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This is to certify that the

dissertation entitled

A Process Tracing Study of the
Strategies Sixth Grade Children Use
in Finding Relations Between Variables

presented by

Judy Hale Dennison

has been accepted towards fulfillment
Doctor ‘5‘?“ reqmremems f0Admi ni strati on and

Philosophy degree in Curriculum

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Major professor

 

[hue November 8, 1982

MS U is an Affirmative Action/Equal Opportunity Institution 0- 12771

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A PROCESS TRACING STUDY OF THE STRATEGIES
SIXTH GRADE CHILDREN USE IN FINDING RELATIONS
BETWEEN VARIABLES

By

Judy Hale Dennison

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Administration and Curriculum

1982

ABSTRACT
A PROCESS TRACING STUDY OF THE STRATEGIES

SIXTH GRADE CHILDREN USE IN FINDING
RELATIONS BETWEEN VARIABLES

By

Judy Hale Dennison

A substantial portion of all scientific knowledge takes the
form of relations among variables. Despite the importance of problems
involving these relations, little is known about the strategies
students use in performing tasks requiring that they find relations
between variables. The purpose of this study was to determine what
some of these strategies might be for sixth grade children.

The study involved the selection of six children based on three
criteria. Each child participated individually in a practice session
and three problem sessions. These sessions involved the child's
performance of a task, immediately followed by stimulated recall, using
videotapes of the child's task performance. After each of the three
problem sessions, the videotape of the task performance was transcribed
and inferences were made about the child's performance from the task
performance alone. The audiotape from the stimulated recall for that
problem was then transcribed and used to validate or disconfirm prior.
inferences, as well as to make additional inferences about the child's
performance. The performance models were then constructed to reflect

the inferences made for the activity and stimulated recall protocols.

Judy Hale Dennison

All of the problem performances were then analyzed to see, first, if

strategies did indeed exist. A strategy was said to exist if a pattern

of processing steps was seen to occur more than once in a subject's

performances. If strategies were identified, they were modeled. An

attempt was made to see how consistent the students were in applying

the strategies found.

The following interpretations of the data were made:

1.

The subjects in this study were accurate in finding rules
involving relations between variables.

The sixth grade children in this study used strategies
when they were asked to find relations between variables,
but they differed in the number of strategies they have in
their repertoire for this purpose.

The nature of the six strategies identified was such that
they were modeled as components of'a performance, rather
then models of the whole performance.

It appears that the rules formulated by the subjects were
meaningful, as indicated by the fact that the subjects
used the rules to make predictions about what would happen
when two elements were tested.

It is clear that the subjects were hypothesis-guided in

much of their attempt to find rules.

DEDICATION

To my husband, Dan, for his enduring patience and support and
to my son, John Michael, for helping me keep my sense of humor.

ii

ACKNOWLEDGEMENTS

The author wishes to express special gratitude to Dr. Edward L.
Smith. His advice, personal direction and expert counsel provided
invaluable guidance throughout this investigation and during the
writing of this dissertation.

The author also expresses grateful appreciation to the members
of her graduate committee, Drs. Glenn D. Berkheimer, William M.
Fitzgerald, and Richard J. McLeod. A special note of appreciation is
extended to Dr. Lee S. Shulman, now at Stanford University, for the
great influence he had on this study. Finally, the author acknowledges
those persons who were on the faculty of the Science and Mathematics
Teaching Center at Michigan State University for their continual

interest and encouragement.

TABLE OF CONTENTS

Page
LIST OF TABLES ........................ vii
LIST OF FIGURES ........................ viii
CHAPTER .
I. THE PROBLEM ..................... 1
General Need for the Study ............. 1
The Knowledge to be Taught ........... 1
The Importance of Strategy Identification. . . . 4
The Problem Relative to the Chosen Curriculum
Model ...................... 6
An Overview of the Procedure ............. 7
The Research Questions ................ 7
II. REVIEW OF RELATED LITERATURE ............. 9
The Representation of Knowledge ........... 9
The Representation of Procedural Knowledge ...... 10
Distinctive Features. . . . .......... 11
Active Structural Networks ....... . . . . 11
Productidn Systems. . . ............ 12
Flow Charts . . . . . . ....... . . . . . 13
The Specific Theoretical Framework for This Study . . 18
The Concept-Task-Strategy Model ........ 18
Content Analysis ............. 19
Task Analysis . . . . . . . . . . . . . . 20
Strategy Analysis ............ 21
What We Know About Strategies ....... , ..... 23
III. THE RESEARCH METHOD AND PROCEDURES. ......... 26

iv

CHAPTER PAGE

Overview of the Study ................ 26
Research Subjects . . ................ 27
The Papulation and Sainple ........... 27
Method of Subject Selection .......... 27

The Screening Instrument ......... _ . . . 28

The Procedure . . . . . . . . . ........... 32
Overview of the Data Collection Procedure . . . 32

The Practice Session. . . . . ...... 32

Three Problem Sessions .......... 33

The Practice Problem. . . . .......... 34

The Three Parallel Problems .......... 35
Description of the Task . . . . . . . . . 35

Description of the Problems ....... 35

Problem 1 .............. 35

Problem 2 .............. 36

Problem 3. . . ............ 40

The Parallel Nature of the Problems ...... 44
Problem and Protocol Development. ....... 48
Stimulated Recall ............... 49
Protocol Analysis . . ............. 49

IV. RESULTS 0 I O OOOOOOOOOOOOOOOOOOOO 57
Overview of the Results . . . . . .......... 57
Rule Formation Data . . . . .......... '. . . . 58
Identification of Strategies. . . .......... 58
Strategies for Testing Rules .......... 65
Strategy I ................ 65

Strategy 11 . .............. 67

Strategy III. . . . . .......... 71

Strategies for Forming Rules .......... 79

CHAPTER ’ Page

Strategy IV ................ 79

Strategy V ................ 79

Strategy VI. . .............. 79

Consistency of Strategy Use ............. 84

smary O O O I O O O O O 00000000000000 89

V. INTERPRETATION OF RESULTS .............. 90

Summary ...... . ................ 95

VI. IMPLICATIONS OF THE STUDY FOR EDUCATION AND RESEARCH 96

Educational Implications. ............. 96

Research Implications ................ 98

Limitations of the Study ............ 98

Conclusions About the Research Methodology. . . 101

Questions for Further Study . . . . . ..... 102

REFERENCES . . . ................. . ..... 104
APPENDICES

A. The Method of Subject Selection and Criterion
Data on Potential Subjects. . ............ 107
8. Description of Particle Sets ............ 109

C. Task Protocol for Determining Correlational
Rules--Particle Test and Observation Record
for Particle Test . . . . . . . . . . . . ...... 111

D. Protocols for the Administration of the Problems
and Stimulated Recall and Observation Records for
the Three Parallel Problems ...... . ...... 115

E. Typical Questions Asked of the Students in
the Stimulated Recall . . . . . . . ......... 123

F. Guidelines for Making Inferences and
Analyzing Protocols . . . . . . . . ......... 124

G. Definitions of the Processes Used in
Modeling the Performances and Strategies ....... 127

vi

LIST OF TABLES

Page
Concepts Network for the Particle Test . .. ...... 29
Concepts Network for Problem 1 ............ 37
Concepts Network for Problem 2 ............ 41
Concepts Network for Problem 3 ............ 45
Rule Formation Data. . . . . . . . . ......... 59
Subjects' Use of Strategies on Each Problem ...... 86
Strategies Used by Subjects on Each Problem ...... 88
Numbers of Rule-Testing and Rule-Forming
Strategies Used by Subjects .............. 92
Summary of Ad Hoc Prediction Data ........... 94
Citerion Data on Potential Subjects. ' ......... 108
Description of Particle Sets ............. 109

vii

LIST OF FIGURES

Figure . Page
1. Flow chart representing a strategy for finding
relations between variables based on preliminary
piloting data. 0 O O O O O O O O O O 0 O O O O O O O O O O 15
2. An example set of materials for the Particle Test. . . . . 31

3. Matrix representing the rods that make up the set

of elements for Problem 1. . . . . . . . . . . . . . . . . 36
4. Matrix representing the pairs of wheels that make up
the set of elements for Problem 2. . . . . . . . . . . . . 39
5. A pictorial representation of a pair of wheels . . . . . . 39
6. Representation of the pattern made when a pair
of wheels was rolled . . . . . . . . . . . . . . . . . . . 4O
7. Matrix representing the wires that make up the set
of elements for Problem 3. . . . . . . . . . . . . . . . . 4O
8. Sample Activity Analysis . . . . . . . . . . . . . . . . . 51
9. Sample Stimulated Recall Analysis. . . ........ . . 52
10. Sample Performance Model . . . . . . . . , . . . ..... 55

11. Strategy I: Testing a rule by controlling variables . . . 66

12. Abbreviated Performance Model of Pilot Subject #2--
Hires PrObleMI O O O O O I O O O I I O I O O I O ..... 68

13. Strategy II: Testing a rule by observing
correspondence between values on the independent
variable(s) and the dependent variable . . . . . . . . . . 72

14. Performance Model of Pilot Subject #1--
Rods Problem . . . . . . . . . . . . . . . . . ..... 73

15. Strategy III: Testing a rule by selecting extreme
values strategy, a special case of Strategy II . . . . . . 76

viii

 

 

Figure ‘ Page
16. Performance Model of Subject #5--Rods Problem ....... 77

17. Strategy IV: Formation of a rule by controlling
variables. . . . . .......... . ......... 80

18. Strategy V: Formation of a rule by observing
correspondence between values on the independent
variable(s) and the dependent variable . . . . ...... 81

19. Performance Model of Subject #5--Wires Problem ...... 82

20. Strategy VI: Formation of a rule by selecting
extreme values, a special case of Strategy V ....... 85

21. The COMPARISON secondary process. Input: A
variable concept, Element A, and Element 8.
Output: A comparative concept relating Element A,
and Element 8 on the input variable. . . . . . . ..... 140

22. The OBSERVE secondary process. Input: element,
observation/measurement procedure, value of
independent variable. Output: value concept for
dependent variable (activation of a node). . . . . . . . . 141

23. The OBSERVEI secondary process. Input: element,
observation/measurement procedure. Output: value
concepts for independent and dependent variables
(activation of nodes). . . . . . . . . . . . . . . . . . . 143

24. The SERIATION tertiary process. Input: A variable
concept, Element A, and Element 8. Output: An
ordinal concept relating Element A, and Element 8
on the input variable. . . . . . . . . . . . . . . . . . . 144

25. The MAXPIC tertiary process. Input: set of elements,
variable concept. Output: element displaying the
maximum value on the variable concept. . . . . . . . . . . 146

26. The INDEPENDENT VARIABLE IDENTIFICATION tertiary
process. Input: set of elements. Output: activation
of a node corresponding to the difference variable
name . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

27. The MINPIC tertiary process. Input: set of elements,
variable concept. Output: element displaying the
minimum value on the variable concept. . . . . . . . . . . 149

28. The GT ELEMENT SELECTION tertiary process. Input:
set of elements, variable concept. Output: element
displaying a greater value on the variable concept
than element(s) already used . . ...... . . ..... 150

ix

Figure

29.

30.

31.

32.

The LT ELEMENT SELECTION tertiary process.
set of elements, variable concept. Output:

Input:
element

displaying a lesser value on the variable concept

than element(s) already used . . . . . . .

The SE ELEMENT SELECTION tertiary process.
set of elements, variable concept. Output:

Input:
element

displaying a value on the variable concept the same

as or equal to element(s) already used . .

The GT ELEMENT SELECTION WITH CONTROLLED VARIABLE
tertiary process. Input: set of elements, two
variable concepts. Output: element displaying the
same value on one variable concept and a greater
value on the other variable concept than element

already used . . . . . . . . . . . . . . .

The LT ELEMENT SELECTION WITH CONTROLLED VARIABLE
tertiary process. Input: set of elements, two
variable concepts. Output: element displaying the
same value on one variable concept and a lesser
value on the other variable concept than element

already used . . . . . . . . . . . . . . .

Page

151

153

154

156

CHAPTER I

THE PROBLEM

A substantial portion of all scientific knowledge takes the
form of relations among variables. In physics, the classical laws of
motion specify relations among distance, time, velocity, force and
other variables with which moving objects are described. In chemistry,
the gas laws specify relations between the temperature and pressure of
a gas and the volume it occupies. Elementary and middle school
programs attempt to teach relations and skill in finding relations
between variables. An activity in the Science Curriculum Improvement
Study (S.C.I.S.), for example, has the children explore the effect that
weight and shape has on how well a paper airplane will fly through the
air. DeSpite the importance of problems involving relations between
variables in the sciences, we know very little about the strategies
students use in performing tasks requiring that they find relations
between variables. The purpose of this study is to determine what some

of these strategies might be for sixth grade children.

General Need for the Study

 

The Knowledge to be Taught

 

In an age characterized by an explosion of knowledge,
conceptualization of learning outcomes has become an important focus in

educational circles as a response to the question: What should be

taught? Shulman and Tamir (1973) refer to this issue as an attempt to
find ". . . what is most learnable under given conditions, (and) what
is most readily retained and transferred to new situations. . ."

(p. 1105).

Prior to the early 1960's, the major emphasis was on facts,
concepts, and principles that were the stable truths of a discipline.
In 1963, Bruner argued for the teaching of the "fundamental structure
of a subject.“ He argued that to “learn structure, in short, means to
learn how things are related" (p. 7). Bruner expected these structures
to serve as mechanisms for learning and transfer to new situations, but
he did not suggest how these structures were to be identified or
described.

Gagne's (1965, 1970) work brought a great deal of attention to
the learning of tasks. These tasks were defined in terms of observable
behaviors. Consequently, the behavioral objective (Mager, 1962) became
a popular way of describing learning outcomes. A Gagneian task
analysis, by its very structure, might lead one to assume that the
outcome of learning a task will be the same for every student.
Bessemer and Smith (1972) point out, however:

While behavioral objectives are sometimes rightfully
criticized as too narrow in scope, or as obscuring the overall
organization of content, the value and necessity of defining
tasks is now commonly-recognized.

Not so commonly recognized, however, is the fact that a
variety of educational outcomes can result from instruction on
a particular task, even when all students fully master the
task (p. 4).

In other words, students can learn different ways of performing a task

which, in turn, might become an altogether different educational

outcome than might have been intended. Bessemer and Smith further

argue that the strategies and skills one learns as one performs a task
may determine the other tasks that may be learned readily. In their
words, ". . . the particular skills which are acquired make a great
deal of difference in what kinds of new situations the student will be
able to handle“ (p. 7).

Modern psychology no longer accepts only a behavioral descrip-
tion of tasks. All theoretical positions, including Gagne's (1974),
have incorporated some information processing into their theories.
Resnick (1976) argues that what is and can be learned is a strategy for
performing a task or a series of similar tasks, and that such strat-
egies can be made explicit as intended outcomes or objectives of
instruction.

A strategy is defined, for the purposes of this study, as a set
of information processing steps that are applicable to a range of
similar situations. A strategy model is differentiated from a per-
formance model in that a strategy model is generalizable to similar
problems and a performance model describes only the steps performed on
a single problem.

Some strategies are more appropriate as learning outcomes than
are others because (1) they are more learnable by the p0pulation, and
(2) they are more generalizable; i.e., applicable to a broader range of
situations and are more efficient. A strategy that is used by some
children in a population is quite likely to be learnable by other such
children. One approach to meeting the criterion of learnability, then,
is empirical analysis--process tracing of strategies found in the
population. A rational analysis of the empirically-determined

strategies can lead to judgments as to the potential generalizability

of those strategies to other situations. Potential learning outcomes
in the form of strategies can be devel0ped and/or identified by taking
into account the models of strategies used by children in the
population.

The purpose of this study is to provide base-line data
concerning what strategies can be found among sixth grade children for
finding relations among variables. It addresses the question of
learnability through empirical analysis; i.e., process tracing the
strategies sixth grade children use in finding relations between
variables. It does not address the question of generalizability as

described above.

The Importance of Strategy Identification

The identification of strategies as potential learning outcomes
is important to curriculum developers, researchers, teachers, and
learners.

1. Curriculum developers should be able to apply the notion of
strategies explicitly in the development of instructional materials.
“If strategies can be adequately represented, then instruction can be
planned to enhance the mastery, workings, selection or retrieval of
these strategies when needed by students" (Shulman & Shroyer, 1976,

p. 15).

2. With adequate representation of strategies, research
regarding the teaching, learning, and transfer of strategies can be
designed.

3. Having determined the more appropriate strategies in terms

of learnability and generalizability, teachers can use this

information to assess whether or not a task has been performed in an
appropriate way.

4. Teachers will be better able to give guidance to the child
having difficulty with the performance of a task if they are aware of
appropriate strategies. “Students adept at solving mathematical
problems may be compared with physicians skilled in diagnosis.

Knowing how 'experts' behave has certain clear implications for how
teachers assist students to perform expertly“ (Shulman & Shroyer,
1976, p. 12). '

5. If appropriate strategies for performing a task can be
laid out explicitly for the student, he will be able to learn selected
tasks more efficiently.

Knowledge of strategies is important beyond information about
potential learning outcomes. Students may come to a situation with an
already acquired strategy. Identification of ineffective or problem-
atic strategies will enable teachers to look for these undesirable
strategies and, knowing where students are to begin with, may enable
the teachers to plan how to teach other strategies; i.e., how to move
students from undesirable Strategy A to desirable Strategy 8.

It may also be that the process the student uses in finding a
relation is not important; i.e., the relation itself is the only
outcome of importance. One would assume, in this case, that how one
finds the relation would not later create a problem in finding other
relations. Having knowlege of strategies that are used by a popu-
lation of students for solving problems similar in nature might aid a

teacher in helping a student become more efficient with “the strategy

of least resistance“ for that student, rather than trying to teach one

that is more difficult.

The Probiem Relative to the Chosen Curriculum Model

 

Smith (1974) conceives of children's scientific knowledge in
terms of three interrelated aspects: concepts, tasks, and strategies.
The major assumption underlying this work is that within a discipline,
concepts of a particular kind (e.g., variables) are associated with
particular tasks for which generalizable strategies may be developed.
A major goal of the work is to examine the role of these three aspects
(concepts, tasks, and strategies) in learning and transfer. The
present study uses Smith's Concept-Task-Strategy Model as its
theoretical framework and is directed at identifying potential
desirable learning outcomes in the form of strategies for science
tasks.

The task of interest in this study is to find relations
between variables:

Given: Set of elements

Observation/measurement procedure for the
dependent variable
Dependent variable name
Required: Correlational rule for independent variable(s)
and dependent variable that holds for the given
elements
The strategy or strategies sought are a set or sets of information
processing steps that are applicable to a range of similar situa-
tions. A strategy model is differentiated from a performance model in
that a strategy model is generalizable to similar problems and a

performance model describes only the steps performed on a single

problem.

An Overview of the Procedure

 

The study involved the selection of six children based on a
set of criteria (see Appendix A). Each child participated individ-
ually in a practice session and three problem sessions. These
sessions involved the child's performance of a task, immediately
followed by stimulated recall, using videotapes of the child's task
performance. After each of the three problem sessions, the videotape
of the task performance was transcribed and inferences were made about
the child's performance from the task performance alone. The
audiotape from the stimulated recall for that problem was then tran-
scribed and used to validate or disconfirm prior inferences, as well
as to make additional inferences about the child's performance. The
performance models were then constructed to reflect the inferences
made for the activity and stimulated recall protocols. All of the
problem performances were then analyzed to see, first, if strategies
did indeed exist. A strategy was said to exist if a pattern of
processing steps was seen to occur more than once in a subject's
performances. If strategies were identified, they were modeled. An
attempt was made to see how consistent the students were in applying

the strategies found.
The Research Questions

This study proposed to answer two questions:
1. What strategies, if any, do sixth grade children use in

finding relations between variables?

2. Is a strategy or elements of a strategy used consistently
by a child when presented three parallel problems

involving the same task over different content?

CHAPTER II

REVIEW OF RELATED RESEARCH

The present chapter reviews the research considered in the
development of this study. The first section reviews literature
related to how knowledge.can and should be represented. The second
section deals with how procedural knowledge can be represented. The
third section describes the specific theoretical framework, the
Concept-Task-Strategy Model, this study employs. Finally, the last
section reviews selected literature related to what is known about

strategies for accomplishing tasks.

The Representation of Knowledge

 

As indicated in the problem statement of this study, there are
a number of differing opinions as to how potential learning outcomes
should be described. The problem is basically one of how knowledge can
or should be represented for educational purposes. Anderson (1976)
distinguishes between two basic kinds of knowledge--declarative and
procedural. He defines declarative knowledge as “. . . knowledge of
facts about the world” (p.78) and procedural knowledge as “. . .
knowledge about how to do something“ (p.78).

Some artificial intelligence psychologists (e.g., Newell and
Simon, 1972) suggest that all knowledge be represented as procedures
(productions, in this example); others find more merit in representing

all knowledge declaratively (e.g., the active structural network of

10

Norman and Rumelhart, 1975). Anderson (1976) contends that any piece
of knowledge can be represented in either form. The representation of
knowledge need not be an either-or dilemma. The question is not how to
represent all_knowledge, but, rather how to best represent a given
piece of knowledge for given purposes. Anderson (1976) cites the
following as criteria for making a choice: '

It is much more economical to represent declaratively

that knowledge which is subject to multiple, different

.uses and without having to incorporate the knowledge

into all the necessary procedures that will use it . . . .

0n the other hand, knowledge used over and over again in

the same way; for example, how to generate sentences, would

seem to be better represented in a procedural format in

which it can be applied more rapidly (p. 118).

Greeno (1976) provides a more general criterion; that is, whatever
representation best fits for educational purposes.

For purposes of focusing on the strategies sixth grade children
use in finding relations between variables, a procedural representation
is most appropriate. It is hypothesized that children will apply the
same strategy, or components of a strateQY. to problems that are
parallel in nature. The fact that the experimenter is interested in a
“how-to“ question and that the strategies are hypothesized to be used
over and over again in the same way, seems to warrant the use of
procedural representation. Further, using Greeno's criterion, a

procedural representation seems to fit best for the educational

applications this study addresses.
The Representation of Procedural Knowledge

Greeno (1976) suggests the use of distinctive features, active

structural networks, and production systems for representing problems

11

where "a situation is presented and a goal is specified, and the
student is required to supply a set of procedures for achieving the
goal“ (p. 136). He uses, as an example of this type of problem, a

problem involving the geometry of angles and parallel lines.

Distinctive Features

 

The role of a network of distinctive features is that of
allowing the subject "to identify certain patterns of relational
properties,“ in the case of Greeno's example, "to identify relevant
relations between pairs of angles“ (Greeno, 1976, p. 137). He uses
a flow chart to represent the network of features, each node in the
network being a decision box concerning whether a given feature is
present or not.

As far as the present work is concerned, this pattern matching
phase of problem solving has not been detailed. It is subsumed in the
processing having to do with scanning the elements and identifying the
variables. The focus of this study is on the manipulation of variables
rather than on the identification and selection of those variables. It
is felt by the researcher, therefore, that the level of detail offered
by the network of features is nonessential for the present work. It

could be added when, and if, it was needed.

Active Structural Network

 

Greeno (1976) uses the active structural network (similar to
those of Anderson and Bower, 1973; Kintsch, 1974; Norman et at., 1975)
to represent the relations among the concepts employed in solving the
problem. The present work employs a network called an analytic network

(the product of the concept analysis of the CTS Model described in

4,

12

the next section) to represent the variables, their values, their
observation/measurement procedures, the correlational rules relating
them to other variables, and the elements they describe. The repre-
sentation is tabular, and, thus, different from the active structural
networks noted above. The analytic network represents the concepts but
not the relationships among them. The relationships are conceived of
as connections between nodes as in the structural networks, but the
relations are described in text rather than diagrammatically. Smith
(1972, 1974), in his Concept-Task-Strategy (CTS) Model, presented the
analytic network in tabular format because the interrelations between
the concepts involved are constant. Thus, use of network diagrams to

display these interrelations is unnecessary.

Production Systems

Greeno (1976) uses the production system to describe the
problem-solving procedure associated with finding a solution to the
problem. His conception of a production system is based on the work
of Newell and Simon (1972). Greeno's example of the network of produc-
tions needed to solve problems about angles and parallel lines is
represented as an active structural network. He contends that knowl-
edge structures like this one are necessary, but not sufficient, for
students to solve the required problems. "An additional requirement is
a system for interpreting a problem, setting goals, and selecting
productions from the knowledge base for use in generating the relations
among components of the problem. This, then, becomes the role of the
interpreter“ (Greeno, 1976, p. 141). Greeno does not Specify how this

interpretation system should be represented.

13

The biggest problem associated with the production system
notions of Newell and Simon (1972) is the technical language and its
inability to communicate to researchers and practitioners that are not
in the field of artificial intelligence. It appears that the notions
of setting goals and sub-goals and evaluating present states as to
whether those goals have been met could be employed in the framework of
Smith's (1974) and Padilla's (1975) flow-charting (to be described in
the next section) without becoming encumbered with the language
barrier. For example, the processes Smith and Padilla refer to as
DECODE, SCAN, IDENTIFY might fall under the goal of identifying the
problem. When a list of possible independent variables has been
generated, then the goal of choosing a rule to evaluate for its truth
value may take over. The notions of goal-setting and goal-searching
might be potentially valuable in thinking about the present work.

Computer simulations, however, are not employed in this work.

Flow Charts

 

Greeno (1976) suggests that flow chart representation is most
appropriate for procedures that are more or less algorithmic in nature,
such as adding fractions. The flow chart outlines the component
processes of a procedure.

In general, the procedure is not unique--there are more

ways than one to calculate the correct answer. Alternative

procedures can be represented in different models, or

incorporated in a single nondeterministic model that allows

different branches to be taken (Greeno, 1976, p. 125).

A procedural flow chart can be general in regard to the represen-
tation of the thing to be operated on or can be made more explicitly

applicable to a given set of materials. As defined in this study, the

q.

14

identification of strategies is the identification of procedures, at
some level, usable in dealing with parallel problems involving the same
task. Thus, a flow chart mode of representation appears to be appro-
priate.

The preliminary flow chart that appears in Figure 1 is similar
to Greeno's flow charts and is general as to the set of materials being
operated on, although it is based on the preliminary piloting data
from a set of pairs of wheels where the independent variables were the
size of the bigger wheel and the size of the smaller wheel, and the
dependent variable was the size circle a pair of wheels makes. These
materials are described further in Chapter III. The preliminary
strategy model shown in Figure 1 and the other models produced in this
study were attempts to conform in language and form to the precedent
models of Smith, McClain, and Kuchenbecker (1972) and Padilla (1975).

Padilla (1975) used flow charts to represent his strategy
information processing models for the seriation of objects having
non-visual variables. Following a precedent set by Smith et al.
(1972), Padilla described the steps in the model as primary, secondary,
or tertiary processes.

The primary processes are the basic building blocks

available for use and are considered to be a unitary

skill; examples are choose, designate, and scan.

Secondary processes are frequently recurring sequences

of primary processing steps; e.g., the comparison process.

Tertiary processes may be defined in terms of both primary

and secondary processes (Smith et al, 1972). Examples of

tertiary processes include the MAXPIC and EDGUESS routines

(Padilla, 1975, p. 101).

Padilla began with processes previously defined by Smith et al. (1972),

but defined new processes as needed while model-building. An example

of a primary process definition is given below:

 

15

 

INPUT:

dependent variable name

set of elements
observation/measuremen
procedure

 

DECODE '
variable
SCAN ,

elements

 

 

CHOOSE
n_elements from
the set of element
at random

 

 

 

L
PERFORM

 

 

 

   

IDENTIFY
list of possible
independent variables

SELECT
one independent
variable

i

procedure on chosen
elements

 

observation/measurement

 

 

 

 

HYPOTHESIZE

‘ about the relationship
of the selected inde- .
pendent variable and
the dependent variable

 

 

 

Hypothetical rule of the form:
The er the independent
variEETe, the er the
dependent variaBTe.

  
 
  

 

CHOOSE
element with value d3] for
selected independentd variable,
P1, and values df
dk for the other mindgpendent

 

 

vaFiables, pm, pn, . . ., pv

 

   

RFORM
observation/measurement
procedure on element

 

 

 

‘To 9. 16

V

Figure 1.

 

Hypothetical relationship of thei
form: The dependent variable
is related to the independent

 

variable.

A

l

 

 

 

CHOOSE
element with value d al for
selected independent3 variable, p].
and values df . adkv
for the other mindgpendent vari-
ables, pm, pn, . . ., p"

 

 

 

observation/measurement
procedure on element

 

To p. 16

W

Flow chart representing a strategy for finding

relations between variables based on preliminary piloting data.

l

CHOOSE
delement with value
d] for gpe, and values

dkv
., pv

 

fm’d
for pm, gpn, . .

 

 

 

 

hypothetical rule to

 

 

   
  

 

 

 

 

 

   
  
    
   
   
     
    
      

 

 

l6

 

Je__
CHOOSE
element with value
d9] for gpe, and values

d
fm 9
,form Pm. gpn. . . fEV l
PERFORM |

observation/measurement

 

 

   
  

 

 

 

 

 

 

 

 

 

 
  
  

  
    

 
   
 

   
 
 

 

 

 

 

   
  
 
   

  
 
 
 
  

 

generate expected value procedure on element .1... _.
for dependent variable r- SELECT
one
PERFORM COMPARE independent]
bservation/measurement values of the L_ ariab]e_,
procedure on element dependent a jig
- variable ,
REJECT
va1ESMS¢REhe , HYPOTHESIS
dependent variable
ith expected valu Are the a
values of the ‘
dependent variable “
the SAME or
DIFFERENT? o
RECOGNIZE
Are the F_ as evidence
values of the E "effigm
dependent variables E
in the 3
expected -
In
6 YES what
direction are
the values of the de- '
pendent variable relative to
RECOGNIZE the values of the se-
as SUPPOVF for lected indepen-
rule RULE

 

 

 

RULE

 

   
 

 

 

 

.Q .
U)
K
g o INVERSE
..z.. RULE
Figure 1. (continued)

[— CHOOSE

element with value da] for
selected independent vari- I
able, p], and values dfm,

d n, . ., dkv for the l
'OEher independent variables

l3.1..11".....p

1'."—

_l

k___.

 

RECOGNIZE
as support
for non-rule

 

 

Th 9- 15

l

 

 

Figure l.

 

F_- SELECT I
one
To p- 15 ~.J independent I

l variable ___]

 

RECOGNIZE
as non-support
for hypothetical
rule

<1)
REJECT * 10
HYPOTHESIS
11
HYPOTHESIZE .
inverse
_]

rule

 

l

 

[

 

 

 

RECONSIDER
collected
data

 

 

)-

RECOGNIZE
as support
for inverse

rule

 

 

k

 

 

 

(continued)

18

SCAN
This is a primary process which represents a rather
cursory, largely visual, exploration of the stimulus field.

It establishes a figure-ground differentiation of objects

and detects a few salient features which may enter short-term

storage. However, only partial information is obtained, even

in the visual modality. Detection of certain salient and/or
relevant features usually terminates the SCAN process, or at
least relegates it to a background role, and triggers some
attentive processing. Thus, the input to SCAN is undifferen-
tiated stimulus information while the Output is one or more
differentiated perceptual objects. In most cases, many
features which are relevant from a formal point-of-view are
not detected by SCAN.

Other processes employed in this study are defined in Appendix G.

The flow-charting of the seriation strategies in this manner
was successful in guiding the planning of instruction for teaching
seriation and in evaluating the success of training in seriation
strategies on performance (Padilla, 1975). Further, the flow charts
rather easily communicate to the reader what was occurring in the

procedure.
The Specific Theoretical Framework for this Study

The Concept-Task-Strategy Model

 

Smith (1974) proposed a model for representing knowledge to be
taught. There are three components to the model; concepts, tasks, and

skills or strategies.

19

Content analysis involved the identification and descrip-
tion of related concepts or sets Of concepts. Task analysis
results in descriptions of what information is initially
given and ultimately required in the performance of the
disciplinary tasks. Strategy analysis specifies at a
psychological level how available information is processed in
the performance of a specific task (Finley, 1977, p. 17).

The sections that follow contain further descriptions of these compo-
nents, including the underlying assumptions for them. In each
section, some discussion as to how that component relates to this study

will also be included.

Content Analysis

 

Assumptions:

1. Any discipline is built around a set of specialized
conceptual systems (Smith, 1974, p. 2).

2. Many of the specialized conceptual systems of a
discipline fall into a small number of categories, each
of which share a common logical structure (Smith, 1974,
p. 2).

Description:
Content analysis involves (1) the identification of

the types of conceptual systems characteristic of a

discipline or subdiscipline, (2) the formulation of a

paradigm or analytic network which represents the structure

of each type of system, and (3) the comprehensive identi-

fication and cataloging of the conceptual systems of a

discipline according to the analytic network they exemplify

(Smith, 1974, p. 2).

The content analysis identifies sets of concepts which belong
to a particular discipline. For this study Of relations between
variables, such a set of concepts includes length, thickness, size of
smaller wheel, and size of bigger wheel. These concepts are similar in
that each names a variable. For this set of concepts (called

“systemic" concepts), a single "analytic” concept can be generated to

20

represent the function of all similar concepts. For example, the
analytic concept “variable name“ can be applied to all the concepts
listed above. “A complete but relatively small number of such analytic
constructs when taken together, constitute an analytic network which
specifies the logical relationships between specific or systemic
concepts of the discipline“ (Finley, 1977, p. 28). The analytic
concepts in the analytic networks for this study are variable name,
variable definition, values (comparative and measured), observation/
measurement procedures (comparative and measured), the correlational
rules, and the elements. The analytic networks for the three problems

of this study appear in Tables 2, 3, and 4 in Chapter III.

Task Analysis

 

Assumptions:

1. Most important competencies related to a discipline, at
least from a general education point of view, can be
presented as manipulations of conceptual systems (Smith,
1974, p. 2). ‘

2. The level of mastery of a conceptual system may be
adequately inferred from a defined set of observable
behaviors (Smith, 1974, p. 2).

Description:

Task analysis involves the identification of perform-
ance requirements relevant to a specific type of conceptual
system. These requirements or tasks are described in terms
of the correSponding analytic network (Smith, 1974, p. 3).
“More specifically, tasks are defined by presenting the

analytic concepts which represent the given information and the
information which is required as Output by the person executing the
task“ (Finley, 1977, p. 29). The task for this study represented

within this framework may be defined at the analytic level as:

21

Given: Set of elements .
Observation/measurement procedure for
the dependent variable
Dependent variable name

Required: Correlational rule for independent variable(s)
and dependent variable that holds for the given
elements

On the systemic level, the task would read for Problem #1, as an
example:

Given: Set of rods
Observation/measurement procedure for how far
down the rod bends
Dependent variable name: how far down the
rod bends

Required: Correlational rule relating length and/or

thickness of rods to how far down the rod
bends that holds for all the rods

Strategy Analysis

 

Assumptions:
1. Common information processing strategies are applicable
to the utilization of conceptual systems sharing a
cannon structure (Smith, 1974, p. 2).
Description:
Skills analysis identifies alternative information
processing strategies by which tasks can be performed.

These are descriptions of behavior at the psychological

level and provide the basis for planning and predicting

transfer among tasks (Smith, 1974, p. 3).

“Skills or strategy analysis represents the psychological
processes by which someone may complete a specified task“ (Finley,
1977, p. 29). Each strategy is modeled in a flow chart, using defined
primary, secondary, and tertiary processes. The primary processes are
defined in terms of an input and output and the Operations that inter-

vene between them. More complex secondary and tertiary processes are

22

defined in terms Of the constituent primary processes. Definitions Of
all the processes used to model the children's strategies in this study
are included in Appendix G.

I “Taken together the products of Content-Task-Strategy analysis
represent the structure of a portion of a discipline. The description
consists of related sets of concepts (conceptual systems), specified
tasks to be performed with those concepts, and strategies which model
at a psychological level how the task can be performed” (Finley, 1977,
pp. 30-31). As mentioned earlier, it is this latter component, the
strategy component, that leads one to consider the possibility of
transfer. Both lateral and vertical transfer have been studied using
the CTS Model (Padilla, 1975; Finley, 1977). The scOpe of the present
study is, however, related only to lateral transfer.

Padilla (1975) defines lateral transfer as occurring “when the
learning of a task in a specific content area is facilitated by prior
learning of the same task in a different content area" (p. 21). The
present study is not a training study (i.e., the children will not be
‘tagght_strategies for solving the problems), so, in that sense, the
experimenter is not interested in transfer of learning. However, one
question of interest does arise from the fact that three parallel
problems involving the same task will be given to the students: Have
the students learned a single strategy, or components of a strategy,

that they will apply consistently over the parallel problems?

23

What We Know About Strategies

 

 

Bessemer and Smith (1972) define skills analysis as "a
description of psychological processes operative during performance of
a given task“ (p. 3). The product of such an analysis is a strategy
for performing the task, a set of information processing steps that are
applicable to a range of similar situations. The skills analysis
is one of three analyses deemed necessary for describing learning
outcomes. Content and task analyses are the other two (Bessemer and
Smith, 1972; Smith, 1974). ’

Three empirical studies that used Smith's Concept-Task-
Strategy Model will be reviewed. The first of these is “Strategies
Used by First-Grade Children in Ordering Objects by Weight and Length"
(Smith and Padilla, 1975). Model strategies were determined in
preliminary pilot work. The study involved 96 students. The most
significant finding was that over two thirds (69%) used a highly
systematic approaCh to the task (i.e., used model strategies). Another
9% were identified as using near model strategies.

. . . the fact that even young children approach quite

systematically at least some tasks they understand suggest

that strategy instruction may be practical. This fact
certainly indicates that attempts to teach tasks should take
into account the learner's capacity and tendency to use

systematic approaches (Smith et al., 1975, p. 20).

At the same time this work was being done, Baylor and Gascon (1974)
published production system strategies for weight seriation. These
models were empirically based on the actual performance of children
varying in ages from six to twelve years. Baylor and Gascon "pre-

sented a language of weight seriation, BG, out of which performance

models can be written that simulate most of the observed behavior

24

. .“ (1974, p. 38). They reported the same three strategies as were
found by Smith and Padilla--the extreme value selection or “find
heaviest" strategy, the insertion strategy, and the little used
rearrangement or heavy-light-sieve strategy. Their study seems to
further substantiate the use of systematic approaches by children, even
though the modeling of those strategies took a different form than that
of Smith and Padilla.

A second study using Smith's Concept-Task-Strategy Model, “The
Teaching and Transfer of Seriation Strategies Using Nonvisual Variables
with First Grade Children“ (Padilla, 1975), was designed to teach the
extreme value selection (EVS) and insertion strategies for nonvisual
variable seriation to first grade children. The children were either
Stage I (nonseriators) or Stage III (operational seriators) on Piaget's
stick task (length seriation). One of Padilla's findings was that most
(more than 80%) of all the first grade children taught a strategy could
learn and use that strategy on the post test. The EVS strategy seemed
to be easier to learn for Stage I subjects. Stage I subjects that were
taught the EVS strategy performed more accurately on the post test than
other Stage I subjects. The data in thisstudy indicates that the
teaching of strategies for some tasks is feasible.

A third study, “Vertical Transfer of Instruction Based on
Cognitive Strategies for a Sequence of Geologic Tasks“ (Finley, 1977),
found that:

1. Students learned the task specific strategies during
instruction.

2. The students used components of the strategies they had
been taught during posttests, and transferred strategy
components to the pretests for the next most closely

q

25

related tasks. Students did not use or transfer the
complete strategies extensively . . . (Finley, 1977,
pp. 2-3 of abstract).

Further substantiation of the use of strategy components rather
than "whole strategies" is reported by Resnick (1976). In a study
conducted by herself and Guy Groen, 4-year-olds were taught to solve
Single-digit problems of the form m + n 8 ? (where m and n ranged from
O to 5) by using an algorithm. Practice sessions followed. The
children were then tested on a device that allowed the experimenter to
collect latency data. In this study,

children are taught a routine which is derived from the

subject matter. After some practice--but no additional

direct instruction-~they perform a different routine, one
that is more efficient. The efficiency is a result of fewer
steps (not, apparently, faster performance of component
operations), which in turn requires a choice or decision on
the part of the child. A strictly algorithmic routine, in
other words, is converted into another routine which turns
out to solve the presented problem more efficiently (Resnick,

1976, pp. 71-72).

In sunlnary, the studies cited provide us with the following
information:

1. Children do approach quite systematically some selected
tasks; i.e., they do use well-developed strategies to perform the
tasks.

2. Children can be taught and can use strategies to perform
selected tasks. In sOme cases, this learning of a taught strategy
improves their task performance.

3. Students, after learning a strategy in instruction,
reorganize that strategy to make it more efficient for themselves,
transferring components rather than "whole strategies" to a new, but

similar task.

CHAPTER III

THE RESEARCH METHOD AND PROCEDURES

The purpose of this chapter is to describe the research method
and specific procedures used in doing this study. After a brief
overview of the study, the population and sample of children used in
the study will be described. This will be followed by discussions of
the problems given to the subjects. Descriptions of the data
collected during the problem sessions and the methods of analysis will

then be reviewed.

Overview of the Study

 

Six children were chosen, three from classroom A and three
from classroom 8, based on criteria set forth in the next section.
Each child participated individually in a practice session and three
problem sessions. These sessions involved the child's performance of
a task, immediately followed by stimulated recall, using videotapes of
the child's task performance. After each of the three problem
sessions, the videotape Of the task performance was transcribed and
inferences were made about the child's performance from the task
performance alone. The audiotape from the stimulated recall for that
problem was then transcribed and used to validate or disconfirm prior
inferences, as well as to make additional inferences about the child's
performance. The performance models were then constructed to reflect

the inferences made for the activity and stimulated recall protocols.

26

27

All of the performance models were then analyzed to see, first, if
strategies did exist. A strategy was said to exist if a pattern of
processing steps was seen to occur more than once in a subject's
performance. As strategies were identified, they were modeled. An
attempt was made to see how consistent the students were in applying

the strategies found.
Research Subjects

The Population and Sample

 

The sample of Sixth grade children used in this work was
selected from a middle school in the greater Lansing, Michigan, area.
This particular population was chosen because the school system is
using an elementary science program, Science Curriculum Improvement
Study (S.C.I.S.), that Offers many Opportunities for the children to
examine relations between variables.

The students in the population ranged in age from 135 months
(11.25 years) to 158 months (13.17 years) with a mean age of 142
months (11.83 years) (5.0. a 4.83 months).

Method of Subject Selection

Three criteria were employed in selecting subjects. The first
two criteria were applied to increase the probability that the
subjects would be able to find relations between variables. These
criteria were: (1) that the subject has been in the school system
and, consequently, in the S.C.I.S. program, for at least three grade
levels; and (2) that the subject scored at least five out of nine on a

screening instrument, the Particle Test. The Particle Test was

28

designed to measure a subject's ability to find relations between two
named, arbitrarily related variables. The next subsection will
describe the screening instrument.

The third criterion, that the subject be described by his
teacher as verbally fluent in his classroom explanations, was applied
since the child's ability to express himself is important in efforts
to infer his strategy. Appendix A illustrates the outcome of applying

these three criteria for subject selection.

The Screening Instrument

 

The Particle Test was designed to measure a subject's ability
to find relations between two named, arbitrarily related variables.
Using Smith's Concept-Task-Strategy Model (Smith, 1974) the task can
be described, in abstract or analytical terms, as:

Given: Set of elements
Two variable names

Required: Correlational rule for the two
variables that holds for the given elements

The variables addressed by the Particle Test are: darkness, sharpness
of points, and size of a Specially constructed set of transparent
plastic particles. Associated with each variable is a set of inter-
related concepts as shown in Table 1. These are called systemic
concepts and correspond to the more abstract analytic concepts listed
in the first column.

The materials are sets of plastic particles cut from trans-
parent, colored plastic and Varying in size, color intensity or

darkness, and angularity. An example set of these materials is

29

.uuo
.aeegm mmme mg» .megeu one
.Lmaeezm msu .emxeou «sh
.Lm—pmsm we» .meeeu ugh
.Emmmpa mg» .emgeeu ugh

=o_uooam:_ pm=m_>

Louzmpp .Loxcec

mm_u_ueea oz» we Lo—ou mo
xu_m=o»c_ Lo mmocxeeu ugh

mmoexeea

mopupaeea upume_a acmeaamcegu nose—cu

.uuo
.goaeegm ogu .gopposm ugh
.Loncegm mgu .emmm_n oz»
.gougapp as» .eoaeegm ozh
.meeeu as» .eoagegm use

cowuumam:_ .mamp>

Aem__=uv
acegm amp. .aneesm

mmpu_ueaa men we mucwoa
poccouxm mg» ea mmocneegm

mmmcagegm

mhmmozoo o~tmpm>m

.uum
.emppeEm mg“ .eogeegm och
.meawa mg» .Loagegm mew
.Lmbgm_F ego .mea.a use

.emxeeu mga .comm_a ugh

eopuuoamc. pezmp>

Lop—eEm .Eommwa

mmpupaaea use
we omen muewgsm ugh

o~pm

amok mpo_ueea map Lou accrumz muamucou

.H anMh

mucoeopm

mo—zm Pecopuepoesou

mgauouoem copue>eomao

Ao>_ueeensouv mospe>

co.u_=_aao 8.3aaaa>

was: m—aawee>

mhmuuzou u~h>4<z<

30

illustrated in Figure 2. The test consisted of nine items, each item
involving a set of five particles that conformed to one of these
possibilities: a direct rule on two variables (e.g., the bigger, the
darker), an inverse rule on two variables (e.g. the darker, the duller
or less sharp), or a non-rule (no relationship between variables).
Three of the items involved direct rules, three involved inverse
rules, and three involved non-rules. Detailed descriptions for each
item are in Appendix B.

The test was administered to each child individually. Two
examples of rules were given before the nine-item test was begun.
Each item, containing five particles each, was presented to the child
with the question, "Is there a rule for (e.g., size) and (e.g.,
darkness)?“ The actual relation might be direct (e.g., the bigger,
the darker), inverse (e.g., the bigger, the lighter), or non-rule (no
relation between the variables). The children were allowed to
continue to reSpond until they were “done" with the item. The
protocol for the administration Of the test appears in Appendix C.

For each item on the test, the experimenter recorded the
child's verbatim response(s) and noted whether or not the child
ordered or superimposed the particles in performing the task.

Dichotomous scoring was used in evaluating a child's perform-
mance on the test. Items were scored as correct (value = 1) if the
responses were the correct comparative rule forms for the two named
variables on the inverse and direct rule items (e.g., Item 1: the
darker, the smaller; or Item 2: the sharper, the darker) or “no rule“
responses for the sets Of particles having no relationship.

Children tended to give a “no rule“ response if they did not

31

 

 

anew upuwugea oga Lo» mpaveoume we pom opasexo =<

ups; oz ”6—3“ .m EouH

N ogamwu

 

32

understand the task. Consequently, in order for a “no rule" response
to be counted as correct, the child was required to have responded
previously with at least one correct rule for an inverse or direct
rule item. All other responses were scored as O's. The item scores
were summed to produce the child's test score.

These procedures were identical to those used in a previous
study (Dennison and Smith, 1976) using these materials. In that study
32.5% (fifty-two out of 160 Sixth grade children) achieved a test
score of five or more out of a possible score of nine. In the present
study, nineteen of the fifty-eight sixth grade children tested (32.7%)

scored at least five out of the possible nine.

The Procedure

 

Overview of the Data Collection Procedure

 

The Practice Session. The first session with the selected
subjects was a practice session. The practice session was designed to
accomplish three things: .

1. To give the subject a chance to practice "thinking aloud"
under the guidance of the experimenter, so that what was intended
became clear (Krutetskii, 1976).

2. To give the subject an Opportunity to view himself on the
video screen and to familiarize himself with the questioning tech-
niques employed in stimulated recall (Kagan, 1976; Smith and
Sendelbach, 1977).

3. To help establish some rapport between the experimenter
and subject, so that both were as comfortable as possible in the

testing environment.

33

The goals of the practice session were met by following the
procedure below:

1. A task dissimilar to the three parallel problems was.
assigned in the practice session. The use of a dissimilar task was
intended to minimize the learning of the task of interest while
maximizing the learning of the data collection procedure.

2. The subject was directed to “think aloud,“ much like he
would do if he were talking to himself while doing his homework. The
experimenter made efforts to assist the subject in "thinking aloud“ as

he worked on the practice task (Krutetskii, 1976), using the same kind
of questioning that was later employed in stimulated recall.

3. The experimenter and subject then reviewed the videotape
Of the task performance together, giving both a chance to practice the
stimulated recall portion Of the procedure.

Three Problem Sessions. The next three sessions with a
subject were devoted to the administration of the three parallel
problems. At each of these sessions, the procedure involved the
following:

1. At least two examples of what was meant by the term "rule"
were presented to the subject.

2. When the experimenter was confident that the subject knew
what a "rule“ is, the problem was introduced and an Observation/
measurement procedure was demonstrated. These first two steps were
directed toward ensuring that the subject knew what the task was.

3. The task was assigned in the form: “Find a rule for
(e.g., these pairs of wheels).“ An additional instruction was for the

subject to “think aloud" if he could. However, no further effort

34

was made to encourage this as it appeared to interfere with
performance when a subject tried too hard.

4. The experimenter did not interfere while the subject
attempted to find a rule or rules for the set of materials.

5. When the subject indicated he was "done,“ he reviewed the
videotape of his performance with the experimenter. The experimenter
probed with questions such as: “Were you thinking anything in
particular when you rolled that pair of wheels?,“ to try to stimulate
recall of what the subject was thinking as he made efforts to solve
the problem.

6. A sub-task was asked of the student if deemed appropriate
for further clarification. In the Concept-Task-Strategy Structure,
that sub-task could be described as:

Given: Two elements
Observation/measurement procedure

Required: Comparative prediction of the dependent variable

value for the two elements when observation/
measurement procedure was applied

The Practice Problem

 

The practice task involved giving the subject a system having
three funnels of different colored water, allowing the subject to
Observe an interaction, and asking that the subject describe what
might be inside the system (which he cannot see) that would explain
the evidence. The subject was given tumblers of the different colored
water and several empty tumblers so that he could mix colors if he
wanted to as an aid to explaining the evidence. This task was chosen
because Of its motivational appeal and because of its dissimilarity to

the three problems of interest.

35

The Three Parallel Problems

 

Description of the Task

Smith (1974) conceives of children's abilities to deal with
' variables in terms of three interrelated aspects: concepts, tasks, and
strategies. The major assumptiOn underlying this work is that within
a discipline, concepts of a particular kind (e.g., variables) are
associated with particular tasks for which generalizable strategies
may be developed. A major goal of the work is to examine the role of
these three aspects (concepts, tasks, and strategies) in learning and
transfer.

The objective Of this study was to examine strategy use by
sixth grade children for a task requiring the discovering of the
relation between a dependent variable and one or both independent
variables for a given set Of objects. Using Smith's Concept-Task-
Strategy Model, the task can be described, in abstract or analytical
terms, as:

Given: Set of elements

-Observation/measurement procedure for the
dependent variable
Dependent variable name '
Required: Correlational rule for independent variable(s)
and dependent variable that holds
for the given elements
This task might be assigned or carried out with any pair of variables
relevant to a given set of elements.
Description of the Problems
Problem 1. The set of elements was fifteen steel music wire

rods that differed in length and diameter. The fifteen rods are

represented below in a matrix (Figure 3).

36

Diameter of rod (in inches)

1/16 3/32 1/8 5/32 3/16

Length . 9 X X X X x
of 12 X X X X
rod 15 X X X
(in 18 X X
inches) 21 X

Figure 3. Matrix representing the rods that make up the set
of elements for Problem 1.

IThe dependent variable was the flexibility of the rods, "how
far down they bend,“ when a constant weight was placed on the end.
The independent variables were the length and diameter of the rods.
Associated with each variable was a set of systemic concepts, repre-
sented in Table 2. These are called systemic concepts and correspond
to the more abstract analytic concepts listed in the first column
(Smith, 1974).

Appropriate responses (correlational rules) to the task, as
can be seen in Table 2, might be "The longer the rod, the more it
bends“ (when the length is held constant), etc. (The part of the
responses given above and in the table that are in parentheses would
not necessarily be expected as part of the child's response.)

Problem 2. The set of elements was fifteen pairs of wheels.
Each pair of wheels was permanently attached to an axle. The pair of
wheels consisted of a “bigger wheel,“ d1, and a "smaller wheel,” d2.

The fifteen pairs are represented below in a matrix (Figure 4).

37

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39

Size of bigger wheel (d1 in inches)

9/8 11/84 13/8 15/8 17/8

Size 7/8 X X X X X
of 9/8 X X x X
smaller 11/8 X X X
wheel 13/8 X X
((12 in 1.5/8 X
inches) X

Figure 4. Matrix representing the pairs of wheels that make
up the set of elements for Problem 2.

The “distance between edges of wheels," 5, was a constant (one inch in
length).

A pictorial representation Of a pair of wheels is given in

,gpfi) .1

Figure 5. A pictorial representation of a pair of wheels.

Figure 5 below.

 

When one of the pairs of wheels was rolled, a double circle formed
with diameters dependent on the Sizes of the “smaller wheel“ and the
“bigger wheel.“ The wheels were coated with carpenter's chalk SO that
a double circle pattern was left on one-inch blocked paper for

Observation. Such a pattern is illustrated in Figure 6.

40

0

Figure 6. Representation of the pattern made when a pair of
wheels was rolled.

The independent variables then were the size of the "smaller
wheel“ and the Size of the “bigger wheel." The dependent variable was
the size circle (outside diameter) the pair of wheels makes. Asso-
ciated with each variable was a set of interrelated concepts as
presented in Table 3.

Problem 3. The set of elements was fifteen nichrome (Chromel A)
wires through which current was passed from an AC-OC rectifier. An
ammeter and a light bulb were also present in the circuit. The wires
differed in their diameters and lengths. The fifteen wires are

represented below in a matrix (Figure 7).

Length Of Wire (in feet)

10 8 6 4 2

Wire 20 X X X X X
Gauge 24 X X X X
28 X X X

32 X X

36 X

Figure 7. Matrix representing the wires that make up the set
of elements for Problem 3.

41

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44

The load voltage from the rectifier remained a constant.

When the circuit was completed, the meter responded by reading
the number of amperes, and the light bulb responded by "coming on.“
The meter reading and the brightness of the bulb, both dependent
variables, depended on the diameter and length (independent variables)
of the wire through which the current passed. Associated with each of
the variables was a set of systemic concepts. These are represented

in Table 4.

The Parallel Nature of the Problems

 

Question 2 of the study addressed whether or not a sixth grade
child used a consistent strategy over three parallel problems. The
three problems were parallel in the following ways:

1. Each problem addressed the same task:

Given: Set of elements
Observation/measurement procedure for the
dependent variable
Dependent variable name
Required: Correlational rule for independent
variable(s) and dependent variable that
holds for the given elements

2. Each problem contained fifteen elements.

3. Only certain fixed combinations of values on the independ-
ent variables were represented in the set of elements. Subjects could
manipulate the independent variables only by selecting among the given
elements.

4. The arrays of available values of independent variables

were parallel in structure as reflected in Figures 3, 4, and 5.

45

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47

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48

Problem and ProtocOl Development

 

Pilot work indicated that the level of difficulty of the
problems was not the same. The problems for the study, then, were -
ordered from easiest to hardeSt: rods, wheels, wires. These reasons,
determined from the pilot work, are given for that ordering:

1. The children had had experiences with "rods" that bend;
e.g., a fishing pole.

2. The Wheels Problem could be reduced to one independent and
one dependent variable instead of two independent and one dependent
variable if the child focused on the difference between the sizes of
the bigger and smaller wheels as the independent variable.

3. The thickness Of the wire in the Wires Problem was the
least salient variable in all of the problems.

In the preliminary piloting of the problems, efforts were made
at structuring the protocols for the problems such that information
about what the subject was doing could be gathered while the subject
was performing the task. This interruption of the subject's perform-
ance of the task interfered with the subject's thinking significantly,
and the information gathered was of no great benefit. The decision was
made to give instructions, asking the subject to ”think aloud" if he or
she could, then allow the subject to perform the task without inter-
ruption, and use the stimulated recall procedure to Obtain as much
information as possible about what the subject was thinking as he did
the task. Protocols for the administration of the problem appear in

Appendix D.

49

Stimulated Recall

 

Norman Kagan and his colleagues (1976) develOped a procedure
called IPR (Interpersonal Process Recall) for use in training
physicians and mental health personnel. He writes, "What we Observed,
in '62, was that if a person is videorecorded while s/he is relating to
another and is thus Shown the recording immediately after the
interaction, the person is able to recall thoughts and feelings in
amazing detail and in depth (Kagan, 1976, p. 1). Smith and Sendelbach
(1977) adapted this procedure for use in their teacher planning study,
where after the teacher had planned a unit Of instruction he reviewed a
videotape of his planning procedure and was asked to stop the tape and
comment on anything he remembered about what was happening at that
moment. They also used the technique with teachers and students to
reconstruct classroom interactions.

With this background information, this experimenter decided to
try this procedure with the sixth grade children. From the preliminary
pilot work, it was clear that, for most children Of this age, "thinking
aloud” while performing a task tended to interfere with their normal
thought processes. Stimulated recall provided a means of getting
verbal information from the children about what they were doing without
interfering with their task performance. The protocol used and a list
of typical questions the experimenter asked of the child are in

Appendix E.

Protocol Analysis

 

The experimenter reviewed the videotapes of the actual problem

performances, making detailed notes. These notes became the written

SO

record of the raw data. Inferences were then made regarding each
subject's mental processes using the actual problem performance data
alone. A sample of a transcribed videotape w/inferences made follows
in Figure 8.

The audiotape of the stimulated recall was then transcribed and
used to validate or disconfirm inferences made on performance data
alone. Additional inferences about the child's performance were also
made where appropriate. A sample of a transcribed audiotape
(corresponding to the sample transcribed videotape) with inferences
made follows in Figure 9.

The child's performance on each problem was then modeled in a
flow chart using processes previously defined by Smith et al. (1972),
Padilla (1975), Finley (1977), and new ones defined for the purposes of
this study. The experimenter constantly referred to the detailed notes
and inferences for evidence while preparing the models. The model
developed for the corresponding videotape and audiotape analyses in
Figures 8 and 9 appears in Figure 10.

Guidelines used in making inferences and analyzing the
protocols are given in Appendix F. Definitions of the processes used
in modeling the performances and strategies are given in Appendix G.

A sample of the videotapes of actual task performance and of
the audio-recorded stimulated recall were reviewed by a colleague,
using the guidelines and definitions of processes, to establish the
validity of the modeling process.

Up to this point, the analysis was, more or less, straight-
forward, once the guidelines for analyzing the protocols were

established and all of the processes were defined. The next phase of

Videotape #VJ
Activity Analysis Record Form
Tape begins @113

51

Page 1 of 1
Subject #5
Task Problem #l-Rods

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S
'5 8 L
E . § § .3 Descriptive Notes Inferences (AI's)
3221.: a ..
A Quit/)8.
O t-a: m
1 113 T E Instruction
2 193 _I S Activity Begins.
3 194 T S S takes #3, tests it. AI1-3a S selects
(length l-thickness 1) thinnest and Shortest
. 4 207 _J;"§L S returns #3., rod. AIl-3b S observes
S 208 T S S takes #4, tests it. . #3.
(length 4-thickness 5) AIl-5a S selects thick-
, 6 218 _1;“§__§_returns #4. est and what s/he thinks
7 219 T S "The thinner around the rod is longest rod; All-5b
is, the further down it will S observes #4; All-5c S
8 bend." is not attempting to
9 221 T E "Would you say that again?" All-7a S has not encode
10 222 T S "The thinner around the rod length values, only
11 is, the further down it will thickness and bending
bend." values.
12 223 T E "Are you sure of your rule?" AI1-7b S rgpggts_nulg._m
13 S S nods.
14 224 T E "Do you want to continue work-
. ,_ ing?"
15 S "NO."
16
17
18
19
20
”'21
22
23
__2:4
25
26
27
28
29
3O
31
322
33
34
35
36
37
.w_38

 

 

Figure 8.

Sample Activity Analysis.

52

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Audiotape #AM Page 1 of 3
. Subject #5
Stimulated Recall Analy51s Record Form Task Problem #1-Rods
Tape beg1ns @ 003
,§ a, Descriptive Notes Inferences (SI'S)
w» U cu ‘-
6 C U Q)
teases
RZpeaa
a e w
1 003 S E Instructions for Stimulated Recall
2 016 S Videotape Begins - Instructions for
Activity
3 052 S E (1-2) "Were you thinking anything in
. 4 particular at this point?"
5 S S "No, not really."
. 6 ___S__§__"Did ouh 11 id
7 was at this point?"
8 S S "Yggh."
9 S E "Do you remember what you were
10 thinking it might be?"
11 S S "Well, it just seems like that the 511-11 5 retrieves
12 thicker it would be, it wouldn't rule - the thicker,
13 bend as easier." the less it bends -
, 14 S E "Is there some reason--is there _g§_gyggtng§i§.____.l
15 something you had done before that
16 ggve you a clue that that might be
17T* the rule here?"
18 5 § "Not really."
19 S E "00 you recall anything like that?"
__20 S S S shook head in the negative.
21 S E "Did you have any idea at this
22 point how you would go ggggt
23 fipding out if that was the
24 ___g ___ 3"
2; ES "NO."
26 064 E 1-3) "The first rm,
27 #3. Was there any particular reason
28 for choosing #3 at this point?"
29 L S "Because that one looked like the $11-29 S selects
30 thinnest one and it w ld thinnest rod. Modi-
31 easier to test just the thinnest fies All-3a;
32 one th 11 l -- _smnantsJLlela—
33 know it would take less time
34 and stuff."
35 E "Did you have any idea about what
3 W
37 put the weight on it?"
38 L15 "I thought it would bend down pretty $11-38 S predicts

 

Figure 9.

Sample Stimulated Recall Analysis.

 

 

53

 

 

 

 

 

 

 

 

 

 

Page 2 of 3
Stimulated Recall Analysis Record Form Subject #5
Task Problem #l-Rods

C
.3 Descriptive Notes Inferences (SI'S)

+3 d) ‘-

§3§§ 23.3

L g. 3 (6

0 (‘6 O U

m l— m a.
8 (A

1 S E far because it's thin and-" value for bending of

__g S E (Tape Begins) "What happened when rod; supports 511-11,

3 you put the wéight on it?"

4 S S "It bent down really far." SI2-4TS’encodéS val-

ues for bending of

5 S E "Is that what you expected?" rod. Confirms All-3b,
6 _L S "Hu-huh." 2-6 5 judges pre-
7 S FE_‘"Did you at this point have any idea diction to be

8 about what to do next to che ck yggr correct.

9 rule?"

, 10 L_§_ "Not really."

11 1686‘s E 1-5 "The next one you picked was
12 #4. Was there any particular reasgn ‘

3 for choosing #4 at this point?"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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s_in tween" implies S is
between to find out. " (looking at extremes. ,
5 §_." id ,
#4 would do at this point when
ou outgthg_yeioht on?"

S S "Yeah, I thought it wouldn't bend SI2-23 5 predicts
down i value for bending of
and-" rod; supports $11-11.

____§_.E Ta e i "W
___lyou put the weight on #4?"

S S "It didn't b nd d w SI2- 28 S encodes
when I put the weight on #3.“ value for bending of

S E "15 th dif red._£nn£i:ms_All_5b_,

. 'S S "Hu-huh." 512- 31 S judges pre-
109 S E (1-15) "Yo id h (diction to be
around it is, the further it bends. _snznegtg

 

 

 

your rule?"

 

Figure 9. (Continued)

54

Page 3 of 3

Stimulated Recall Analysis Record Form Subject #5

Task Problem #I-Rods

 

Descriptive Notes

Inferences (SI's)

 

"No .II

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

cecnkecncoce to ro‘utu rerervhgrvhoua we rubururdrahd
aa~30101anea 1- xeco~4 aunt» racaxo¢n~q cusseahawac>u>a3~40101aw» we

 

 

 

Figure 9.

(Continued)

 

55

PERFORMANCE MODEL

 

Subject #5
Problem #1 - Rods

 

INPUT: set Of rods
observation procedure

for amount of bendin

 
  
  
  

 

 

 

   

 

 

 

  

 

 

 

 

 

 

   
   
 

    

   
   

variable name: amoun
of bending
Instructio
DECODE
INDEPENDENT observation procedure
logically ‘VARIABLE SCAN for amount of bending
necessary IDENTIFI- rods variable name: amount
for SIl-ll CATION of bending
Instructions
All-7b
rule relating amount of ‘
bending to thickness DESIGNATEl MINPIC PREDICT VALUE
(the thicker the rod, th rule for amount
less easily it bends) as hypothesi~ ,thinnes ) of bending

      

 

 

 

 

 

I logically

 

 

 

 

 

 

 

 

 

 

$11-29
SIl-ll necessary for
SIl-38, $12-23 All-3b, OBSERVE
512-4 rod #3
AIl-Sb REDICT VALUE MAXPIC JUDGE PREDICTION
$12-28, OBSERVE or amount of
rod #4 bending thick- (correct)
512‘23 SIZ-l4a 512-6

 

 

 

JUDGE PREDICTION JUDGE HYPOTHESIS

(correct) (correct)

 

 

 

 

512.31 logically

necessary
for All-7b

Figure 10.

REPORT
ule: The thinner around th
rod is, the further down it

will bend.

      
 
   
   

 

All-7b

JUDGE RULE
(sure)

 

Sample Performance Model.

56

the analysis, moving from the performance models to strategy models of
some kind, was now eXploratory. It was anticipated that when one
observed the patterns of a single individual across the three parallel
problems that a single “Best Fit“ or strategy model could be built for
that individual. The anticipation of a possible "Best Fit“ or strategy
model for a single individual over the three parallel problems also
presupposed that the individual would be consistent, more or less, in
his/her strategy use. This part of the analysis was difficult, at
best, with the data available, as the experimenter's expectations
regarding the matter of consistency were not borne out. The actual
analysis used is more fully described in Chapter IV, and the

implications of it are discussed in Chapter V.

CHAPTER IV

RESULTS

This study proposed to address two issues: (1) the
identification of strategies Sixth grade children use in finding
relations between variables given the following task:

Given: Set of elements

Observation/measurement procedure
for the dependent variable
Dependent variable name
Required: Correlational rule for independent variable(s)
and dependent variable that holds for the
given elements
and (2) the determination as to whether a strategy or elements of a
strategy are used consistently by a child when presented three
parallel problems involving the same task over different content.

The two children in the formal pilot are included here because
they reflect strategies not encountered with the six children in the
final study. The children from the formal pilot will be referred to

as Pilot Subjects.

Overview Of the Results

 

The sixth grade children in this study were able to find rules
relating one or both independent variables to the dependent variable.
Performance models were built for each Of the eight students on each

of the three problems for a total of twenty-four models.

57

58

Strategies were identified for the students' performances.
These strategies were modeled as components of a performance, rather
than models of the whole performance, as had originally been expected.
The strategies fell into two categories: rule-testing strategies and
rule-forming strategies. For any given performance, a student used one
or some combination of several strategies to find the rule. Some
students used strategies in both categories for a given performance:
rule-testing and rule-forming. Other students used a strategy or
strategies from the rule-testing category only; i.e. they apparently
retrieved a rule from long-term memory immediately as they began the
task and proceeded in a rule-testing mode until the problem perform-

ance was completed.

Rule Formation Data

 

Every subject formed at least one rule for each problem
presented. The eight students had a total of twenty-four opportuni-
ties to find rules; a total of twenty-seven rules were reported. Of
these twenty-seven rules, nineteen were simple rules and eight were
compound rules. A simple rule was defined as a rule that relates only
one of the two independent variables to the dependent variable. A
compound rule is a rule that relates both independent variables to the
dependent variable. Twenty-four rules were correct; three were incor-

rect. This data is presented in Table 5.

Identification Of Strategies

 

The strategies the sixth grade children in this study used in

solving problems Of the aforementioned type were found to be of two

59

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61

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62

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63

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64

kinds; (1) strategies for testing rules and (2) strategies for forming
rules. In each of these categories, three strategies were found.
They are listed below:
1. Strategies for Testing Rules
(a) Strategy 1: Testing a Rule by Controlling Variables
(b) Strategy II: Testing a Rule by Observing
Correspondence Between Values on the Independent
Variable(s) and the Dependent Variable
(c) Strategy III: Testing a Rule by Selecting Extreme
Values, a Special Case of the Testing a Rule by
Observing Correspondence Between Values on the
Independent Variable(s) and the Dependent Variable
2. Strategies for Forming Rules

(a) Strategy IV: Formation of a Rule by Controlling
Variables

(b) Strategy V: Formation of a Rule by Observing
Correspondence Between Values on the Independent
Variable(s) and the Dependent Variable
(c) Strategy VI: Formation of a Rule by Selecting
Extreme Values, a Special Case of the Formation of
a Rule by Observing Correspondence Between Values
on the Independent Variable(s) and the Dependent '
Variable
It should be noted that the Strategies for Testing Rules and the
Strategies for Forming Rules are parallel in nature. The method for
selecting elements to observe are similar for Strategies I and IV, 11
and V, and III and VI. The difference in these strategies lies in the
fact that elements are selected in Strategies I, II, and III for the
purpose of testing a rule; those selected in Strategies IV, V, and VI
are for the purpose of trying to form a rule.
Models of these strategies, some narrative describing the
strategies, and an example of a subject's performance where each

strategy is used follows.

65

Strategies for Testing Rules

 

These strategies were employed when the subject had either
retrieved a rule from long-term memory or had formed a rule in a
previous set of processes.

Strategy I: Testing a Rule by Controlling Variables. This
strategy allows one to test a rule by first choosing an element to
test and then selecting successive elements such that the independent
variable of interest is allowed to vary while the other independent
variable is controlled. A model of this strategy appears in Figure
11. The guidelines used for making inferences about processing steps
are listed in Appendix F. Some of these are reviewed here to clarify
the meaning of the steps in the strategy model.

When the subject and the experimenter viewed the videotape in
stimulated recall, they discussed each element selected. A line of
typical questioning was as follows:

(1) “Has there any particular reason for choosing # _?“

(2) "Did you expect f__ to do anything in particular when

you tested it?“ '
If the answer to #1 was “yes“ with some explanation, it was inferred

that the subject selected that element, rather than chose it, more or

 

less, randomly. If the answer to #2 was "yes” with some explanation,
it was inferred that the subject predicted a value for the dependent
variable before observing it. If the subject did make a prediction
before he or she tested the element, the experimenter inferred that
the subject was testing a hypothesis he or she generated before or at
the time the element was selected. Furthermore, the experimenter

inferred that the subject judged the prediction correct if he or she

66

 

INPUT-—--)‘

 

RETRIEVE or FORM RULE
relating dependent
variable to independent
variable

 

 

  

    

 

DESIGNATEl -CHOOSE
rule as LEMENTmSEEEgTION
hypothesis '

 

 

 

 

 

 

PREDICT VALUE
for dependent
variable

 

 

 

 

‘JUDGE PREDICTION,

  
   
 

  

OBSERVE
element

 

 

 

LT or GT

 

 

 

PREDICT VALUE I
for dependent

variable

 

ELEMENT

 

 

SELECTION
WITH

 
 

 

. OBSERVE
element

 

 

CONTROLLED

   

 

JUDGE PREDICTION

 

 

 

NO

    

 

[1 REPORT

 

JUDGE RULE

rule

    

 

JUDGE HYPOTHESIS

 

 

 

YFG

sure?

 

Figure ll.

 

Strategy 1:

 

 

 

Testing a rule by controlling variables.

67

answered the question, "Is that what you expected?", in the
affirmative when the element was tested.

Controlling variables was not inferred unless the subject
mentioned that he or she was attempting to control variables. Merely
selecting two or three elements where one of the independent variables
remained constant was not viewed as sufficient evidence.

The inference that a hypothesis was judged to be correct was
made when a subject reported a rule in the activity protocol or other-
wise indicated that to be the case in the stimulated recall. The
experimenter inferred the subject judged the hypothesis to be
incorrect when another hypothesis took its place or when the subject
otherwise indicated that to be the case in the stimulated recall.

JUDGE RULE is an artifact of the protocol itself. When the
subject reported a rule, the experimenter asked the question, "Are you
sure of your rule?“ If the response was “yes,“ the experimenter
indicated that the rule was judged correct. If the reSponse was "no,“
the experimenter indicated that the rule was judged incorrect.

The example of a subject using Strategy I is that of Pilot
Subject #2. (See Figure 12.) Values describing the numbered elements
(the wires) are presented in the Key. You will note that the subject
actually used Strategy I twice in testing rules in this part of the
protocol for the Hires Problem.

Strategy II: Testing a Rule by Observing Correspondence
Between Values on the Independent Variable(s) and the Dependent
Variable. This strategy allows one to test a rule by choosing or

selecting elements and noting whether the direction of the values of

68

KEY: WIRES MATRIX
Length of Wire

 

10 ft- Lita

6 ft. 4 ft. 2 ft

 

20 #5 #10
(21 1(4JSZI 3(4!
24 #15

 

#9 #4
1221/4) (231. L23 1/2)

#3 #8 #13
Hire 28 (l8 112+§l9#314A§2l 114mg2221122
Gauge

1
L14 1/2) (17) (20 1 4 ,

#11 °

 

 

 

 

 

 

 

32 #l4 #6
jjl) (16')
36 #12
(9*)

 

 

 

 

*Actual performance of this problem by this subject
involved a rather lengthy procedure that led to the
discovery of the second independent variable (thick-
ness). This part of the performance was omitted in
this figure to highlight the use of Strategies 1,

 

 

 

 

 

 

OBSERVE
wire #1

  

 

 

 

 

 

 

 

     

and IV.
Input*
CHOOSE
wire # l4
2: GT ELEMENT
SELECTION
3y OBSERVE - NITH
-: wire #14 CONTROLLED
4‘5 VARIABLE
a; (thicker, same
length)
i— GT ELEMENT
— r SELECTION
PREDICT VALUE NITH

 

 

 
 
   
   
 
 
   

ORM ULE

elating how far the nee-
le moves over to thick-
ess: If the wires are

he same length, the
thicker the wires, the far
h r

 

 

  

 

    

 

 

 

for how far CONTROLLED
the needle VARIABLE DESIGNATEl
(thicker, rule as
same length) hypothesis

 

Figure 12. Abbreviated Performance Model of Pilot Subject #2--

Wires Problem.

av I

St

OBSERVE
wire #4

 

69

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

PREDICT VALUE

 

 

 

 

 

 

JUDGE PREDICTION MINPIC r-fl for how far
___? (correct) (thin- the needle
n mgvgs gyg: ,
GT
ELEMENT L- JUDGE PREDICTION OBSERVE
SELECTION (correct) wire #12
WITH
CONTROLLED
VARIABLE
(thicker,

 

 

LT

 

   
 

ELEMENT

 

 

 

 

 

 

PREDICT VALUE

  
  

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

  
 
 
  

 

 

 

 

   

OBSERVE SELECTION
*2 "IT" 312 22:32"
CONTROLLED
VARIABLE
(thinner,
mm)..— OBSERVE
wire #6
PREDICT VALU ’ MAXPIC —J
WITH
the needle VARIABLE COPVEC
m°V95 OVEV (thickest,
OBSERVE JUDGE PREDICTION‘ UDGE HYPOTHESIS
wire #11 (correct) (correct)
" FORM RULE
elating how far the needle
"CIIAC ves over to length: The
CONTROLLED ess times the wire is
VARIABLE rapped around, the farther
(longest DESIGNATEI h needle moves over.
’ ru e as
same
thickness) hypothesis
0 C
P' h‘ Figure 12. (continued)

 

 

I

 

  

PREDICT VALUE
for how far ,
the needle
moves

 
 

 
  

 

7O

 

 

OBSERVE
wire #5

 

 

JUDGE PREDICTION
(correct)

 

 

 

 

OBSERVE
wire #13

 

 

 

JUDGE PREDICTION
(correct)

 

 

 

Str

 

 

 

 

J

 

! WITH A
CONTROLLED

MAXPIC

VARIABLE
(longest.

vi

 

 

samfi Egick-

  
 

PREDICT VALU
L— for how far
the needle

  

_1_.

~MINPIC
(short-

‘ est) 1

 

 

 

for how far
the needle

 

 
  
 

 

  

OBSERVE
wire #15

 

 

[__

 

JUDGE HYPOTHESIS
(correct) '

 

JUDGE PREDICTION
(correct)

 

 

 

 

 

REPORT

combined rule: The thicker
and the less times it goes
around, the higher it'll

read on the meter.

__\\\‘__"

Figure 12.

 

 

JUDGE RULE

 

 

(continued)

71

the independent variable(s) of interest and the dependent variable are
consistent with the direction predicted by the rule. A model of
Strategy II is found in Figure 13. If a prediction is found to be
inconsistent with the actual values observed, it may lead the subject
to either ignore that data or, perhaps erroneously, to judge the
' hypothesis incorrect. Strategy II seems to work only because the
subjects tested many elements when that strategy was applied. This
testing of many elements, and the fact that some evidence is ignored
when it is not consistent with predictions, indicates that Strategy II
is probabilistic in nature. The performance model of Pilot Subject #1
on the Rods Problem exemplifies the use of this strategy. (See
Figure 14.)

Strategy III: Testing a Rule by Selecting Extreme Values, a
Special Case of the Testing a Rule by Observing Correspondence Between
Values on the Independent Variable(s) and the Dependent Variable
Strategy (Strategy II). This strategy is very similar to Strategy II,
except that the elements selected have extreme values on the inde-
pendent variable(s). Selecting elements with extreme value(s) on the
independent variable(s) was not inferred unless the subject used the
superlative term; e.g., biggest, longest, thinnest, in his or her
description of the selections made. Strategy III also tends to be
more efficient than Strategy II, in that attending to extreme values
typically requires fewer observations before the subject is willing to
report a rule than when one does not attend to extremes. Figure 15 is
a model of Strategy III. Subject #5's performance on the Rods Problem

is given as an example of this strategy. (See Figure 16.)

72

 

' RETRIEVEl
INPUT or
FORM RULE
relating dependent
variable to independent
5 .

 

 

   

DESIGNATEl
rule as
hypothesis

I CHOOSE

element

 

 

 

 

 

PREDICT VALUE
OBSERVE . for

or
element dependent SELEETVDN
variable

- ' OT‘
l THO VARIABLE

JUDGE PREDICTION

   
   
      

 

 

   

 

 

 

 

 

 

 

 

JUDGE HYPOTHESIS

 

correct?

 

 

 

NO

JUDGE RULE REPORT

rule

 

YE

Figure 13. Strategy 11: Testing a rule by observing corre-
Spondence between values on the independent variable(s) and the
dependent variable.

 

KEY: RODS MATRIX
_Lgng‘h of Rodv
, 25 i 2l in. 17 in. _1§gin. 9 in-
7/32 #l3 #4 #l5 ’ #lO #12
(ll) (7) (3 l/§)_ (2) (1)
3/16 #6 #ll #7 #8
Thick- (l3) (7 l/2) (4) L2).
ness 5/32 #l4 #5 #l
of (15) (7) (3 l/Z
Rods l/B #12 #9
(incheS) (l6 Hg) £7)
3/32 3 '
(l9)
INPUT: set of rods
observation procedure
for amount of bendin
variable name: amoun
of bending
Instrgctions
L
INDEPENDENT 0 DECODE d
VARIABLE bservation proce ure for
IDENTIFI- )6— ch" k-i amount of bending
CATION r0 5 Variable name: amount of
(tmkness) Mm
RETRIEVEl
rule relating amount of
bending to thickness: The
thicker, they wouldn't bend
as much as the thinner ones.
rule as rod #13 or bending o d #13
hypothesis rod ro
I:
W - r—l—_,.
PREDICT VALUE ELEhENT JUDGE PREDICTION
“'1; “3“"9 E—SELECTION '
0 r0 3 (thinner)
O
'—

 

Figure 14.

73

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Performance Model of Pilot Subject #l--Rods Problem.

 

 

 

 

 

74

 

 

 

 

 

 

 

 

 

 

 

 
       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
    
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LT
OBSERVE ' JUDGE PREDICTION, ELEMENT
rod #9 (incorrect) SELECTION
' (thinner)
'JUOGE PREDICTION OBSERVE Pfigf‘g:fl:¢:35
(correct) rod #3 of rods
JUDGE HYPOTHESIS REPORT
(correct) l——-—a rule: The thinner they are,
the more they bend when you
put the weight on, and the
thicker, they don't bend as
much.
7"? EAE;QSE NDEPENDENT
GE EETION VARIABLE DESIGNATEl JUDGE RULE
Iltnger DENTIFI- rule as (not sure)
thicker) CATION , hypothesis
H) -
I _ L +
g; PREDICT VALU OBSERVE JUDGE PREDICTION
: for bending rod #15 ‘ (incorrect)
V of rod
JUDGE HYPOTHESIS
(incorrect)
h
r- __L.
_, OBSERVE PREDICT VALU "guzlc
> for bending ‘
rod #12 MAXPIC
>. of rod
m (shortest,
-; , thickest)
a 21..
U, N

 

Figure l4. (continued)

 

 

75

L

JUDGE PREDICTION
(incorrect)

 

 

 

 

I

FORM RULE
relating amount of bending to
thickness and length: The
thicker and shorter they are,
the less they bend.

___l

REPORT
rule: The thicker and
shorter they are, the
less they bend.

\J

 

 

 

 

 

 

 

 

 

JUDGE RULE]
(sure) I

 

 

 

Figure 14. (continued)

76

 

 

INPUT

‘4‘”

 

relating dependent
variable to independent

RETRIEVE) or
FORM RULE

variable(s)

 

 

DESIGNATEI

rule as
hypothesis

 

 

 

 

 

 

OBSERVE
element

 

PREDICT VALUE
‘for dependent
variable

      

MINPIC
or
MAXPIC

 

 

 

 

JUDGE PREDICTION

 

 

 

NO sure?

/\

Figure 15.

a

 

 

JUDGE HYPOTHESIS

 

 

Strategy III:
values strategy. a special case of Strategy II.

 

NOT SURE

 

    

correct?

 

JUDGE RULE

 

  

REPORT
rule.

   

 

 

 

 

Testing a rule by selecting extreme

KEY:

 

RODS MATRIX
25 in. 2] in- 17 in 13 in. 9 in
7/32 #13 #4 #15 #10 #12
(11) (7) (3 1 2 (2) (1)
“3716 #6 (#11 #7) #8
. (13) 7 2) 4 2)
Th““' 5732 #14 #5 #1
ness
of (15) (7)
R d 173 #2 #9
(‘1’ Shes) (16 112) 17)
"° 3/32 #3
(l9)
INPUT: set of rods
Observation procedure
for amount of bending
variable name: amount
of bending
Instructions
INDEPENDENT DECODE
VARIABLE SCAN , observation procedure
IDENTIFI- rods for amount of bending
CATION variable name: amount
(thickness) of bending
| Instructions
RETRIEVEl 1
rule relating amount of
bending to thickness: --*°E§:$:AIE‘ MINPIC
The thicker the rod, the h othesis (thin-
_‘ less easily it bends. yp
EA PREDICT VALUE
4; for amount
‘3 JUDGE PREDICTION OBSERVE of bending
vi (correct) rod #3 -
E3
6.
O
TWP
Figure 16. Performance Model of Subject #5--Rods Problem.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
    
   

 

 

 

  
   

 

   
   

 

 

 

 

MAXPIC

(thick-A

est)

 

 

 

78

 

PREDICT VALUE
for amount --—1
of bending

 

OBSERVE
rod #4

 

 

 

 

 

JUDGE PREDICTION

(correct)

r___.|,____.

JUDGE HYPOTHESIS
(correct)

 

 

 

 

 

 

 

 

REPORT
rule: The thinner around the

 

 

 

 

 

 

 

--m rod is, the further down it
will bend.
\J
JUDGE RULE
(sure)
Figure 16. (continued)

79

Strategies for Forming Rules

 

These strategies were employed when the subject had not yet
formed a rule and was testing elements in an effort to determine what
relationships between variables might exist.

Strategy IV: Formation of a Rule by Controlling Variables.
This strategy allows one to form a rule by first choosing an element
to test and then selecting successive elements such that the inde-
pendent variable of interest is allowed to vary while the other
independent variable is controlled. Again, controlling variables was
not inferred unless the subject mentioned that he or she was attempt-
ing to control variables. Strategy IV is modeled in Figure 17. Use
of Strategy IV is demonstrated in Figure 12.

Strategy V: Formation of a Rule by Observing Correspondence
Between Values on the Independent Variable(s) and the Dependent
Variable. This strategy allows one to form a rule by choosing or
selecting elements and noting whether a pattern develOps, enabling one
to form a rule. The model of Strategy V appears in Figure 18. An
example of a subject using this strategy is given in Figure 19.

Strategy VI: Formation of a Rule by Selecting Extreme Values,
a Special Case of the Formation of a Rule by Observing Correspondence
Between Values on the Independent Variable(s) and the Dependent
Variable Strategy (Strategy V). This strategy is very similar to
Strategy V, except that the elements selected have extreme values on
the independent variable(s). Again, selecting elements with extreme
value(s) on the independent variable(s) was not inferred unless the

subject used the superlative term; e.g., biggest, longest, thinnest,

BO

 

CHOOSE

INPUT element

01‘
ELEMENT
SELECTION

 

 

OBSERVE
element

LT or GT
ELEMENT
SELECTIONf-——~
WITH '
CONTROLLED“

 

 

 

 

 

OBSERVE
element

NO

 

 

:1
relating depen-
dent variable to
independent

 

JUDGE RULE

 

 

 

rule NO REPORT
formed? rule

 

 

 

DESIGNATEl
rule as
hypothesis

JUDGE HYPOTHESIS‘

 

 

 

 

 

Figure 17. Strategy IV: Formation of a rule by controlling
variables.

81

 

CHOOSE

INPUT element or
ELEMENT
SELECTION

or

TWO VARIABLE
ELEMENT
SELECTION

 

 

 

OBSERVE
element .

 

 

 

     

FORM RULE

 

 

N0

DESIGNATEl
rule as
hypothesis

 

 

 

 
      
   
 

___—

JUDGE HYPOTHESIS

 

 

 

YES

 

NO , JUDGE RULE REPORT

rule

 

 

Figure 18. Strategy V: Formation of a rule by observing
correSpondence between values on the independent variable(s) and the
dependent variable.

 

 

 

 

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

KEY:
WIRES MATRIX
Ln h 0 ' ‘
10ft. 8ft. 6ft. 4f.
'21? #5 #1 m #4 #11
(21 1/4)(21 3/4, 1 23
24 #15 #8 #13
Wire (18 1/2 (19 3/4, 21 1 4 22 l 2
Gauge 28 -' #2
14 l/ 1 0
32 #14 #6
(ll) (16')
36 #12
(9*)
INPUT: set of wires
observation procedure for
how far the needle moves
over (and brightness of
bulb)
variable name: how far the
needle moves over ( and
brightness of bulb)
Instructions
DECODE
, Observation procedure for
how far the needle moves
SCAN ‘ over (and brightness of
elements bulb)
Variable name: how far the
- * needle moves over ( and
brightness of bulb)
.Llnstnuptinns
F. INDEPENDEN GT
CHOOSE IDENTIEILE ll ‘ OBSERVEl ,__,, ELEMENT
wire #9 CATION- wire #9 1 SELECTION
_ (length) (longer)
> ,
”'3 FORM RULE L
3 relating length or wire
3 5., to brightness of the bulb;'—" OBSERVE
°° (The shorter the wire, the wire #10
5‘ less bright the bulb
o burns.
y...
L. 1!
Figure 19. Perfbrmance Model of Subject #5--Wires Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Strategy II

_1

 

DESIGNATEl
rule as
hypothesis

83

 

 

 

 

Strategy 11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

LT
ELEMENT
SELECTION ”'91::EDBEIgXIEUE—1 OBSERVE
(shorter) ness of bulb w1re #12
BL
' ‘ SE JUDGE PREDICTION
Jgggvgggggggve amen #— (We)
:SELECTION
ness of bulb _ (same
.___lengthlgn

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T——__L_.
OBSERVE '
Wire #13 ___+JUDGE PREDICTION ___JJUDGE HYPOTHESIS
(incorrect) (incorrect)
FORM RUEE—E '1;‘
relating length of wire GT
DESIGNATE1 to brightness of the ELEMENT
rule as bulb: the longer the SELECTION
hypothesis wire, the brighter the (longer)
' 1L bulb.
PREDICT VALUE
for bright- __—
ness of bulb .___y
OBSERVE JUDGE PREDICTION
wire #15 (correct)
1*
gr LT
ELEMENT
OBSERVE PREDICT VALUE ’ SELECTION
wire #6 for bright- (Shorter)
ness of bulb
1..
REPORT

(correct)

 

JUDGE PREDICTION)

 

 

--# JUDGE HYPOTHESIS‘

(correct) rule:

 

 

 

 

 

The shorter

the wire is, the
duller the bulb and
the needle won't

move up_as far.

JUDGE RULE , 1
(sure)

 

 

Figure 19.

(continued)

 

 

 

84

in his or her description of the selections made. Figure 20 is a model

of strategy VI. Its use is exemplified in Figure 14.

Consistency of Strategy Use

 

Table 6 shows the strategies used on each problem, with the
exception of the Wires Problem of Subject #3. Conflicting data in the
Activity Protocol and the Stimulated Recall Protocol made the modeling
of that problem performance impossible.

The experimenter had anticipated that a strategy might be
formed for the whole task and that a subject would be either consis-
tent or inconsistent in the use of that strategy across problems. As
one can see in Table 6, these expectations were not met. Rather,
strategies for parts of the task were usually strung together in order
for the subjects to complete the entire task. An alternative analysis
had to be considered. Table 7 displays the strategies used by subjects
on each problem in a different format. Looking at the data this way
allows one to look at the number and identity of the strategies in each
subject's repertoire. It also allows one to examine the number of
subjects using each strategy.

It is interesting to note that five of the eight subjects used
neither of the controlling variables strategies and that one of these
five, Subject #4, used only the two strategies associated with looking
for correspondences between the values on the independent variable(s)
and the dependent variable. It is further interesting to note that
both Pilot Subject #1 and Pilot Subject #2 employed all six strategies
identified.

85

  

MAXPIC
OP
MINPIC

 
 
  

INPUT

 
 

 

  
 
   
 
 

' OBSERVE
element

 

 

   
 

FORM RULE
elating indepen-
tent variable(s)
0 dependent

 
 

DESIGNATEl
rule as
hypothesis

 

 

JUDGE HYPOTHESIS

  
    

 

 

 

NO

  
 

NOT SURE or ,
NO '

   

correct?

   

REPORT

 

rule

  

 

JUDGE RULE
(sure)

  

 

 

Figure 20. Strategy VI: Formation of a rule by selecting
extreme values, a Special case of Strategy V.

86

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88

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89

Summar

Data was reported as to the nature of the rules formed by
the sixth grade students in this study; i.e., whether the rules were
simple or compound rules and whether the rules were correct or not.
The nature of the strategies identified was such that they were modeled
as components of a performance, rather than models of the whole
performance, as had originally been expected. Six strategies that
these Sixth grade children used in finding relations between variables
were identified and modeled. Three of the strategies were used in
testing rules; three were used in forming rules. The numbers of
strategies each subject had in his/her repertoire were determined from

the performance models of each problem by each subject.

90

CHAPTER V

INTERPRETATION OF RESULTS

It is clear that the eight sixth grade children (two from the
formal pilot and six from the actual study) were acCurate in finding
rules involving relations between variables (89% correct). It is
additionally clear that these sixth grade children used strategies when
they were asked to find relations between variables, but that they
differed in the number of strategies they have in their repertoire for
this purpose. (See Table 7.) The strategies identified were compo-
nents of the whole problem performance, rather than strategies for the
whole problem, as had originally been expected.

Performance models were built for each of the eight students
on each of the three problems for a total of twenty-four models. The
experimenter had originally expected to construct a "Best Fit" or
strategy model for the student that would describe the student's
performance on the whole task. Initial efforts found it possible to do
so for a couple of the students, but much difficulty was encountered
when the "Best Fit" approach was applied to the other six students'
performances.

A finer analysis revealed that a problem performance model
could be divided into components and examination of these components
led to the identification of the strategies used by these children. A
given performance model was divided into component sets of processes,

the first set becoming a tentative strategy. Examination of other

91

components in that performance model and in the performance models for
the other two problems revealed whether or not this set of processes
was used in multiple replications. If it was, this set of processes,
by definition, was identified as a strategy. Consistent use of this
methodology to examine all components of the twenty-four performance
models led to the identification of the six strategies found in this
study.

The extent to which the subjects were hypothesis-guided in
finding their rules was not anticipated. Hypothesis formation was
only inferred if, in the stimulated recall session, the subject
indicated that he or she was testing a hypothesis and/or if the
subject predicted values for the dependent variable that indicated the
subject was testing a hypothesis. Strategies I, II, and III, the
rule-testing strategies, all depend upon prior retrieval or formation
of which is a rule, then designated as a hypothesis to be tested. You
will note in Table 8 how often these strategies are used (36 times).
One subject, Subject #6, used only Strategies II and III, implying
that he/she was in a rule-testing mode at all times on all three
problems.

One might speculate that the populations from which the
Children in the pilot work and in the study may be different in some
respect. Whereas, the subject selection procedures were identical, it
is interesting to note that five of the six children in the study are
similar in that they used neither Strategy I nor Strategy IV, the
controlling variables strategies. The two Pilot Subjects, on the

other hand, are similar to each other, but different from the six

92

m»

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m

mum hum
mHg»o»

«H

NO MN mm

Nu—a I HO u—h—c

Nil-4

mgHEgoHIaHga
ag»»mahuaHgm

mgHEgomuaHgm
ag»»mahuaHgm

mgHELoHIaHgm
ag»»mahuaHgm

mgpschIaHgm
ag»»maguaHgm

mgHEgomuaHgm
ag»»mahuaHga

mgpsgoHVaHzm
ag»»mahuaHgm

mgHsgoHVaHgm
ag»»mapuaHgg

mgHsgomuaHgg
ag»»mahua—gm

eaHgogg mag»:

HH

HN HH

NH NC

HH

HO c—n—u NH

agHsgomnaHgm
ag»»mahuaHgm

agHEgoauaHgm
ag»»mahnaHgm

mgHEgoHaaHgm
ag»»mahuaHgg

mgHELoHTaHga
ag»»mahnaHgg

agHELomuaHga
ag»»mahuaHga

mgHEgoguaHgm
ag»»mahuaHza

agHagoHuaHga
ag»»mahnaHgm

mgHsgoHuaHgm
ag»»mapiang

saHgogg mHaagz

(No—4
H

NH HF" NH Ho HO HO Hl-G

mgHsgomuaHam
ag»»mahuaHgm

mgHsgomuang
mgH»mahuaHgg

mgHELoHIaH=m
ag»»mahuaHga

mgHEgomaaHgm
ag»»mahuaHgg

mgwsgouuang
ag»»mapuaHgm

mgHsgoHuang
ag»»mahuapgx

mgHsgoguaHgm
ag»»mahnaHgm

agHENOHIaHgg
ag»»mahsaHga

eangga mega

m»uanggm xg nan: mapma»gg»m mg_Egom1aH=a uga ag»»mahuaHgm No «sagas:

mum
hum

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gN gaahggm
mN gaagggm
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we »uann=m

HN aaanggm

.m a—aah

93

subjects in the actual study, as they employed all six identified
strategies.

Cross-referencing the strategy use data with the rule for-
mation data, one finds that all three incorrect rules were reported
for the Wires Problem and all three rules reported incorrectly
involved the length variable. In each case, the rule reported was
some version of “The longer the wire, the more the needle moves over."
This data suggests that the Wires Problem was, as was anticipated from
the pilot work, the most difficult problem.

Lastly, the experimenter considered the issue of whether or
not the rules reported by the subjects were meaningful to them. One
indication of meaningfulness of the rules would be the subjects'
subsequent use of them in a new task. For example, would the subjects
spontaneously use their rules to make predictions about what would
happen when two Specific elements were tested? A rather ad hoc part
of the interview with each subject after the stimulated recall
session had the subject predict what would happen when pairs of
elements of the experimenter's choosing were tested. A summary of
this data is presented in Table 9.

It appears that the rules formulated by the subjects were
meaningful. Subjects' predictions were consistent with the rules they
had reported 77 percent of the time. Evidence that the subjects used
their rules is most dramatic when an incorrect rule yields an
incorrect prediction consistent with the rule. Predictions from
incorrect rules were consistent 86 percent of the time. Additional

evidence can be found in that, when the variable not mentioned in the

94

ueH\~

acm\~H

am~\mm

n-\mHH

»uaggougH mg: ga>Hm aHgg gag:
»ga»mngougH mgoH»quagg No
ama»gaugag\gage=z

»uaggougH mg: ga>Hw aHgg gag:
»ga»mngcu mch»u_gagg No
amg»gaugag\gags=z

ga>Hw ang g»»3
»ga»mngougH mgoH»quagg No
ama»gaugag\gage=z

ga>Ha aHam g»H3
»ga»mngou mgoH»uHuagg No
ama»gaugagxgagE:z

38 83962.. 8: 2 No Pages .a as:

95

rule was controlled by the experimenter, every prediction was
consistent with the rules given by the subjects, with one exception

(30 out of 31).
Summary

The following interpretations have been made of the data:

1. The subjects in this study were accurate in finding rules
involving relations between variables.

2. It appears that the rules formulated by the subjects were
meaningful; i.e., the subjects used the rules to make predictions
about what would happen when two elements were tested.

3. The sixth grade children in this study used strategies
when they were asked to find relations between variables, but they
differed in the number of strategies they have in their repertoire for
this purpose.

4. It is clear that the subjects were hypothesis-guided in
much of their attempt to find rules.

5. It appears that the pOpulations frOm which the children in
the pilot work and in the study may be different when one compares
their strategy use.

6. It appears that the Wires Problem may be more difficult in
content than the Rods and Wheels Problems, in that all the incorrect
rules (3) were given for this problem. Perhaps prior knowledge or

familiarity with the content of the problems is a factor.

CHAPTER VI

IMPLICATIONS OF THE STUDY FOR EDUCATION AND RESEARCH

This study proposed (a) to identify strategies sixth grade
children use in finding relations between variables and (b) to
determine whether a strategy or elements of a strategy are used
consistently by a child when presented three parallel problems
involving the same task over different content. The primary purpose
for conducting this Study was to gather strategy-use baseline data for

use in formulating explicit educational Outcomes.

Educational Implications

 

The nature of the strategies identified in this study has
implications for how process objectives are viewed. The strategies
identified were modeled as components of the whole task, rather than as
a single strategy for the whole task. Consequently, the experimenter
referred to the set of strategies that a subject demonstrated in
his/her problem performances as a subject's repertoire of strategies.
These repertoires of strategies have implications for how one thinks
about outcomes or process objectives. Perhaps educators should
conceptualize such outcomes as changes in the number and kind of
strategies found in a student's repertoire. '

Six strategies were found to be used by the sixth grade

children in this study to find relations between variables, given a

set of elements, an observation/measurement procedure for the dependent

96

97

variable, and the dependent variable name. These strategies, as well
as any that may be identified through additional research, need to be
evaluated for their appropriateness in the follOwing educational
applications:

1. Curriculum developers could apply the notion of strategies
explicitly in the development of instructional materials. Knowing how
children deal with problems of this type, the developer could sequence
activities with strategy steps clearly defined that would enable the
students to proceed efficiently and directly to the relationship
sought. If the developer was most interested in the process by which
the students find relations; i.e., if he/she was interested in assist-
ing the students in controlling variables, for example, knowledge of
the other strategies for finding relations would hopefully assist the
developer in avoiding pitfalls in sequencing of activities and describ-
.ing steps of the process. If the developer was more interested in the
relationship itself, for example, how pressure affects the volume of a
gas, he/she could suggest the alternative strategies to the teacher so
that the teacher would have at his/her disposal several ways to assist
the students in reaching the goal. The emphasis here is on communi-
cating to teachers and students the strategies that are available.

2. Knowing what strategies are likely to be present in a popu-
lation of students trying to solve these types Of problems might allow
teachers to assess whether or not a task had been performed in an
appropriate way. For example, if the objective is that students
control variables in order to find the relation, knowing explicitly
what other strategies would yield the same result might assist the

teacher in knowing whether that objective had really been met.

98

3. Teachers might be better able to give guidance to the child
having difficulty with the performance of this task if they were aware
of approDriate strategies. In this sense, knowledge of the strategies
would assist the teacher in a remedial function.

4. If appropriate strategies for performing the task were laid
out and taught explicitly to students, it might enable all students to
learn selected tasks more efficiently.

Potential uses for the identified strategies that need to be
researched have been briefly discussed. Beyond that, the argument that
students who cannot yet control variables should not be asked to deal
with situations where relations between variables are sought needs to
be evaluated. If the relationships are important for children to
understand more of the world around them, or if the relationships grow
from an interest expressed by the children, it would seem that alter-
native strategies might be used in order to deal with these relation-
ships, since alternative strategies that yield correct rules do indeed
exist within the population. Furthermore, evidence was found in this
study to show that these rules are meaningful to the children. The
concern would be what effect, if any, teaching alternative strategies
might have on one's eventual ability to control variables. This is an

important issue, needing further research.

Research Implications

 

This section has been divided into three parts: (1) the limi-
tations Of this study, (2) conclusions about the research methodology

for further study, and (3) questions for further study.

99

Limitations of the Study

 

It must be recognized that all research of this kind, where
either "thinking aloud" or the stimulated recall method is employed, is
considered by some critics to be somewhat suspect. G. A. Miller,

E. Galanter, and K. H.-Pribran (1960) outline the potential dangers of
“thinking aloud“:

. . . the task of talking may inhibit the thought

processes, or slow them down, it may make the process

more coherent and orderly then it would otherwise be,

the referents for some of the utterances are not clear,

the subject may fall silent at just the critical moment

when the experimenter would most like to know what he is

doing. But when the method is used intelligently and

conscientiously, it can provide a tremendous amount of

information about the detailed process of thought (p.304).

These same dangers may be posited for stimulated recall.
Shulman and Elstein remind us, however, that de Groot, Kleinmuntz,
Clarkson, as well as Piaget, are among those who “. . . accept verbal
reports as legitimate data and agree that knowledge of the process by
which a problem is solved is at least as important to pyschology as
observing that it was solved” (1975).

It should also be pointed out that the stimulated recall method
used in this study was used as a systematic check of the validity of
the videotaped performances, rather than the sole source of infor-
mation. It would appear that its use in that way becomes a method-
ological strength rather than weakness.

A further limitation is that flow-charting is an abstract
representation of a process with distinct pieces or boxes—~one process

occurs, produces an output, then feeds into another process--a

distinctly mechanical linear process. The mental processes of an

100

individual may not be linear or serial. In fact, Neisser (1963)
proposes that thought is best described by multiple processes rather
than by sequential processes.

My thesis is that human thinking is a multiple activity.
Awake or asleep, a number of more or less independent trains
of thought usually coexist. Ordinarily, however, there is a
'main sequence' in progress, dealing with some particular
material in step-by-step fashion. The main sequence corres-
ponds to the ordinary course of consciousness. It may or may
not be directly influenced by the other processes going on
simultaneously. The concurrent operations are not conscious,
because consciousness is intrinsically single: one is aware
of a train of thought, but not of the details of several.

The main sequence usually has control of motor activity.

Cases where it does not (where behavior does not correspond to
consciousness) impress the observer as bizarre or patholog-
ical (p. 316).

Neisser seems to be saying that there is a main stream of processes
that function in consciousness, but that this main stream may be
influenced by multiple processing not occurring in consciousness.
Caution should, therefore, be applied in interpreting the flow charts

as other than models that help us understand what we believe to be the

 

main stream thought processing that leads to the solution of a problem.
The models are not meant to imply that the actual processes are either
linear or serial in the strictest sense.

Finally, a caution about generalizability needs to be given.
Mention has already been made Of the fact that the study subjects and
the pilot subjects appear to have come from two somewhat different
populations. Five of the six children in the study are similar in that
they used neither Strategy I nor Strategy IV, the controlling variables
strategies. The two Pilot Subjects, on the other hand, are similar to
each other, but different from the six subjects in the actual study, as

they employed all six identified strategies. Even given that

101

difference, however, it should be noted that strategies I, II, III, V,
and VI do appear in both populations.

Additionally, a reminder needs to be made that the subjects in
the study were chosen partially on the basis of a screening instrument,
the Particle Test. Only subjects who scored at least five out of nine
on this test were considered for the study. Those finally selected had
to meet two other criteria: (1) that the subject had been in the
school system and, consequently, in the S.C.I.S. program, for at least
three grade levels; and (2) that the subject be described by his or her
teacher as verbally fluent in his/her classroom explanations. When the
screening instrument was administered to the population of students
from which the study subjects were selected, 32.7% scored at least five
out of the possible nine. In a previous study (Dennison et al., 1976),
32.5% of the sixth grade students achieved a score of five or more on
the instrument. This data would suggest that some generalizability

beyond the immediate population could be made.

Conclusions About the Research Methodology

 

The stimulated recall technology proved to be an essential
ingredient in the discerning of differences between student's strat-
egies. The guidelines for analyzing the stimulated recall protocols,
appearing in Appendix F, are some indicator that this part of the
Inethodology was used conservatively. The stimulated recall protocols
were used primarily to validate or disconfirm evidence from the
activity protocol, although they did provide valuable additional

'insight into the performance of the students.

102

It should be noted, too, that the process of transcribing and
analyzing both the activity and stimulated recalls is very tedious and
time-consuming. The objective of one's endeavor should clearly dictate
such procedures; they should not be pursued when other methodologies
might produce comparable quality results.

Finally, the point should be made that the modeling of both
performance and strategies is still in its infancy and can and should

be continually refined as additional studies of this kind are pursued.

Questions for Further Study

The following areas need additional study:

1. Studies of this kind need to address problems that require
students to find relations between variables that are more curriculum-
based; e.g., the study of how students determine how weight affects the
flight of a paper airplane in Science Curriculum Improvement Study
(S.C.I.S.).

2. As mentioned in the section on Educational Implications,
studies need to be conducted to determine if learning one taught
strategy for finding relations between variables influences one's
ability to learn another strategy at a later point; e.g., if being
taught the extreme value selection strategy at one point would affect
one's ability to learn to control variables at a later point.

3. Studies to determine whether there is any developmental
relationship to the number and/or type of strategies in one's reper-
t<3ire need to be carried out. The patterns seen in Table 7 seem to

iridicate there might be.

REFERENCES

REFERENCES

Anderson, J. R. Lan ua e, memor , and thou ht. Hillsdale, New Jersey:
Lawrence Erlgaum Associates, 1976.

Anderson, J. R., & Bower, G. H. figmgn gssggiative mgmgry. Washington,
D. C.: V. H. Winston, 1973.

Baylor, G. W., & Gascon, J. An information processing theory of
aspects of the development of weight seriation in children.
Eggnitive Psychology, 1974, 6, 1-40.

Bessemer, D. W., D Smith, E. L. The role of skills analysis in
instructional design (TN 2-72-50). In D. W. Bessemer &
E. L. Smith (Eds.), The integration of content, task, and
kill i t hni i i r ti n .
Southwest Regional Laboratory, 1972.

Bruner, J. The process of education. New York: Vintage Books, 1963.

Dennison, J. H., & Smith, E. L. Determination of relations between
visual variables by sixth grade children. Paper presented
at the National Association for Research in Science Teaching,
San Francisco, California, April, 1976.

Finley, F. N. Vertical transfer of instruction based on cognitive

strategies fOr a sequence of eolo*ic tasks. UnpubliShed
30ctora1*diSsertation, Michigan State University, 1977.

Frija, N. H. Simulation of human long-term memory. Psychological

Bulletin. 1972. 21 (11. 1-31.

Gagne, R. U. Essentials of learnin for instruction. Hinsdale,
Illinois: *Dryden Press, 19 42

Gagne, R. U. The conditions of learning. New York: Holt, Rinehart,
and Winston,T1965.

Gagne, R. U. The conditions of learning (2nd ed.). New York: Holt,
Rinehart, and Winston, 1970.

Greeno, J. 6. Cagnitive objectives of instruction: Theory of
knowledge for solving problems and answering questions. In
D. Klahr (Ed.), C nition and instruction. Hillsdale, New
Jersey: Lawrence rlbaum Associates, 1976.

Kagan, N. IPR-media in_glinical and humgg interaction supervision.
East Lansing, Michigan: Michigan State University, 1976.

 

104

105

Kintsch, W. The representation of meaning in memory. Hillsdale,
New Jersey: Lawrence Erlbaum Associates, 1974.

Krutetskii, V. A. The psycholggy of mathematical abilities in school
age Children (JT’KiTpEtrick76 I. Wirszup, Eds. and J. Teller,
Trans.). Chicago: University of Chicago Press, 1976.

 

 

Mager, R. F. Preparing instructional objectives. Belmont,
California: Fearon PubliShers, 1962.

 

Miller, G. A., Galanter, E., & Pribram, K. H. The formation of plans.
In P. C. Wason & P. N. Johnson-Laird (Eds.), Thinking &
reasoning. Baltimore: Penguin Books, 1968.

Neisser, U. Cpgnitivg psychology. New York: Appleton-Century-Crofts,
1967.

 

Neisser, U. The multiplicity of thought. In P. C. Wason & P. N.
Johnson- Laird (Eds. ), Thinking,& reasoning. Baltimore:
Penguin Books, 1968.

Newell, A., & Simon, H. A. Human problem solving. Englewood Cliffs,
New Jersey: Prentice-Hall, 1972.

Norman, D. A., & Rumelhart, D. E. Explorgtjons in cognition.
San Francisco, Freeman, 1975.

Padilla, M. J. Thg teaching and transfer of seriation strategies
us1'ng nonvisual variables with first grade clhildren. Unpub-
lished doctoral dissertation, Michigan State University, 1975.

 

Egplicgtion manual of thggAmerican Ps cholo ical Association
(2nd ed.). Washington, D. C.: American Psychological
Association, 1974.

 

Resnick, L. 8. Task analysis in instructional design: Some cases
from mathematics. In D. Klahr (Ed.), C nition and instruc-
tion. Hillsdale, New Jersey: Lawrence rlbaum Associates,
I976.

 

Shulman, L. S., & Elstein, A. S. Studies of problem solving, judgment,
and decision making: Implications for educational research.
In F. N. Kerlinger (Ed.), Review of research in education, 3.
Itasca, Illinois: Peacock, 1975.

Shulman, L. S., & Shroyer, J. ,Esychologypand mathematics education
revisited: 1976. East Lansing, Miéhigan: Michigan State
University,71976.

106

Shulman, L., & Tamir, P. Research on teaching in the natural sciences.
In R. Travers (Ed.), Second handbook of research on teaching.
Chicago: Rand McNally, 1973.

Smith, E. L. Analytic concepts and the relation between content and
process in science curricula (TN 2-72-56). In D. W. Bessemer
& E. L. Smith (Eds.), The integration of contenti task, and
skills analysis techniques in instructional design. Southwest
REgional Caboratory, 1972.

 

Smith, E. L. Techniques for instructional design. Paper presented at
the American Educational Research Association Annual Meeting,
Chicago, Illinois, April 16, 1974.

Smith, E. L., McClain, J. J., & Kuchenbecker, S. A skills analysis of
selected primary level science tasks (TN 2-72-60). In D. W.
Bessemer & E. L. Smith (Eds.), The integration of contentL
tasks, and skills analysis techniques in instructional design.
Southwest"RegiOna1 Eiboratory, 1972.

Smith, E. L., & Padilla, M. J. Strategies used by first-grade children
in ordering objects by weight and length. Paper presented
at the National Association for Research in Science Teaching
Annual Meeting, Los Angeles, California, March 18, 1975.

Smith, E. L., & Sendelbach, N. Development and tryout of the science
teacher planning simulatibn system. East Lansing, Michigan:
MiChigan State Ufiiversity, I977. .

APPENDICES

APPENDIX A

THE METHOD OF SUBJECT SELECTION
AND
CRITERION DATA ON POTENTIAL SUBJECTS

107

The Method of Subject Selection

'Three criteria:

1. that the subject had been in the school and, cOnsequently,
in the S.C.I.S. program, for at least three grade levels;

2. that the subject score at least five out of nine on a
screening instrument, the Particle Test; and

3. that the subject be described by his teacher as being
verbally fluent.

All of the subjects listed below met the second criterion;
‘i.e., had scored at least five out of nine on the Particle Test. The
Tactual score is given in parentheses after the letter identifying the
subject. An X in the columns headed “Criterion 1" and ”Criterion 3"
indicates that these criteria were met. If the subject did not meet
(:riterion 1, the teacher was not queried as to whether they met
<:riterion 3. These subjects have blanks in the column for criterion 1
and question marks (7) in the column for criterion 3.

The column headed ”Subjects Identified by Number Used in the
Study“ indicates the subjects that were actually selected from those
‘ttmat were considered potential subjects based on their Particle Test
performance. The numbers are their subject identification numbers.

Table 10.

Subjects Identi-
fied by Number
in the
Study

Classgoom A

3
5

Classroom 8
6
2
4

Subjects
That Met
Criterion 2

DOW)

f-KCHHIG'HM

me'UOZ

Criterion Data on Potential Subjects

(7)
(7)
(7)
(9)

(5)
(6)
(5)
(6)
(6)
(5)
(6)
(8)

(5)

(5)
(5)
(6)
(5)
(5)
(7)

108

Criterion 1 Criterion 3

XXX

xxx

xx

><><><><><

XXXX

'90s)

XXX

Comments

out with
appendici-
tis

on vacation-
study time
schedule did
not permit
waiting for
subject's
return

APPENDIX 8

DESCRIPTION OF PARTICLE SETS

109

v N H gnN
N m N aim
H H m 0..H
m e c one
m m m tum gzogn
m m m cum
e e v ate
m H m uuH
N m N uum
H N H qu was
H N v niN
N m N aim
m H H uuH
v v m one
m m m aim gross
m m H aim
e v m one
H m m gum
m N e anN
N H m anH was
m m N gum
v e m use
m m H uum
N N v 01N
H H m 61H 630.5
H N m aiN
N m o vim
m H m guH
c v N use
m m H uum maps

aHgggog

aaaLHe

aHgggog

amgang

aaagpe

amga>gH

gmmmzx¢<o mmmuzm¢<zm NNNHm szHmua mogou mm>h wgaz

m»am aHuH»gag No goH»gngmao

.HH aHga»

ua»gHag »og
aNHm egg mmagggggm

gagegg ag» .gammHg ag»

ga»gHag »og

mmagxgou egg aNHm

ga—HgEm ag» .Eaggagm agh

gaggagm ag» .gaxgag agh

eaNgNHH ag» .gaNNHg ag»
Nggg

H
:th

lIO

.uooHnm .ucmue .uomam .uomnN

.uoHuH

"ago magHo> ag» .aH»maHo »gagoomgag» ag» goN .»gH» ae oa»mHH ag» go oamag ago mag—g) mmaggggo agHg

. cmum . cone . calm . ONHIN . omHuH "ago
magHa> agH .m»gHoo .maHaH»goo ag» Hg gaggom maHoga gnga»gH ag» go gamma ago maoHo> mmagogogm agHm

.Eumum ..EoH\H Nuv ..EUN-m ..suN\H HiN ..EoH-H "ago ga»aso_o amaga>o ag» go oamgg .maoHo> a~

_a afiN

.agHo>

mmagogogm g»g=oN ag» Low gmHmao »gagaNNHo a mH egies aHng agHg> mmagogogm ogHg» ag» Low gmHmao
a m» scum: mogh .aoHo> mmagogagm guoa go» a>HN .oam: agaz mgmHmao aHuH»goo agngo a>»»-»»ga3»H

oa»aHag »og
gag aHgggog mmagogggm ogg mmagxggo

UUDU‘UUU?QQUU~~U
mQMNHHNMGmLflVMNv—O

ang »aagHo gammHg ag» .gaogogm agh

ogagm
agHg amga>gH mmaH ag» .gaxgao agp

HNMQLONLOHQ’MMLDt—ONQ’
WQMNHHNMVLOLDQ'MNH
NWHQ‘MHNMVU’MVHMN

mmmzxm<o mmmzmm<zm “NHm zmHmua moHou mm>h mgaz mgam
HuaagHugouv mpwm uglo¢<m mo onhmHaumma

:th

APPENDIX C

TASK PROTOCOL FOR DETERMINING
CORRELATIONAL RULES -
PARTICLE TEST
AND
OBSERVATION RECORD FOR PARTICLE TEST

Example 1

111

TASK PROTOCOL FOR DETERMINING
CORRELATIONAL RULES -
PARTICLE TEST

Introduction

1. Present in triangular arrangement the three cylinders,1

2. WHICH IS
WHICH IS
WHICH IS

3. NOW PICK
WHICH IS
WHICH IS
WHICH IS

THE TALLEST CYLINDER ?
THE NEXT TALLEST CYLINDER ?
THE SHORTEST CYLINDER 7

UP EACH CYLINDER TO SEE HOW HEAVY IT IS.
THE HEAVIEST 7

THE NEXT HEAVIEST 7

THE LIGHTEST ?

4. WE CAN MAKE A RULE FOR THE HEIGHT AND WEIGHT OF THE CYLINDERS.

THE RULE

IS “THE TALLER THE CYLINDER, THE HEAVIER IT IS.“

00 YOU UNDERSTAND THE RULE ? (If not, state the order of the
objects on the two variables and repeat the rule.)

CAN YOU TELL ME THE RULE? (If not stated correctly, state the
rule and continue.)

1The cylinders were cut from the same metal material at different
lengths, so that height and weight were directly proportional.

112

Example 2

WE HAVE MADE A RULE FOR THE HEIGHT AND WEIGHT OF THE CYLINDERS. NOW
LET‘S TRY TO FIND ANOTHER RULE.

1.

Present in triangular arrangement the three bottles.1

SHAKE EACH BOTTLE TO SEE HOW THICK EACH LIQUID IS.
WHICH HAS THE THICKEST LIQUID 7

WHICH HAS THE NEXT THICKEST LIQUID ?

WHICH HAS THE THINNEST LIQUID ?

NOW TURN EACH BOTTLE UPSIDE DOWN TO SEE HOW FAST EACH MARBLE FALLS.
WHICH FALLS THE FASTEST 7

WHICH FALLS THE NEXT FASTEST 7

WHICH FALLS THE SLOWEST 7

WE CAN MAKE A RULE FOR THE THICKNESS OF THE LIQUID AND THE SPEED
OF THE MARBLE. THE RULE IS, “THE THICKER THE LIQUID, THE SLOWER
THE MARBLE FALLS.“

DO YOU UNDERSTAND THE RULE? (If not, state the order of the
objects on the variables and then repeat the rule.)

WHAT IS THE RULE ? (If not stated correctly, repeat the rule and
continue.)

1One bottle contained water, the second a mixture of Karo syrup

and'water, and the third pure Karo syrup. Each contained a marble.

113

TEST QUESTIONS

 

WE MADE A RULE FOR THE HEIGHT AND WEIGHT OF THE CYLINDERS. WE MADE
ANOTHER RULE FOR THE THICKNESS OF THE LIQUID AND THE SPEED OF THE
MARBLE. SOMETIMES THERE ARE RULES LIKE THESE AND SOMETIMES THERE ARE
NO RULES.

NOW I AM GOING TO SHOW YOU SOME OTHER THINGS. I WOULD LIKE YOU TO SEE
IF YOU CAN FIND ANY RULES FOR THEM.

I AM GOING TO TAKE THE TIME WE SPEND ON EACH TASK, BUT YOU DO NOT NEED
TO HURRY. TAKE AS MUCH TIME AS YOU NEED TO GIVE ME YOUR ANSWER. YOU
MAY MOVE THE THINGS I GIVE YOU IF YOU LIKE.

REMEMBER THAT SOMETIMES THERE ARE RULES AND SOMETIMES THERE ARE NO
RULES. DO YOU UNDERSTAND WHAT YOU ARE TO DO?

For each item, present the particles in a random pile partially
overlapping. Make sure they are all right side up.

IS THERE A RULE FOR THE AND OF THESE PARTICLES?

Guidelines

 

If unclear whether or not S is finished and a statement is intended as
his answer, ask, “IS THAT YOUR ANSWER?“ (DO not stop the watch unless
he says “yes.")

If the time reaches 60 seconds and no response has yet been given, stop
the watch and repeat the question. If no response is given in 5
seconds, record “no response." Record a time of 61 seconds.

If the child's statement is not understood, ask “WHAT DO YOU MEAN BY
7“ Avoid open-ended probing.

 

If the child orders the objects, record the order of the objects on the
variable used to order.

114

 

m»gHoo
No mmagogogm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ago mmagggog (zeal m
aNHm ogg m»gHoH «Ho
No mmagogogm mxo m
mugwqm ,
No mmagogggm >zH
ogg mmagxggo gxo N
aNHm oga m»g_og
No mmagogagm zoz m
mmaggggo gHo
ego aNHm oxm m
mmagxgag 1111
oga aNHm zcz e
aNHm ogg m»gHog >zH
No mmagogogm mxo m
1m»g_om
No mmagogggm «Ho
ogo mmagxggo gxo N
.wwuumuqa. >zH
oga aNHm oxm H
mhzmzzou Huumv macaw mmzogmmz onpmmao “gag .oz
quh zth zuhH
gmhmm» H.o: az<.m¢>v
goozum
sat:
.m»w3ao.gH mega» No .oz bmmh uguHh¢<o
gaguoa» mom macaw: onh<>aummo

 

a»ao

APPENDIX D

PROTOCOLS FOR THE ADMINISTRATION
OF THE PROBLEMS
AND STIMULATED RECALL
AND
OBSERVATION RECORDS FOR
THE THREE PARALLEL PROBLEMS

115

PROTOCOL FOR THE
ADMINISTRATION OF THE
PROBLEM: COLORED WATER
AND STIMULATED RECALL

(Name), this is not a test. We are interested in how you go
about trying to find a solution to a problem so we can design activ-
ivities to help other students your age do them.

Have you every been videotaped before and seen yourself on TV?
Mr. Dennison has been videotaping us and will let us see it now.

I have a science task for you to do. Mr. Dennison will be
videotaping what we do here today. We will get to see it later. Try
not to pay any attention to the camera, but rather focus on what I am
going to ask you to do.

Now, as you are thinking about or doing something with the
problem I give you, I want you to think aloud. You do this sometimes,
don't you, when you are solving a problem alone at home? Just say out
loud whatever comes into your head. Don't worry about us understand-
ing. You can explain later.

Take as much time as you need to give me your answer to the
problem. Tell me your answer whenever you think of one, but keep
working until you are very sure of your answer. 00 you understand
these instructions?

I have this box over here. I have poured colored water in
these funnels--red here, blue here, and yellow here. You are to try to
figure out what might be inside the box that explains what you are.
about to see. Watch carefully.

Over here we have more colored water and some tumblers.
Without using the box, you may do whatever you want to with the water
to try to figure out what might be inside the box that explains what we
just saw happen. You may use that pencil and paper, too, if you want
to. Do you have any questions?

As you know, we have a Video recording of your activity. We
are now going to watch that recording. As you were doing this activ-
ity, many thoughts probably passed through your mind. (Some of these
you may have written down or said out loud.) As we watch the tape, 1
would like you to recall any thoughts or feelings that occurred to you
at that particular point during the activity. For example, you may
have remembered other things, either from your classroom or home. I
want to know about all these things. As we watch the tape, I want you
'to tell me when to stop it whenever you recall anything that you
‘thought at that point in the activity, I want to know as much as I can
about what you were thinking while you were doing this activity. 00
.You have any questions about this procedure?

116

PROTOCOL FOR THE
ADMINISTRATION OF THE
PROBLEM: RODS
AND STIMULATED RECALL

I have another science task for you to do today. Mr. Dennison
will be videotaping what we do just like he did (day).

Now, as you are thinking about or doing something with the
problem I give you, I want you to think aloud. Just say out loud
whatever comes into your head. Don't worry about g5 understanding.
You can explain later.

Take as much time as you need to give me your answer to the
problem. Tell me a rule whenever you think of one, but keep working
until you are very sure of your rule. 00 you understand these
instructions?

The first day I met with you we did the activity with the
plastic particles. Do you remember?

Let's review a couple of the rules we found that day. Do you
remember what they were? Can you tell me the rules?

This is a rod holder and these are rods. Notice that the rods
all have a notch on one end. The rod holder works like this: you slide
the rod in until it touches the backboard and won't slide any more,
make sure the notch is on top, and then screw it down. You can then
hang this weight on it. See how the rod bends?

I have given you this whole set of rods. You are to try to
find a rule for these rods. You may use as many of them as you want to
before you tell me your rule. You may also use pencil and paper, too,
if you want to. Remember to try to think out loud as you work. What I
am most interested in is hg!_you are doing the activity.

As you know, we have a video recording of your activity. We
are now going to watch that recording. As you were doing this
activity, many thoughts probably passed through your mind. (Some of
these you may have written down or said out loud.) As we watch the
tape, I would like you to recall any thoughts or feelings that occurred
to you at that particular point during the activity. For example, you
may have remembered other things, either from your classroom or home.

I want to know about all these things. As we watch the tape, I want you
to tell me when to stop it whenever you recall anything that you
thought at that point in the activity. I want to know as much as I can
about what you were thinking while you were doing this activity. 00
you have any questions about this procedure?

117

PROTOCOL FOR THE
ADMINISTRATION OF THE
PROBLEM: WHEELS
AND STIMULATED RECALL

I have another science task for you to do today. Mr. Dennison
will be videotaping what we do just like he did (day).

Now, as you are thinking about or doing something with the
problem I give you, I want you to think aloud. Just say out loud
whatever comes into your head. Don't worry about us understanding.
You can explain later. "'

Take as much time as you need to give me your answer to the
problem. Tell me a rule whenever you think of one, but keep working
until you are very sure of your rule. 00 you understand these
instructions?

Let's review a couple of the rules we have found. 00 you
remember what they were? Can you tell me the rules?

In front of you is a piece of paper, some pairs of wheels, and
a container of chalk dust. Roll a pair of wheels around in the chalk
dust, put it down on the paper, and give it a push like this. See how
the pair of wheels rolls to make a circle?

I have given you this whole set of pairs of wheels. You are to
try to find a rule for these pairs of wheels. You may use as many of
them as you want to before you tell me the rule. You may also use
pencil and paper, if you want to. Remember to try to think out loud as
you work. What I am most interested in is hgw you are doing the
activity.

As you know, we have a Video recording of your activity. We
are now going to watch that recording. As you were doing this
activity, many thoughts probably passed through your mind. (Some of
these you may have written down or said out loud.) As we watch the
tape, I would like you to recall any thoughts or feelings that occurred
to you at that particular point during the activity. For example, you
may have remembered other things, either from your classroom or home.

I want to know about all these things. As we watch the tape, I want
you to tell me when to stop it whenever you recall anything that you
thought at that point in the activity. I want to know as much as I can
about what you were thinking while you were doing this activity. 00
you have any questions about this procedure?

118

PROTOCOL FOR THE
ADMINISTRATION OF THE
PROBLEM: WIRES
AND STIMULATED RECALL

I have another science task for you to do today. Mr. Dennison
will be videotaping what we do just like he did (day).

Now, as you are thinking about or doing something with the
problem I give you, I want you to think aloud. Just say out loud
whatever comes into your head. Don't worry about gg understanding.
You can explain later. '

Take as much time as you need to give me your answer to the
problem. Tell me a rule whenever you think of one, but keep working
until you are very sure of your rule. 00 you understand these
instructions?

Let's review a couple of the rules we have found. 00 you
remember what they were? Can you tell me the rules?

On the board in front of you is attached a light bulb, a meter,
and a power source. Over here you see boards with wires wrapped around
them. The boards can fit into this slit. Then you can attach the
wires like so. Each time I will turn the power source to 10. See how
the needle on the meter moves? ‘

I have given you this whole set of wires. You are to try to
find a rule for these wires. You may use as many of them as you want
to before you tell me the rule. You may also use pencil and paper, if
you want to. Remember to try to think out loud as you work. What I am
most interested in is 22: you are doing the activity.

As you know, we have a Video recording of your activity. We
are now going to watch that recording. As you were doing this
activity, many thoughts probably passed through your mind. (Some of
these you may have written down or said out loud.) As we watch the
tape, I would like you to recall any thoughts or feelings that occurred
to you at that particular point during the activity. For example, you
may have remembered other things, either from your classroom or home.

I want to know about all these things. As we watch the tape, I want
you to tell me when to stop it whenever you recall anything that you
thought at that point in the activity. I want to know as much as I can
about what you were thinking while you were doihg this activity. Do
you have any questions about this procedure?

119

USING THE OBSERVATION
RECORDS FOR
THE THREE PARALLEL PROBLEMS

The experimenter records on the observation record the sequence
of each element observed by placing an appropriate numeral (1, II, 111,
etc.) in the appropriate cell of the observation record form.

120

 

NM\m

 

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Nm\m

 

mH\m

 

 

 

 

 

 

 

NM\N

 

N humamzm

zu4moam moom
mam smegma zo~h<>ammmo

121.

 

m\mH

 

m\mH

 

m\HH

 

m\m

 

 

 

 

 

 

 

m\~

 

Q:

N panamam

mme

m\MH mxHH

twqmomm mHmm:3_
mom amouwm chh<>¢ummo

m3

122

 

om

 

 

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mN

 

eN

 

 

 

 

 

 

 

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.»N m .»w m

zmgmcmm mmzH:
mom amoun: onh<>¢mmmo

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APPENDIX E

TYPICAL QUESTIONS ASKED OF
THE STUDENTS IN THE
STIMULATED RECALL

123

Typical Questions Asked of the
Students in Stimulated Recall*

1. Did you have any ideas about what you were supposed to do
at that point?
2. Had you thought of a rule by this time?

3. The first one you picked was #4.
Was there any reason for your choosing #4?

4. Were you looking for something in particular?

5. Did you expect anything in particular to happen when you
tested #4?

6. Was there some reason you thought it would (do whatever
was predicted)?

*Encourage more complete answers when the child says only "yes.“
Do not probe further where the child says ”no.“

APPENDIX F

GUIDELINES FOR MAKING INFERENCES
AND ANALYZING PROTOCOLS

124

Guidelines for Analyzing Protocols

For each problem, you are given the following materials:
1. A description of the problem

2. An activity protocol

3. A problem matrix

- #5, #8, etc. represent the labels (chosen randomly)
on the set of elements.

- The numbers in parentheses, ( ), are the values of the
dependent variable for that element.

- I, II, III, etc., are the moves to test elements that
the subject made.

4. A stimulated recall protocol
5. Definitions of processes used to model performance

6. An example analysis

Analyzing the Activity Protocol

1.

Read through the entire activity protocol, referring to the
problem matrix, to get a feel for what the subject was doing
and what s/he saw. This overall sense of what is going on will
assist you in making inferences.

Inferences for the Activity Protocol will be referred to as AI'S
and should be recorded to the far right of the sheet. An
inference should be labeled. All-17 means an inference made from
the activity protocol, page 1, beginning on line 17. You may want
to make more than one inference for a single line in the protocol.
Inlthgt case, employ a's, b's, etc.; for example, All-17a,

AI - b.

125

Analyzing the Stimulated Recall Protocol

1. Using the activity protocol and the problem matrix, review the
stimulated recall protocol.

2. Inferences for the Stimulated Recall Protocol will be referred to
as SI's and should be recorded to the far right of the Sheet. An
inference should be labeled. SI3-4 means an inference made from
the stimulated recall protocol, page 3, beginning on line 4.
Again, you may want to make more than one inference for a single
line in the protocol. In that case, employ a's, b's, etc; for
example, SI3-4a, SI3-4b.

3. Three kinds of inferences should appear in the Stimulated Recall
Analysis.

a) Inferences that support AI's or SI's that appear
earlier in the protocol. You should declare and label
' the inference, then indicate that it supports an A1 or
SI. For example, S predicts value for bending of
rod; supports $11-11.

b) Inferences that disconfirm AI's or 51's that appear
earlier in the protocol. You should again declare and
label the inference, then indicate that it disconfirms
an A1 or 51 above. Identify the earlier inference by
its label.

c) Inferences that are based on new information in the
stimulated recall.

Specific Decision-Making Guidelines

1. Example: S takes #3, tests it.

Interpretation: S selects #3. If it is the
shorEesE or longest or thinnest or
whatever, this should be included,
such that the inference might look like:

All-3a S selects thinnest and
shortest rod.

Interpretation: After 5 selects #3, s/he observes it.
An additional inference based on this
same piece of information in the activity
protocol might be:

AI1-3b S observes #3.

126

Specific Decision-Making Guidelines (continued)

2.

Failure to select elements where the variables are controlled
consistently is taken as evidence that the subject was not inten-
tionally trying to control variables, unless of course, s/he
mentions an attempt to control variables.

When a subject gives a rule after doing his/her tests on the
elements, you assume the subject encoded information about the
variables mentioned in the rule while doing the tests. An
additional comment that can be made is that 5 reports rule.

If S predicts a value for the dependent variable, assume that the
prediction was hypothesis-generated.

Do not assume 5 has attempted to select an element with extreme
value on one or both variables unless the superlative terms (for
example, biggest, smallest, thinnest, etc.) are used by the
subject.

If S indicates s/he made a prediction about the value of the
dependent variable, and answers in the affirmative when asked, “Is
that what you expected?" you may infer that S judges prediction

to be correct. If s/he answers in the negative, you may infer

that 5 judges predigtipp to be incorrect.

S selects an element only if some justification for doing so is
indicated in the stimulated recall. Otherwise, S chooses or

 

chooses 1 elements.

It may be necessary to indicate in a single square box that subs
ject MAXPIC'S on one independent variable and MINPIC'S on the
other independent variable (or some other combination) simulta-
neously, if S is, indeed, attending to both independent variables
at the same time.

Only indicate the retrieval of a rule if no observations have
been made.

APPENDIX G

DEFINITIONS OF THE PROCESSES
USED IN MODELING
THE PERFORMANCES
AND
STRATEGIES

127

DEFINITIONS OF PROCESSES

LEGEND: No Symbol Smith et.a1., 1972
* Padilla, 1975
Finley, 1977
Newly defined process
for purposes of this

study

**
+

PRIMARY PROCESSES RELATED TO LONG TERM MEMORY

Several processes involve gaining access to information avail-
able in the individual's long-term memory. The demands made on a
model of long-term memory in defining the primary processes include
specification of the nature of the information stored, the kinds of
information which can be used to gain access to stored information,
and the major processing steps distinguished.

Frijda (1972) describes a model of long-term memory, some
version of which is utilized in nearly all information processing
theories and simulations. According to this View, information stored
is an associative network of items or nodes, each leading to any
number of other nodes-—the associations of the first node. The stored
items or nodes are generally considered to be concepts or ideas
themselves rather than names used to refer to them or images exempli-
fying them. Although this is a somewhat vague position, the important
point seems to be that what is stored is not words or images, but
rather information from which words, images and actions are recon-
structed, as proposed by Neisser (1976). Thus, once activated or
accessed, a node makes immediately available a number of operational

options. Nodes are accessible by way of other nodes to which they are

128

linked, by way of items or stimuli that in some sense resemble them
(i.e., that resemble some level of reconstruction), or through the

decoding of labels that refer to them.

DECLINE.

This is the primary process by which an associative network is
entered by way of verbal label for one of the constituent concepts.
The input for the process is the verbal label. Decoding of the label
results in the activation of a concept or node in the network. This
does not necessarily result in the reconstruction of images, actions,
or verbal entities. In effect, the DECODE process Opens the way to
many possibilities, but it remains for the next step(s) to take
advantage of one or more of them. The possibility that the individual
is set to perform another step which then follows automatically from
the decoding need not concern us here. The point is that access to
the storage network must be gained as a result of processing the
verbal label. This is the function of the DECODE process.

+ The use of DECODE in the present study acknowledges that»
nonverbal communications, as well as verbal labels, may be input for
the activation of a concept or node in the network. Consequently,
access to the storage network may be gained as a result of processing

some nonverbal comunication.

129

RETRIEVE

Once a node in an associative network has been activated; e.g.,
by DECODE, access is gained to other nodes in that network. However,
some directing process insures that the appropriate node(s) is
activated next. This involves the RETRIEVE primary process. The
nature of this directing mechanism is not further elaborated here. At
present it seems sufficient to say that it is capable of directing the
RETRIEVE process to a connected node which is related to the original
node in a specific way. Thus, the input of RETRIEVE can be charac-
terized as one concept and its output as another. Just as was the
case with DECODE, RETRIEVE does not output any images, words or
actions although it does make such further steps an immediately
available Option. RETRIEVE can usually avoid retrieving a recently
retrieved node through short-term recall of associated information.
This allows the process to recycle efficiently until appropriate

information is obtained.

*RETRIEVE 1

 

RETRIEVE 1 is a primary process similar to RETRIEVE in that it
is a directing process that insures that the appropriate node(s) is
activated. However, RETRIEVE 1 deals in part with short-term memory
as well-as long-term memory. It involves the retrieval of values from
long-term memory and the retrieval of the salient characteristics of
the objects to which the values belong as well as the connection

between the values and the objects.

130

INPUT STIMULUS ANALYZING PRIMARY PROCESSES

Several primary processes are defined which seek and analyze
input. .Input is viewed as containing an enormous amount of infor-
mation, only a portion of which is attended to or detected by the
individual on a given occasion. Analysis of the input is viewed as
taking place at different levels, each level involving its own unique
kind of processing. Preattentive processes have a large capacity for
parallel activity. They construct perceptual "objects” in a figure-
ground differentiation sense. These processes are limited, however,
in the level of detail and precision they represent. Basically, they
signal when more detailed analysis of particular input by other
processes is warranted. The higher level processes which require
attention are linear. They construct detailed images and are more

selective.

SCAN_

This is a primary process which represents a rather cursory,
largely visual, exploration of the stimulus field. It establishes a
figure-ground differentiation of objects and detects a few salient
features which may enter short-term store. However, only partial
information is obtained, even in the Visual modality. Detection of
certain salient and/or relevant features usually terminates the SCAN
process, or at least relegates it to a background role, and triggers
some attentive processing. Thus, the input to SCAN is undiffer-
entiated stimulus information while the output is one or more differ-
entiated perceptual objects. In most cases, many features which are

relevant from a formal point-of-view are not detected by SCAN.

131

CHOOSE

 

This is a primary process which operates on a set of stimulus
objects previously differentiated; e.g., by SCAN. The output is one
object which then becOmes the focus of attention. The criteria for
this selection are not formal. Rather, such factors as Visual
accessibility, proximity to the observer, and the relative saliency of
detected features are employed. From a formal point-of-view, the
process is essentially a random selection. One exception is that
CHOOSE can usually avoid selecting previously chosen objects by
utilizing feature information stored in short-term memory. This

information may well be otherwise irrelevant to the task at hand.

*CHOOSE 1

CHOOSE 1 is a primary process similar to CHOOSE in nature, but
differing from CHOOSE in that some criterion is used for the choice.
CHOOSE implies a certain randomness of choice, or at least a choice
based on such non-salient factors as proximity to the chooser or
visual accessibility. CHOOSE 1 implies a choice which is non-random,
which is based on some salient criterion. CHOOSE 1 might compare a
value for one element which is encoded and stored in short-term memory
to a series of perceived values of elements and choose the one element
from the series which best approximates the value of that one element.
In this case, CHOOSE 1 has provided an approximation of the value of

the original element.

132

A91_

This is the process of acting on an object in such a manner as
to obtain a particular kind of input (e.g., color or temperature
information). This might involve orientation of the required organs,
exploratory movements such as visual scanning or tactile exploration,
and/or manipulation of Objects such as hefting or squeezing. Perform-
ance of ACT requires a prior retrieval of the appropriate action from
long-term memory; i.e., activation of the observation action node in
an associative network. This activation makes available the informa-
tion from which a control program can be reconstructed. For present
purposes, no distinction will be made between the construction
process. It may eventually prove necessary or useful to break it down
further. The input for ACT includes the observation action concept
and the differentiated object on which the action is to be performed.
The output is the resulting input to the individual. Analysis of the

input is carried out by other processes.

SELECT

 

This is a primary process which sorts relevant information
from irrelevant. In particular, it filters out almost all information
except for that for the variable (or variables) judged relevant to the
task at hand. Thus, the input is undifferentiated input and the
variable concept. The output is information on the relevant variable
about the perceived object. Actually, the process is not simply a
next step following complete execution of ACT. Rather, along with ACT
it forms an active system with a feedbaCk capability which allows
modification of the detailed functioning of ACT until the appropriate

input has been made available. This represents a monitoring function

133

of SELECT. Such feedback mechanisms are probably involved in many
primary processes. The large number makes it cumbersome to make them
all explicit in the task routine. This aspect of the primary process

is probably important to keep in mind, however.

2199.95.
This primary process analyzes in detail information which has I
been attended to; e.g., as a result of SELECT. The general nature of
the information has already been determined (note the nature of ACT
and SELECT) and it remains for ENCODE to make a determination about
this specific case. For exaMple, ENCODE might be present to analyze
texture information. ACT and SELECT have made such information
available. ENCODE determines whether or not the texture information
is novel and, if not, categorizes it in some manner based on
previously experienced texture information. If the information is
novel, a new category is created. Thus, ENCODE involves long-term
memory. In terms of an associative network, the analysis of texture
information activates a node representing a texture value concept or
else forms a new node paralleling other texture value nodes. The
input for ENCODE is selected non-verbal sensory information. The
output is a value concept (the activation of a node). Undoubtedly,
some additional contextual information about the experience will enter

short-term memory. Some may also enter long-term memory.

134

OTHER PRIMARY PROCESSES

PAR

This primary process determines the comparability of two
encoded units of information; e.g., encodings of texture information
for two objects. COMPARE essentially monitors the node or nodes
activated as a result of the encodings. If the same node is activated
on both occasions, a judgment of comparability is made. The output of
COMPARE can itself be viewed as the activation of a node in a network.
This network includes nodes corresponding to the concepts “same“ and
"different“ (and perhaps others). The activation of one of these
nodes makes immediately available certain operational alternatives
including verbal output. The particular alternative to be executed,
if any, is determined by some controlling mechanism which represents

the strategy being employed by the individual.

PLACE

This primary process involves a spatial placement of an
element to indicate its membership in a set. The criterion for
placement is unspecified in the process itself although it will
usually be retained in short-term memory from earlier steps. The
input to the set is an element currently attending to and an affirm-
ative result from the application of the criterion for set membership.
The output is the element in its new spatial location. A variety of
contextual information placed in short-term memory usually enables the

individual to recognize the subset previously set aside by PLACE.

135

111m

This primary process is closely related to PLACE Since it
involves spatial placement of an element to indicate nonmembership in
a set defined by a criterion from a previous step. However, DISCARD
is not simply PLACE using the inverse criterion since DISCARD implies
that the element is of no further interest, at least temporarily.
Previously discarded elements can subsequently be reconsidered for
further processing, however. DISCARD can be used to form more than
one discard set during the performance of a single task. Furthermore,
the permanency of the discard may differ between sets; e.g., one set
may be discarded for the time being while another is permanently

discarded.

282.5%.
This is a primary process which attends to and assesses the
magnitudes of two differing encoded units of information. ORDER
sequentially evaluates the two magnitudes and then hierarchically
orders them from lesser to greater. This primary process then,
basically monitors the nodes activated as a result of the encodings.
The COMPARE secondary process usually precedes and determines whether
or not different nodes were activated during encoding. If this
results in a judgment of non-comparability, it is the function of
ORDER to evaluate the two nodes successively and to seriate them
appropriately. The output of ORDER can itself be viewed as an ordinal
concept; i.e., the activation of a node in a network. This network
includes nodes corresponding to the concepts of “more“ and “less“ (and

perhaps others). The activation of one of these nodes makes immedi-

ately available certain operational alternatives including verbal

136

output and appropriate serial positioning of the elements. The
particular alternative to be executed, if any, is determined by some
controlling mechanism which represents the strategy being employed by

the individual.

REPORT

 

This is the process by which verbal responses are made. The
input is a concept. The output is a verbal label for the concept
embedded in an appropriate linguistic context (not necessarily a

complete or correct sentence).

DESIGNATE

This process assigns a specific role to an element or set of
elements for use in further processing. For example, one element may
be assigned the role of model for formation of a subset. Subsequent
processing steps treat the element in a manner appropriate to the
assigned role.

This process can be conceived as a temporary association of iden-
tifying features of the element with a cOnceptual node representing
the specific role assigned. However, the role concept is not an
integral part of a conceptual network including the specific variable,
values, observation action, etc.. Rather, it is part of a network
associated with the strategy. The DESIGNATE process is somewhat
similar to the RETRIEVE process in that part of the input comes from
some directing mechanism or representation of the strategy, and not
from the previous processing steps. In this case, the perceptually
differentiated element is the output of preceding processing steps,

but the specific role to be assigned is not. The nature of the

137

controlling mechanisms and the representation of the strategy in
memory have not been further elaborated.

In the context of the processing routine, the input is the
perceptually differentiated element, and the output is that element
assigned to the specified role. This description of the output is
vague, but the effect of this processing step is reflected only in the

way the element is employed in future steps.

+ DESIGNATE 1

 

This process is similar to DESIGNATE. It acts on an inde-
pendent variable or rule by assigning it the role represented by
another concept. The role concept, however, is not input to the
process, but is part of the strategy knowledge itself. For example,
a rule may be assigned the role of hypothesis for further testing
(DESIGNATE 1 rule as hypothesis). The rule would be input to the
process. That the rule would be assigned the role of hypothesis is
part of the knowledge structure of the strategy.

DESIGNATE 1 assigns an independent variable or rule to a role,

whereas DESIGNATE assigns an element to a role.

+ PREDICT VALUE

 

The input for this process is a correlational rule and an
independent variable value. The process outputs a value for the
dependent variable corresponding to the inpUt value of the independent
variable. For example, the thickest rod has been chosen or selected.

This rod has a thickness value of "thickest." That value, along with

138

the rule, "the thicker the rod, the less it will bend” is the input
for the PREDICT VALUE process. The process outputs some expected

value for how much the rod will bend; i.e., "very little" or "the

least.“

+ JUDGE PREDICTION

 

This process usually follows the processes PREDICT VALUE
(primary) and OBSERVE (secondary). It inputs the expected value for
the dependent variable of an element and the obtained value of that
dependent variable for that element. It compares these values and

Outputs a decision as to whether the prediction was correct or not.

+ JUDGE HYPOTHESIS

 

This process inputs the hypothesis (correlational rule) and
the activated node, "correct“ predictions or “not correct” predic-
tions. It outputs an activated node, ”correct“ hypothesis or "not
correct" hypothesis, depending on whether predictions are correct as

they relate to the hypothesis.

+ FORM RULE

 

The input for this process is a value for an independent
variable and a value for a dependent variable. The process outputs a
rule relating the independent variable to the dependent variable. For
example, a subject may OBSERVE 1 a pair of wheels. S/he encodes that
the ”bigger wheel“ is small and that the size circle the pair of
Wheels makes is small. The output of the FORM RULE process, in this
Case, would be a rule: The smaller the “bigger wheel", the smaller

the circle.

139

COMPARISON (variable concept, Element A, Element B-——+ comparative
concept)

 

This is a secondary process which takes as input a variable
concept (i.e., the node activated by decoding of variable name or an
appropriate retrieval process) and an ordered pair of elements. It
compares the elements on the given variable and outputs a comparative
concept applicable to the ordered pair of elements. Thus, the COM-
PARISON process does not produce a verbal report although it makes
such a report immediately possible. Alternative steps might be
carried out next instead. The identities of the elements and the
comparison variable are maintained. Figure 21 indicates a parallel
execution of processing steps. This indicates the desirability of
near simultaneous observation of the two elements. "Parallel
processing“ in the technical psychological sense is not implied.
Furthermore, feedback from the selecting and encoding steps to the ACT
step undoubtedly occurs creating an active subsystem. Such feedback
systems are very common, but to avoid excessive complexity, are not
always diagrammed.

+ OBSERVE (element, observation/measurement procedure, value for
ndependent variable--+’value concept for dependent
variable)

OBSERVE is a secondary process that takes as input a selected
element and an observation/measurement procedure. It acts on the
element, selects relevant information regarding the dependent
variable, and encodes that data; i.e., the output is a value concept

for the dependent variable (the activation of a node). See Figure 22.

140

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

COMPAR-
ISON
RETRIEVE l'
observation
l action
ACT
on Element
A
SELECT
Element A
feature
ENCODE
Element A
feature

 

 

 

 

    

COMPARE

 

 

 

ACT
' on Element
8

 

 

 

 

SELECT
Element B
feature

 

 

 

 

 

ENCODE
Element 8
feature

 

 

Element A
and Element

 

     
    
 

return

 

Figure 21. The COMPARISON secondary process. Input: A

variable concept, Element A, and Element 8.

Output: A comparative

concept relating Element A, and Element B on the input variable.

141

 

OBSERVE

 

 

 

 

 

 

 

ACT SELECT
an element value of depen-
dent variable

ENCODE

value of depen-
dent variable

4

return

 

 

 

 

 

 

 

 

 

 

 

Figure 22. The OBSERVE secondary process. Input: element,
observation/measurement procedure, value of independent variable.
Output: value concept for dependent variable (activation of a node).

142

OBSERVE 1 (element, observation/measurement procedure-—-4)value
concepts for independent variable(s) and dependent

variable)

OBSERVE 1 is similar to the secondary process OBSERVE. It
differs in that the value of the independent variable(s) has not yet
been encoded. The output then is a value concept for both the
independent variable(s) and the dependent variable (the activation of

nodes). See Figure 23.

SERIATION (variable concept, Element A, Element B-—-—)ordinal concept)

This tertiary process (see Figure 24) uses as input a variable
concept and a pair of elements. It initially processes the elements
utilizing the COMPARISON process. If the elements are of the “same"
magnitude on the variable observed, SERIATION outputs a comparative
concept applicable to the elements. If the elements are not of the
same magnitudes, SERIATION assesses the relative magnitudes of the
elements using the ORDER process. This process outputs an ordinal
concept, “greater than“ or "less than.“ The identities of the
elements must be maintained and coordinated with the ordinal concept.
The SERIATION process does not produce a verbal report although it
makes such a report immediately possible. Motor manipulation and
sequential ordering of the elements themselves are also possible. The
identity of the seriation variable is maintained.
*MAXPIC (set of elements, variable concept-—-———aelement displaying

the maximum values for the chosen variable)

MAXPIC is a tertiary process which acts upon a set of elements
and Chooses the element displaying the maximum value on some

designated variable. It is the basic subroutine in the extreme value

 

143

 

OBSERVEl

 

 

 

 

 

 

 

SELECT

ACT
1 value of depen-
on element ldent variable

 

 

 

 

 

ENCODE
value of depen-
dent variable

_L

return

 

 

 

 

 

 

Figure 23. The OBSERVEl secondary process. Input: element,
observation/measurement procedure. Output: value concepts for
independent and dependent variables (activatidn of nodes

144

SERIA-

TION

 

 

 

 

perform
COMPARISON
on Element
A and
Element 8

 

 

 

 

     

ORDER
Element A
and Element

TglLtea

 

   

 

return

(___

 

 

 

Figure 24. The SERIATION tertiary process. Input: A variable
concept, Element A, and Element 8. Output: An ordinal concept relating

Element A, and Element 8 on the input variable.

145

selection strategy, and it involves the repeated comparison of each
element in a set to the maximum element found so far. Input require-
ments are a set of elements differing on the named variable and the
variable concept. The element displaying the maximum values for the
Chosen variable is the output. See Figure 25. ‘

+ MAXPIC, in this study, is used to indicate that some similar
series of processes results in the subject's finding an element that
has a maximum value on the selected independent variable.

INDEPENDENT VARIABLE IDENTIFICATION (set of elements-—-—* difference
varfabTe name)

This is a tertiary process which takes as input a set of
elements, usually previously differentiated perceptually by the
primary process SCAN. It retrieves a variable name, compares the set
of elements to see if any pair differs on this variable, and if the
pair does differ on the variable, outputs that variable name as an
independent variable.

(NOTE: This tertiary process, INDEPENDENT VARIABLE IDENTIFI-
CATION, is more like the directed comparison task previously defined
by Smith et al.* than the difference variable identification task
defined by Smith et al.* In the difference variable identification
task, all elements are unique on the difference variable. This is not
the case with the set of elements inputed for the INDEPENDENT VARIABLE
IDENTIFICATION tertiary process. There are five different values for
the difference variable, but more than one element may have the same

value on that variable.) See Figure 26.

146

 

 

 

 

CHOOSE DESIGNATE
MAXPIC ""—' an unused element as
element maximum so far

 

 

 

 

 

 

 

 

    
  

CHOOSE
an unused
element _e_

 

 

Perform
SERIATION
on element
_e_ and max

 

 

 

 

 

DISCARD
max

DESIGNATE

element 3 as
maximum so far

SCAN 1

elements

 

 

 

DISCARD
element e_

 

 

 

 

 

 

 

 

 

   
   

  

'ny
unused
elements

 

return

     
 

 

 

Figure 25. The MAXPIC tertiary process. Input: set of
elements, variable concept. Output: element displaying the maximum
value on the variable concept.

147

 

INDEPENDENT
VARIABLE

IDENTIFI-
CATION

 

 

 

 

 

 

 

 

 

 

 

 

       
       

 

 

 

 

 

 

 

 

 

 

 

 

  

RETRIEVE
an unused ancsggigd
variable element
YES, DESIGNATE
retrieved? element as a
model
perform 7 , J: _
COMPARISON
on element ' CHOOSEd
and model an unuse
i element
U1
1.1.1
)-

PLACE any
elements in -—---N SCAN unused
subset for elements lement

11.0 I ‘ ‘2

 

 

 

 

NO

 

 

Figure 26. The INDEPENDENT VARIABLE IDENTIFICATION tertiary
process. Input: set of elements. Output: activation of a node
correSponding to the difference variable name.

148

+ MINPIC (set of elements, variable concept-—-——P element displaying
the minimum values for the chosen variable)

MINPIC is the same as the tertiary process, MAXPIC, except
that it chooses the element displaying the minimum value on some
designated variable, in this case, the selected independent variable,
instead of the maximum variable. See Figure 27.

+ GT ELEMENT SELECTION (set of elements, variable concept-———9 element

displeying a greater value on the variable concept than
element(s) already used)

 

GT ELEMENT SELECTION is a tertiary process which acts upon a'
set of elements and chooses an element displaying a greater value on
the variable concept than elements already used. It involves the
repeated comparison of elements to an element designated model until
an element having a greater value on the variable concept is found.
Input requirements are a set of elements differing on the named
variable and the variable concept. The element displaying a greater
value On the variable concept is the output. See Figure 28.

GT ELEMENT SELECTION is similar to MAXPIC, differing only in
that the GT ELEMENT SELECTION returns to the routine when an element
with a greater value on the variable concept is found, while MAXPIC
returns to the routine only when the element with the greatest value
is found.

+ LT ELEMENT SELECTION (set of elements, variable concept-—e element
diSpTBying a Tesser value on the variable concept than
element(s) already used)

LT ELEMENT SELECTION is the same as the tertiary process, GT
ELEMENT SELECTION, except that it chooses an element displaying a
lesser value on some designated variable, in this case, the selected

independent variable, instead of a greater value. See Figure 29.

 

 

 

 

Figure 27.
variable concept.
variable concept.

MINPIC 1_.

149

 

 

CHOOSE
an unused
element

 

—#

 

 

 

return

 

The MINPIC tertiary process.

 

DESIGNATE
element as
minimum so far

 

 

   

  
   
   

CH
an

element 9_

OOSE

 

unused

 

 

 

P
SE
on
E

 

erform
RIATION
element
and min

 

 

 

 

DISCARD
element 5

 

 

 

SCAN
elements

 

     

 

DISCARD
min

 

 

 

DESIGNATE

element e_

as minimum
so far_

 

 

J

 

 

Input: set of elements,

Output: element displaying the minimum value on the

150

 

 

 

GT
ELEMENT CHOOSE DESIGNATE

*'—-‘ an element r-—l' element e
SELECTION g_already used' as model"

CHOOSE

element Ln_
from unused
elements

 

 

 

 

 

 

 

 

 

 

 

 

 

Perform
SERIATION
on element
_e_ and ele-
ment m_

 

 

 

 

 

 

 
   

 

  
   
   
 

DISCARD

element _e_
DISCARD DESIGNATE
element m m as > _e_

 

 

 

 

SCAN
elements

 

 

 

YES

 

return

 

Figure 28. The GT ELEMENT SELECTION tertiary process. Input:
set of elements, variable concept. Output: element diSplaying a
greater value on the variable concept than element(s) already used.

 

 

LT
ELEMENT
SELECTION

151

 

 

CHOOSE DESIGNATE

 

 

 

 

an element _e_ element _e_
already used as model

 

 

 

 

 

    

CHOOSE
element,p_

 

 

Figure 29.

from unused
elements

_.L__

Perform
SERIATION
on element
5 and ele-
ment g_

 

 
  

 

 

 

 

 

DISCARD
element _e_

DESIGNATE
gascg

 

 

   

DISCARD
element LIL

    

 

 

 

 

SCAN
elements

 

 

YES

 

 

The LT ELEMENT SELECTION tertiary process. Input:

set of elements, variable concept. Output: element displaying a lesser
value on the variable concept than element(s) already used.

152

+ SE ELEMENT SELECTION (set of elements, variable concept-—-eelement
displaying a value on the variable concept the same as or
equal to element(s) already used)

SE ELEMENT SELECTION is the same as the tertiary process, GT
ELEMENT SELECTION, except that it chooses an element displaying the
same or equal value on some designated variable, in this case, the
selected independent variable, instead of a greater value. See
Figure 30.

+ GT ELEMENT SELECTION WITH CONTROLLED VARIABLE (set of elements,
two variable concepts—9 element displaying the same value
on one variable concept and a greater value on the other
,variable concept than element already used)

GT ELEMENT SELECTION WITH CONTROLLED VARIABLE is a tertiary
process which acts upon a set of elements and chooses an element
displaying the same value on one variable concept and a greater value
on the other variable concept than an element already used. It
involves, first of all a repeated comparison of elements to an element
designated model until elements are found having the same value on the
designated independent variable. Then, this tertiary process uses a
second repeated comparison of these matched elements until an element
having a greater value on the second variable concept is found. The

element displaying a greater value on this second variable concept is

the output. See Figure 31.

153

 

SE
ELEMENT
SELECTION

 

 

—-—-—~ CHOOSE * DESIGNATE

an element 3 element 3
already used as model

 

 

 

 

 

 

 

 

 

CHOOSE
element _n_1_
from unused
elements

‘ Perform

SERIATION
on element
e_ and ele-
mentgg

 

 

 

 

 

 

 

 

DISCARD
element

L

 

 

 

 

 

 

 

 

DISCARD DESIGNATE
element m g_as T e
SCAN
elements

 

 

 

  

return

 

 
 
 

 

Figure 30. The SE ELEMENT ELECTION tertiary process. Input:
set of elements, variable concept. Output: element diSplaying a
value on the variable concept the same as or equal to element(s)
already used.

154

 

 

 

 

 

 

 

 

 

 

 

 

 

      
   
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GT
ELEMENT
SELECTION CHOOSE DESIGNATE
WITH 1 an element e ‘1 element 5
CONTROLLED already usea'. as model
VARIABLE ,
—”'DESI_JF—_GNA El 1
independent
variable
to be held
perform 7 Perform
SERIATION CHOOSE MATCH
on element e 0" element e
and element 5- element m and unused eTe-
(uncontrolleH' from matchEd ments
variable) elements (controlled
variable)
YES DISCARD
element 5
DISCARD DESIGNATE
element E E as > g
.__.___ L
SCAN .
elements
return
NO 1

 

 

 

Figure 31. The GT ELEMENT SELECTION WITH CONTROLLED VARIABLE
tertiary process. Input: set of elements, two variable concepts.
Output: element displaying the same value on one variable concept and
a greater value on the other variable concept than element already used.

155

+ LT ELEMENT SELECTION WITH CONTROLLED VARIABLE (set Of elements,
two variable concepts-—e»element dispTéying the same value
on one variable concept and a lesser value on the other
variable concept than element already used)

LT ELEMENT SELECTION WITH CONTROLLED VARIABLE is the same as
the tertiary process, GT ELEMENT SELECTION WITH CONTROLLED VARIABLE,
except that it chooses an element displaying the same value on one
variable concept and a lesser value, instead of a greater value, on

the other variable concept. See Figure 32.

 

 

 

 

156

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
   

  

 

 

 

 

 

DISCARD DESIGNATE
element _111 L“. as ‘ S.
SCAN
elements
return

 

 

LT
ELEMENT
SELECTION CHOOSE DESIGNATE
WITH an element e element e
CONTROLLED already useH' as model"
VARIABLE
independent
variable
to be held
Perform er orm
SERIATION CHOOSE MATCH
on element e 0" 9161118711: 3
and element 5' element m 30d unused
(uncontrollea' from matcfiEd Elements
variable) elements (controlled
variable)
DISCARD
element 3 _

Figure 32.
tertiary process.

The LT ELEMENT SELECTION WITH CONTROLLED VARIABLE
Input: set of elements, two variable concepts.
Output: element displaying the same value on one variable concept and
a lesser value on the other variable concept than element already used.