr. Howard's planning, as compared with the other
two teachers, was more lab-oriented. It was from the lab
experiments that. Mr. Howard drew' the unit's major con-

clusions that were eventually applied in the solution of

numeric problems.

97

Summarx

Chapter Four contained four sections. First, a
description of the schools and the classrooms were pre-
sented. Second, a description of the participant teachers
was given. Third, an overview of the textbooks used by the
teachers was considered. Finally, it presented a brief
account of the teacher's theories on planning, as well as
how this process was actually conducted for a ‘unit on
dynamics.

The inclusion of a large pool of background information
in Chapters Three and Four was needed because of the
important rglg that the information plays in relation to how
a teacher constructs an instructional sequence, —- especial-
ly how the different topics of a physics unit are put
together by the teacher. A knowledge of the teachers
(planning, characteristics, etc.), classrooms and textbooks,
as well as knowledge of how the researcher proceeded in the
interpretation and construction of the findings will help
the reader to understand how the three participant physics
teachers enacted (in real time) an instructional sequence on

dynamics.

C3LAPTER.FFVE

SEQUENCING SUBJECT MATTER IN
HIGH SCHOOL PHYSICS

Introduction

This chapter returns to the :major question of the
study: How is content knowledge enacted by experienced
teachers? The question specifically focuses on the nature
of the relation between the different topics (coherence) as
they are enacted in real time by physics teachers. In order
to shed light on these questions, "story-lines" have been
reconstructed from the teachers' discourses of a physics
unit on dynamics.

Analysis of the teachers' discourses as well as the
actions accompanying such discourses led the researcher to
take into consideration the fact that content knowledge is
enacted at two levels: macro-level and micro-level. A
macro-analysis yields the nature of the global coherence of
the unit of instruction (i.e., dynamics). It gives a sense
of how different topics are put together to 3produce a
coherent whole (Agar & Hobbs, 1985). On the other hand, a
micro- analysis gives specific details of how a single topic

is enacted in the context of a much larger unit. In this

98

99

study "macro-sequence" will be referred to as the construct
that results from a macro-analysis of a series of major
topics during the development of a theme (e.g., dynamics).
Similarly, "micro-sequence" will be referred to as the unit
that results from a micro-analysis of a specific topic.
Generally speaking, it could be said that the macro-
sequence is an abbreviated version of subject-matter inform-
ation content embedded in the story-line being enacted by
the teacher. It focuses on specific details of content-
knowledge organization and sequencing of a particular unit
of instruction. By the same token, a micro-sequence would
represent a map connecting the main statements presented in
a discourse segment focusing on a single topic of that unit.

The chapter is organized in two different parts. Each
part deals with a set of questions. The first part focuses
on the nature of the instructional macro-sequence (on dynam-
ics) as constructed by teachers. The second part deals with
the nature of the instructional micro-sequence (on Newton's
second law).

The results of this chapter will yield evidence for the
assertion that: experienced physics teachers differentially
construct subject matter at both macro and micro-levels. In
this sense, the subject matter is enacted in organic units
(topics) whose structure and elaboration vary from teacher

to teacher. At the macro level, we find that the topics

100

covered by the teacher are not necessarily the same as those
covered. by another' teacher' when. dealing' with a similar
theme. In addition, similar topics are enacted through
different sets of instructional events. At the micro-level,
the content organization is enacted through logical rela—
tionships (among similar concepts) that are differentially

structured by teachers.

PART 1
Constructing a Macro-Sequence on Dynamics

This section of the study compares the way three
experienced, physics teachers delivered. a ‘unit. on intro-
ductory dynamics to high school students. The main purpose
is to shed light on the following guiding question: What is
the nature of the coherence (global) of a unit on introduc-
tory dynamics as it is enacted by the participant teachers?
In particular, the study focuses on what topics are actually
enacted and how the topics are sequentially and logically

taught through time.

Story Lines on Qynamics

The nature of the coherence will be explained through
story-lines that show how individual teachers put together
different topics to eventually form a macro-sequence. Each
story-line was developed from a data source composed of

three entries: participants' verbalizations, participants'

101

actions and researcher's interpretation. In constructing
the story line, emphasis was made on the information content
being dealt with as well as the "enacted environment"
(Erickson, 1982) through which the information content was
manifested and delivered. The following story-lines present
three different accounts of individual teachers who strived
to communicate the theme of dynamics. The vignettes de-
scribe a day-to-day account of the way in which teachers
introduced new topics, the information content of each topic
and how the topics were related to one another. In addi-
tion, the vignettes also describe how participants inter-
acted with the immediate environment (books, worksheets and
lab equipment) through which topics, and the information
content embedded in them, were delivered.

Each story-line is first introduced, then followed by
the researcher's interpretation in the context of the
question being addressed. Mr. Simon's story-line is
presented first, followed by Mr. Ellis' and, finally, Mr.

Howard's.

gr. Simon's Story-Line on Qynamics

The following vignettes attempt to describe an
abbreviated story-line showing how Mr. Simon dealt with an
introductory unit on high school physics. The theme of the
unit is dynamics: i.e., the study of motion and its causes.

The purpose of the story-line is to describe the nature of

102

the global coherence across the different topics and
relationships among concepts being dealt with in the unit.
The history begins after Mr. Simon had concluded a unit
on Kinematics (i.e., the study of motion) and it concludes
prior to a unit on circular motion. The vignettes were
derived from a series of eight consecutive class observa-
tions, three of which were videotaped and transcribed.
Figure 5.1 shows in sequential-temporal order, the different
topics introduced by Mr. Simon during his teaching of an

introductory unit on dynamics.

Day 1 Introduction to Chapter 3: "Differences Between
Kinematics and Dynamics."

Day 2 The principle of inertia.
Day 3 Vectors.

Day 4 Exercise on vectors.

Day 5 Newton's Laws.

- Newton's law of Inertia.
- Newton's second law (a=F/m).
- Newton's third law.

Day 6 Experiment on Newton's second law (a=F/m).

Day 7 Egg drop competition.

Day 8 Quiz -- paper due.

Figure 5.1. Chronology of major topics and activities in

Mr. Simon's sequence on dynamics.

The story-line will tangentially touch on an activity

that developed parallel to the teaching of the unit on

103

dynamics. The activity was referred to by Mr. Simon as the
"egg drop competition" and he explained in an interview:
"Such an activity is to raise students' interest in physics
. . . and it is not related to the concepts and ideas being
taught in the unit." (Interview, September 22, 1986).

The story-line began after Mr. Simon had completed a
unit on kinematics in which students learned about average
velocity (Ad/At) and average acceleration (Av/At). In doing
so, they analyzed strobe records (ticker tape) of objects
moving in a straight line.

The story-line that follows is intended to describe the
nature of the coherence across the different topics talked
about in the development of the unit on dynamics. The day-

to-day account on dynamics is as follows:

Day 1 Introduction to Chapter 3
7:50 a.m.

After listening to the principal's announcements, Mr.
Simon began today's discourse making reference to the 19th
annual celebration of the egg-drop competition. He referred
to previous experiences, rules and winners of a competition

that takes place every year during physics classes.

8:07 a.m.
After indicating he would be providing the class with

more information about the competition, Mr. Simon made his

104

final opening statement on the next unit: "Well, today we
need to get started on Chapter 3~and we have a demonstration
for tomorrow . . . I'm going to do a demonstration on
inertia . . . a very interesting one." After that, Mr.
Simon distributed a worksheet and an outline for Chapter 3

(see Appendix A).

8:55 a.m.

During the 40 minutes from 8:07 until the end of the
class period, students were left alone to work on the work-
sheet that contained a set of questions students had to
answer by reading from the textbook. The questions focused
on issues such as: the difference between kinematic and
dynamic (this chapter), Newton's principles -- equilibrium,
balanced, unbalanced and net forces. (Fieldnotes, September

22, 1986.)

Day 2 The Principle of Inertia
7:45 a.m.

At the outset of the class, Mr. Simon again referred to
the egg-drop competition. He then distributed a handout on

inertia.

8:05 a.m.
Mr. Simon:
Well, today . . . we look at one grand underlying

principle of physics . . . very simple idea . . .
but it prevails everywhere . . . it extends not

105

only in the surface of the earth, but out in

space. Inertia is the property of all matters to

resist change in motion. Objects at rest remain

at rest . .. . objects in motion remain in motion

unless acted upon by an external force (principle

of inertia). In other words, if we have something

moving, it tries to keep whatever motion it has.

Okay. Let's do a little test to see if that's

true.

He then did six demonstrations having to do with
inertia at the demonstration table. The first three focused
on the need to eliminate friction to almost zero in order to
make things move at a constant speed. For this occasion,
Mr. Simon first slid a wooden block across the table, then a
similar block on a ‘track, and finally, the same block
mounted on a dry-ice disk. They did this to observe how
friction could be minimized, which allows objects to move at
a constant speed.

He made reference to Galileo's work on constant speed
and friction. The three other demonstrations that followed
focused on exerting a sudden force (kick) upon over-hanging
objects, and observing that the objects remained in place.
An example of this was to hang a 1 kg. object from a metal
rod with a thin string. A sudden force was applied to the

object by pulling a piece of string hanging from the bottom

of the object. In this case, only the lower string broke.

8:35 a.m.
After reinforcing the principle of inertia several

times (once after each demonstration), Mr. Simon summarized

106

the day's lesson: "Well, today we've shown you some
ridiculous and some not ridiculous examples. We've seen
inertia of massive objects . . . a block of steel (rolling
down an inclined plane) and so on. Does air have inertia?"
A student's answer: "It should."
Mr. Simon went to get an air propeller and a candle and
showed hoe the flame moved every time he spun the propeller

with his finger.

8:40 a.m.

Next, students were given an optional puzzle to think
about. Mr. Simon dropped a hollow and a solid metal disk,
both of the same weight, onto an inclined plane at the same
time. Observing that the solid disk slid to the bottom of
the ramp first, he posed the question: "Why does the solid

one get down first?"

8:45 a.m.

The above question (left unanswered) marked the end of
Mr. Simon's lecture. On their own initiative, students
began to fill out the worksheet Mr. Simon had distributed

earlier.

8:48 a.m.
While students filled out the worksheet, Mr. Simon
restated, the principle of inertia and announced tomorrow's

topic. To this effect he added:

107

What we are going to do next is look at another
property of motion. And that is . . . you accel-
erate under the influence of a force . . . in
order to take a close look at the fact that forces
point in a certain direction . . . so we have to
look at the properties of what we call vectors.

Any question on what we've done? (no comment) .

Then you will stand at ease until tomorrow when we

get involved with vectors and forces.

8:55 a.m.

As soon as Mr. Simon stopped addressing the class,
students engaged in different activities. Some of them, for
example, decided to complete the worksheet they had been
using throughout the lesson. In doing so, they borrowed
their peer's work. Others played around with the equipment
displayed on the demonstration desks. By the time the bell

rang, most students had already filled out the worksheet.

(Videotape and fieldnotes, September 23, 1986.)

Day 3 Vectors
8:30 a.m.

On the third day of Chapter 3 (dynamics), Mr. Simon
first distributed a set of three worksheets on vectors. He
suggested students grab a ruler and a protractor from his
desk, as they would be needed in the next two class periods.
Mr. Simon then started talking about the definition of a
vector, how to represent a vector (and an angle), and the
difference between scalars (mass, time, etc.) and vectors

(acceleration, velocity, field and force). Next, he talked

108

about the representation of a vector using an appropriate
scale. This short lecture was followed by the students
working on a set of four vector-related problems. One
example that is 'worth. mentioning 'was one that required
students to represent 12 Newtons. While working on this
problem, Steve (one of my closest neighbors) asked, "Mr.
Simon, what is a Newton?" The question was apparently
ignored. by the teacher, even ‘though two other students

raised the same concern later.

8:37 a.m.

At this point in time, most students had already solved
the problems at hand. Mr. Simon explained the "tip to tail"
method of adding vectors. The explanation was followed by
another set of problems for students to work on with Mr.

Simon's constant assistance.

8:53 a.m.

Mr. Simon: "Tomorrow, you will do an experiment
involving vectors." (Most students had finished the pre-
vious task.) "Okay, get ready to apply what you have

learned about addition, representation and so on of

vectors." (Fieldnotes, September 24, 1986.)

109

Day 4 vectors
8:00 a.m.

At the outset of the lesson (after taking care of daily
administrative procedures), Mr. Simon summarized what they
had covered on vectors the previous day. However, today's
task was to get serious about page 3 (problem set on vector
addition). He then suggested students spend the rest of the

hour on that task.

8:55 a.m.

For 40 minutes, students worked in groups or alone on
the task at hand. They were continuously assisted by Mr.
Simon who answered students' individual questions as they
worked on the problems set that he has given them. At the
end of the class, Mr. Simon picked up the worksheets
students had been working on. (Fieldnotes, September 25,

1986.)

Day 5 Newton's Laws

Day 5 began with Mr. Simon circulating a one-page
worksheet entitled "Newton's Laws of Mbtion" (see Appendix
B). After spending a few minutes talking about grades, he

moved to the blackboard, ready to start his lecture.

7:45 a.m.
He began by introducing today's lecture as a "pretty

powerful language . . . the greatest single achievement . .

110

. ever taken." He then said that physics "emerged from
confusion and disagreement . .. . because understanding the
universe began with Newton's contribution and his

principles."

7:55 a.m.

Mr. Simon stated,

Well, let's look at his (Newton's) laws of motion.

There are three of them. The first one you are

familiar with (from the lecture on Tuesday), the

so-called law of inertia. It says bodies at rest
remain at rest. Bodies in motion remain in motion

. . . straight line . . . constant speed . . . and

that's the law of inertia.

(Students followed Mr. Simon with the worksheet that they
needed to fill out accordingly.) Next, he talked about the
conditions and results under which the first law holds:

1. No unbalanced forces act (2F = 0). (Mr. Simon
elaborated on this idea by showing that the sum of
all the forces (four) acting over a piece of wood
resting on his desk was zero.

2. Velocity is constant.

3. Acceleration is zero.

8:05 a.m.

Having explained the conditions under which the first
law holds, Mr. Simon pointed out students already had a
pretty good idea of the first law. Seconds later, he

shifted to another topic, Newton's second law.

111

Let's go on to the second one . . . the biggy one

. . . the second law. It says if you do have an

unbalanced force, then you have acceleration . . .

and these are Newton's words. An unbalanced force

causes an acceleration, in the same direction and

proportional to the net force. That means that

acceleration is proportional to the force . . .

but the net force.
At this point in time, the board read:

2F ,=4 o

a Garnet

Next, he emphasized that a (acceleration) and "F"
(force) were vectors. He continued as follows: "Now the
second part of that (law) says that it (acceleration) is
inversely proportional to mass. That is to say, acceler-
ation is proportional to the inverse of the mass." The

board showed:

1
a _
06M

8:07 a.m.

After giving a couple of examples to illustrate the
relation a oil/m, Mr. Simon's next activity was to describe
the conditions under which the second law held. These
conditions can be summarized as follows:

1. There is net force . . . and that's what causes a

body to accelerate (F f 0).
2. As a result of this (force), the speed is not
constant and the acceleration is not zero . . .

and the object will:

112

a. accelerate
b. decelerate
c. change direction
With respect to the last statement, he added: "It is a
curve ball which does not make sense at this point . . . but

later."

8:10 a.m.
The immediate next step was to try to solicit from the
class some examples in which both laws applied. The final

result of this activity is indicated below:

Examples

Newton's first law: air track - car at constant speed
stopped car - ball on the shelf
weight on table

Newton's second law: speeding car

burning rocket (accelerating)
baseball as hit by a bat

Observe that some of these examples were discussed

earlier.

8:15 a.m.

Another set of examples followed. This time students
were given, in a worksheet, a series of v-t (velocity-time)
graphs: and they were asked to identify which one of the two
laws applied in each case. It was generally agreed that in

cases where V (velocity) was constant or zero, Newton's

113

first law applied. If acceleration was not zero, then

Newton's second law applied.

8:17 a.m.

Mr. Simon: "Let's go back to look at the equation form
of Newton's second law." He then referred to the two
statements made above (achnet and a cal/m) and pointed out
that Newton's second law could be expressed (mathematically)
as: a = F/m which could be read as: "Acceleration is
proportional to 'F' (force) and inversely proportional to

'M' (mass)."

8:20 a.m.

From the equation of Newton's second law, Mr. Simon
derived "Newtons" (Kg m/secz) as the units of force, and at
the very end of this explanation he communicated: "So,
that's where that Newton's business comes in . .. . that we
told you about before." (In previous classes he had used
the ‘word "Newton" ‘without explicitly' explaining ‘what it

was.)

8:22 a.m.

At this point in time, Mr. Simon began to distribute a
handout with a set of problems that required the application
of Newton's second law (a = F/m). Just before the students
started this task, he added: "I want you to write something

down you probably won't get out of your mind . . . silly

114

ideas involving these two terms. I want you to write down
the difference between what we refer to as mass and what we
call weight." He then explained that "weight is a force
caused by gravity. It varies because gravity varies from
place to place." He expanded on this concept by giving
several examples in which gravity varied. Seconds later he
moved on to the concept of mass: "Mass is the same as
inertia. In fact, mass is what we use to measure inertia,
and it is not affected by position . . . as gravity is."

The board read:

Weight:
1. Force caused by gravity.
2. Weight varies from place to place.
Mass:
1. Is the same as inertia.
2. Constant . . . not affected by position.
8:25 a.m.

Once students had copied down the information from the
blackboard, Mr. Simon proceeded:

Well, let me just tie this (lecture) up with a
little chat about Newton's third law. Newton's
third law is not mathematical (as the second law).
It is a sort of common sense law. In his prin-
ciple, Newton says, 'To every reaction there is
always an Opposite and equal reaction, ' or the
mutual action of two bodies upon each other are
always equal and directed to contrary parts.

115

He added that it was "easy to put it as for every reaction .
. . there is an equal and opposite reaction. Forces always
exist in pairs." The above statements were followed by a
series of examples in which the third law applies:
1. The earth pulling. on bodies (action) and bodies
pulling on the earth (reaction). -
2. The baseball bat hits the ball, the ball exerts a
force on the bat.
3. A man pulls on a donkey, the donkey pulls on a

man .

8:31 a.m.

Mr. Simon then demonstrated this law by blowing up a
balloon and asking the students to explain its motion in
terms of Newton's third law. Holding the full balloon, he
waited for several seconds for an answer. As students kept
silent, he explained that: "As the balloon goes up, it
pushes the air down, or the air is pushed down. There is
another force that pushes the balloon up causing it to
accelerate in the other direction (up)." He then restated
Newton's third law and suggested that students start working

on the problem set he had distributed.

8:34 a.m.
Students began to work on the set of problems with Mr.

Simon looking over their shoulders.

116

8:55 a.m.

Students ‘worked. on. the set. of problems ‘until five
minutes before the bell rang. As students waited to leave,
Mr. Simon referred to "tonight's tough game" between the
school football team and another local high school team.

(Videotape and fieldnotes, September 26, 1986.)

Day 6 Newton's Second Law Experiment
7:55 a.m.

At the beginning of the class period, Mr. Simon
reminded students about the egg-drop competition that would
take place tomorrow (Tuesday) after class. He then spent a
few minutes explaining the rules of the competition, as well

as what students needed to do in order to participate in it.

8:00 a.m.
Mr. Simon:
The experiment . . . we are going to do today is
going to be a class experiment. We are going to
have different people involved in analyzing the
data. And the last few minutes we are going to
assimilate our data . . . just a quick review of
the way we are going to analyze our data.
He first explained that there would be two groups. One
group of students (four) would keep the mass constant and
vary the force. A second group ‘would keep the force
constant and vary the mass. These two groups would obtain

the data (ticker tape) that would be analyzed by the rest of

the class. Mr. Simon explained that the rest of the class

117

would take the ticker tape to measure the velocity at the
beginning and the end of the tape, or to calculate the

acceleration of the body (cart).

8:05 a.m.

The first two groups were chosen arbitrarily and sent
to the two lab stations. Each station was already equipped
with: bricks, carts, ticker timers (one), ticker tape, pul-
leys and small weights (200 gr). Just before they started
to work, they were given a lab worksheet (see Appendix K) to

fill out.

8:10 a.m.

While the two groups worked at the lab tables, Mr.
Simon divided the rest of the class into eight groups of
three students each, who would analyze the ticker tapes

obtained by the first two groups.

8:20 a.m.

Both groups worked at their lab tables. They were
constantly assisted by Mr. Simon who checked to see if they
were varying the mass (group 1) and the force (group 2)
accordingly. Once students finished running the tapes, Mr.
Simon assigned them to the rest of the class (one tape per
group). Each tape had been marked as to whether the mass
and the force were constant or variable. The board showed

these labels:

118

Group 1
mass = 1, 2, 3, 4 (bricks)
force constant

Group 2
force = 1, 2, 3, 4 (weights)

mass constant

8:25 a.m.

While students worked on the data analysis, Mr. Simon
circulated around assigning identification numbers to the
students who were to participate in the egg-drop competi-
tion. He was constantly consulted about how to analyze the
ticker tapes, particularly about how to calculate "V1"
(velocity at the beginning of the tape), "V2" (velocity at
the end of the tape), and "T" (time interval between those

two instances).

8:40 a.m.

Mr. Simon: "Okay, Let's tie this up . . . if we can."
He sketched a four column table on the board and asked each
individual group for the acceleration value they had
obtained. As he moved along filling out the table on the
board, he stopped for a few seconds (staring at the board)
and added: "There is something wrong in here . . . errors

of 10000 percent." He completed the table as shown below:

119

 

 

 

 

 

 

 

Mass Acceleration Force Acceleration
1 669 1 15.3
2 2285 2 75
3 120 3 1020.5
4 4.7 4 52.7
8:55 a.m.

As soon as Mr. Simon realized that the acceleration
values were inconsistent with Newton's second law (the
acceleration should decrease in the second column, and it
should increase in the fourth column). He suddenly decided
to stop referring to the experiment and to Newton's second
law. Instead, he opted to ask for more volunteers to
participate in tomorrow's competition. (Videotape and

fieldnotes, September 29, 1986.)

Day 7 Egg-Drop Competition

On. the seventh. day students submitted. the: egg-drop
boxes and then were allowed to complete their papers (see
Appendix A) which were to be collected the following

morning. (Fieldnotes, September 30, 1986.)

120

Day 8 Quiz -- Papers Due
Once the papers were collected, a test on Newton's laws
was given. The test marked the end of the unit on dynamics.

(Fieldnotes, September 31, 1986).

Interpretation of Mr. Simon's Story-Line

The above story-line shows hOW' Mr. Simon and his
students interacted among themselves and with the immediate
environment (lab equipment, worksheets, books, etc.) to
construct an instructional macro-sequence on dynamics.
Figure 5.2 shows Mr. Simon's macrosequence on dynamics. The
major focus was on Newton's three laws of motion. These
were not presented in a lineal fashion. Instead, they were
developed in conjunction with the egg-drop competition
(unrelated to Newton's laws), and with two class periods on
the topic of vectors. The unit on dynamics began by having
students read about unbalanced and net forces and by pro-
viding them with an overview of what the unit was about.
The end of the unit was clearly marked by a quiz, though
content-wise one could affirm that the experiment on
Newton's second law closed the theme on dynamics. From then
on, Mr. Simon did not explicitly talk about the subject-
matter content pertaining to this topic.

The major topics enacted were:

1. Vectors

2. Newton's first law or law of inertia

121

1.0. Principle of Inertia.
"Objects at rest remain at rest . . . objects in
motion remain in :motion, unless acted upon. by an
external force."

2.0. Vectors: addition, representation and subtraction.

3.0. Newton's Law.

3.1.

Figure 5.2.

Newton's First Law.

This law works under the following conditions:
a. there are no unbalanced forces (ZF=0)

b. there is no acceleration

c. speed is constant

Newton's Second Law
Acceleration is proportional to the net
(unbalanced) force (a OLFnet)

Acceleration is proportional to the inverse of
the mass (a ocl/m).

Newton's Second Law works under the following
conditions:

a. there is an unbalanced force (1F f 0)

b. the acceleration is not zero

c. the velocity is not constant

Newton's Second Law is stated as a = F/m.

3.3. Mass and Weight
"Weight is a force caused by gravity and
gravity varies from place to place . . .
so weight changes from place to place."

"Mass is the same as inertia (resistance
to change motion) . . . it is not affected
by position . . . so it is constant."
Newton's Third Law.
"To every action there is always an equal and
opposite reaction."

"Forces always exist in pairs."

Mr. Simon's macro-sequence on dynamics.

122

3. Newton's second law (a = F/m)

4. Newton's third law

In addition to the above topics, there were also
subtopics. One of the most relevant subtopics was the
difference between mass and weight that followed the
discussion of Newton's second law.

A close look at the story-line above shows that
Newton's first and second laws were anaphorically linked to
the concept of net and unbalanced forces, and to the con-
cepts of velocity and acceleration described in the unit on
kinematics some days before. However, the three laws were
introduced in a rather discrete manner with no explicit
connection among themselves. The events dealing with these
laws seemed to have an end in themselves, for example,
during the topic shift that marked the introduction of the
law of inertia (Newton's first law). There was no explicit
anophoric reference to what students supposedly had read in
the textbook the day before (day 1). In the process of
elaborating on this law, through a series of classroom
demonstrations, one topic ‘that. emerged. was the idea of
friction "which should be minimized as to try to keep a body
moving at a constant velocity." This idea did not emerge
again during day 5, when the conditions under which the
first law held were explained. This is probably an example

of topic decay (Tannen, 1984) in which friction was no

123

longer a fundamental concept in the teacher's discourse.
Another example would be the notion of a vector that was
briefly mentioned in the events that led to the formulation
of Newton's second law.

The idea of discreteness among topics and subtopics can
be explained in the same vignettes in the story-line. In
the first vignette, Mr. Simon introduced the mathematical
equation of Newton's second law (a = F/m), and then
explained the difference between mass and weight. He
indicated that, "Weight is force caused by gravity. . . and
it varies from place to place," while mass "is the same as
inertia . . . and it is not affected by position." However,
no reference was made to Newton's second law.1

The second vignette took place on day 6 when Mr. Simon
conducted a cflass experiment on Newton's second law. Even
though he indicated how students were going to proceed to
study the relationship between acceleration, force and mass,
Mr. Simon did not make explicit reference to how to measure
the acceleration of the object being used, an instructional
event that had taken place a week before. A careful look at
the fieldnotes of that day showed that such an instructional
event took place at the end of a class period and lasted

only about two to three minutes.

 

18ince gravity (9) had already been introduced, Mr.
Simon could have indicated that since F = ma and a = 9,
then F (weight) = mg.

124

Mr. Ellis' Story-Line on Dynamics

Mr. Ellis' story—line on dynamics differed in several
respects from that of Mr. Simon, despite the fact that both
teachers used the same textbook, Project Physics. The
macro-sequence was developed over a period of nine consec-
utive class periods during eight school days (see Figure
5.3). All classes, except day 1 (Newton's first law), day 2
(test on vectors) and day 8 (test review) were properly
videotaped and transcribed. Days 1, 2 and 8 were
fieldnoted.

The following description represents a brief story-
line of how Mr. Ellis dealt with major topics during the
construction of his macro-sequence on dynamics. Its purpose
is to show the nature of the coherence (macro) across topics
and activities during the time the unit was being developed.
The story-line focuses primarily on topic shifts and on the
activities undertaken by participants during the development
of these topics.

Here again, the story-line was derived from a data
source that shows main entries: teacher's verbalization,
participants' actions and researcher's interpretation of
these actions.

As shown in Figure 5.3, Mr. Ellis focused on the

following major topics: Newton's first law, Newton's second

125

law, friction, difference between mass and weight, free fall

and terminal velocity, and Newton's third law.

Day 1 Newton's first law.

Day 2 Test on vectors.

Day 3 Newton's first and second law, friction.

Day 4 Newton's second law (demonstration).

Day 5 Weight and mass.

Day 6 Weight, free fall and terminal velocity.

Day 7 Newton's second law experiment (first hour).

Newton's third law (second hour)
Day 8 Test Review (Newton's Laws).
Figure 5.3. Chronology of major topics developed in Mr.
Ellis' macro-sequence on dynamics.

The following story-line describes in more detail how

major concepts were dealt with by participants.

Day 1 Newton's First Law
10:10 a.m.

Having spent the first ten minutes of the class period
on a test review for the next day's test on vectors, Mr.
Ellis announced a new topic: "In your own words, state
Newton's first law of motion. When you get through, bring
it back." While students read the textbook (yesterday, Mr.
Ellis asked them to bring it to class), Hr. Ellis prepared a

lab demonstration at his desk: he piled up a set of wooden

126

blocks (5 x 5) on the top of the table. David was the first
student to get up and show his work. He was given a candy
for it. Other students immediately followed. As soon as
most students had shown their work, Mr. Ellis began to hit
pieces of wood out from under one another with a metric
ruler. He then (without further explanation) looked for his

"package" (set of readings and assignments).

10:18 a.m.

Mr. Ellis began to skim through his package and quickly
assigned problem number three in handout 31. Students read
the problem that dealt with a body travelling at a constant
speed. Mr. Ellis commented that in this case the net force
(from unit on vectors) acting on the body was zero, and that

therefore, its acceleration was zero.

10:26 a.m.
At this time, Mr. Ellis moved to problem number four.

He added, "Okay, state Newton's first law of motion . . .

the law of maintaining the status quo." As students kept
quiet, he added: "Objects at rest keep at rest, unless
there is a force acting on them." David said the same law

could be phrased as, "Objects keep moving forever . . . if
there is no friction." Without further comment on David's
statement, the teacher stated that Newton's first law is

also called law of inertia, where inertia means, "resistance

127

to start moving or to change motion." Mr.- Ellis also

elaborated on the idea that "inertia is a measure of mass."

10:39 a.m.

At this point in time, Mr. Ellis picked up the wooden
blocks again and-piled them up on his desk. After hitting
them out from the bottom up, he commented that the top ones
did not move because, "They don't have time to as the hit is
applied very quickly." Following this demonstration, a bag
of apples was hung from the ceiling with a thin string.
Another piece of string was attached to the bottom of the
bag. He then asked: "If I pull here (bottom), which string
will break first?" The students' answers varied. Mr. Ellis
then pulled very slowly observing that the top one broke
first. He then pulled very quickly, breaking the bottom
string. He explained that the top string had not time to

MOVE .

10:46 a.m.

Having finished the demonstration, the teacher referred
to the application of Newton's Law to explain how difficult
it is to walk on slippery roads during the wintertime due to
the small frictional force between the road and the shoes.
He then assigned problems "36-37 and 38 . . . for tomorrow."
He reminded students that there ‘would. be no school on

Wednesday because of parents' conference and Thursday

128

because of the SAT test. (Videotape and fieldnotes, October

17, 1986.)

Day 2. Test Day (Vectors)

The main activity to date consisted of students taking
a test on the previous unit on vectors which had been devel-
oped the previous week. The students learned about vector
properties: addition, subtraction and representation of
vectors. The notions of balanced forces and equilibrium
were also discussed. Halfway through the class period, Mr.
Ellis wrote down on the board: "Section 3.7" and later
referred to individual students to read that section of the
text as they left the room. That section of the textbook
deals with Newton's second law. (Fieldnotes, October 20,

1986.)

Day 3 Newton's Second Law

On this day, the lesson dealt primarily with Newton's
second law and the relationship between the net force
applied to a body and the acceleration that the body
acquires. Concepts such as net force, unbalanced force and
force of friction were central topics in the discussion.

This discussion was briefly summarized as follows:

10:03 a.m.
After checking attendance, Mr. Ellis made a brief

comment on Newton's first law, focusing on some "wrong"

129

statements made the previous Friday. He added, "What you
said is not correct. You said, 'if friction does not exist,
an object will coast forever.‘ Well, that is not the first
law of motion. You don't have to talk about friction to
define it." Mr. Ellis elaborated on the idea that the first
law deals with inertia as the "capacity of a body to main-
tain its motion." "Inertia," he added, "is measured in
kilograms, and it is an intrinsic property. . . that does
not change with position." When elaborating on this idea,
Mr. Ellis asked a girl to compare the inertia of two objects
(light and heavy) by shaking them, observing that the heavy

object was harder to shake than the light one.

10:25 a.m.
Mr. Ellis added that Newton's first law deals with
equilibrium where,
The net (unbalanced) force is zero. Under a net
force of zero, a velocity of a body does not
change. However, if an unbalanced force acts on a
body, then it causes the body to accelerate and in
this case we talk about Newton's second law.
Newton's second law "indicates that an unbalanced force . .
. causes something to accelerate" (Mr. Ellis wrote down:

Fnet = ma). He added, "This is a cause-effect

relationship."

130

10:30 a.m.

The mathematical formulation of Newton's second law was
followed by an explanation of the units in which forces are
usually expressed. Mr. Ellis substituted kg and slugs for
"m" (mass), and m/sec2 and ft/sec2 for "a" (acceleration),
and concluded that there were two force units: Newtons (kg

m/secz) and pounds (slugs feet/secz)."

10:35 a.m.

At this point in time, Mr. Ellis looked for his package
and asked students to open it to Handout 32 (see Appendix
J). From then on the class worked on a set of five problems
dealing with the application of Newton's first and second
laws. The first three problems dealt with the idea of how
friction affects the net force. During this discussion, Mr.
Ellis actually measured the force of friction between the
floor and a cart by pulling a girl across the room on the
cart. The force of friction could be read on a scale the
girl was holding while being pulled by the teacher. (This
experiment would be conducted next week.) The force of
friction obtained on the scale was eight Newtons. Following
this demonstration, Mr. Ellis added that the force of
friction was equivalent to the resultant force (from last
week) and to the unbalanced or net force. The first three
problems on friction and Newton's second law were followed

by two different problems. The first one of these asked the

131

students to calculate the acceleration of a body being
pushed by a force of 1,000 Newtons up a 60° incline. Before
going into the solution, Hr. Ellis remarked, "That's why we
need to study vectors . . . as they are powerful to solve
these kinds of problems." In this problem, Mr. Ellis split'
the 1,000 Newtons vector into two components, indicating
that the net force would be the component in the direction
of the motion. He then substituted the respective values (m
and Fnet) in the equation Fnet = ma. The last problem
proposed required the application of some kinematics equa-
tions (first unit developed two weeks earlier), as well as
Newton's second law equation. It consisted of calculating
the net force applied to an ice puck given its initial
velocity, distance traveled and mass. Having solved this
last problem, Mr. Ellis pointed out that a similar situation

would be presented to students in the hallway next week.

10:40 a.m.

Mr. Ellis assigned problems to be solved for tomorrow.
He pointed at the board and added: "Those are questions
involving Newton's second law." During the remaining ten
minutes, students worked quietly on the set of assigned
problems. Hr. Ellis remained at his desk assisting a girl
(Nana) who was concerned about her test on vectors.

(Videotape and fieldnotes, October 22, 1986.)

132

Day 4 Newton's Second Law Demonstrations

In today's lesson, Mr. Ellis first showed qualitatively
that in Newton's second law, the acceleration of a body
(cart) was proportional to the net force applied to it, and
secondly, that the acceleration was also proportional to the
inverse of the mass of the body being moved. The following
description indicates major events developed during the 50

minute class period.

10:02 a.m.

After briefing students on the previous evening's
parent conference, Mr. Ellis pointed at the board where he
had already written the equation for Newton's second law
together with a set of Kinematic equations (Pnet = ma, Vf2 =
Vo2 + 2ad, and V = Vo + at). He rewrote Newton's second law
in terms of acceleration (a = Fnet/M) and began to elaborate
on the idea of how the mass of a body affects its
acceleration. Relying on two newspaper articles, Mr. Ellis
emphasized that when the mass of a body is small, the
acceleration is larger and vice versa. Such is the case of
gymnasts who are given medication to retard their normal
growth, and the case of old Mig airplanes that accelerated

slowly due to their dependence on heavy metals.

133

10:05 a.m.

The teacher put the articles away and began to set up a
demonstration with a wooden cart on a wooden platform being
pulled by a rubber band. (He did not explain what he was
going to do.) Mr. Ellis asked for Melissa's assistance to
hold the cart on one side of the platform while he stretched
the rubber band and waited for Melissa to set the cart free
so that he could catch it on the other end. He then showed
that as he increased number of the rubber bands from one to
four, the speed of the cart increased at a rate difficult to
be perceived by the eye. Once these four trials had been
completed, Mr. Ellis moved back to the board and explained
that Newton's second law gives a relation between three
variables (F, a and M) and that to examine two of them, "we
had to keep the third one constant." In this case, the
constant variable was the mass of the cart (1/2 kg). He
added:

If we keep the mass constant, then we have a

direct proportion . . . between acceleration and

the net force (rubber bands). (The board showed:

a afiFnet.) What this means is that as we double .

. . or triple the force, we double or triple the

acceleration.

Mr. Ellis remarked that this statement could be expressed

as:

32 F2

134

Having established this relation, the teacher filled out a
table (handout 32) in which individual students were requir—
ed to apply the above equation to find the values for a, F

and m accordingly.

10:22 a.m.

Once the class had completed the previous exercise, Mr.
Ellis moved back to the demonstration table to vary the mass
and keep the force constant (rubber band). Assisted by
Melissa, Mr. Ellis added one, two and three bricks (1 1/2 kg
each) on top of the cart and had students observe how the
acceleration decreased as the number of bricks increased.
Mr. Ellis then stated that, "It is difficult to learn about
reciprocal relationships . . . such as the case of acceler-
ation and mass. As one gets bigger (mass), the other gets
smaller (acceleration)." He expressed this statement as
follows:

a 0(1/m

and concluded that the above equation could be written

in the following way:

31 m1

32 11"2

135

10:22 a.m.
Mr. Ellis: "Let's go to question 5." In the next
eight minutes, students were individually asked to apply the

above equation to solve for a, F and m in question 5.

10:30 a.m.

Before Mr. Ellis stopped to summarize what they had
covered up to that time, he gave a third related exercise.
Mr. Ellis found his unit schedule (pink sheet he had
distributed earlier) and briefly referred to what he had
covered since last Friday. He also made reference to the
hallway experiment on Newton's second law next week. "This

would be another day on Newton's second law," he said.

10:35 a.m.

Mr. Ellis assigned homework. He pointed at the set of
problems already written on the board and shortly thereafter
students began to work on them until the end of the hour.
While students worked on these problems, Mr. Ellis circu-
lated around the room showing each student the grade she/he
had obtained on the previous test. (Videotape and field-

notes, October 24, 1986.)

Day 5 Weight and Mass
The lesson centered on the distinction between weight

and mass.

136

10:02 a.m.
At the outset of the lesson, after complaining about
students' tardiness, Mr. Ellis opened the lesson as follows:

"This is a concept which I am not naive enough . . . to know

that it is confusing . . . and this is the difference
between mass and weight. People use them interchangeably,
which adds to the confusion." He indicated that usually

chemistry teachers "across the hall" were primarily
responsible for students' misunderstanding of the distinc-
tion between these two fundamental concepts in physics.
This discussion was followed by Mr. Ellis' elaborating on
the following statements related to the concepts of mass.

- mass measures inertia (in kilograms)

- mass is an intrinsic property built into the

object
- mass is measured using a balance (not a scale)

- mass does not change with position

10:16 a.m.

Having established the definition of mass, Mr. Ellis
first explained the difference between a balance (to measure
mass) and a scale (to measure weight), before going into the
concept of weight. The following interaction showed how

this concept was introduced.

137

Mr. Ellis: Now, weight . . . I weight unfortunately
about 200 pounds. What does it mean when I say I
weight 200 pounds . . . see . . . that (students keep
quiet) (5 sec.) . . . that's not an intrinsic property.
That's not something that belongs to me. What does it

mean . . . when I say I weight 200 pounds?"

Student: You are pulling down on the earth with 200

pounds.
Mr. Ellis: But why am I pulling down?
Student: Gravity . . . force of gravity.

Mr. Ellis: But what causes gravity? The bottom line

here is . . . I weight 200 pounds because the earth

loves me. It attracts me. It pulls down on me with
200 pounds. It likes me more than it likes you.
(laugh)

From here on Mr. Ellis explained that because gravity
changes, weight also changes as opposed to mass which is
always the same. He explained that weight is a force that
depends on the interaction of bodies with their surround-
ings. Using a small scale, Mr. Ellis showed that a 1 kg
object weighs 10 Newtons at "this position of the earth"
(lab). He indicated that the net force acting on net mass

(1 kg) was zero because there was an equal force acting in

138

the opposite direction. As soon as the object was released
it would be in a free fall situation in which the only force
acting on it would be the force of gravity. Following the
previous discussion, Mr. Ellis substituted the values of m
(= 1 kg) and a (= 10 m/secz) into Newton's second law (F =
ma) and concluded that, "Indeed, the force acting on a 1 kg
object in free fall was 10 Newtons." The argument led Mr.
Ellis to affirm that mass and weight are related by Newton's
second law (F = ma) for the special case in which "a"
(acceleration) is equal to "g" (acceleration of gravity).
In this case, weight then could be determined using the

equation: F = mg.

10:21 a.m.

Having established the difference between weight and
mass and the equation that related both terms, Mr. Ellis
solved a set of three problems (from the package) that

required the application of the weight equation.

10:35 a.m.

At this point in time, Mr. Ellis found his pink sheet
(unit schedule) and indicated: "This is block 5 . .. . and
there are five questions assigned for today. They deal with
the difference between weight and mass." He insisted that
students turn in their work on time, and, "At the beginning

of the class period. Otherwise, it won't count."

139

10:50 a.m.
Once the problem had been assigned, students worked
quietly on it until the class period was over. Few of them

requested any help from Mr. Ellis.

Day 6 Weight, Free Fall and Terminal velocity

The main issue of this day's lesson centered on the
concept of free fall and its relation to weight, mass and
acceleration of gravity. A second major topic dealt with
was the concept of terminal velocity that was characterized
as the velocity reached by a body where the net force is

equal to the air resistance.

10:01 a.m.

At the outset on the lesson, once students had handed
in their assignments, Mr. Ellis referred to the 1 kg object
(it was there yesterday) hanging from a hook above Mr.
Ellis' desk. He mentioned that the reading on the scale was
a measure of weight and not mass as some students had

written on some of their assignments.

10:02 a.m.

Mr. Ellis picked up a couple of toy gun and jumped over
his desk. From there, he described that one gun was loaded
with a single dart, while the second was loaded with a dart
with a ballbearing attached to it. He then asked (hands

touching the ceiling), "If I stand up here and drop both of

140

these darts, which one will strike the floor first?" Most
students answered that both would drop at the same time
because of the acceleration due to gravity. Mr. Ellis then
asked a second question: "Is there any difference between
dropping them and firing them? If I fire them, which one
will strike first?" (with the gun loaded). The answers
went two ways: "same time," and the "ball bearings." Mr.
Ellis explained that since both guns were exactly the same,
both darts would receive the same force but that one (ball
bearing) was heavier (had more inertia) and, therefore, it
would be harder to move initially. He then fired both guns,
observing that the lighter dart struck the floor first. He
repeated the demonstration firing both guns in the hori-
zontal direction. This time the heavy dart fell behind the

light dart.

10:10 a.m.

As soon as Mr. Ellis jumped off his desk, he looked for
his package and added: "Handout 33 . . . (5 sec) . . . you
can have some ideas about mass and weight and Newton's
second law, but this question will puzzled students . . .
and this is question 4 . . . 4a. Tell me, what is meant by
'free fall?'" As the students kept silent, Mr. Ellis stated
that "free fall means that we neglect any resistance and
that the only force acting is the weight of the body." He

then posed a second question: "Why then don't heavy objects

141

fall faster than lighter objects? Why doesn't the heavy
dart fall faster than the light dart?" After a lengthy
discussion on how objects are attracted by the earth, Mr.
Ellis said that "motion depends on two things . . . from
Newton's second law . . . those two things are force and
mass." Mr. Ellis commented that students were looking at
only one thing, which was acceleration (or gravity). He
moved to the board and wrote down:

Fg = mg

g = Fg/m
He explained that acceleration (g) depends on the weight and
the mass of the body, and that as the mass increased, so
does the weight. He finally added, "Though it is true that
heavy objects have a bigger force acting on them, they have
more inertia, the acceleration is the same as indicated by

the relation Fg/m."

10:25 a.m.

Having explained that heavy objects fall in free fall
at the same rate as light objects. Mr. Ellis described how
air resistance can exert a force in the opposite direction
to the weight (force). He explained. that as the air
resistance gradually increased, the net force (weight-air
resistance) decreased. "When these two forces become equal,
then the body is not in free fall any more and the body is

moving with what is called terminal velocity." He added:

142

"In this case, the net force would be zero and the air

resistance would balance the weight of the body."

10:10 a.m.

Mr. Ellis talked about some examples in everyday life
where air resistance could balance weight (e.g., skydiving).
He then selected two problems from the package (Handout 34)
that required the application of Newton's Second Law, the
concepts of weight and vectors. The first problem used the
"Atwood Machine." (There were two demonstration set ups of
this machine in the room.) He showed how the acceleration
of two bodies with different masses could be calculated.
They were attached with a common string that passed through
a pulley system. The second problem dealt with a similar
system, but this time one of the masses was allowed to slide
on top of a table. In both cases, Mr. Ellis carried out
demonstrations before going over the solution to the problem

on the overhead projector.

10:41 a.m.

At this point in time, Mr. Ellis looked from his pink
schedule sheet (this was a sign that the lecture was already
over) and briefly described the material covered in block
six. He then suggested that students read about block seven
in their books: Newton's Third Law. He added: "For every

reaction there is an equal and opposite reaction." The

143

third law would be discussed in the second hour of the first
double period on Thursday. The first hour would be devoted
to Newton's Second Law Experiment (block 4). Students were
advised to go over the sample test on Newton's laws for

Friday.

10:55 a.m.

As soon as Mr. Ellis put away his pink sheet, students
engaged in all sorts of conversation (there was no home-
work), and played around with some of the stuff left on the
lab tables. (Videotape and fieldnotes, October 28, 1986.)
Day 7 Newton's Second Law Experiment and

Newton's Third Law

This was the last lesson devoted to the unit on
dynamics. This was a double-hour class period. In the
first. period. Mr. Ellis conducted. a class experiment to
measure the mass of a student by pulling a cart along the
hallway in front of the physics classroom. Pulling consis-
ted of a constant force that was measured using a scale held
by the student whose mass was to be measured. The second
hour was devoted to the idea that "forces come in pairs"
(Newton's Third Law). The following story-line describes
how these two lessons were dealt with, beginning first with

Newton's Second Law Experiment.

144

First Hour: Newton's Second Law Experiment
9:19 a.m.

At the outset of the lesson, Mr. Ellis circulated
around handing back the test on vectors (taken last Friday).
He reviewed some of the questions and complained about the
poor grades obtained by some students in spite of the amount

of time spent on the vectors unit.

9:20 a.m.

After' collecting' the test answers. and.jputting' them
away, Mr. Ellis remarked:

Again, take your package . .. . turn to Newton's

experiment . . . it would be in the end of Chapter

3 . . . after handout 39 . .. . two experiments.

Skip the one on adding forces . . . and the spring

scale . . . that's another one on Newton's Second

Law. Read the first two paragraphs please.
While students read, the teacher began to search for some
lab equipment: a scale used to :measure the force of
friction the previous week, the cart used to carry a student

while measuring such a forces, timers, and a plastic red

hat.

9:23 a.m.

Having placed the equipment on his desk, Mr. Ellis
circulated a handout entitled: "Newton's Second Law Experi-
ment" (See Appendix D). Then, he asked for a rider for the
cart. Jim stood up and Mr. Ellis put the red hat on his

head before pulling him across the room at a constant speed.

145

The scale (held by Jim) read 7. While Mr. Ellis was

pulling, the following interaction took place:

Mr. Ellis: What am I measuring? (pulling the cart
with Jim on it) This is coasting along. What is the

net force?

Student: Zero.

Mr. Ellis: Zero . . . no force. How hard am I

pulling?

Student: Seven.

Mr. Ellis: Seven. So, that must be the force of
friction. So, what we are doing here is determining
the force of friction. How hard must I pull to keep it
rolling at a constant speed? It is not accelerating,
there is no net force . .. . so in the first line (of

the handout), write seven.

9:25 a.m.

After determining the force of friction (between the
floor and the cart wheels), Mr. Ellis asked for a puller.
John volunteered, and Mr. Ellis asked him to pull Jim (on
the cart) with a force (on the scale) of 40 Newtons. They
practiced pulling at least three times in front of the

class. Mr. Ellis insisted John keep the scale reading at 40

146

Newtons. The next thing Mr. Ellis did was to ask a third
student, Chris, to go out to the hallway to use tape to mark
the starting and the stopping lines, separated by a distance
of approximately 10 meters. Before giving the order "Let's

go out," two girls were assigned to control the time.

9:30 a.m.

In the hallway, John pulled Jim (on the cart) at least
eight times. They carried out three trials before taking
any measure. Mr. Ellis was in charge of giving the order
"ready, set, go." Each time he insisted John keep the
reading at 40. At the end of each run, he asked the time
keepers to read the time it took John and Jim to cross the

finish line.

9:40 a.m.

Back in the room, Mr. Ellis first asked for the times,
and then copied them on the board: "6.0, 7.03, 6.6, 8.90,
6.82, 7.23, 7.26."

He then crossed out the two extreme values (6.0 and
8.90) and computed the average of the remaining ones. He
got 7.03. The next step was to calculate Jim's acceleration
which could be "kinetically done using the equation d = Vt
+ 1/2at2." (This equation had been on the left and right

hand sides of the board since last week.) Since the initial

147

velocity was zero, and the distance between the starting and

stopping lines was 11.20, acceleration was given by:

 

d = Vot + 1/2at2
2 x 11.20

a = = .40 m/sec2
7.032

10:43 a.m.

At this point in time, Mr. Ellis added, "The problem is
not over . . . that's acceleration. Now, mass is . . . net
force over acceleration. We look back to the first line (in
the handout). What is the force of friction? (He had

written on the board m = Fnet/a°)
Student: Seven.
Mr. Ellis: Seven. How hard was John pulling?
Student: 40.
Mr. Ellis: 40. What was the net force?
Chris: 33 Newtons

Mr. Ellis: Even though John was pulling with 40, seven
of them overcame friction . . . that's the net force

John was pulling.

He then wrote the following on the board:

m = Fnet/a Friction = 7 Newtons Fnet = 33 Newtons

148

The next step was the substitute the values for the a
and Fnet in the equation m = Fnet/a to get m. The value
obtained was 81.68 kg. Jim (the rider) was surprised and
complained that "he did not weigh that much." Mr. Ellis
went into his office and came back with a bathroom scale and
asked Jim to step on it. He added that "although this was a
scale (not a balance), it could read kilograms and pounds."
Jim stepped on it (wearing the red heat and holding the
cart) and the reading was "80 kilos." Mr. Ellis subtracted
6.8 kg (weight of cart) from that figure and asked Jim, "Do
you weigh about 72 kilos, Jim?" Jim nodded his head affirm-
atively. Finally, Mr. Ellis commented that "we were off by
2 percent . . . hope this (experiment) will make you true

believers in Newton's Laws."

9:45 a.m.
From now until the end of the class period, students
and teacher engaged in friendly conversation, occasionally

making reference to the experiment they had just finished.

Second Hour: Newton's Third Law
10:01 a.m.

During the 10 minute break, Mr. Ellis cleared the board
and put lab equipment away. He replaced the one kilogram
object hanging from the ceiling above his desk with the 16

pound black bowling ball he used when describing the idea of

149

inertia the previous week. At the beginning of the lesson,
Mr. Ellis suggested that students prepare "the sample test
for tomorrow . . . which would be the last class on Newton's

laws.

10:02 a.m.

The teacher picked up a cloth ball from his desk and
said: "Newton's Third Law . . . I have a Nerf ball here. I
confiscated it from two students last year. They have not
come to pick it up yet." He went on, "On Newton's Third
Law, I am going to go over some demonstrations . . . that I
think . . . its complexity gets harder and harder. So, if
you would turn to your reference handout 35 . . . on
Newton's Third Law . . . question 2." Seconds later Mr.
Ellis kicked the cloth ball and asked if his foot exerted a
force over the ball or vice versa. Some students imme-
diately responded, "both," while the others said, "the foot
on the ball."

In "view of this confusion," Mr. Ellis looked for a bat
and hit the hanging bowling ball and asked: "Does the bat
exert force on the ball, or does the bowling ball exert a
force on the bat?" Again, the answers were split into two
groups -- one group agreed that, "it is the ball that exerts
a force on the bat," and the second group believed in the
idea that "both" were exerting forces. Mr. Ellis then

looked for the cloth ball, kicked it again and students

150

reiterated that he was exerting a force on the cloth ball.
Mr. Ellis pointed out, "There would seem to be some incon-
sistencies here as students were of the idea that when he
hit the bowling ball with the bat, there was a force acting
on the bat, but when he kicked the cloth ball, the force was
acting on the cloth ball."

Having concluded with the previous two demonstrations,
the teacher asked, "What's Newton's Third Law?" .After
waiting for a few seconds for an answer, he added,

It comes down . . . usually . . . as for every

action . . . there is an equal and opposite

reaction. Actually, that is not the third law.

It says for every force . .. . there is an equal

and opposite force. Forces do not come alone.

They are always paired up, they are equal in size

and they act on different bodies . . . or

different objects.

He elaborated on the idea that every time he hit the
cloth ball (or the bowling ball) there was a force of the
same size acting in the opposite direction. He explained
that one body might be slower than the other because of
inertia (resistance to move) "that is, heavy masses move

slower than lighter ones under the influence of the same

force."

10:10 a.m.
At this point in time, Mr. Ellis asked students to
identify the "action-reaction" forces as indicated in seven

different everyday situations described in the package. In

151

closing’ the previous discussion, he Icommented: "forces

always come in pairs."

10:17 a.m.

As soon as the previous discussion. was over, the
teacher took two carts and placed them on the floor (in
front of the class). He then announced "problem 8." While
students read what this problem was about, he asked two
volunteers to come up to the front and step on the carts.
He gave them a yellow rope to hold and suggested they keep
it seven meters apart. Mr. Ellis told one of the students:

"Mike, you will pull, okay?" Looking at the second student

he added: "Kathy, would you hold?" Next he posed the
question: "Who's going to move?"
"Both." "Mike will move" were the answers that

followed. Both students ended up in the front row after Mr.
Ellis had asked Mike to pull the rope. Mr. Ellis elaborated
that in fact both students were pulling with the same force
and that Mike, who was heavy, had moved the shortest dis-
tance .because of his greater' mass, and. therefore, more
inertia. He insisted that the action and reaction forces
were not Mike pulling Kathy or Kathy pulling Mike, but "Mike
pulling on the rope, the rope pulling on Kathy and Kathy

pulling on the rope and the rope pulling on Mike."

152

10:29 a.m.

After restating that the force of action and reactions
were equal in size and opposite in direction, Mr. Ellis
performed three more demonstrations that he explained in

terms of Newton's Third Law.

10:45 a.m.

At this time, Mr. Ellis began to take away the
equipment he had used in the demonstration, allowing stu-
dents to circulate around and interact with the equipment if
they wished to do so. There was no assignment. (Videotape

and fieldnotes, October 30, 1986.)

Day 8 Test Review (Newton's Law)

Interpretation of Mr. Ellis' Story-Line

The above description indicates that Mr. Ellis focused
on three major topics: (a) Newton's First Law, (b) Newton's
Second Law and (c) Newton's Third Law. In addition, he
focused on the subtopic of inertia. The subtopics friction,
mass versus weight, and free-fall and terminal velocity were
developed as an extension or application of Newton's Second
Law. Figure 5.4 shows a summary of the information content
being delivered by Mr. Ellis in the unit on dynamics.

In constructing the first law, Mr. Ellis drew from the
concept of net force that he had explained in the previous

unit on vectors. From the first law (objects at rest keep

153

Newton's First Law.
"An object at rest stays at rest unless there is a net
(unbalanced) force acting on it."

Newton's Second Law.

"If there is a net (unbalanced) force acting on a

body, it creates an acceleration" (F=ma).

2.1. "Friction is a net force that affects motion."

2.2. "Acceleration is proportional to the net force
(a d Fnet) ."

2.3. "Acceleration is proportional to the inverse of
mass (a C(1/m)."

2.4. Mass and weight.
"Mass is resistance to change a body motion . .
. it is an intrinsic property . . . which does
not change with position . . . it is measured in
a balance."

"Weight is a special case of Newton's Second Law
where the acceleration of the body is equal to
the acceleration of gravity. It changes with
position . . . and it is measured with a scale."

2.5. Free fall and terminal velocity.
"An object is in free fall when the net force
acting on it is equal to its weight and the air
resistance is zero."

"An object reaches its terminal velocity . . .
when the net (driving) force is equal to the air
(resistance)."

Newton's Third Law

"For every force there is an equal and opposite force.
These forces are equal in size and opposite in
direction."

Figure 5.4. Mr. Ellis' macro-sequence on Dynamics.

154

at rest unless there is a fbrce acting on them), the idea
that inertia is the capacity of a body to maintain its
motion was established. After indicating that friction had
nothing to do with the first law, he established Newton's
Second law, "If an unbalanced force acts on a body, then it
causes the body to accelerate." This statement was followed
by a series of events dealing with "friction as a net force"
or resultant force, and with the application of Newton's
First and Second Laws in the solution of numerical problems.

The development of Newton's Second Law (explained in
detail in Part II of this chapter) was anaphorically
(Halliday and Hasan, 1976) done by Mr. Ellis drawing on the
concepts of acceleration and inertia. In this sense, he
established that "acceleration is proportional to the net
force" and "acceleration is proportional to the inverse of
the mass" (or inertia). Newton's Second Law was used to
explain the distinction between mass and weight and the
ideas of free fall and terminal velocity.

Newton's Second Law was demonstrated again later (day
7) during a laboratory experiment. The content of the
experiment was anaphorically linked to most of the topics
already taught. A close look at the vignette on day 7
(first hour) shows the application of the following topics:
friction, weight and mass, Newton's Second Law and accel-

eration. The experiment was also a link between the

155

previous theme on kinematics (observe the application of
kinematic equations) and the theme on dynamics.

Mr. Ellis' elaboration on Newton's Third Law was less
explicitly linked to previous ideas and topics taught.
Instead, he began the topic of Newton's Third Law by probing
the students' knowledge of the topic. However, there was
one instance in which he referred to the idea of inertia to
explain the action of‘ the pair’ of forces on different
bodies. This instance is indicated on pages 149 and 150.
There, two students were described: Mike (heavy one) and
Kathy pulling on a rope. On that occasion, Mr. Ellis
explained that Mike moved a shorter distance compared to
Kathy, because he had more inertia and, therefore, was

harder to move.

Mr. Howard's Story-Line op Dynamics

Mr. Howard's macro-sequence of the introductory unit on
dynamics was constructed over a period of 11 consecutive
days. The first ten classes were videotaped and eventually
transcribed. During this time period, three experiments
dealing with the relation between force and acceleration
were performed. Each experiment was analyzed by the class
(individually), and the analysis was subsequently used by
Mr. Howard to derive the major conclusion of the theme being

developed.

156

Figure 5.5 indicates the main topics that Mr. Howard
discussed during 11 consecutive days he developed the theme
of dynamics. Since Mr. Howard's class was "activity-
oriented" and "lab-centered," emphasis was placed on the
main activities that took place around the topics being
discussed. A careful look at the videotape transcripts, for
Day 1 Galileo's constant motion and procedures for

Experiment 20: What forces do to motion.
Day 2 Conducing Experiment 20.
Day 3 Data Analysis of Experiment 20.

Galileo's constant motion and friction.
Forces cause a constant change in velocity.

Experiment 21: How force and mass affect
acceleration.

Day 4 Data Analysis of Experiment 21.

Day 5 Conclusions of Experiment 21.

Day 6 Wrap-up of Experiment 21 (F = ma).

Day 7 Experiment 22: Inertial versus gravitational
mass.

Day 8 Conclusions of Experiment 22.

Day 9 Conclusions of Experiment 22.

Mass and weight -- solving problems.

Day 10 Solving HDL's. (home, demonstration and
laboratory).

Day 11 Reviewing HDL's.
Introduction to new unit on projectile motion.

Figure 5.5. Chronogram of major topics and activities in
Mr. Howard's macro-sequence on dynamics.

157

indicated that topics were explained through statements,
without giving them a specific name. For example, while the
previous two teachers explicitly mentioned Newton's First
Law and Newton's Second Law, Mr. Howard did not make
reference to these labels, in spite of the fact that he
explained what the topics were about.

The following is a day-to-day story-line describing how
Mr. Howard constructed the unit on dynamics. Three major
topics were covered:

1. Galileo's constant motion and friction.

2. The effect of force on the velocity of a body.

3. Inertial versus gravitational mass.

This summary indicates the temporal order' in.‘which
topics were developed. The story-line that follows attempts
to describe how these concepts were coherently connected
across time, through the major events undertaken by Mr.

Howard's class.

Day 1 Experiment 20: Galileo's Constant Motion

On day 1, Mr. Howard briefly referred to Galileo's
constant motion. Then, he moved on to the purpose and
procedure of the experiment that followed: how force

affects motion.

158

9:10 a.m.

During the first 15 minutes of the class period, Mr.
Howard discussed students' grades from the previous week's
test on vectors. Having collected the tests, he found his
textbook (PSSC) and said:

Let's look at what Galileo says. . . . Now that we

know all about motion, and how it is described, we

begin to take a look at things that affect motion.

So, the whole unit which consists of a fairly long

chapter . .. . lot of HDL's there . .. . we don't

get away from vectors . . . what we have to do is

to take a look at ideas about force and motion . .

. how force and motion relate.

Then, Mr. Howard discussed Galileo's idea of constant
motion: "Objects move at constant speed . . . if there are
no forces (friction) acting on it." Next, he briefly
described the pendulum and inclined plane as two situations
in which Galileo's ideas apply, then pointing out "the need
to investigate the acting of forces over the velocity of a
body, which is the purpose of Experiment 20." The purpose

and procedures for Experiment 20 followed (on the

blackboard):

Experiment 20: Force and motion

Purpose: to determine how a force affects the velocity
of a body.

Procedure: force is a pull of one rubber band

stretched 40 cm from the cart front.

159

1. Practice giving a cart a run and then hook a timer

and run a recording tape for a v-t graph of this

trip.
2. One tock is four time intervals of tick.
3. Make a record of a push and let the cart coast.

4. Two trials:
a. a cart and one brick.
b. a cart and two bricks.
5. Plot v-t graph of each type on a sheet of graph
paper.
oc. [Observe that at this point students are familiar
with v-t graph (velocity time graph): and with the
analysis of the tapes. The only new concepts are:

push (or force) and the bricks.)

10:00 a.m.

As Mr. Howard elaborated the procedures (occasionally
skimming over the lab book), he showed the students how to
hook the timer and stretch the rubber band to pull the cart
along the lab table. Having finished with the procedures,
he added: "Let's go to work." Students found their part-
ners (same as last week) and moved to the tables in the
back. Each table contained a cart, a timer, ticker tape and
a meter stick. Students had to get the bricks from a shelf
and the rubber band from Mr. Howard. Once they had gathered

the equipment, they practiced pulling the cart with the

160

rubber band stretched at 40 cm or pushing it along the table
until the end of the hour. In both cases, they hooked the
ticker tape to the timer to record the motion of the cart.

(Videotape and fieldnotes, February 4, 1987.)

Day 2 Conducting Experiment 20
9:20 a.m.

At the outset of the lesson, Mr. Howard pointed out, "I
want to get some consistent data today . . . don't know . .
. try to pull back from 40 to 30." (The previous day
students had a hard time trying to keep a constant stretch
of 40 cm in the rubber band.) He then refreshed the
students concerning the procedures -- suggesting they do a
small push first and then a big push. (This was a new pro-
cedure.) As soon as students were given the order to go to
work, Mr. Howard went back to the board and wrote down:

Part 1. The coasting of a cart to see how small forces

affect the velocity of graph.

Part 2. The pulling force of one rubber band on two

masses to see how it affects the velocity graph (force

30 cm).

Some students wrote the above information in their lab

report (to be) before engaging in any work.

161

10:05 a.m.

Following the lab procedures, students obtained four
ticker tapes (small push, big push, one rubber band and one
brick, one rubber band and two bricks). They worked on
running the experiment until the end of the class period
when Mr. Howard suggested students "get their v-t graph"
from the table as well as the acceleration (they had worked
on these concepts in the previous chapter). Before students
left he added: "Try to get a conclusion formulated on these
two (parts) . . . for tomorrow, so that we can begin to take
a look at what we are saying here. We'll run into further
experiments." Some students had already started analyzing

their tapes. (Videotape and fieldnotes, February 5, 1987.)

Day 3 Conclusion of Experiment 20
9:10 a.m.

Immediately after checking attendance, Mr. Howard
stated: "Who's got a graph to take a look at? Let's take a
look at coasting first." He looked around for two graphs

(see Appendix E) and sketched them on the board as follows:

‘/////’////,Galileo's ideal
A

ctual motion (big push)

V

¢————Actual motion (small push)

 

 

 

162

He explained, using the v-t graph, that the speed of
the cart increased to a point at which the cart began to
coast. Hewever, he added: "The bodies ought to keep the
same velocity. If there is not friction . . . or force
acting on it" (referring to the dotted lines in the graph).
The graph showed, according to Mr. Howard, that because of
friction with the lab desk, the velocity was not constant
during coasting as predicted by' Galileo. .According to
Galileo, "when no force is acting (as in the dotted lines),
a body will coast with a constant velocity if there is no
friction." Having stated Galileo's idea of constant motion
and friction, the teacher wrote down on the board the first
two major conclusions:

1. Small forces cause a small constant decrease in

velocity or deceleration.

2. Friction forces do not depend on speed.

9:30 a.m.
At this point in time, Mr. Howard borrowed another set
of graphs (velocity-time) for the other two trials (part 2),

and sketched them as follows: (see Appendix F.)

163

v 1 brick

2 bricks

 

 

He explained that what these graphs indicated was that
"forces cause a constant change on velocity, or a constant
acceleration." He added that with respect to the effect of
mass "one cannot say anything on its effect on the accel-
eration because they had used only two bricks" (so a conclu-
sive statement could not be reached at this point).
Instead, "further research is needed" and "this was the
purpose of Experiment 21 in which the effect of mass and

force on the acceleration would be investigated."

9:38 a.m.

Mr. Howard found his lab book and said, "Let's take a
look at Experiment 21. Maybe we can resolve the problem."
Shortly thereafter, he began to elaborate on the purpose and

procedures of Experiment 21.

Experiment 21: Force, acceleration and mass.
Purpose:
1. To find out how forces affect the acceleration

value.

164

2. To find out how masses affect the acceleration.

Procedures:

1. Stretch one rubber band to 30 cm and keep mass
constant.

2. Use 1, 2, 3 and 4 rubber bands as forces.

3. Sample change in velocity to estimate
acceleration.

4. Plot acceleration versus force.

He added that these procedures corresponded to Purpose

1 above.

9:40 a.m.

Having elaborated on the procedures one at a time, Mr.
Howard gave the order: "All right, let's try that . . . get
these four acceleration and those four forces that go with
them. Let's go to work." Students worked at the lab tables
that already had the equipment to be used on them: bricks,
ticker timer, tape, meter stick, etc. Under Mr. Howard's
supervision, students (in groups of two) worked at the lab
tables until the end of the class period. They simply
hooked the cart to a ticker tape to record the motion, and
pulled it four times with one, two, three and four rubber
bands stretched at 30 cm (as indicated by the meter stick).
Some students did not get beyond the second rubber band
though. As students left the room, Mr. Howard remarked:

"Remember now . . . a force causes a constant change in

165

velocity . . . or a constant acceleration." (Videotape and

fieldnotes, February 6, 1987).

Day 4 Data Analyzing Experiment 21
9:15 a.m.

Mr. Howard initiated. the lesson. by' doing "a quick
review on the procedures" (Part 1). He insisted students
did not need to plot the whole tape, but they needed to
check in which part of the tape "they did the best job on
pulling" as to obtain two consecutive velocity values to
compute the acceleration that corresponded to the respective

pulling (or force).

9:20 a.m.

Mr. Howard added the procedures that went along with
purpose two of the experiment (i.e., how :masses affect
acceleration). Students were to run this part today. "This
is procedure 5," he said. "Use one rubber band and vary the
number of bricks . . . one, two, three, four. Also, graph
acceleration versus mass. . . . have four points here."
These two procedures were added to the four previous pro-
cedures that had remained on the board since yesterday.
Having explained these procedures, Mr. Howard suggested that
students move to their tables and continue the experiment.
Most students worked on part 1 (varying the force) either

repeating the trials and beginning from the point they left

166

off the previous day, or analyzing the tapes they had

obtained.

9:50 a.m.
While students worked at the lab tables, the teacher

sketched the following graph on the board:

(acc)

 

_

m (inertial mass)

With respect to the graph, he commented: "In this graph,
this is inertial mass . . . may I have everybody's attention
for a minute . .. . I'm trying to get a conclusion here on
what the acceleration should do as you put more bricks" (few
students had even run this experiment yet). A discussion
continued as to whether the acceleration increased or
decreased with the mass until Mr. Howard suggested that it
appeared to be an "inverse relation" between mass and
acceleration. In view of these situations, students were
advised to "add a new procedure . . . . (7) to plot a versus
inertial mass . . . instead of a versus mass" (as indicated

in procedure 6).

167

The previous discussion created some confusion among
the two students who had run part 2 of the experiment
because they' thought. they’ had. to repeat the experiment

again.

10:05 a.m.

During the last 15 minutes of the class period, most
students worked on part 2 of the experiment: varying the
mass of the load (one, two, three and four bricks) and
pulling the cart with one rubber band stretched at 30 cm as
measured with the meta stick. (Videotape and fieldnotes,

February 9, 1987.)

Day 5 Conclusions on Experiment 21
9:10 a.m.

Having checked attendance and taken care of students'
individual questions, Mr. Howard sketched the following
graph on the board (students had already started working on

their graphs):

 

—
_
—
_

1 2 3 4 FOECe

168

He also wrote down the following statement:

Acceleration and mass: large mass has small accelera-

tion and constant force . . . this suggests an inverse

function that plots force (1) over acceleration (a)

versus inertial mass.

Without any further discussion on the information
presented on the board, Mr. Howard began to move around
supervising students' work and answering individual

questions.

9:13 a.m.

Mr. Howard: "Any question on this graph (a versus
force)? I'm going to try the conclusion of this today. I'm
going to see if we can come out with something . . . No. 20
(lab report) is due." Seconds later he asked for an accel-

eration versus force graph and sketched it on the board:

 

 

Force

169

He commented that "the graph shows that two-thirds of
the force was lost to friction . . . with the lab table" and
that from the previous graph a general conclusion could be
reached: "Force is directly proportional to the acceler-
ation if one inertial mass (Mi) is constant." He further
indicated that this (statement) could be mathematically
formulated as: F oCa.

Mr. Howard went on to say that "the question left to be
answered is to find out how the two variables (F and a) are
directly related. If we double F, do we also double a?" He
then placed a question mark on the expression "Foca" and

added that "more work needed to be done."

9:30 a.m.

Following the previous discussion, Mr. Howard moved to
the right hand-side board where yesterday he had sketched a
graph of "1/a versus Mi-"

He commented that "one, two, three and four represent
inertial mass . . . and we have not really defined these
terms . . . but that's one of our jobs this week." He then
borrowed a student's graph and sketched it over the

previous one.

170

1/a

 

L—
r—
I

/ ll
12

As most students had not finished this graph yet, Mr.
Howard decided to delay a full discussion of the graph
because, "some further thinking was needed . . . specifical-
ly in trying to interpret what the intersect meant . . . and

about the kind of relationship between l/a and Mi-"

9:26 a.m.

While students worked on their analyses, Mr. Howard
suggested that they "try to wrap it (lab report) up today."
Some of them, after consulting with Mr. Howard, had to
repeat some parts of the experiment again. But this time
they were focusing on that part of the experiment that dealt

with varying the mass.

10:00 a.m.

As the end of class was approaching, and the students
were preparing to leave, Mr. Howard said: "All ready to
conclude this devil? We'll spend a little time on HDL's

tomorrow." During the last 20 minutes, he had been

171

circulating around, reading students' graphs and assisting
them in the analysis of the ticker tapes. (Videotape and

fieldnotes, February 10, 1987.)

Day 6 "Wrap Up" of Experiment 21 (F = ma)
9:10 a.m.

Beginning the class period, the teacher stated: "Let's
try to wrap up today. Take a look at page 229 to 231
please" (PSSC textbook). Students and teacher then talked
about a set of strobe photographs that showed the motion of

a body under the influence of a constant force.

9:12 a.m.

Mr. Howard put his PSSC book away and exclaimed:
"Okay. Here we go. Now yesterday we tried to generalize .
. . who's got a graph?" (moving around the room). He went
to the board and sketched the following graph: (see

Appendix G.)

 

 

4.
a 1.25 -
1.00 -
.75 -
.50 -
.25 -

l i l 4 t

1 2 3 4

172

He indicated that, "it does not show 'friction' . . .
because I have translocated it" (i.e., move the straight
line toward the left so that it passes through the origin).
He remarked. that since these ‘were: a one-to-one corres-
pondence between force and acceleration, then a "big
conclusion" could be drawn from that graph:

Acceleration is directly proportional to the applied

force if the mass is constant" (Mi = K).

He added that the above statement could be numerically

expressed as: "F 04 a."

9:16 a.m.
Having explained the force versus acceleration graph,
Mr. Howard sketched "l/a versus H," which appeared as: (see

Appendix H)

 

\‘

173

As in the previous analysis, Mr. Howard indicated that

"if we doubled the mass then l/a also doubled." This led
him to conclude that: "The acceleration is inversely
proportional to the inertial mass if force is constant." He

went on to assert that numerically, this could be expressed

as: "l/a a m. "

9:20 a.m.

Mr. Howard again referred to the above two statements
on both sides of the board and explained that they could be
considered in a mathematical expression such as: "F Oi Mia."

Finally, from his last expression, it could be
concluded that "force was equal to mass times acceleration"

or F = Mia.

10:05 a.m.

Having established the force equation, Mr. Howard
substituted the units of acceleration (m/secz, cm/secz) and
mass (Kgl, gr) to obtain the units of force (Newtons and
dynes). The next major activity was to assign HDL's that
required the application of the equation F = ma. As the
class period was about to conclude, he pointed out that
tomorrow they would be starting on Experiment 22 dealing
with "gravitational mass" versus "inertial mass."

(Videotape and fieldnotes, February 11, 1987.)

174

Day 7 Inertial versus Gravitational Mass
9:10 a.m.

As soon as students arrived and without even checking
attendance, Mr. Howard directed their attention to the
equation: F = Mia. He remarked that the next task was
Experiment 22, and that they "would be dropping that 'i' . .
. today from that equation." He then wrote down the purpose
of the experiment (how gravitational and inertial mass

compare to one another) followed by five procedures.

9:36 a.m.

After fully explaining each procedure and demonstrating
to the students how to operate the equipment, Mr. Howard
suggested that they move to the lab tables and start work-
ing. At each lab table, Mr. Howard had placed clamps,
chronometers, balances and an inertial balance. Students
first familiarized themselves with the inertial balance, and
then they began to take measurements of the frequencies (of
the inertial balance) as the mass hooked to it was varied.
The obtained values were put into a table of data given in

the procedures.

10:05 a.m.
By the time the bell rang, students (under Mr. Howard's
supervision) were still taking measurements. (videotape and

fieldnotes, February 12, 1987.)

175

Day 8 Here on Experiment 22
9:10 a.m.

Upon arrival, the students went straight to the lab
tables where they continued the work they had started the
previous day. They worked at the lab tables for about 30
minutes before starting to analyze the data they had

gathered.

9:50 a.m.

At this point in time, Mr. Howard, who had been
assisting and checking students' work, called their atten-
tion to the kind of graph (outcome) they should get. He
sketched a T (period) versus Mi (inertial mass) graph as

follows: (see Appendix I.)

 

V

"1

Using this graph, students could compare the period of
known mass (in kilograms) and find out that "inertial and

gravitational mass are proportional but not equal." In this

176

sense, grams and kilograms were proportional to clamps,
bricks, etc., which are examples of inertial mass.
Day 9 Conclusion of Experiment 22.
Mass and Weight. Solving Problems.
9:10 a.m.

After reminding students about the set of HDL's
assigned two days earlier (students should be working on
this task), Mr. Howard checked on the final conclusion with
respect to Experiment 22. After sketching a graph of
"period versus mass" he had borrowed, he concluded that
"gravitational (Mg) mass is proportional to the inertial
mass (Mi) (Mi x k = mg). From this point, Mr. Howard
elaborated on the difference between mass and weight: "mass

does not change with position, weight depends on gravity."

9:31 a.m.

Having gone through the difference between mass and
weight, the teacher pointed out: "Let's take a look at
HDL's." Students immediately found their textbook and began
to skim over the assigned problems. However, instead of
focusing on the task at hand, Mr. Howard went on to talk
about everyday life situations that required the application
of the idea of force as a vector quantity. These situ-
ations included: "swinging," "standing on a rope," "pulling

an object uphill," etc.

177

9:42 a.m.

Mr. Howard: "Let's go back to HDL's." From this time
on until the bell rang (10:05), Mr. Howard worked on the
first six problems (HDL's) he had assigned two days earlier.

(Videotape and fieldnotes, February 17, 1987.)

Day 10 Solving HDL's

This day's class was devoted to solving most of the
problems he had assigned earlier. The problems required the
application of the equation: F = ma, as well as the con-
cepts and relations students had learned in the previous two
units (kinematics and vectors). Halfway through the class,
while students worked on their own, Mr. Howard called to
their attention, by listing on the board, a summary of the
major fundamental physics equations they had learned thus
far. These equations would be useful in solving most of the
assigned problems. (Videotape and fieldnotes, February 18,

1987.)

Day 11 Review on HDL's

The first 40 minutes of the class period were spent
reviewing all of the previously assigned HDL's. Students
were constantly given the opportunity to ask questions or
raise concerns about the tasks at hand. Fifteen minutes
before the bell rang, Mr. Howard was already introducing the

new unit: "Motion at the earth's surface . . . it's what we

178

are going to take a look at next." This statement was
followed by Mr. Howard elaborating on the major issues dealt

with in this unit.

Interpretation pf Mr. Howard's Story-Line

As pointed out before, and as it has been described in
the story-line, Mr. Howard's construction of the theme on
dynamics was carried out through a series of three consec-
utive lab experiments. Three major topics were clearly
identified: (a) Galileo's constant motion (equivalent to
Newton's First law), (b) the effect of a force on velocity
(F=ma) (equivalent to Newton's Second Law), and (c) inertial
versus gravitational mass. Figure 5.6 shows a summary of
the information content delivered by Mr. Howard in the unit
on dynamics.

In the construction of the above sequence, the story-
line also indicates a common pattern indicating how the
coherence across topics is determined. In this sense, Mr.
Howard first established the procedures to follow for each
experiment, then analyzed the properly gathered data, and
finally established the conclusions. Through this strategy,
Mr. Howard was able to deliver the information content
described in the story-line. At each of these phases, Mr.
Howard constantly drew on information from previous events.
For example, when introducing Experiment 20, he refreshed

students' memories about how to determine velocity and

179

acceleration from the ticker tape. Similarly, he introduced
Experiment 21 by indicating that Experiment 20 was incon-
clusive in determining the relationship between force, mass
and acceleration. At the time he introduced Experiment 22,
he again referred to the need to work on the relation: F =

mia by "dropping that i."

1.0. Galileo's constant motion and friction.
1.1. "The velocity of a body is constant if there is
no friction."
1.2. "Small forces (friction) cause a small constant
decrease in velocity or deceleration.

2.0. The effect of a force over the velocity of a body.

2.1. A force causes a constant change on velocity (or
acceleration).

2.2. A force is directly proportional to the acceler-
ation if the "inertial mass" is constant (Fol
a).

2.3. The acceleration is inversely proportional to
the inertial mass if force is constant (aCZ
l/mi)°

2.4. Force is equal to mass times acceleration (F =
mia).

3.0. Inertial versus gravitational mass.
3.1. Inertial and gravitational mass are proportional

(Mixk = Mg).
3.2. Mass and weight.

Figure 5.6. Mr. Howard's macro-sequence

A look at the nature of the "global coherence" (Van
Dijk, 1985) imbedded in the information content enacted by
Mr. Howard in his daily interaction with students and the
immediate environment, reveals some degree of discreteness

among the different topics being taught. In Grimes' terms,

180

we are in the presence of a "logically loose sequence"
(Grimes, 1975). In this sense, the teacher's discourse on
dynamics shows some discontinuity.

The following vignette sheds light on the above
assertion. Having established (after Experiment 20) that
"small forces cause a small constant decrease on velocity or
acceleration" and that "friction forces do not depend on
speed," Mr. Howard had the students study the effect of
force and mass on acceleration. At this point in time the
connection between these two instructional events was logi-
cally consistent since the data from Experiment 20 was not
sufficient enough to draw any conclusion on the relationship
between mass, acceleration and force. As they moved along,
Mr. Howard explained that the mass that students were
working with was, in fact, inertial mass, and it would be
the topic of the following experiment.

At the time in which Newton's Second Law was formally
established based on the graphs students had obtained, the
term inertial mass was being used without having elaborated
on its meaning. This situation led Mr. Howard to indicate
that "force is equal to mass times acceleration" if the
units of acceleration, mass and force were appropriately
chosen. In this sense, after having indicated that "force
is proportional to mass (inertial) times acceleration"

(F'o2mia), Mr. Howard ignored the nature of the proportion-

181

ality and moved on to indicate that force could be defined
as "mass times acceleration."

Even though Mr. Howard explicitly referred (in
Experiment 21) to the need "to drop the 'i' from Newton's
Second Law," a close look at the events that took place
around that experiment, indicate that no further reference
was made with respect to Newton's Second Law and its
relation to mass or inertial mass.

Summary and Conclusions on the Theme
"Dynamics" as Taught by Teachers

As has been described in the previous vignettes,
teachers usualLy act on school knowledge (e.g.; dynamics),
and structure them into macro-sequences. These macro-
sequences vary in terms of the topics being delivered and
the nature in ‘which these topics are organized through
instructional events. In this sense, teachers act upon
bodies of existing knowledge (discipline) and individually
organize them to communicate the information they consider
necessary for students to learn. In doing so, they
purposely anticipate the instructional events and control
the process through. which that information needs to be
delivered (Magoon, 1977: Kelly, 1954) for learning to take
place. As Kitchener (1986) put it, teachers construct the
cognitive schema, categories, concepts and structures

necessary for learning.

182

The analysis of how three experienced teachers
constructed their unit on dynamics yields several con-
clusions with respect to subject matter, organization and
sequencing in high school physics. These conclusions will
be summarized under the following headings: "The Nature of
the Global Coherence on Dynamics," and "The Nature of the

Information Content and the Immediate Environment."

Ihe Nature of the GlobaI Coherence

Topics can be organized in macro-sequences, as a
convenient way to represent the overall (global) coherence
of a theme. These macro-sequences vary across teachers with
respect to the information content enacted. The micro-
sequences on dynamics developed from a discourse analysis of
the way three physics teachers actually dealt with such a
theme over a period of several days, indicates that each
individual teacher delivered different sets of information
content for the same theme. Table 5.1 shows a summary of
the different topics delivered by each of the participant
teachers.

Table 5.1 clearly indicates a distinction between Mr.
Howard's and both Mr. Ellis' and Mr. Simon's macro-
sequences. The fact that Mr. Howard relied on a different
textbook may explain such a difference. Mr. Howard followed
the PSSC textbook while Mr. Ellis and Mr. Simon relied on

Harvard Project Physics. Neither Mr. Ellis nor Mr. Simon

183

included the topic on "gravitational versus inertial mass."
In addition, Mr. Howard did not explicitly address Newton's
First Law and inertia, though he talked about Galileo's
constant motion. Furthermore, while the notion of friction
was considered as a consequence of bodies "not being able to
keep at constant motion" in the case of Mr. Howard, the same
topic is discussed under Newton's Second Law by Mr. Ellis

who defined friction as a "net force that affects

 

 

 

 

acceleration."
Table 5.1: Topics Delivered by Individual Teachers on
the Theme Dynamics.
Ieacher Topics
Mr. Simon Principle of inertia
Vectors
Newton's First Law
Newton's Second Law
- Mass and Weight
Newton's Third Law
Mr. Ellis Newton's First Law -- Inertia
Newton's Second Law
- Friction
- Mass and Weight
- Free Fall and Terminal Velocity
Newton's Third Law
Mr. Howard Galileo's Constant Motion and Friction

Newton's Law (F = ma)
Inertial Versus Gravitational Mass

 

184

A second topic, not included in Mr. Howard's sequence
was Newton's Third Law. When asked about this issue in an
interview, Mr. Howard responded: "There was no need to . .
. teach that concept and that the chapter dealt only with
Newton's law."1 However, he pointed out that he would be
dealing with the topic (i.e., Newton's Third Law) later in
the unit on momentum. How can one account for the fact that
Mr. Howard spent more class periods on the unit on dynamics
than the other two teachers? First, he dealt with each
topic at a much deeper level than the other two teachers.
Secondly, during the whole school year he does not "go
beyond the unit on Kinetic energy" -- a topic covered by the
other teachers by mid-February. In this sense, Mr. Ellis
and Mr. Simon covered a larger number of topics during the
whole school year.

There were also other differences in the content
delivered by both Mr. Ellis and Mr. Simon. The first
teacher, for example, introduced Newton's First Law once he
had finished a unit on vectors. For Mr. Simon, the inform-
ation content on vectors was presented as a prerequisite to
introduce Newton's Second law. Another striking difference
is the idea of friction. The story—lines show that the idea

of friction was not fully considered by Mr. Simon. It was a

 

1This issue has been addressed by Aaron who stated that
one of the weak points of the PSSC textbook is that it does
not deal with Newton's laws in a coherent manner.

185

fundamental issue in the case of Mr. Ellis, who constantly
made reference to it as he moved through the unit on dynam-
ics. A second topic discussed by Mr. Ellis was that of
"free fall and terminal velocity." There was no indication
that Mr. Simon referred to this topic. Several reasons may
account for this difference in information content between
two teachers using a similar textbook. One reason is that
Mr. Ellis covers a smaller number of units throughout the
school year (as explained in an interview). On the other
hand, Mr. Ellis rarely‘ covers the 'units on. atomic and
nuclear physics. A second explanation is Mr. Ellis'
reliance on a "package" of instructional material that is
used daily to complement the information given in the
textbook. The use of this package allows Mr. Ellis to treat
individual topics in more depth than Mr. Simon.

The way different topics were logically connected
varied among teachers and, hence, the nature of the global
coherence across topics. The following vignettes show how
topics were put together in the theme on dynamics as taught
by three different teachers.

The first teacher, Mr. Simon, structured the theme on
dynamics as follows. He explained that inertia is the prin-
ciple by which "objects in motion remain in motion unless
acted upon by an external force." But objects accelerate

under the influence of a force, and forces are vectors. The

186

principle of inertia is the same as Newton's First Law which
holds that if there are no "unbalanced forces acting on the
body, the ‘velocity’ is constant and the acceleration is
zero." If there are unbalanced forces acting upon it, then
an acceleration is produced in the same direction (vector)
and proportional to the net force. This acceleration is
also inversely proportional to the mass (of the body being
moved). Under the action of such a force, objects would
accelerate, decelerate or change direction.

The previous discussion was then followed by two
loosely connected topics, mass and weight and Newton's Third
Law. Weight is a force caused by gravity and it varies from
place to place (as gravity does) while mass is the same as
inertia and it is constant. The discussion of mass and
weight was followed by Newton's Third Law according which
is: "to every reaction there is always an equal and
opposite reaction" or "forces always exist in pairs."

Mr. Ellis structured the theme on dynamics in a rather
different manner. He first introduced Newton's First Law as
the property by which "an object at rest stays at rest
unless there is a net (unbalanced) force acting on it."
However, if there is a net force acting on a body, it
creates an acceleration (Newton's Second Law): friction is
a net force that also affects motion. The introduction of

Newton's Second Law was then followed by Mr. Ellis' elabor-

187

ating on the idea that in the case of Newton's Second Law:
(a) the acceleration is proportional to the net force, and
that (b) acceleration is proportional to the inverse of the
mass. Newton's second law can be applied to explain the
difference between mass and weight. Mass "measures iner-
tia," "it is an intrinsic property" which "does not change
with position." Weight, on the other hand, is a special
case of Newton's Second Law where the acceleration of the
body is equal to 'the acceleration of gravity; ‘Weight
changes as position changes. It follows that "an object if
in free fall then the net force acting on it is equal to its
weight and the air resistance is zero." If the air resis-
tance becomes equal to the driving force, the object would
move at a constant speed called "terminal velocity."

As in the case of Mr. Simon, Mr. Ellis introduced
Newton's Third Law in a loosely connected manner. It was
presented immediately after an experiment on Newton's Second
Law. The argument went as follows: for every force there
is an equal and opposite force. These forces are equal in
size, opposite in direction and act on different objects.

Finally, Mr. Howard, presented the subject matter-
content information as follows. The velocity of a body is
constant if there is no friction (Galileo's constant
motion). In cases where friction exists, it then causes a

small constant decrease in velocity or deceleration. In

188

general, forces cause. a constant change in ‘velocity or
acceleration, and the rate of change can be (experimentally)
determined by the numerical equation: F = Mia, where Mi is
the inertial mass of the object being moved. Inertial mass
(measured. in. bricks, marbles, etc.) can. be compared. to
gravitational mass measured in kilograms.

The previous discussion concerning the nature of
coherence in the teaching theme dynamics by three experi-
enced teachers led to the opinion that physics lessons are
not preset entities, but that they are differentially
constructed by teachers and students to achieve their goals.
In this sense, "classroom conversations" in high school
physics are not scripts to be followed rotely by teachers
and students (Green & Harker, 1982). This situation, as
Green Harker stated, allows for "breaches" in the cohesion
of the lesson as conversations develop. The idea that
classroom conversations are not scripts seems to explain why
the three participant teachers ended up enacting differently
organized bodies of knowledge for a common unit. In organ-
izing this knowledge, each individual teacher employed
different types of "coherent relations" (Hobbs, 1983) to
connect the topics being delivered in the unit on dynamics.
For' example, some topics were linked to ‘previous ones,
others were introduced once and eventually ignored. Others

were carried over into new topics and still others emerged

189

without explicit connection with what had been presented
before.

In the story-lines we observed that Mr. Howard
initiated his teaching on Newton's Law (i.e., Newton's
Second Law) by making explicit reference to the experiment
on "Galileo's coasting," and to the lack of data from that
experiment to establish a relationship between mass, accel-
eration and force. The other two teachers (Mr. Ellis and
Mr. Simon), however, elaborated on Newton's second law by
making explicit reference to "net force" and its effect on
the acceleration of a body. These are examples of "linkage
relations" (Hobbs, 1983) among topics. These were also
examples of linkage relations between topics and subtopics,
for example between "Newton's Second Law" and "mass and
weight" as taught by Mr. Ellis and Mr. Simon. The story-
lines indicate that in the case of Mr. Ellis, there was a
strong linkage relation between Newton's Second Law and the
difference between mass and weight since the latter was
derived by applying the first one. In the case of Mr.
Simon, the relation was weak in the sense that he elaborated
on the same subtopic without making explicit reference to
"Newton's Second Law." Another example was the subtopic
friction. FTiction as taught by Mr. Ellis was taught as a
net force that affects acceleration (direct application of

Newton's Second Law). However, in the case of Mr. Simon, he

190

introduced the idea of friction in the context of Newton's
First Law as something that "needs to be eliminated" to make
objects move at a constant speed.

There are also topics that were introduced once in the
classroom discourse and eventually ignored. As Tanner
(1984) stated, "they eventually decay." Examples of these
topics were vectors and the difference between mass and
weight (Mr. Simon's class) and friction (Mr. Howard's case).
However, there were topics that, once introduced, were
carried over into subsequent events dealing with different
topics or with the application of topics already discussed.
In this sense, we talk about "strong temporal relations"
(Hobbs, 1983) between topics in which previous information
has a strong impact on what happens next in the discourse.
Examples of this situation were the instructional events
that led Mr. Howard to establish Newton's Second Law. He
first had students experimentally derive the relations
between acceleration and mass and acceleration and force
before concluding that "force is equal to mass times
acceleration." A similar event took place in Mr. Ellis'
sequence on dynamics. This happened when he was conducting
the experiment on Newton's Second Law. During the dev-
elopment of the experiment, Mr. Ellis' made explicit

reference to the concepts of inertia, friction, mass and

191

weight and Newton's Second Law. Coherent relations of this
nature were very rare in Mr. Simon's sequence on dynamics.

The final point to be made is with respect to topics
that are not properly linked to what was presented before,
or in other words, the non-existence of explicit linkage
relations between topics. Examples of this situation were
Mr. Simon's elaboration on Newton's Third law as an entity
in itself without making explicit reference to Newton's
First and Second Law or Mr. Howard's elaboration on the
topic "inertial mass versus gravitational mass" without
explicitly referring to Newton's Second law, which was the
immediate antecedent topic.

In summary, teachers in their daily interaction with
students and classroom. materials construct, for similar
instructional units, different structures of subject matter
(macro-sequences) by breaking those units into topics which
may or may not be logically connected. In this sense,
teachers enact different underlying structures (or macro-
structure) for themes that are usually expected to convey
the same type of information. In Grimes' (1975) terms, the
three macro-sequences can be categorized as "logically
loose" sequences in the sense that teachers enact topics in
a theme, following a temporal and logical order without an

explicit connection among them.

192

In effect, if one looks at the theme dynamic as a
organic instructional unit, it can be observed that there
was no direct connection between the topic of Newton's
Second Law" and "vectors" and Newton's Third Law as taught
by Mr. Simon. Similarly, there was not a direct logical
link between the topic of Newton's Second Law and the topic
"difference between inertial mass and gravitational mass" as
taught by Mr. Howard. Perhaps the link was that the term
inertial mass (Mi) appears in the equation of Newton's
Second Law, however, this issue was not explicitly addressed
in Mr. Howard's discourse. The story-lines do indicate
that teachers establish logical connections among some of
the topics such as vectors, Newton's First Law and Newton's
Second Law (Mr. Simon): between Newton's First Law and
Newton's Second Law (Mr. Ellis); and between Newton's First
Law (Galileo's coasting) and Newton's Third Law (Mr.
Howard).

This analysis seems to support the idea that "there is
not one logical sequence in which the truths of a subject
must be communicated" (Hirst, 1975).

The data also support the assertion that important
logical connections among topics of an instructional unit
are not made clear to students. Generally, these

connections are subtle and to miss them is to miss the

193

"logical grammar" (Hirst, 1975) of physics, making it
incomprhensible to high school students.

atu e of the n o tio ont

and Epvironmgpr

The macro-analysis of the teachers' discourse on
dynamics indicated that the information content was
differentially enacted by teachers. There were variations
in the subject matter organization as well as variations in
the nature of the "environment through which tasks were
accomplished." These environments were enacted in
fundamentally different ways. Tables 5.2, 5.3 and 5.4 show
an overview of the physical materials individual teachers
used when delivering similar and different topics related to
the unit on dynamics. As Erickson (1971) pointed out:
"These materials contain cues towards steps and strategies
that are necessary in the completion of the subject matter
task (p. 171) . The story-lines above give evidence that
these steps and strategies are context-specific.

It'can be observed, for example, that Mr. Simon relied
on a worksheet that the students needed to fill out, as he
simultaneously elaborated on Newton's three laws. He also
performed classroom demonstrations on Newton's First Law.
However, compared to Mr. Ellis, Mr. Simon did not perform
classroom demonstrations while elaborating on Newton's

Second Law. It can be observed, for example, that Mr. Ellis

194

 

Table 5.2: Mr. Simon's Enacted Topics and Physical
Materials.
Topic thsicaI Materials

 

Principle of inertia

Vectors

Newton's Second Law

 

Worksheet, textbook:
balls, strings, wooden blocks,
dry ice, metal desks.

Worksheet

Worksheet, bricks, carts, ticker
timers, ticker tape, weights and
pulleys.

 

 

Newton's Third Law Worksheet

Table 5.3: ZMr. Ellis' Enacted Topics and Physical
Materials.

Topic Physical Materials

 

 

Newton's First Law

Newton's Second Law

Newton's Third Law

Package of materials, textbook,
wooden blocks, weights, strings
and balls.

Package, schedule sheet, scales,
balances, carts, rubber bands,
bricks, darts, weights, stop
watches and rulers.

Package, cloth balls, cart, rope,
and scales.

 

195

 

 

 

Table 5.4: Mr. Howard's Enacted Topics and Physical
Materials

Ionic thsi_<m_1__IMer_i_als

Galileo's Constant Textbook and lab reports:

Motion rubber bands, carts, bricks,

ticker timer, ticker tape,
graph paper and rulers.

The Effect of Force Textbook and lab reports:

Over Velocity rubber bands, carts, bricks,

(Newton's Second Law) ticker timer, ticker tape,
graph paper and rulers.

Inertial Versus Textbook and lab reports:

Gravitational Mass clamps, balances (inertial),
chronometers, weights, graph
paper.

 

carried out demonstrations ‘with carts, rubber' bands. and
bricks to show how mass and force relate to acceleration.
Mr. Simon initially established the relationships among
these variables as given though they were tested the follow-
ing day in a class experiment that yielded inconsistent
results. On the other hand, Mr. Ellis conducted a "hallway
experiment" to calculate the mass of a student from the
relation m = F/a. In both cases, they were applying the
already established Newton's Second Law in two different
specific situations.

The third teacher, Mr. Howard, produced a different
kind of environment in which the information content was
delivered. The story-line on Mr. Howard shows a different

type of organization with respect to the "physical stuff"

196

(Erickson, 1982) through which the information content was
delivered. He relied on the textbook materials (textbook
and lab manual) and lab equipment such as carts, bricks,
ticker tape and graph 'tape, etc. as Ihe «elaborated. the
information content on "Galileo's Constant Motion"
(equivalent to Newton's First Law in Mr. Ellis' and Mr.
Simon's terms) and. "the effect of force. over 'velocity"
(equivalent to Newton's Second Law). The equipment changed
again for the demonstration on inertial and gravitational
mass. When Mr. Howard and Mr. Ellis and Mr. Simon are
compared, as shown in the story-line, it is clear that even
similar physical materials have different purposes and
usages as teachers construct subject matter for topics and
units that convey the same information. Mr. Howard, for
example, had students interact with the equipment in order
to gather data that would be represented in the graph papers
for later use. The information contained on these graphs
was eventually used to draw the conclusions on the topics
being dealt with at different instances. The story-line on
Mr. Howard gives evidence of three lab reports elaborated by
students and borrowed by Mr. Howard to establish these
conclusions.

The above discussion shows that teachers enact
different environments as they organize similar pieces of

classroom subject matter. And even though the environments

197

may be similar (e.g., same physical stuff), sometimes its
organization and purpose varied across teachers. In this
sense the "steps and strategies" (Erickson, 1982) imbedded
the physical materials through which subject matter is
delivered are not only context-specific but also topic-
specific. This finding is consistent with a constructivist
view of teaching in which teachers enact different environ-
ments to communicate the necessary information students need

to learn.

Part II -- Constructing Macro-Sequences on
Newton's Second Law

The previous account does not specifically focus in
detail on the variation in the way particular pieces of
academic work are constructed by teachers. Its purpose was
to give a sense of the overall structure (global coherence)
of a unit of dynamics as constructed by the three partici-
pant teachers. It gives the reader a story-line of how that
theme was sequenced across time. To begin to probe on
specific details, the researcher has selected videotape
segments that contain information concerning how teachers
dealt with a common topic. The micro-analysis that follows
will primarily shed light on the following guiding question:
What is the nature of the coherence of the information con-
tent delivered in a single topic as taught by high school
physics teachers? 'The analysis is geared. towards more
specific questions that focus on: (a) how is the selected
topic connected to other topics within the unit; (b) how is
the topic introduced and concluded: and (c) what are the
enacted logical relationships being delivered in a common
topic across teachers. The analysis will also focus on the
question: What is the nature of the task. environment
through which the topic was delivered?

The topic selected for micro-analysis is Newton's
Second Law (F = ma). This topic is considered to be a

fundamental concept in the study of dynamics and the causes

198

199

of motion. IDn addition to its importance within the theme
on dynamics itself, Newton's Second Law is a physics concept
that is carried over and linked to teaching other topics
such. as: circular' motion, Kepler's laws, momentum. and
energy. It can be assumed that understanding how such a
concept is taught can have strong implications on how future
concepts are also organized and connected to the concepts
already taught.

For the purposes of the analysis, it was decided to
select out the teachers' discourses on Newton's Second Law
from the entire data source on dynamics. In this sense, a
careful scrutiny of the data sources was carried out so as
to partition (Brown & Yule, 1983) the discourse in segments
which would indicate the precise moment at which Newton's
Second Law commenced being a topic as well as the moment at
which it was no longer a topic. For example, even though
two of the teachers (Mr. Simon and Mr. Ellis) performed an
experiment on Newton's Second Law after the discourse had
taken place, it was not considered as part of the discourse
on Newton's Second Law. Instead, these a-posteriory
instructional events can be categorized as applications of
Newton's Second Law. In the selection of the discourse
segments on Newton's Second Law, specific attention was
focused on the moment in time when teachers explicitly dealt

with the relations between mass, force and acceleration for

200

the first time. The micro-analysis of Newton's Second Law
will now be discussed.

The analysis will proceed as follows. First, the data
for each of the teachers will be presented, followed by an
interpretation. based on the interpretive framework that
guides this study. Second, a comparison of the three
participant teachers use of the topic of Newton's Second Law
will follow. The comparison is fundamentally based on how
the topic is connected to other topics within the same unit
(i.e., dynamics), how the topic is concluded, and what is
the nature of the task environment or physical stuff
(Erickson, 1982) through which the topic is delivered.

The segments on Newton's Second Law are presented in
tables that have three main columns: verbalizations,
participants' actions and immediate interpretation of these
actions as seen Iby the researcher (after ‘Yorke, 1987).
Though the micro-analysis could be focused on particular
utterances, a global view of the segments has been pursued
in order to compare the "grown" (Agar & Hobbs, 1985) micro-
sequences that result from the micro-analysis of these
segments. Analysis of the coherence of a text (discourse)
can be appropriately used as a tool to derive how the
"intended meaning" has been "grown" from the participant's
actions and the analysis of these actions. A micro-

sequence, then, can be viewed as the intended meaning

201

implicit in the teaching of a single topic (e.g., Newton's
Second Law).

The micro-analysis of the discourse segments on
Newton's Second Law leads to a consideration of the follow-
ing general assertions: Newton's Second Law, as taught by
three experienced high school teachers is differentially
constructed. A careful analysis of the teachers' discourse
reveals the existence of variations in the process of how
such a law is connected to other topics and how the same law
is formally introduced and terminated to students. In addi-
tion, Newton's Second Law is enacted through a series of

logical steps (micro—sequence) which vary among teachers.

Mr. Simon's Discourse on Newton's Second Law

Mr. Simon introduced Newton's Second Law immediately
after reviewing Newton's First Law, which was a topic he had
enacted three days earlier. Before beginning to elaborate
on Newton's Second Law, Mr. Simon referred to the conditions
and results of applying Newton's First Law. In this case,
after stating Newton's First Law as: "Bodies at rest remain
at rest . . . bodies in motion remain in motion . . .
straight line . . .," Mr. Simon indicated that this law
holds under the condition that there are no unbalanced
forces ( zF = 0), and that the result of these balanced
forces is that a body moves at a constant velocity and the

acceleration is zero. During the events that surrounded

202

the teaching of Newton's Second Law, Mr. Simon first
established the given relations that "acceleration is
proportional to net force" and "acceleration is inversely
proportional to mass." However, this was not followed by a
discussion on the conditions and results of applying
Newton's Second Law. Before concluding with the
mathematical equation that defines Newton's second Law,
examples of both Newton's First and Second Laws were
solicited from the class. The formulation of this equation
was followed by a brief discussion on the difference between
mass and weight, and a short lecture on Newton's Third Law.
Mr. Simon's discourse on Newton's Second Law (see Table
5.5) lasted about 20 minutes and students followed it with a
worksheet with spaces to be filled in as the lecture

progressed (see Appendix B).

2(33

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204

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no.a5oxo vsu osmu o_z» .amn.u ecu 0»
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ago: mo.n6oxo we «no» zuoo .soa
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210

Discussion of Mr. Simon's Micro-Sequence
on Newton's Second Law

The purpose of this section is to discuss Mr. Simon's
discourse on Newton's Second Law in terms of the interpre-
tive framework of this study. As has been indicated before,
an analysis of people's discourse as well as the actions
enacted simultaneously with a discourse can lead the dis-
course analyst to "map out" the intended meaning (Brown &
Yule, 1983) being communicated. Specifically, one can study
the nature of the coherence or the "underlying task struc-
ture" (Erickson, 1982) being displayed in the discourse. As
Erickson (1982) has indicated in, the case of classroom
events, this task structure is simultaneously enacted and
manifested through a series of steps and strategies
contained in the "physical stuff" used by teachers and
students to deliver information.

In the case of Mr. Simon, the immediate "physical
stuff" used to deliver information relative to Newton's
Second Law consisted of a worksheet (see Appendix B) and the
blackboard. Students were expected to fill out the work-
sheet as the teacher explained the content on the board. As
Appendix B indicates, the worksheet contained a series of
steps that were carefully followed. by' Hr. Simon as he
delivered Newton's Second Law. Specifically, it contained a
written statement about Newton's Second Law as well as black

spaces under the headings: conditions, results and examples

211

applied to Newton's Second Law. In addition, it contained a
series of examples, or self-tests, to be completed by the
students. It also contained cues as to the location in the
worksheet where students were expected to write down the
mathematical equation of Newton's Second Law.

A careful look at the way the information content is
organized through time yields evidence about the nature of
the local coherence (Brown & Yule, 1983) imbedded in the
teacher's discourse on Newton's Second Law. The discourse
segment shows that not all that is said is strictly related
to Newton's Second Law. It is also related to Newton's
First Law as illustrated by the fact that he discussed
Newton's First Law immediately after he had finished talking
about the results of Newton's Second Law. In spite of these
breaks (Brown & Yule, 1983), it was possible to map out the
structure of the information content he delivered. One is
able to determine the structure from the teacher's verbal-
ization and actions (e.g., what was written on the board),
as well as the immediate interpretation of them. The
following statements determine the nature of the coherence
of the information content being delivered by Mr. Simon:

The second law . . . it says that if you do have

an unbalanced force, then you have an acceleration

. and these are Newton's words . . . that
means that the acceleration is proportional to the

force" (written a o<Fnet).

Now the other part of that (equation) says . .
.that it (acceleration) is inversely proportional

212

to mass . . . that's to say . . . acceleration is

proportional to the inverse of the mass . . . if

you make the mass bigger the value of this

fraction a oLl/m) becomes less.

Let's go back to look at the equation form of

Newton's second law (8 sec) . . . I think . . . on

your sheet . . . there is above "test yourself"

and it says "written" . . . Newton's second law is

written this way . . . acceleration is propor-

tional to "f" and inversely proportional to "m"

(written a anym) . . . and if I choose the units

right . . . I can make that (proportion) an equal

(written a = F/m).

As has been indicated before, the enactment of Newton's
laws, as taught by Mr. Simon, was not done in a linear type
of fashion. Instead of organizing the information content
in a linear fashion, Mr. Simon initiated a break in which he
elaborated on the conditions under which the law applies,
the results of applying that law, and examples of the law.
All this took place immediately after the first two state-
ments (a 04 l/m and a o: Fnet) indicated above. A second
related break took place when Mr. Simon probed students'
understanding of Newton's First and Second Laws. It was not
until this last instructional event ended that Mr. Simon
finally established the mathematical formulation of Newton's

Second Law (see Figure 5.7).

 

 

I I I r |
I I I """""""""" I """"""""""" I net I Fnet I
| | | conditions | examples of | no: | a 0 |
| aocl'net | sod/m | and results | Newton's First | m | m |
| | of Second Law | and Second Lsusl | |
I I l I I I I
Figure 5.7. Temporal representation of Mr. Simon's micro-

sequence on Newton's Second Law.

213

The nature of Mr. Simon's local coherence on the topic
of Newton's Second Law indicates that even though not all of
the instructional events are logically' connected. tot one
another, there are events that strictly depend on what has
been said before (Grimes, 1975). In Grimes' terms, Mr.
Simon's sequence on Newton's Second Law can be categorized
as a logically loose one. Even though he elaborated on the
relations a d—Fnet and a 00 l/m before concluding that a =
Fnet/mr in a logical manner, Mr. Simon introduced two
breaks (Jefferson, 1972). The first one was to explain the
conditions and results of Newton's Second Law, and the
second one was to engage students in a problem solving
activity dealing with the application not only of Newton's
Second Law, but also of Newton's First Law (see Figure 5.7).
In this sense, Mr. Simon could have waited to formally
establish Newton's Second Law, and then engage students in
an activity dealing with the application of it or comparing
it with other laws. This interpretation is consistent with
Hirst's (1974) jig-saw metaphor. It is Hirst's view that
"the logical order does not prescribe a series of steps
which must be taken. There are a variety of ways in which
the jig-saw can be made up and the same is true in teaching

science" (Hirst, 1974:122).

214

Mr. Ellis' Discourse on Newton's Second Law

Mr. Ellis' discourse on Newton's Second Law (see Table
5.6) took place over a period of two consecutive class
sessions of 50 minutes each. In the first period, after
elaborating on the concept of inertia and Newton's First
Law, Mr. Ellis established, as given, the numerical equation
that defined Newton's Second Law (Fnet = ma). He next gave
the students a set of numerical and qualitative questions in
which they were required to apply the equation. In the
discussion that followed the solution to these problems, one
of the topics that emerged was the notion of friction, a net
force which affects the acceleration of a body.

During the second class period, Mr. Ellis further
elaborated on the logical relations that can be derived from
Newton's Second Law. He conducted two classroom demon-
strations that led him to conclude that "force (net) is
proportional to acceleration" (Fnetoca) and "acceleration is
inversely proportional to mass" (a ol_l/m). Each of the
above equations was later applied to a set of numerical
problems, and students were called on to answer questions
posed in each problem. Next Mr. Ellis summarized the topics
already covered, and referred to the future activities
(experiment) related to Newton's Second Law and other unit
topics. Ten minutes before the end of class, the teacher
assigned problems that required the application of topics

they covered, and more specifically, Newton's Second Law.

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227

Discussion of Mr. Ellis' Micro-Sequence
on Newton's Second Law

The focus of this section of the study will be on the
nature of the "enacted task environment (Erickson, 1982) and
the nature of the coherence across the information content
being delivered by Mr. Ellis. At this point of the
discussion, it is pertinent to remind the reader that Mr.
Ellis used the same textbook (Project Physics) as Mr. Simon.

The enacted task environment through which the subject
matter was delivered, in Mr. Ellis' case, consisted of "the
package" of written materials, and a set of laboratory
equipment made up of carts, rubber bands, bricks and a piece
of plywood. Each one of these materials played an important
role in the teacher's subject matter organization as it
relates to Newton's Second Law. For example, Handout 32 (in
the "package") (see Appendix J) was referred to on three
occasions. 'These instances usually’ marked. a change of
activity which generally consisted of having students work
on a particular problem or set of problems related to either
Newton's First or Second Law.

The lab equipment, however, served a different
function. It was used to qualitatively demonstrate that
acceleration is proportional to net force and that acceler-
ation is inversely proportional to mass. The second part of
the segment on Newton's Second Law (October 24, 1986)

contained information that describes how the lab equipment

228

was organized to enact the two statements mentioned. With
respect to the first statement, Mr. Ellis had students
observe how the acceleration increased as he increased the
force (number of rubber bands) being applied to the cart
moving along a horizontal surface of wood. The force varied
from one to three units. Similarly, the second statement
was elaborated by having the students observe how the accel-
eration of the cart decreased every time the number of
bricks was increased.

Through the interaction with the immediate environment
and the students, the teacher was able to communicate a
series of logical relationships between force, ‘mass and
acceleration. These relationships were not enacted in a
linear fashion but were intertwined with other instructional
events that were not necessarily related to Newton's Second
Law. In Mr. Ellis' case, the following statements could
well determine the underlying subject matter structure
imbedded in his teaching of Newton's Second Law.

It takes an unbalanced force to cause things to move .

. . and that is Newton's Second Law . . ." (written

Fnet = ma).

Newton's Second Law . . . in terms of acceleration . .

. standing below . . . is equal to the net force

divided by mass . . ." (written a = Fnet/m)-

If you keep the mass constant then we have a direct

proportion . . . between acceleration and the net force

. . . (written a oéFnet).

Now if the force is constant . . . the relationship
between acceleration and mass is a reciprocal one . . .

2229

as one (mass) gets bigger . . . the other (acceler-
ation) gets "smaller" (written a cxl/m).

The above statements yield evidence as to how Mr. Ellis
structured the relations between acceleration, mass and
force. Although these statements were taught in that order,
a careful look at the discourse segment shows the existence
of several "breaks" (Brown & Yule, 1983) in which subsequent
"pieces" of subject matter were linked to Newton's Second
Law (see Figure 5.8). For example, he introduced Newton's
Second Law equation as Fnet = ma, where the force is
measured in pounds and Newtons. He then engaged in a
problem solving activity in which Newton's First and Second
Laws were applied. Several related concepts were dealt with
on that occasion, such as: net force (or unbalanced force),
acceleration and force of friction. The force of friction
was a subtopic that was manifested through a couple of

demonstrations using a cart and a scale.

| | Break | | Break | |
I I --------------- I l --------------- I I
| | Problem | | Demonstration | a o‘Fnet |
| Fnet = ma | solving | a = Fnet/m | leading to | |
| | (friction) | | ach | |
I I | I | |
| Break | Break | | Break |

I ------------- I --------------- I I --------------- I

I Example | Demonstration | | Example on |

| on aocF | leading to | a otl/m | a Oil/m |

I l '3 “Um I I I

I I I l I

Figure 5.8. Temporal representation of Mr. Ellis' micro-

sequence on Newton's Second Law.

230

The last three statements given above were elaborated
in a sort of linear fashion. Their elaboration depended
heavily on the already established Newton's Second Law. So,
the three events that surrounded these statements were
logically connected to the first event. The whole sequence
could be categorized as a logically loose connected sequence
in which one event does not necessarily have another as a
consequence (Grimes, 1975). In this sense, the problem-
solving activity, that had taken place the day before the
last two statements above were delivered, were not logically
connected. What this means is that Mr. Ellis could have
elaborated on these two important statements without having
students engage in the problem-solving activity dealing with
Newton's Second Law. From an educational point of view it
would be better to "unravel" the logical relations that
derive from Newton's Second Law before engaging in instruc-

tional events that require the application of such a law.

Mr. Howard's Discourse on Newton's Second Law
Mr. Howard's discourse on Newton's Second Law (see
Table 5.7) lasted about 13 minutes. It took place during a
class period in which Mr. Howard announced the need to reach
the conclusions of the experiment: "The effect of force and
mass on acceleration." Students had been working on the
experiment for four class periods. The two major purposes

of the experiment were "to find out how forces affect the

231

acceleration value" and "how masses affect the acceleration"
(Videotape, February 6, 1987). Assisted by Mr. Howard,
students were expected to derive two different graphs, one
for each purpose: One was a representation of the "acceler-
ation versus force" when a brick was pulled by stretched
rubber bands, and the other was a representation of the
"inverse of the acceleration versus the mass (inertial)" of
a set of bricks being pulled by a stretched rubber band.
During the discussion of the experiment's conclusions,
Mr. Howard borrowed a student's set of graphs and sketched
them on the blackboard. He first derived the logical
relationship between acceleration and force (F 0(a), and
secondly, the relationship between acceleration and mass
(1/a 04 Mi). From here, Mr. Howard moved on to establish
that "force is equal to mass times acceleration" (F = Mia).
Throughout the entire discourse, most students ‘took; Mr.
Howard's suggestion and copied the notes he had written on

the blackboard.

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241

Discussion of Mr. Howard's flicro-Seguence
9n Newton's Second Law

The focus of this section of the study is the nature of
the local coherence in the subject matter delivered by Mr.
Howard, as he taught Newton's Second Law, as well as the
nature of the "physical stuff" or "materials" (Erickson,
1982) through which the subject matter was delivered to
students. The segment on Newton's Second Law yields
evidence to the effect that Mr. Howard first established
logical connection between acceleration and mass and
acceleration and force before deriving Newton's Second Law.
In this sense Newton's Second Law (F = ma) was "chained"
(Brown & Yule, 1983) or linked to previously derived
relations between acceleration, mass and force.

The enacted task environment through which Newton's
Second Law was delivered will be considered first. As shown
in the discourse segment above, Mr. Howard relied on the
textbook (PSSC) particularly pages 228 and 231. He also
relied on a set of graphs he borrowed from one of the
students. These graphs contained a substantial amount of
information that was eventually used by Hr. Howard to draw
the major conclusions with respect to Newton's Second Laws.
It is important to point out that these graphs were the
result of two consecutive lab experiments in which students
were expected to find out about the relationships between

force and mass and acceleration and mass, in that order.

242

This instructional event lasted five consecutive class
periods.

A second important point to consider is the nature of
the local coherence or structure of the subject matter
organization imbedded in the teaching of Newton's Second
Law. Several statements, either written on the board or
verbalized by Mr. Howard give a sense of the nature of the
coherence between acceleration, force and mass as follows:

Acceleration is directly proportional to the applied

force if the mass is constant (Mi = k) (constant)"

(written l/a oz Mi) .

The "a" (acceleration) is inversely proportional to the

inertial mass if "F" (force) is "K" (constant) (written

1/ a oz Mi) .

If we take a serious look at that (F/a QCMi) I can make

life easier . . . if I define force as the product of

mass and acceleration . . . I resolve the only problem

. . . I can search for a constant of proportionality .

. . that will make force equal to mass times

acceleration . . ." (written F = mia).

The three statements above were delivered by Mr. Howard
without having to resort to breaks in the discourse. The
first statement was a conclusion he had drawn from the graph
on force versus inertial mass, which he had borrowed and
sketched on the board. The second statement was the con-
clusion he arrived at, after discussing the graph "inverse
of acceleration versus inertial mass." The third statement
was a direct derivation from the first two statements.

In a sense, Mr. Howard's micro-sequence on Newton's

Second Law could. be categorized as a "logically tight"

243

sequence (in Grimes' terms), meaning that the events dealing
with the construction of the equation F = Mia were
logically linked to the previous events dealing with F<x a,
and a Gil/mi which led Mr. Howard to conclude that "force is
equal to mass times acceleration." In Mr. Howard's segment
on Newton's Second Law (see Figure 5.9), it could be
observed, that compared with the other two teachers, there
were no "breaks" (Jefferson, 1972) that engaged the students
in an application of the logical relationships being
established. Table 5.7 shows that "problems" or "HDL" were
assigned .once the conclusions on Newton's Second Law had
been reached.

Folo 1/a azni F/a acnia

FCKHfi rerun

Figure 5.9. Temporal representation of Mr. Howard's
micro-sequence on Newton's Second Law.

A Comparative Analysis on Newton's Second Law
as Taught by Teachers

This section of the study offers a comparative analysis
on the way the three participant teachers organized the
subject matter, as they delivered the topic of Newton's
Second Law. It also compares the nature of the immediate
task environment through which the subject matter was

manifested. With respect to the first issue, a description

244

of how Newton's Second Law was presented, in the context of
the unit on dynamics, is given. Emphasis is made on how the
topic was connected to others within the unit and how the
topic of Newton's Law was "closed" (Brown & Yule, 1983).
Related also to the first issue, this section also provides
a comparative analysis of how the information content on
Newton's Second Law was structured through time. Finally,
this section discusses the nature of the enacted environment

through which each individual teacher delivered the topic.

Connecting Newton's Second Law to Previous Topics

 

 

In order to guide the discussion that follows,
"previous topics" will refer here to the main concepts that
preceded the teaching of Newton's Second Law. These
concepts include acceleration, velocity, vectors, inertia
and unbalanced net force. The concepts of acceleration and
velocity as well as the operations that they imply are
considered to be background information already taught by
the three participant teachers in the unit on kinematics.

A look at the discourse segments shows that both Mr.
Ellis and Mr. Simon introduced Newton's Second Law immedi-
ately after Newton's First Law of inertia. Both teachers
drew from the concept of "unbalanced force" that produces an
acceleration.

Both teachers also indicated the vectorial nature of

Newton's Second Law. After introducing Newton's Second Law

245

(F = ma), Mr. Ellis discussed the "units" of force. On the
other hand, Mr. Simon preferred to elaborate on two main
statements: "acceleration is -proportional to the net
force," and "acceleration is proportional to the inverse of
the mass." This was followed by a discussion of the con-
ditions under 'which Newton's laws hold. as ‘well as the
results and some examples of that law. This discussion
would be considered to be a "break" that was terminated once
the numerical equation of Newton's Second Law was formally
introduced (a = F/m). At this point, it is important to
point out the difference in the way both teachers formulated
Newton's Second Law.

Mr. Ellis shifted gears to do a problem solving
activity that involved the application of Newton's First and
Second Laws. During this activity, the concept of friction
(force) was fully explained. The following class period he
picked up on Newton's Second Law again and relied on class-
room demonstrations to show that "acceleration is propor-
tional to the net force" and that "acceleration is inversely
proportional to the mass." The following day, he moved on
to a discussion of mass and weight.

The third teacher, Mr. Howard, did not explicitly
introduce Newton's Second Law as such. (In an interview
with him, he referred to the expression F = ma as "Newton's

Law.") Before deriving the relation P = ma, Mr. Howard

246

summarized, in two major statements, the information gath-
ered from the laboratory work the class had been engaged in
during the previous six consecutive days. These statements
were as follows:
1. Acceleration is directly proportional to the
applied force if the mass is constant (F<X.a).
2. Acceleration is inversely proportional to the
inertial mass if F (force) is constant.
The two previous statements were "collapsed" into a

single mathematical relation in the form of F = ma.

Topic "glosipg" or Terminapion

A topic is considered to be "terminated" when the
speaker moves on to a subject of a different nature (Brown &
Yule, 1985). In this case, it was pragmatically decided to
"close" a topic as soon as a topic-shift occurred in the
teacher's discourse. Precautions were taken to find evi-
dence ‘that the ‘teacher' was not elaborating’ on. Newton's
Second Law as an indication that such a topic had been
terminated. For example, Mr. Simon "closed" his formal
introduction of Newton's Second Law as follows:

Let's go back to look at the equation form of

Newton's Second Law (8 sec) . . . I think your

sheet . . . there is above "test yourself" and it

says "written" . . . Newton's Second Law is

written this way . . . acceleration is

proportional to "f" and inversely proportional to

"m" (a at f/m) . . . and if I choose the units
right . . . I can make that (proportion) an equal

247

. . . not a proportionality. (a = f/m) (see page
204)

The previous segment was then followed by a subtopic
dealing with the unit of force and an operational rule on
how to operate the variables "F", "a" and "m" when applying
the equation F = ma in the solution of numerical problems.

Mr. Ellis' closing on Newton's Second Law was rather
different. Immediately after elaborating on the idea that
the relationship between acceleration and mass is a
reciprocal one, he summarized the Iblock. he .had already
covered to indicate the tasks to come (global coherence).
The following excerpt clarifies this point:

Block one . . . I believe we did it last Friday .

. . block two last time we met on Wednesday . . .

block three . . . the hallway experiment . . .

we'll probably get it next Thursday . . . if at

all possible, I'd like to have the experiment on

the double hour. (see page 210)

The above event. was followed. by' a jproblem solving
activity that focused on the application of Newton's Second
Law. The following class period Mr. Ellis dealt with the
distinction between mass and weight.

The third teacher, Mr. Howard, closed the discussion on
Newton's law (F = ma) after collapsing the two statements:
"Force is proportional to acceleration," and "acceleration
is inversely proportional to mass" into a single statement:

"Force is the product of mass and acceleration." After he

established this equation, he made a topic shift to derive

248

the units of force by substituting the units of acceleration
(M/secz) and mass (kg) in the already established Newton's
law (F = ma). The following excerpt shows how the topic of
Newton's Law was terminated: "In this experiment, we define
force . . . force is the product of the acceleration and
mass (F = ma) . . . Let's see what it looks like unit wise .
. . well, you know that . .. . any problem with that. . ."
(see page 225).

The discussion on units was followed by Mr. Howard
assigning a set of problems in which students would apply

the equation: F = ma.

The Structure of the Information Content

The micro-analysis of the nature of the coherence on
Newton's Second Law showed an important variation on the way
academic information content is organized. in real time.
This variation emerged from a detailed analysis of the
synthesis imbedded in the discourse segments on Newton's
Second Law. A synthesis is a sequence strategy that shows
how' concepts are logically related (Van Patten et al.,
1986). The analysis that follows shows how teachers syn-
thesized the concepts of mass, acceleration and force when
they taught the relation: "Force is equal to mass times

acceleration."

249

Figure 5.10 shows how the three micro-sequence
structures vary among teachers. These structures or cog-
nitive maps represent a global view of how Newton's Second
Law was logically organized by the participant teachers.
They represent the underlying organization of the inform-
ation content (Erickson, 1982) included in the teaching of
Newton's Second Law. The maps have been developed from a
detailed analysis of the logical connections between the
different pieces of segments dealing with Newton's Second
Law. Attention was paid to the content given in the
discourse, the actions that such a discourse conveyed as
well as the researcher's immediate interpretation of these
actions.

A close look at Figure 5.10 indicates that both Mr.
Howard and Mr. Simon's micro-sequences are strikingly
similar, in spite of the fact that different textbooks were
used. However, this similarity is very superficial in terms
of how each sequence was constructed. While Mr. Howard, for
example, spent six consecutive class periods empirically
deriving' Newton's Second. Law, Mr. Simon spent about 15
minutes. In addition, Mr. Simon started off from the given
statement of "unbalanced force which produces acceleration."
Mr. Howard's notion of force was represented by rubber bands
used to pull objects. A third important comparison between

the two sequences lies on the idea of mass. In the case of

250

Mr. Simon's Micro-Sequence Hr. Ellis' Micro-Sequence
aCXFnet (200) a 0(l/m (203) Fnet I ma (215)
a (xF/m (207) /= Fnet/m (219)
a = F/m (207) a Oanet (215) a czl/m (225)
a1 1 F1 a1 1"2
__ = __ (223) __ = __ (225)
a2 F2 a2 m1

Mr. Howard's Micro-Sequence

F Ola (234) Emmi (237)
a
F /
Oimi (237)

31

F amia (237)

F = mia (238)

Figure 5.10. Micro-sequence structures on Newton's Second
Law compared.

Note 1: The numbers in parenthesis show the page location
of that statement in the respective discourse
segment.

Note 2: i stands for inertial, O< stands for proportional
to, m stands for mass, F stands for force, and a
stands for acceleration. F is given in Newtons and
pounds, a in m/secz, and m in kg and slugs.

251

Mr. Simon, mass is a measure of inertia or resistance to
mover and it is accelerated when an unbalanced force is
applied to ix; Instead, Mr. Howard introduced the idea of
inertial mass measured in bricks (later inertial mass and
gravitational mass would be compared).

Mr. Ellis' micro-sequence is also surprising,
particularly when it was compared with Mr. Simon's sequence
(both teachers used the same textbook: Prpject Physics).
Both teachers introduced Newton's Second Law as a given
relationship. However, Mr. Simon first elaborated on the
facts that "acceleration is proportional to force" and that
"acceleration is inversely proportional to mass"
(gravitational). These two expressions were then combined
to form a single one (F = ma). To the contrary, Mr. Ellis
first stated Newton's Second Law and then elaborated on the
same given facts (a O‘Fnet and a.o<l/m). While elaborating
(using a class demonstration) on these two relationships,
Mr. Ellis made use of exactly the same laboratory equipment
used by Mr. Howard's students to derive the graphs that
would show the relationships between "acceleration and
force" and between "acceleration and inertial mass." This
is also an indication that the enacted. environment ‘was

different among teachers.

252

Information Content and Envipopmgnt

The micro-analysis of the discourse segment on Newton's
Second Law indicates that teachers not only enact different
sequences of logical operations when teaching a similar
topic, but also that these logical operations are simul-
taneously manifested through distinct environments. The
following vignettes will shed light on the above assertion.
The vignettes describe the nature of the environment (as
defined by Erickson, 1982) being simultaneously enacted as
the three participants/teachers elaborated on the relations
between acceleration, mass and force. As shown in Figure
5.7, the four' major' mathematical relationships teachers
referred to when constructing Newton's Second Law are:
F = ma, a ct F, a oLl/m and FoLm/a.

The first teacher, Mr. Simon, delivered the topic of
Newton's Second Law by having students follow along with a
worksheet entitled "Newton's laws of motion" (see Appendix
B). (It was usually the case that students had to copy down
relevant statements which, for the most part, were express-
ively written on the board.) This worksheet contained blank
spaces for students to fill in. As indicated in the dis-
course segment, Mr. Simon first established (as "given") ,
the relation a QCFnet and for a few seconds elaborated on it

by making reference to the relation between acceleration and

253

force in cars with big engines. The second step was to
elaborate on the relation a all/m.

It is important to point out that the worksheet did not
contain blank spaces for these relationships to be written
down. However, in the next step that followed, space was
provided to write down the conditions under which Newton's
Second Law held, it's results, examples and the written
format of the proportionality a<fo/m. Having established
this proportionality, Mr. Simon immediately' moved. on 'to
state that "if I choose the units right . . . I can make the
(proportion) an equal" (a = F/m). He then identified each
one of these variables before explaining the units in which
acceleration, mass and force are expressed.. At each one of
these steps, students filled in the corresponding blanks on
the worksheet.

Mr. Ellis' story on Newton's Second Law and the
immediate environment through which it was delivered was
rather different (remember that both Mr. Ellis and Mr. Simon
used the same textbook). He spent two consecutive class
periods in the enactment of the information content deliver-
ed on Newton's Second Law. In the first meeting (October
22, 1986), Mr. Ellis first reviewed. Newton's first law
before introducing the equation: Fnet = ma, and elaborating
on the units of force, mass and acceleration. His lecture

on this subtopic was followed by a problem solving activity

254

initiated by having students "open their package . . . in
handout 30." Four problems were worked dealing with
Newton's First and Second Laws. The third problem was of
particular significance, since on this occasion, the idea of
friction was discussed. It was important because this topic
would be linked to other events that happened afterwards.
The problem consisted of calculating the force of friction
between the teacher's desk and a wooden block, and between a
cart (with a girl standing on it) and the classroom floor.
In the second meeting (October 24, 1986), Mr. Ellis'
enacted environment was even more complex because he elabor-
ated on two relations linked to Newton's Second Law, that
is: a oi Fnet and a o< l/m. He had already added the
equation of Newton's Second Law to the list of kinematic
equations on both sides of the blackboard. After rewriting
(on the board) Newton's Second Law in the form: a = Fnet/mr
Mr. Ellis suggested that students "open their package in
Handout 32." While students read the first problem assign-
ed, he called for Melissa's assistance to run a demon-
stration. On this occasion, he gave Melissa a wooden cart
being to be pulled by a rubber band. He first tried one
rubber band (first force), then two rubber bands (second
force), and finally, three rubber bands (third force). The
cart accelerated faster each time. After the demonstration,

Mr. Ellis called students' attention to the package and

255

elaborated on the idea that "if you keep the mass constant
(one cart), then we have a direct proportion between
acceleration and the net force" (a 0L Fnet) . The above event
was followed by a numerical exercise.

Having established (qualitatively) that acceleration is
proportional to net force, Hr. Ellis next engaged in a
second demonstration dealing with the idea that acceleration
is inversely proportional to mass. Assisted by the same
student as before, Mr. Ellis added onto the cart one, two
and then three bricks (varying the mass) and had students
observe that the acceleration was smaller each time, if the
cart is pulled with one rubber band (constant force). Next,
he finally established the relation to be: a ocl/m.

As before, the demonstration with carts, rubber bands
and bricks was followed by a numerical problem from the
package in which the relation (a at l/m) was applied. Mr.
Ellis then briefly referred to the blocks (from the schedule
sheet) already covered as well as to future activities (lab
work and assignment).

The history of how Mr. Howard enacted the information
content on Newton's Second Law, through "physical materials"
(Erickson, 1982), is different from Mr. Simon's and Mr.
Ellis' accounts. The sequencing of the physical materials
and the cues that they contained to accomplish the task at

hand ran parallel to the sequencing of the information

256

content being delivered. At a general level, the segment on
"Newton's law" (as he later called it) shows that Mr. Howard
referred students to information in the textbook (page 229
and 231) (see Appendix H) and questioned students on the
information indicated there. He next borrowed two graphs
that students had been working on during the previous three
class meetings. Mr. Howard sketched the first graph on the
board. He showed that acceleration was directly proportion-
al to the applied force if the mass was constant (F a a).
The next step was to sketch the second graph that contained
information on the relation between acceleration and mass.
On this occasion he sketched the inverse of the acceleration
(l/a) versus mass (one, two, three and four bricks). The
graph led him to conclude that: "a" (acceleration) is
inversely proportional to the inertial mass, if "F" (force)
is "K" (meaning constant).

The two statements indicated above were combined by Mr.
Howard into one single expression given by: F ocnqa, after
which he would define force as F = mia.

It is important to point out the events just described
were preceded by other series of events that were considered
to be already known to the students (and to the readers,
too). For example, the graphs indicated above had been
obtained from a laboratory experiment whose purpose was to

determine how a force affects acceleration and mass. Each

257

graph contained information being derived from the
procedures. On the discourse segment, Mr. Howard referred
several times to "one, two, three or four" (reading the
horizontal axis). In the case of the first graph
(acceleration versus force), he was making reference to "one
rubber band, "two rubber bands," "three rubber bands" and
"four rubber bands." For the second graph (inverse of
acceleration versus mass), the meaning was different. He
meant: "one brick," "two bricks," "three bricks" and "four
bricks" (examples of inertial masszmi).

We can observe here that both Mr. Howard and Mr. Ellis
relied on practically the same physical stuff to elaborate
on the relations F = ma, F oca and a ail/m. The difference
lies in how the materials were sequenced through time. On
one hand, Mr. Ellis preferred to qualitatively show the
nature of these relations, without. having' students 'take
measurements or draw graphs. On the other hand, Mr. Howard
had students discover by themselves the relations by having
them measure accelerations (on a ticker tape) and plotting

the acceleration versus force and mass.

gesults and Conclusions pn Newton's Secong an

The preceding vignettes and assertions describing how
teachers organized the presentation of the topic Newton's
Second Law reveals several conclusions. In general terms,

it can be stated that Newton's Second Law was differentially

258

constructed (Magoon, 1977) by teachers. First, teachers
"differ from each other in their construction of events" and
in doing so they anticipate and organize these events
accordingly (Kelly, 1955). We Ihave observed. how' three
experienced physics teachers structured a series of
instructional events as they strove to communicate the
possible logical relationships that could be derived from
the concepts of acceleration (a), mass (m) and force (F).
Indeed, a micro-analysis of the teacher's discourse on
Newton's Second Law revealed the existence of different
patterns with respect to how teachers structured and
organized logical relationships over time. In one case, for
example, Mr. Simon, who started out by elaborating on the
given relationships: "force is proportional to
acceleration" and "acceleration is inversely proportional to
mass" until he eventually concluded that "force is equal to
mass times acceleration." A second teacher, Mr. Ellis,
using the same textbook as Mr. Simon, began by indicating
that "force is mass times acceleration." From here, he
demonstrated (qualitatively) that "force is proportional to
acceleration" and "acceleration is inversely proportional to
mass." The third teacher, Mr. Howard, who relied on a
different textbook, structured Newton's Second Law in a
different manner. His first step was to have students

experimentally determine the relationships between acceler-

259

ation and force and acceleration and mass. From here, Mr.
Howard synthesized that "force is equal to mass times
acceleration."

A second major conclusion related to the one above lies
in the nature of the local coherence (Agar & Hobbs, 1985)
among the different events dealing with a specific topic.
The fact that teachers anticipate different instructional
events as a specific topic such as Newton's Second Law is
enacted, results in story-lines whose temporal and logical
sequence vary in terms of the information content delivered
and the logical relationships imbedded in that content. In
this sense, the teachers made use of "coherent relations"
(Hobbs, 1983) to connect the different pieces of information
content they want to communicate. As the segment on
Newton's Second Law indicated, one of the most common
coherent relations put in practice by the three participant
teachers was that of "expansion relation" (Hobbs, 1983).
Teachers very rarely stopped to evaluate their discourse
(evaluation relation) to explain what happened before
(temporal relation) or to explicitly explain what the actual
message was about (linkage relation). Expansion relation in
a discourse refers to statements are made by teachers to
move between specific and general statements (Hobbs, 1983).

This idea can be expanded as follows.

260

A close look at the teacher's discourse on Newton's
Second Law shows, for example, that a common expansion
relation is to make a general statement and then exemplify
it by having students work on numerical problems. This was
the case of Mr. Ellis and Mr. Simon, who after-elaborating
on the statements F = ma, F oé a and a OCl/m had students
work on a set of numerical problems where these relations
were applied. The difference between the two teachers lay
in that Mr. Ellis, for example, gave out a first set of
problems right after he had established the equation F = ma,
and a second one after he had elaborated on the other two
relations. On the other hand, Mr. Simon presented the
examples (problem) immediately after he had elaborated on
the ideas that "force (net) is proportional to acceleration"
and "acceleration is proportional to mass." He also posed a
second set of problems after he had eventually established
the relation F = ma.

The third teacher, Mr. Howard, delivered Newton's Second
Law following a rather different organization. He first
established the general statements that surrounded Newton's
Second Law and eventually assigned a set of numerical prob-
lems for students to work on. The shifting from a general
statement to an exemplification situation can be categorized
as a break (Jefferson, 1972). In this sense, one could say

that both Mr. Ellis and Mr. Simon, after elaborating on a

261

general statement introduced. a topic shift (Brown & Yule,
1983) by having students work on numerical problems until
they eventually returned to the topic being enacted. How-
ever, this was not the case of Mr. Howard, who decided to
quickly lay down the general statements that surrounded the
teaching of Newton's Second Law. It is through the use of
breaks (Jefferson, 1972) and coherent relations (Agar &
Hobbs, 1985) that teachers enact different types of logical
sequences when delivering a common topic. We have observed
that in the cases of Mr. Ellis and Mr. Simon, both con-
structed logically loose sequences when enacting Newton's
Second Law. However, Mr. Howard enacted the same law by
following a "tight logical sequence" (Grimes, 1976).

A third major conclusion with respect to how teachers
construct a single topic in physics is related to the
inclusion of breaks, the type of logical sequence, and the
way information is actually derived. For example, Mr. Simon
and Mr. Ellis, who frequently introduced breaks in their
discourses on Newton's Second Law, established the logical
relationships that surrounded Newton's Second Law as if they
were "given" statements that could be empirically (through
demonstration) supported. However, Mr. Howard, for whom
breaks were infrequent, experimentally derived the logical
relationships that surrounded the deviation of Newton's

Second Law. In this sense, breaks seem to be associated

262

with logically loose sequences in which logical statements
are established as "given," and as such, they need to be
expanded through specific examples.

Finally, there is a conclusion that needs to be made.
As had been indicated in Chapter II, teaching is a
constructivist process (Magoon, 1977; Green & Harker, 1983;
Yorke, 1987) in which teachers act upon the subject matter
and organize it accordingly to be able to communicate
(verbally and nonverbally) the information content which the
students are expected to learn. In this process, teachers
and students interact with the immediate environment (books,
worksheets and lab equipment) through which such information
is delivered. In the micro-analysis of Newton's Second Law,
it was found that the elements of immediate environment
varied among teachers with respect to: (a) their location
in the discourse sequence, (b) the steps and strategies
implemented by teachers with respect to their location in
the discourse sequence, and (c) the steps and strategies
implemented by teachers to communicate information. In the
case of Newton's Second Law, one teacher (Mr. Simon), for
example, relied on a worksheet with spaces to fill in and
the blackboard. Hr. Ellis relied primarily on a package of
written materials and lab equipment for classroom demon-
stration. Finally, the third teacher, Mr. Howard, made use

of students' graphs to establish Newton's Second Law.

263

The preceding conclusions lead to the consideration of a
final question, "Why do teachers organize the teaching of a
single topics and units differently?" One possibility is
that teachers (such as Mr. Ellis and. Mr. Simon) have
different interpretations of the information content
imbedded. in the textbook. and the ‘use of equipment for
delivering that information content (through classroom
demonstrations, handouts, worksheets, etc.) , so that they
enact different relationships among the, concepts and
generalizations. .A second possibility' is ‘that ‘teachers
bring into their classroom information from their own
experience drawn from previous courses, readings and the
like. This information, added to the textbook information,
undoubtedly leads to discourses with different underlying
structure in terms of the organization of the subject matter
being delivered.

A third possibility is that teachers change the
textbook structure in order to assist students in the
comprehension of subject matter. This modification of the
textbook structure takes place at unit level (macro) and at
topic level (micro). Detail analysis of the teacher's
discourse of Newton's Second Law showed, for example, that
teachers construct logical sequences in ways that are not
directly prescribed in the textbooks. In doing so, teachers

introduce "breaks" in the sequence in order to carry out

264

demonstrations or solve numerical problems that illustrate
and expand specific logical relationships imbedded in the
sequences.

One important point to be made here is that even though
the participating physics teachers modified the textbook's
logical sequence (as they constructed subject matter), the
purpose of this modification was not explicitly geared
towards changing students' previous conceptions of the
subject matter being constructed as was. the case of
Minstrell's (1984) work on Newtonian dynamics. Based on
empirical research on students' own conceptions about the
relationship between force and motion, Minstrell modified
the traditional way of sequencing Newton's Laws in order to
help high school students to overcome the preinstruction
idea that "a constant unbalanced force should result in
constant velocity" and instead be able to accept the view
that "a constant unbalanced force would produce a constant
acceleration." In trying to help students overcome the idea
that an unbalanced force results in constant velocity,
Minstrell (1984) designed an instructional sequence for
teaching Newton's Laws that basically consisted of four
major points: (a) engagement of initial conception, (b)
firsthand experiences relating to their initial conception,
(c) treating the concrete constant acceleration case before

the abstract logical consequence of the constant velocity

265

case, and (d) the discussions encouraging rational thought
to resolve discrepancies between initial ideas and firsthand
experiences.

In conclusion, what Minstrell did in terms of organizing
subject matter for students' comprehension was to change the
traditional sequence in which Newton's Laws are presented in
high school textbooks. In this sense, he started off by
first introducing Newton's Second Law and then treating
Newton's First Law (or law of constant velocity) as a
particular case of the second law.

Contrary to what Minstrell (1984) did, the three
participating teachers of this study did not explicitly
address students' conceptions as they constructed their
units on dynamics. However, this does not necessarily lead
to the conclusion that students did not overcome the
conception "an unbalanced force results in constant
velocity." This is an issue that needs to be further
explored through more empirical research as will be

described later.

CHLAPTER.SDK

OVERVIEW, CONCLUSIONS AND IMPLICATIONS
FOR PRACTICE AND RESEARCH

This final chapter is divided into three main parts.
The first part describes an overview' of the study and
includes research questions, methodology and findings. The
second part discusses the major conclusions of the research.
The third part addresses the implications the study has in
terms of the effects it may have on areas such as:
inservice and preservice teacher education and future

research.

Overview

The present study has been an empirical effort to learn
how teachers construct and enact classroom academic content.
This issue has been established as a fundamental problem in
research on teaching and teacher education (Doyle, 1986) .
It has been said that school knowledge is constructed as
teachers and students interact to achieve their goals
(Yorke, 1987: Erickson, 1982). This study was carried out
with the intention of learning how school knowledge is made
available to students and how that knowledge is organized.

This is what Cazden (1986) referred to as a "micro-sociology

266

267

of knowledge" or "how’ educational knowledge: is socially
defined and made available."

In order to shed light on the above question, the
researcher "negotiated entry" (Erickson, 1986) with three
experienced physics teachers to study and learn about their
teaching. During the six months of intensive observation,
the researcher recorded classroom observation on different
topics in high school physics including optics, waves,
kinematics, dynamics, electricity, etc. For the purpose of
analysis, the theme on dynamics was chosen in order to
describe the way school knowledge is differently enacted by
teachers.

The primary questions addressed in this ethnographic
study had to do with the organization of physics topics by
high school teachers. The general question remained the
same throughout the school year (see Chapter Three);
however, during the data analysis process it was soon
discovered that the specific questions were too broad to be
answered. The literature review that followed and "the
understanding of events" (Erickson, 1986) under analysis led
to a more focused set of questions. Three main questions
that guided the final analysis as follows:

1. What is the nature of the coherence of the subject

matter-information content (story-line) in the

268

unit on dynamics as enacted by three high school
physics teachers?

2. What is the nature of the coherence of the subject
matter information content delivered on a single
topic (dynamics) as taught by three high school
physics teachers?

3. What is the nature of the enacted environment
through which the information content is
delivered?

These questions remained constant during the final
analysis. The first question was methodologically addressed
through the construction of "story-lines" which showed how
teachers dealt, through time, with different topics, and the
way the topics gradually emerged and decayed (Tannen, 1984)
as the target theme (dynamics) was developed. The purpose
of the story-line was to describe, not only the topics being
enacted but also how they were enacted. The second question
was addressed by carrying out a micro-analysis of the seg-
ment on Newton's Second Law that was common to the three
participant teachers. These two analyses led to the
establishment of "the underlying structure" (Erickson, 1982)
of the subject matter being enacted at two different levels:
macro-level and micro-level. At the macro-level, it was
noticed that the topics taught in a unit on introductory

dynamics, as well as its organization, vary among teachers

269

—- even those teachers following the same overall
curriculum. At the micro-level, it was found that the
teachers enact different sequences of "logical operations
and steps" (Erickson, 1982) when dealing with common topics.
The third question was also addressed at both levels. The

conclusions will now be discussed.

W

Erickson (1982) pointed out that the school "subject
matter" can be defined according to four constitute aspects:
(a) the subject matter information content: (b) the sequenc-
ing of recursive steps in logic of subject matter compre-
hension; (c) the "meta content" cues toward completion of
the task; and (d) the physical materials through which tasks
are accomplished. This section of the study presents some
of the major conclusions in terms of how the three
participant teachers dealt with the above four aspects.

The study of the global and local coherence (Agar &
Hobbs, 1985) as these three participant teachers delivered a
theme on introductory dynamics, revealed that "school
knowledge" (Doyle, 1986) or school "subject matter"
(Erickson, 1982) was differentially enacted by teachers, as
shown by the subject matter content and its organization.
The subject matter content, manifested in the form of
topics, and organized in macro-sequence and micro-sequence,

vary in terms of what topics are delivered by teachers and

270

in the form in which each individual topic is enacted.
Also, the study of global and local coherence in teacher's
discourse, as well as the actions being displayed as the
discourse was elaborated, yielded evidence with respect to
subject matter organization and its enactment through
physical materials.

A general conclusion that can be drawn from this study
is that experienced qualified physics teachers
differentially organize subject matter at both macro-level
and micro-level. At a macro-level, teachers constructed
different structures of subject matter by breaking a piece
of knowledge (i.e., unit) into topics which may or may not
be logically connected. The way in which individual topics
were treated ‘varied among teachers, even among the two
teachers who were using the same textbook. Also, the topics
enacted by one teacher were not necessarily the same as
those enacted by a different teacher. In addition, the
logical connection between successive topics, as carried out
by a teacher, were totally different to the connections made
by another teacher, even though they may be dealing with
similar topics taught in the same temporal order. In this
sense, teachers generally relied on different "coherent
relations" (Hobbs, 1983) to properly connect the topics in
similar units of instruction. A topic may be initially

introduced and eventually ignored, or it may be transferred

271

and used in the context of an instructional event dealing
with another topic or set of topics. This situation is
somehow similar to Jefferson's notion (Jefferson, 1972) of
"termination" and "break." In a termination, a topic is
shifted from one area to another, and the first area is
never picked up again in the development of the discourse's
general theme. In a break, a topic is elaborated, then a
"topic shift" (Brown & Yule, 1983) occurs that shifts the
discussion into a different area and later another topic
shift eventually brings the initial topic back. It is
through this process of connecting topics that teachers
enact subject matter structures which vary with respect to
the nature of the information content being communicated to
students.

The analysis of the unit on dynamics' global coherence
as constructed by the three participant teachers of this
study yields evidence as to how "breaks" and "topic shifts"
emerged while individual teachers actively engaged in the
process of communicating the information content imbedded in
that unit. The story lines that described the nature of
the global coherence, indicated that teachers made use of
"topics shifts" as they constructed subject matter, and they
eventually ended up ignoring the logical connections between
related topics. The end product of these actions was the

construction of "logically loose sequences" (Grimes, 1976)

272

with. gaps that students ‘were expected to interpret and
comprehend. Three specific instances of "topic shifts" in
which three participants ignored the logical connection
between two contiguous topics are worth mentioning.

In the following three instances, the three participant
teachers did not make explicit reference to the preceding
topic (Newton's Second Law): Mr. Simon's elaborating on the
difference between mass and weight, Mr. Ellis dealing with
Newton's Third Law, and Mr. Howard's teaching the difference
between inertial mass and gravitational mass.

At a micro-level, the nature of how school subject
matter is differentially organized by physics teachers
becomes more detailed. In effect, a micro-analysis of the
"local coherence" (Agar & Hobbs, 1985) of the way three
experienced teachers strived to communicate the topic of
Newton's Second Law revealed that teachers enacted subject
matter through a series of successive steps containing
information organized under different underlying structures
(Erickson, 1982) which do not necessarily follow the same
logical and temporal order.

In this study, we have defined the term micro-sequence
as of the underlying structure imbedded in the teaching of a
particular topic. A macro-sequence gives a sense of the
synthesis of the topic that teachers tried to communicate

through their discourse. In effect, this study showed that

273

teachers break topics into small pieces of knowledge (state-
ments) and organize them under different logical steps.

As in the case of global coherence, teachers relied on
"coherent relations" (Hobbs, 1983) to construct on specific
topics. At a micro-analysis level, these relations are
easier to detect. In the case of the discourse analysis on
Newton's Second Law, the most frequent relations being used
were linkage :relations, temporal relations. and. expansion
relations (in Hobb's terms). Expansion relations were
frequently used by the two teachers (Mr. Simon and Mr.
Ellis) who established Newton's Second Law in a series of
successive logical relationships between acceleration, mass
and force. waever, strong temporal relations and linkage
relations were more common in Mr. Howard's discourse on
Newton's Second Law. The fact that teachers implement
expansion relations, such as examples after establishing a
general statement (e.g., a otF or a CLl/m) leads teachers to
establish "breaks" (Jefferson, 1972) or "breaches" (Green &
Harker, 1982) in the discourse as conversation develops.
This way, teachers leave the impression that they establish
logical relationships in a "jig-saw" (Hirst, 1974) fashion.
That is, there is a great variety of ways in which a topic
can be taught and the logical order emerges as you go along

(Hirst, 1974).

274

In the construction of Newton's Second Law, breaks
were introduced by teachers and the discourses served
different purposes. For example, Mr. Simon made use of
breaks to exemplify specific logical "given" relations
(a‘XFnet and a crl/m) before establishing the equation that
defined Newton's Second Law. On the other hand, Mr. Ellis
first established Newton's Second Law, and then exemplified
it by solving numerical problems. His next major step was
to carry out empirical demonstrations that led to the
conclusions of two logical relations as indicated above.
The third teacher, Mr. Howard, did not introduce breaks in
his discourse when he constructed similar logical relation-
ships. The difference between Mr. Howard and the other two
teachers was his reliance on students' lab reports to
elaborate the logical relationships that surrounded the
construction of Newton's Second Law.

The above discussion suggested that breaks are more
common in micro-sequences constructed out of a given
relationship and for which no empirical work is previously
anticipated by teachers. This study also shows that when
breaks are introduced in the construction of specific
topics, the result is a "logically loose sequence" (Grimes,
1976) in which teachers need to clarify each one of the
statements begin made. However, in the absence of breaks,

the result is a "logically tight sequence" (Grimes, 1976) in

275

which teachers rely on empirical information already
available for its construction.

In addition to variations in the order in which logical
relationships are enacted by teachers at a micro-level and a
macro-level, there are also variations on the nature of the
enacted environment through which these logical relation-
ships are manifested and delivered. The enacted environment
is determined by the physical materials through which
subject matter is manifested (Erickson, 1982) . The steps
and strategies imbedded in these materials are important
ingredients in the structuring of subject matter and play a
fundamental role in how information is delivered. In the
teacher's discourse on Newton's Second Law (F = ma),
teachers simultaneously relied on worksheets (Mr. Simon), a
package of lab equipment (Mr. Ellis) and students' graphs
(Mr. Howard). Each one of these tools contained different
sets of information which in conjunction with the teacher's
verbalizations and actions determined the intended meaning
delivered by the three teachers in the topic of Newton's
Second Law.

The previous discussion on findings is quite consistent
with Hirst's view of school content, logical organization
and sequencing. According to Hirst (1974), similar themes
and topics may have different logical organization as they

are enacted. He pointed out that "there is . . . no one

276

logical sequence in which the truth of a subject must be
communicated, even in these subjects which seem most

strictly sequential" (Hirst, 1974:125).

m at'ons o u a ion e a ch and P ac 'ce:
Epeseryicg, Insepyice Teacnez Education
and Student Lgnpning

It has been suggested that learning how to construct
and enact a classroom curriculum is a fundamental problem in
research on teaching (Doyle, 1986). The present study has
been an attempt to learn about the way teachers actually
construct subject matter in high school physics. Learning
about curriculum enactment of school academic content has
important. implications for 'teacher' education .and. student
learning because one of the main purposes of schooling is
the appropriate delivery of knowledge so that students can
make sense of it. In the process of making students
comprehend such knowledge, teachers not only interact with
students, but also with curriculum materials enacting what
is usually referred to as the manifest curriculum.
Students, for whom this curriculum is directed, acquire
skills and learn about logical relations between different
concepts, topics and related pieces of school knowledge. In
this sense, describing how experienced teachers, on a daily
basis, assist students to acquire those skills and the logic

of subject matter has strong implications for those concern-

277

ed with education in general and with subject matter in
particular.

Two major important conceptual contributions for
curriculum development and research have emerged as a
byproduct of the present study. The first contribution,
borrowed from discourse analysis, is the notion of 13293-
In this study, it. has been shown how' two conceptually
organized physics curricula (PSSC, Harvard Project Physics)
were transformed by experienced qualified teachers and
eventually presented to students in a series of sequential
topics. The second major contribution, also borrowed from
discourse analysis, is the idea of coherence (local and
global) and the notion of how individual topics are
logically constructed and connected among themselves as
teachers interact daily with students and curriculum
materials. Both constructs will hopefully contribute to the
language of those concerned with the study of subject matter

knowledge and pedagogical training and practice.

Preservice Teacher Education

How experienced teachers actually organize and select
different. bits of academic content. has implications for
preservice teacher education. Prospective teachers, for
example, can be informed of the content variations that
exist as similar pieces of subject matter which are enacted

by experienced teachers. Written vignettes and videotapes

278

such as the ones described in this study (see Chapter 3) can
be used as sources of information for this purpose. Story-
lines of "naturally occurring events" (Erickson, 1982,
1986b) describing the nature of the coherence among related
tapics delivered over a period of several days can be used
for discussion dealing with the way academic content is con-
structed through the teacher and student interactions with
the immediate environment. Similarly, videotaped segments
showing how a topic is dealt with by experienced teachers
can be used as a learning tool to assist prospective
teachers in their understanding that different sets of
logical relationships may emerge in the enactment of the
topic. This also implies that prospective teachers can
implement their own set of relationships from their analyses
of videotaped segments.

Another important related implication of this study for
prospective teachers, particularly for physics teachers, has
to do with the understanding that although teachers may use
similar textbooks (such as Mr. Ellis and Mr. Simon) and that
the overall coherence of the discourse on a common theme may
on the surface look the same, the content organization of
specific topics may be enacted in strikingly different ways.
This is the case of the well-studied topic of Newton's

Second Law discussed in Part II of Chapter Five.

279

Teacher educators engaged in preservice education, need
to recognize that. experienced teachers do not follow' a
particular curriculum in a linear fashion. Instead, they
develop their own instructional strategies in order to anti-
cipate what topics to include, what statements to make in
each topic, and how to organize them when dealing with a
specific instructional unit. This point was recognized by
Porter et al. (1986) in their study of mathematics content
taught by elementary schools. In addition, teacher edu-
cators need to recognize that experienced teachers rely on a
variety of physical materials, whose organization and use in
the act of teaching play a fundamental role in the nature of
the subject matter communicated to students. The purposes
and uses of those materials vary among teachers in terms of
the "steps and strategies" (Erickson, 1982) implemented as
subject matter is enacted.

Day to day accounts of how experienced teachers strive
to communicate information to students can also be a
resource for staff development (Erickson, 1986b). Indeed,
prospective teachers can be properly guided to learn and
deliberate about how experienced teachers enact subject
matter in real-life through their daily classroom routines.
Prospective teachers, then, have the opportunity to reflect
on whether or not what is being said makes sense to them.

In this reflective process, prospective teachers can be

280

encouraged to suggest changes in the subject matter sequence
being enacted in order to make it more understandable and

accessible to students.

Insepyice Teacher Education

The findings of this study as well as the data
presented have implications for inservice teachers. On one
hand, there is a need for teachers to reflect and write upon
their own practices (Clark & Florio, 1982; Erickson, 1986b)
in order to improve their own teaching and "to participate
in the generation of a knowledge base on teaching" (Porter,
1986:23). The story-lines described in this study as well
as the videotaped transcripts and the videotapes themselves
can be made available to participant teachers in order to
learn about their own perception of how a particular set of
topics was coherently organized and what changes may be
needed in future teaching. Teachers, for example, can be
asked for their own interpretation of the way topics are
segmented through time and how topics are logically
connected. Informal conversations with the three
participant teachers gave evidence that the teachers' views:
on how they organize content is rather different from how
that content is actually enacted in real life. This point
is consistent with Doyle's suggestion that many teachers,
including those considered to be effective, do not have a

"rich semantic grasp" of their content (Doyle, 1986).

281

However, this is a matter of empirical verification through
further research.

A second implication of this study is concerned with
the implementation of knowledge-based inservice programs
that are "consultative" (Clark, 1987) rather than prescrip-
tive. In this sense, teacher educators can exemplify
through the use of case studies, such as the ones described
in this study, how experienced teachers actually organize
school academic content, instead of indicating how it should
be organized. As Clark (1987) stated, "The best consultants
are those who leave us with something interesting and
provocative to think about as we continue to wrestle with
the complexities of our own local problematic situation"
(Clark, 1987:3). Indeed, teachers deal daily' with the
specific situations that need to be reflected upon. One
particular situation is the organization of different pieces
of knowledge in a coherent manner to make them understand-
able to students. Informing inservice teachers concerning
the way experienced teachers strive daily to organize
content knowledge will contribute to more effective

teaching.

Spudent Lenrning

The present study also has implications for student
learning. In this study, it was observed that contents in

three distinct high school physics classrooms are organized

282

differently. The study also indicates that similar high
school populations are being delivered differently organized
school knowledge. At a macro-level, it has been observed
that a topic enacted in one classroom may not necessarily be
taught in a second classroom, even in the case in which both
classrooms use the same textbook. This is, for example, the
case of free fall and terminal velocity that was taught by
Mr. Ellis but not by Mr. Simon. When comparison across
classes are made, it can be observed that for example.
Newton's Third Law, is not taught in the same logical
progression by all teachers.

At a micro-level, it can be observed that teachers
enacted different sets of logical relationships when
elaborating on a topic such as Newton's Second Law. These
'mariations in content organization suggest that each
individual group of students is learning different sets of
topics and logical relationships among the topics under the
theme dynamics. However, the fact that teachers construct
different logical relationships between topics and concepts
does not necessarily lead to the conclusion that students
comprehend those relationships as they are enacted by the
teachers. Students possess their own "scripts" (Schank &
Adelson, 1977) and "mental models" (Johnson-Laird, 1980) to
interpret and understand the subject matter imbedded in the

teacher discourse. In this sense, understanding the nature

283

of the subject matter, as constructed by individual students
out of a teacher's discourse is and important issue for
further research. This difference in learning may have
strong implications for research and policy on student
testing. As Porter et al. (1979) stated, "Understanding
what teachers teach and how they decide what to teach will
help educators understand more fully why students differ in

what they learn" (p. 3).

Im i a ' s or s

The findings from this study point toward new avenues
for research in curriculum development and science teaching
and learning. In the context of a more general ethnographic
work, a constructivist approach has been proposed to inter-
pret and describe how teachers in their daily interaction
with students enact subject. matter; In this sense, a
detailed analysis of three teachers' discourses and actions
was conducted in an effort to represent and describe the
nature of the logical connections among the topics and
concepts enacted in a unit on dynamics taught by the three
teachers. One of the first general questions that emerges
from this study is the perception that the participant
teachers might have about the description and representation
of the subject matter as carried out by the research

analyst. In this way, we may' have the 'teacher's own

284

viewpoint of the "semantic grasp" (Doyle, 1986) implicit in
the content they teach.

A second. major theme is related. to the notion of
coherence among the different instructional units that
constitute a ‘whole year's curriculum.;program. In high
school physics, teachers anaphorically enact subject matter
by making reference to topics already taught in previous
units. How these topics are constructed and eventually link
to other topics needs to be empirically studied since any
possible gap in previous instructional units may have
profound consequences on how students interpret and
understand later units. Apart from describing in detail how
topics in an early unit are anaphorically linked to later
topics in subsequent units, the study of the discourse as
teachers move from one unit to the next may give important
insights in terms of the nature of the coherence between
contiguous units. This shift is usually very short in time,
so the use of special devices (audiotapes and videotapes)
may be required to capture it.

A third point that needs to be made is related to the
nature of the knowledge constructed by students as a
byproduct of their interaction with teachers and curriculum
materials. It is the teachers' responsibility to evaluate
and check for students' understanding and comprehension of

subject matter knowledge. The teachers' discourse can give

285

specific details of instructional events in which teachers
intervene to eNaluate and probe students' understanding of
the information content they are expected to learn. In
this sense, if a teacher is engaged in teaching for con-
ceptual change (Minstrell, 1984), looking at the relation-
ship between what teachers construct and what students learn
can provide us with empirical evidence as to why students
change (or do not change) their pre-instructional ideas they
bring into the classroom. What has been suggested, then, is
to investigate the process by which students come to con-
struct subject matter and the role played by teachers in
that process. It is possible that a student resists
accepting a new scientific concept, not because the student
lacks the cognitive skills required to comprehend and
interpret it, but because of possible missing links (Brown &
Yule, 1983) in the teacher's discourse, which, if included,
would make explicit connection between related topics.

A final issue that needs further research is also
related to student learning and subject matter construction.
As has been clarified in a series of story-lines and
vignettes throughout the body of this dissertation,
experienced, qualified teachers create environments in
fundamentally different ways when they deliver subject
matter to students. In this sense, the elements of the

environment and their sequential organization are important

286

ingredients in the process of how subject matter is
constructed. In the case of high school physics, one of the
most common elements of this environment is the physical
equipment used for empirical demonstrations and laboratory
work. This study has shown that even similar physical
equipment may have different purposes in the organization of
similar bodies of subject matter knowledge. Knowing this,
an issue that needs to be investigated is the extent to
which a specific environment is more helpful than others in

assisting students in their construction of subject matter.

APPENDIX A

HR. SIMON'S "UNIT PLAN" ON DYNAMICS

HR. SIHDN'S

287

APPENDIX A

“UNIT PLAN” ON DYNAMICS

 

 

Chapter 3 Outline Name

Hour Date
Schedule
Mon Sept. 22 Tue 23 Wed 24 Thur 25 Fri 26
Intro to Demo Work Exp. Newton's
ch 3 lecture session "force Laws
Study Q's "inertia" "vectors" vectors" Prob. Set
Part A Prob. Set
Mon 29 Tue 30 Wed Oct. 1
Exp. a = F/m Egg Day Quiz Ch3

Objectives
If Given:
Descriptions

2 vectors

F = ma

List the descrip-
tive phrases

Eapeps Qne

 

Be able to:

1.
2.
3.
4.
5.

6.

7.

8.

9.

10.

Identify those situations in
equilibrium or not.

Name upper and lower unit of their
sums.

Watch defining and description.

Find vector sum (resultant).

Given and resultant, name the
equilibrant.

Pick true statements about vectors.
Name 3 vectors and 3 of Newton's
Laws.

Identify which applies from:

a) strobe photographs or graphs

b) word descriptions

Solve problems including the
equation.

Identify which are true for nnss and
which are true for weign .

288

Physical situation,
object in

Assignmenps:

1.
2.

equilibrium 11. Identify and describe all forces
acting on the body including
friction.
Study questions, Ch 3, Part A Read all parts of
"Inertia" demo notes Chapter 3.

3.
4.
5.
6.
7.
8.
9.

Vectors work sheets

Study questions Ch 3, Part B
Force board experiment
Newton's Laws notes

Newton's Laws problem set
Exp. a = F/m

(Document, September 22, 1986)

APPENDIX B

HR. SIMON'S WORKSHEET ON NEWTON'S LAWS

289

APPENDIX B

HR. SIHDN'S WORKSHEET ON NEWTON'S LAWS

 

 

ewton' w Ho '0
One of mankind's great achievements. Name
Hour Date
I. Newton's First Law of Motion -- otherwise known as the
law of .
"Bodies at rest remain at rest,
and bodies in motion remain
in motion in a straight line
by constant speed."
II. Newton's Second Law
Conditions Results Examples

"An unbalanced (net)
force causes an
acceleration in the
same direction as,
and proportional to,
the net force
acceleration is
inversely propor-
tional to mass."

Written:

 

290

Test yourself . . . are these examples of first law or
second law?

 

 

 

 

 

 

a) V = O b) v c) v = lO/m sec
a = 0 a f 0
t
d) o e) o
o o
o strobe o
o o
o
f) v g) V h) V
t t t

 

measured in (units)

Where: a =

III. Two confusing terms: (read about this in Chapter 3)

Weigh; is: gass is:

291

III. Newton's Third Law or:

"to every action there is
always opposed an equal
reaction: or, the mutual
actions of two bodies upon

each other are always equal

and directed to contrary parts."

Samples:

(Document, September 26, 1986)

APPENDIX C

MR. ELLIS' UNIT PLANNING ON DYNAMICS

292

APPENDIX C

MR. ELLIS' UNIT PLANNING ON DYNAMICS

Physics Assignment Sheet: Chapter 3

1.

Newton's 1st law (law of doing nothing different!)
Text: 3.5-3.6
HO-31: Selected questions and problems will be
discussed and demonstrated in class.
Bulletin Board: Look! There are some great cartoons
illustrating inertia.

Newton's 2nd law (Fnet = ma) Note: The unit of

Text: 3.7 force, the newton (N).
HO-32: 21,22 dimensionally has units
of kg m/s2

F = ma ---- N = kg m/sz
Hallway Experiment: Get your mass moving.

Newton's 2nd law
HO-32: 10,11,14,27

Mass vs. Weight (causes bald physics teachers)

Text: 3.8

HO-33: 9,10,11,12,13 Selected problems will also be
discussed in class.

Terminal velocity, Atwood's machine and other
niceties (putting assignments 1,2
and 5 together)

HO-33: Examples in class

HO-34a: Examples in class

HO-34b: Great exercise for Mickey Mouse

Newton's 3rd Law (F12 = -F21)

Text: 3.9-3.10

HO-35: Selected problems will be discussed and
demonstrated in class.

Test

(Document, October 24, 1986)

APPENDIX D

MR. ELLIS' EXPERIMENT SHEET

ON NEWTON'S SECOND LAW

293

APPENDIX D

MR. ELLIS' EXPERIMENT SHEET
ON NEWTON'S SECOND LAW

trial 1 trial 2 trial 3

"Ffrictional (Ff)
Fpulling (Pp) =
Fnet (Fn) =‘Fp’Ff =
Distance traveled (d) =
Journey time (t) =

Kinematic determination of the
acceleration (starting from rest)

d = 1/2 at2 a = 2d/t2

Dynamic determination of the load (mass)

Fn = ma m = Fn /a

Embarrassing (perhaps) determination of the mass

% difference"

(Document, October 30, 1986)

APPENDIX E

GRAPH OF VELOCITY VERSUS TIME:

"GALILEO COASTING'

294

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#5! 7524!.

APPENDIX F

GRAPH OF VEIDCITY VERSUS TIME:

ONE AND TWO BRICKS PULLED BY

A RUBBER BAND

295

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fat)?“

APPENDIX G

GRAPH OF ACCELERATION VERSUS

FORCE (uAss CONSTANT)

 

- ~~ ..¢

APPENDIX H

GRAPH OF ACCELERATION VERSUS

INERTIAL MASS (FORCE CONSTANT)

297

 

 

 

 

 

 

APPENDIX I

GRAPH OF PERIOD VERSUS INERTIAL MASS

298

 

 

 

 

 

 

 

 

 

 

 

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0019M)» fl} ; (C lamp:

APPENDIX J

THE FLASH PHOTOGRAPHS:

FORCE AND ACCELERATION

299

 

(to the right) in each time interval. By measuring the successive displace-
ments, we can calculate how the avenge velocity changed. As the caption
under Table I shows, in each ‘95. second after the motion started. the aver-
age velocity increased by about 5.8 cal/sec. a constant amount within the
limits 0! accuracy of our experiment. Dividing the change in velocity of
5.8 cut/sec by the time interval 0! “iii see, we see that the average velocity

at the constant rate of 14 cm/sec’. Since the average velocity
changed at a constant rate throughout the motion, we can safely assume
In: the instantaneous velocity also changed at the same constant rate.

 

 

 

"flunk ”In mule l4m/sx’
~ avenge vaccm' \
\ n4 mama. \ ounce m
mat. mm AX/Al - menace m
m. 3(a) «cu/rum) Mar/m)
l 4.1 4.1
2 10.4 6.3 2.2
3 19.2 8.3 2.5
a 31.4 11.2 2.‘
5 44.0 13.6 2.4
6 60.1 16.1 2.5
1 78.6 18.5 2.4

 

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glaciers-reel. henna-n

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In: [lulu

.4
2.! flash: /aee tell: .
eat/flesh)" “Jinks/are) - SAM/mhmmduwmends

 

The particular value 14 em/see' occurs in this experiment because we
pulled with a particular force on a particular object. When we pull with
other forces or pull on other objects. we usually obtain other values of the
acceleration. But all experiments like the one just described show that
under influeme o! a constant force the acceleration is constant.

229

Figure 1t-I

The flash photograph shows the puck
being pulled to the right. The light
flashes were separated by 10/24
see. A constant lorce was applied
by keeping the loop extension con-
stant. The displacement at the puck
in each interval marked on the
photograph has been measured and
appears in Table 1.

Table 1
Data from Experiment Shown
MP to

300

231

Figure 11-10
To apply twice the original lorce. we
attach m idential loops to the puck

 

 

 

 

Table 2
. avms mean
or v“ m 331% Experiment Shown in
mat. IA: ovum
tn. 2(a) (or/nan) Mar/rust)

1 1.4 8.4

2 21.5 11.1 4.1
1 39.1 11.! 4 1
4 61.9 22.6 4.8
5 19.1 21.4 4.1

flu an the yen-In of a "prom" h nldeh 1k applld force we:
uh Ila! and in the/in! "when! (Table I). The/lull me In: again
l‘Mlfiflm '11-"- . L 1 . .,“—n... . .I ..
(kl-Imam nleelly bimniaugmlulr ask/ere.

APPENDIX K

MR. SIMON'S WORKSHEET ON NEWTON'S

SECOND LAW EXPERIMENT

301

APPENDIX K
MR. SIMON'S WORKSHEET ON NEWTON'S
SECOND LAW EXPERIMENT
Class Analysis::::

1. Identify your tape

mass mass

constant with A of 1, 2, 3, 4
force force
(circle) (circle) (circle)

Tape analysis:

d1 =

d2 =

v1 =

v2 =
No. of internals

t = ( ) .0083 sec = sec.
V2 "V2

a = ____—_ = cm/sec2

total

302

 

 

 

 

 

 

 

 

 

 

2. Class analysis
Constant Force Constant Mass
Mass Acceleration Force Acceleration
1 1
2 2
3 3
4 4

 

 

 

 

 

 

 

(a) With a constant force, how does mass change the
acceleration?

(b) With a constant mass, how does force change the
acceleration?

(c) Try combining the two ideas above into a word model,
then a mathematical model.

(Document, September 29, 1986)

APPENDIX L

HANDOUT 32: NET FORCE AND ACCELERATION

2303

 

q

60-32 fict Force and Acceleration "Isaac's 2nd"
1. a)‘what is the relationship between Force Acceleration
the net force actinc on an object F u m/s4
and the acceleration of the ob- 2F 8
ject? How could you experimen- F 12

04..

tally test it? -r

b) Complete the table in the mar- {F
gin which lists some accelera- 5F
tions resulting from applying 10

varying forces on a given object.‘ . ' 3

A force F gives a Chevette an acceleration of 5 m/sz.'What

’ force is needed to ziye the car an acceleration 8f:

a) 1 m/sZ_ b) 2 m/s c) 7 m/s2 d) 10 m/s

A slot car has an acceleration of .5 m/s2 when a net force of
6 newtons acts on it. What's the acceleration when the net
force is increased to 18 newtons? - .

a)°If a ball is rolling at 20 cm/s and no net force-acts on it,
what will its speed be after 5 s? - °

b) Suppose that a car increases its velocity so that it travels
first at 30 mph, 35 mph at the end of the next second, 40
mph at the end of the next second after that, and so on.

' what can you say about the net force acting on the car?.

c) If the force of friction acting against a sliding object is
10 newtons, how much force must be applied to maintain a
constant velocity? What is the resulting net force in this
case? The acceleration?

d) If we find an object which we know to be acted on by a force,
but which is not moving, what inference can we draw?

a) what term is used to express the mass acceleration

 

amount of inertia any object has? n 30 57s2
b) How does the mass of an object 2m ~15 .
influence the acceleration of an m
object? Express your answer both .m
mathematically and in words. .2m
c) Complete the table in the margin h5m
which lists some accelerations ,-3
resulting from applying equal ' 75
forces to objects of different
mass.

3) A pick-up truck can accelerate at 3 m/sz. What is its accel-
eration if it is towing another truck like itself?

b) A coffee can is balanced by three identical soda bottles on
a balance. A certain force accelerates the coffee can at
2 m/sz. How much will the same force accelerate one of the
bottles? Two of the bottles?

7.

10.

ll.

12.

13.0

14.

15.

Alt give

3(14

1A force gives a 15 kg object an acceleration of 12 m/sz. What

would the acceleration be if the mass were:
a) 5 kg b) 10 kg c) 30 kg d) #0 kg

a) What is Newton's 2nd law of motion? Express your answer
both mathematically and in words.

b) What are the units of mass in the metric (EJS) system?
The units of force? ‘

c) What are the units of mass in the English (FPS) system?
The units of force?

a) A little league pitcher exerts a net force of 90 newtons
(90 N) on a .3 kg baseball. What is the ball's acceleration?
b) An EL athlete exerts a 150 N force on a shot while putting
it with an acceleration of 20 m/sz. What is the shot's mass?

How much force is needed to give a'2 kg object the same accel-
eration that a 25 N force gives to a 6»kg object?

A force of 5 N gives a mass m an acceleration of 8 m/sz, and
a mass m an acceleration ofԤQ m/sz. What acceleration would
Ehe two when they are fastened together? ”

A pull P applied to a laboratory cart gives it a measured
acceleration. A load of i kg is then placed on the cart and
now the same pull P is-found to give only 3/4 of the previous
acceleration. What can you say about the inertia of the cart
compared with the inertia of the Q kg load? . - . - ‘ . '

a) Explain the concept of net force, and how the force of
friction enters into the determination of the net force.

b) A sled having a mass of 10 kg is being pulled by an 18 N

- force. If the force of friction is 2 N, what is the sled's'
acceleration?‘ ‘ ' "%

c) A 6 N force is applied to a 2 kg cart in the lab. The accel-
eration is measured at 2 m/sz. Find the frictional force.

d) A 2 kg book is pulled across the table with a 20 N force.
It actually accelerates at 6 m/sz. Find the frictional force.

A man pushes a box along a rough horizontal floor, exerting a

gush of 40 N. Friction exerts an opposite drag of 10 N on the
ox.

a) What is the actual accelerating force?

b) how hard should the man push, if friction stays the same,

  

to double the acceleration of the box? ,\
A 75 kg track star, at the start of a sprint, )1z'7zéf’.
pushed on the ground with a measured force of ' A
2000 H at an angle of 60‘, as shown at the \/;

right. What forward acceleration was pro- ,' ..-,‘ .
duced? . ,"1‘ r. '1' r
,S_ ‘H~jh?~ \

 

22.

25.

26.

27.

3(35

A 1500 kg car is traveling at 2? ale and collides with another car
during a demolition derby at the state fair. The car moves 3 meters
forward while it is being brought to rest. What force (assumed
constant) is exerted on the car during the collision?

A 6 kg object is moving at a constant speed of 15 n/s. What force
is needed to bring the object to rest in 9 5?

An astronaut 100 n from his speceship observes a 200 kg maternid
drift past him toward the ship at 11 n/s. If the astronaut can'
gain a hold on the meteroid and the astronaut's rocket gun is
capable of delivering a force of 100 N, can he stop it before it
hits the sp ccship? (Neglect the mass of the astronaut.)

The driver of a 600 kg sports car, heading directly for a railroad

crossing IOO meters away, applies the brakes in a panic step. The

car is moving at 40 m/s and the brakes can supply a force of 4500 N.

a) how fast will the car be moving when it reaches the crossing?

b) Will the driver escape collision with a freight train which, at
the instant the brakes are applied, is still blocking the road
and still requires 6 s to clear the crossing? '

A boy runs beside a wagon, pushing it into the wind until the wagon
is going 6 n/s; then he jumps on. The combined mass of the boy and
wagon is 50 kg. The wind exerts a force of 25 N on the boy and

'wagon in the opposite direction that the wagon is coasting.

a) At what rate will the wagon's speed decrease? (Find acceleration)

b) For how many seconds will the wagon coast forward before caning
to a stop?

c) If the boy stays on the wagon after it stops, how fast will the
wind accelerate the wagon backward?

A 60 kg boy junps from a window ledge 1.25 meters above a hard floor.
Estimate the force exerted on him by the floor while he is stopping,
by answering the questions below. Suppose that he foolishly forgets
to bend his knees while landing so that the total "give" of his feet,
etc., is only .025 meters (1 inch), in compression of floor, shoes,
feet, ankles, spine, etc., during the stopping process.

a) Show that the time of fall is .5 s.

b) Find the speed of the boy at the end of his fall, just before
landing.

c) To calculate the time taken by the landing process we must find
the boy's average speed during the landing process. Write down
his speed just before he lands and his speed when he has finished
landing; take the average. Use that average speed to find how
long he takes for the process of landing, that is, how long he
takes to travel .025 meters.

d) You know his speed before landing and his speed after landing, so
you know his change of speed; and you also know how long he took
to make that change of speed. Calculate his acceleration during
landing. .

e) Using f - na, calculate the force the floor exerted on him during
landing. Express this force in tons, using 1 ton - 10.000 newtons.

3(36

HO-JZ (Con't.) "May the Force be with you."

16.

17.

21.

All three phenomena - rest, uniform motion, and acceleration -
could be more or less reasonable explained by an Aristotelian.
Compare the Aristotelian and Newtonian explanation of the
following phenomena:

2) an apple sitting on the desk

b) an apple dropping from a tree branch

c) an apple thrown through the air

d) a cart load of apples being transported to market

 

 

The graph to the right shows the :
speed at various times of Fonzie I I
cruising the "strip". 03. . D

 

L0

"Fonz"?

 

b) when is the greatest net
force in action?

a) Which section(s) indicate no
c) Which section(s) indicate - \.

:3

(L
65
N

 

t EEO (Hr/"1)

\

a force acting in the

 

net force acting on the

 

 

 

 

 

 

 

opposite direction of A E
motion?
'd) Which section(s) indicate ’0 (9 IL I8 1'1- 30

that the direction of . ng (5)
motion was reversed? '
e) If Ponzie and his "chopper" have a
mass of 250 kg, find the acceleration
and net force during interval CD.

A 220 kg rocket-driven sled develops a thrust of 6600 N.
a) Hhat is the sled' s acceleration? '
b) If the rocket fires for 20 s., how fast will the sled be going?

A 1500 kg car is advertised in a popular magazine to accelerate from
a standing start to 60 mi/hr (27 m/s) in 10s. Find

a) the car' 3 acceleration

b) the net force exerted on the car

. c) the distance traveled in those 10 s.

A hockey puck(.25 kg)slides on the ice for 100 meters before it stops.
If its initial speed was 20 m/s, what was the retarding force of
friction between puck and ice?

A £0'kg toboggan is coasting along with a speed of 10 m/s over
smooth snow and ice. It enters a rough stretch of ice 6 meters long
in which the retarding force of friction is 120 H. With what speed
does the toboggan emerge from the rough?

APPENDIX’H

TRANSCRIPTION CONVENTIONS

 

307

APPENDIX H

TRANSCRIPTION CONVENTIONS
(Adopted from Lemke, 1982a)

Citation: Videotape, Oct. 12, 86 means the videotape was
taken on October 12, 1986.

Speakers: The teacher is the speaker’ unless otherwise
indicated. On many occasions the teacher's names are
identified by Mr. Ellis, Mr. Simon and Mr. Howard (not
their real names). Sometimes the letter T is used,

instead.

Students names appear under pseudonyms. If the
name cannot be identified, then we see ST (for student)
and ST (for another student).

Dialogue: The Dialogues are shown as if speakers (students
and teachers) alternate. In this sense, no overlapping
is shown in spite of the fact that overlapping is
common in classroom dialogues.

Symbols: (( . . . )) enclose analyst's note of nonverbal
information.

) with blank interior is speech not
resolved or unintelligible.

. . . is used for minimal pause or hesitation.
(5) gives time in seconds or longer pauses.

. followed by a capitalized word other than proper
name is used to end a sentence and begin a new one.

? questioning intonation.
! exclamatory intonation.

n " speaker's exact wording.

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1970-74

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1979-83

1984-86

VITA

B.S. Physics and Education, Instituto
Universitario Pedagogigo de Caracas, Venezuela.

Physics Instructor, Instituto Pedagogico de
Caracas.

Diploma in Science Education, Chelsea College,
University of London (U.K.).

M.Sc. (Physics and Education), Reading Univer-
sity, Reading (U.K.).

Assistant Professor, Universidad de los Andes,
Venezuela.

Research Assistant, Institute for Research on

Teaching, School of Education, Michigan State
University.

319

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