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Evaluating Students' Motivation in Predicting
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EVALUATING STUDENTS’ MOTIVATION IN PREDICTING
MATHEMATICS AND SCIENCE PERFORMANCE: A DEVELOPMENTAL
PERSPECTIVE

By
Leland S. Cogan

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Counseling, Educational Psychology, and Special Education

1996

ABSTRACT
EVALUATING STUDENTS’ MOTIVATION IN PREDICTING
MATHEMATICS AND SCIENCE PERFORMANCE: A DEVELOPMENTAL
PERSPECTIVE
By

Leland S. Cogan

This study employs concepts associated with a general expectancy -
value model of motivation to explore students’ motivation within a
developmental perspective. It examines how specific aspects of motivation,
i.e., interest, importance, career relevance, perceived competence, and success
attributions to natural talent and hard work, are related to students’
achievement in mathematics and science. The present study had two main
goals: 1) to examine the relationships among students’ subject matter interest,
importance, career relevance, perceived competence, and success attributions
at three developmental levels, and 2) to evaluate the usefulness of these
aspects of motivation in predicting students’ performance on a mathematics
and science achievement test. The study employs structural equation
modeling to evaluate the usefulness of these motivational constructs in
predicting students’ performance as a function of students’ developmental

level and the academic domain assessed.

For my father.

iii

ACKNOWLEDGMENTS

Despite the considerable investment of time and effort necessary to
complete this project, I am acutely aware of the contribution a number of
individuals have made along the way that has enabled me to bring this
project to fruition. For all the support and encouragement provided, I am
profoundly grateful.

I am particularly thankful for my committee members who facilitated
this ”mountain conquering” experience. Dr. Ralph Putnam provided
Challenging ideas about students and classroom learning. He also offered
personal encouragement and support during the writing process. Dr. Ellen
Strommen has served as a mentor in my interest and thinking about social
development issues. She always made herself available to me to listen to my
ideas or read drafts and provide the appropriate and needed response.

Special thanks goes to Dr. William Schmidt who took me on as a
member of his research team for the Third International Mathematics and
Science Study. Through his leadership in this project, he has served as a

mentor in educational research, research methodology, and data analysis.

iv

Without his assistance and encouragement this project would not have been
possible.

My advisor, Dr. Evelyn Oka, also deserves special thanks. Throughout
my program she has provided stimulating intellectual guidance and practical
professional advice. Our discussions about motivation, Children’s learning
and development, and the role parents play in their children’s development
plumbed the depths of theory but she always brought us back to the practical
implications of these for teachers, parents, and others. I am particularly
grateful for her example, patience, and prodding during this project.

I am indebted to my family and offer them my everlasting
appreciation. The prayers and words of encouragement of my parents as well
as my mother-in-law and father-in-law proved to be an invaluable source of
comfort and support. My children, Scott, Rebekah, Ruth, and Chip were a
constant source of inspiration and never complained about my absence at
special school functions or the amount of time I needed to devote to
completing this dissertation. Their frequent inquiry, ”How much of your
dissertation have you completed?” provided a gentle prod and an incentive
to finish. Because they deserve it, we have a great family vacation planned.

Finally, I express my profound gratitude to my wife, Ioella, who has
been my biggest fan and staunchest supporter. Her faith enabled me to try, to

work hard, and to succeed. I have been truly blessed.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. v

LIST OF FIGURES ......................................................................................................... Vi
CHAPTER 1

INTRODUCTION AND BACKGROUND ................................................................. 1

Introduction ......................................................................................................... 1

Background ........................................................................................................... 4

Motivation ................................................................................................ 4

Motivation and Development ............................................................. 7

Interests and Values ............................................................................... 8

Competence .............................................................................................. 9

Success Attributions ............................................................................. 11

Career Relevance ................................................................................... 13

Subject-Matter Specificity .................................................................... 15

Assessing Achievement ...................................................................... 17

Motivation Related to Achievement ............................................... 21

Research Questions and Hypotheses ............................................................ 23
CHAPTER 2

METHODOLOGY ........................................................................................................... 26

Research Design ................................................................................................. 26

Sample ................................................................................................................. 27

Instruments ........................................................................................................ 31

Student Background Questionnaires ................................................ 31

Achievement Tests ............................................................................... 35

Data Collection ................................................................................................... 39
CHAPTER 3

RESULTS ......................................................................................................................... 43

Describing Student Motivation ...................................................................... 43

Hypothesis 1: Decreasing Motivational Means .............................. 51

Hypothesis 2: Attributions to Hard Work and Talent .................. 52

Hypothesis 3: Perceived Competence and Success
Attributions ................................................................. 53

vi

Hypothesis 4: Career Relevance and Other Aspects of

Motivation ................................................................... 54
Hypothesis 5: Relationship Between Mathematics and
Science Motivation .................................................... 58
Relating Motivation to Achievement .......................................................... 6O
Hypothesis 6: Interest, Importance, Perceived Competence
and Achievement ...................................................... 62
Hypothesis 7: Career Relevance and Achievement ...................... 65
Hypothesis 8: Mathematics and Science Motivation ,
Related to Achievement ........................................... 66
CHAPTER 4
DISCUSSION AND CONCLUSIONS ....................................................................... 72
APPENDIX A
Items used to assess Students’ Mathematics Motivation ..................................... 97
APPENDIX B
Items used to assess Students’ Science Motivation ............................................... 98
APPENDIX C
Item Content Categories and Type by Book and Population ............................. 100
REFERENCES ............................................................................................................... 103

vii

LIST OF TABLES

Table 1 - Description of Student Sample by Grade ................................................ 31
Table 2 - Motivation Means (Std Dev) by Grade Level and Subject .................. 44
Table 3 — Summary of MANOVA on Students’ Motivation .............................. 46
Table 4 - Correlations Between Perceived Competence and Success

Attributions by Subject and Grade ........................................................... 53
Table 5 - Correlations Between Career Relevance and Other

Motivation Variables by Subject and Grade .......................................... 57
Table 6 - Correlations Between Corresponding Aspects of Mathematics

and Science Motivation by Grade ............................................................ 60
Table 7 - Correlations Between Motivation and Achievement Scores by

Subject, Score Type and Grade .................................................................. 61
Table 8 — Goodness of Fit Measures for Two Models ............................................ 70

Table 9 — Path Coefficients (Std. Error) for MIMIC Model by Subject and
Grade .............................................................................................................. 72

viii

LIST OF FIGURES

Figure 1 — Aspects of Motivation Related to Achievement ................................ 23
Figure 2 - Differences Between Mathematics and Science Motivation

Means by Grade .......................................................................................... 47
Figure 3 - Mean of Mathematics and Science Motivation Variables by

Grade ............................................................................................................ 49
Figure 4 —Motivation Means for Mathematics and Science ................................ 50

Figure 5 — Correlation Between Mathematics Career Relevance and
Other Aspects of Mathematics Motivation by Grade ......................... 55

Figure 6 — Correlation Between Science Career Relevance and Other
Aspects of Science Motivation by Grade ............................................... 56

Figure 7 — Correlation Between Aspects of Mathematics and Science
Motivation by Grade ................................................................................. 59

Figure 8 — Correlations Between Mathematics Motivation and Multiple
Choice Score by Grade ............................................................................... 63

Figure 9 —Correlations Between Mathematics Motivation and Open-
Ended Score by Grade ................................................................................ 63

Figure 10 — Correlations Between Science Motivation and Multiple
Choice Score by Grade ............................................................................... 64

Figure 11 —Correlations Between Science Motivation and Open-Ended
Score by Grade ............................................................................................ 64

ix

CHAPTER 1: INTRODUCTION AND BACKGROUND

Introduction

In a recent conversation, an eighth grader indicated that very few of his
peers thought that school was important. When asked what he thought was
important to his peers he said, ”friends and other activities like sports.” His
comment, while not particularly surprising, did seem to be a rather unusual
description for a class that had developed a reputation among the school’s
staff, students, and parents for being academically oriented and motivated.
The student mused further that some students didn’t seem to be trying as
hard or doing as well in school as they had in earlier years. When prodded as
to why he thought that might be, he paused and considered, ”Perhaps they
aren’t trying because they don’t think it’s that important...there are other
things they’re more interested in. Or maybe they’ve just gotten tired of trying
and not doing as well as they’d like. I guess they aren’t trying as hard or doing
as well as they could.”

These comments from an eighth grader illustrate the role that
motivational issues often play in efforts to understand and explain students’
academic achievement behavior. While it is a human trait for people to
attempt to understand the behavior of others (Brunet, 1990), educators and

policy makers are professionally motivated as well in attempting to make

2
sense of students’ academic achievement. Educators and policy makers are

interested in understanding the factors that affect students’ academic
achievement so that they might improve student learning.

Those interested in students’ motivation have sought explanations of
students’ achievement behavior at the individual, classroom, and system
levels (Thomas, 1993; Brown, 1993; MCCaslin & Murdoch, 1991). Although
researchers and educators alike acknowledge the strategic and important role
that motivation has in students’ cognitive and academic development,
assessment of aspects of students’ motivation are typically not a part of
academic achievement tests (Scarr, 1981; Paris, 1991). The prevailing View
that students’ academic motivation plays an important role in their
achievement behavior is supported by a considerable amount of research.
The vast majority of this research has related students’ motivation to specific
strategies, classroom grades, short tests for research purposes, and future
curricular/course-taking decisions - not to achievement tests.

Many achievement tests have become ”high stakes” assessments which
have major implications for educational policy and curriculum if not for an
individual student’s immediate educational future. However, assessing
students’ motivation and relating this to their performance on this type of
”high stakes” assessment is rare. The important role students’ motivation
has in achievement and the importance afforded achievement tests has

prompted one set of researchers to argue that,

3
Tests should measure more than what students know; they
should assess students’ perceptions of their abilities, their own
effort and goals, their interests in the material, their relative
satisfaction with their own performance, and their preparation
for the tests. Personal control, efficacy, ownership, and self-
regulation are critical constructs for achievement and deserve to
be assessed. (Paris et al, p. 18)

A distinguishing feature of the present study is that it examines students’
motivation in relation to their performance on a ”high stakes” achievement
test.

Embedded in the student’s comments noted earlier are references to
two motivational constructs, expectancies and values, that are the basis of a
general model of motivation which has informed many productive research
programs (e.g., Eccles, 1983; Grolnick 8: Ryan, 1987; Harter, 1983; Nichols,
Cobb, Wood, Yackel, & Patashnick, 1990; Pintrich & DeGroot, 1990). Inherent
in his comments is the idea that, not only do students’ behaviors change over
time, but what they expect from themselves (they’re ”tired of trying and not
doing as well as they’d like) and their underlying reasons (”there are other
things they’re more interested in”) may also change. Thus, a students’
academic behavior may be understood in terms of her evaluation of her
personal resources relevant to the task (expectancies) and her evaluations of
the task (values) — all of which are subject to change as the student grows and
matures.

The current study focuses upon the way different aspects of students’
expectancies and values are interrelated and relate to their performance on a

specific achievement test. This study draws upon concepts associated with a

4
general expectancy-value model of motivation to address the two main

purposes of this study: 1) to examine the interrelationships among students’
subject matter interest, importance, career relevance, perceived competence,
and success attributions at three developmental levels with respect to two
academic domains (e.g., mathematics and science), and 2) to evaluate the
usefulness of these aspects of motivation in predicting their performance on

an achievement test in mathematics and science.

Background

Weiner (1989) notes that there have been two traditional perspectives
on human motivation and behavior: behavior generality and behavior
specificity. Theorists who favor behavior generality tend to view individual’s
behavior as a function of internal states or drives which are expressed in a
relatively invariant manner over time and across settings. According to this
view, motivation is considered an aspect of personality, a stable attribute that
functions in an essentially consistent and predictable manner across all
situations or contexts.

In contrast, theorists who hold a behavior specificity perspective regard

an individual’s internal states or drives as temporary states that are a function

5
of the specific situation or context. According to this View, an individual’s

motivation is a function of both the individual’s personality and the specific
context. For example, Rotter (1954) claimed that the proper focus of
investigation in matters of personality and motivation was ”the interaction
of the individual and his meaningful environment” (p. 85).

Rotter’s emphasis upon the interaction between the individual and the
environment is compatible with more recent cognitive and socio-
psychological conceptions of motivation. These perspectives emphasize an
individual’s motivation and behavior as an adaptive response on the part of
an individual to specific situations in which personal resources are flexibly
applied (Bandura, 1986; Maehr & Braskamp, 1986; MCCaslin 8: Murdock,
1991). This emphasis has emerged as a corollary to the recognition of the
fundamental social nature of human thought and development. Humans
are uniquely social and strive to make sense out of their surroundings and
interactions (Bruner, 1990; Kozulin, 1990). The aspects of motivation
employed in this study may be viewed as cognitive constructs employed by
individuals as they attempt to understand themselves and their
environment.

The specific aspects of motivation employed in this study are associated
with a general expectancy-value motivational model. Rotter (1954) originally
proposed the general principle that the potential for any behavior could be
viewed as a function of an individual’s expectancy of a reward associated with

the anticipated behavior and the value assigned by the individual to the

6
expected result or goal of the behavior. He broadly defined expectancy as the

”probability held by the individual that a particular reinforcement will occur
as a function of a specific behavior on his part in a specific situation” (Rotter,
1954, p. 107).

About the same time, Atkinson and his colleagues employed the
concepts of expectancy and value more specifically to understanding and
explaining achievement behavior (Eccles, 1983; Weiner, 1992; Wigfield, 1994).
Subsequently, these two basic motivational components have been expanded
and refined by researchers investigating motivation for a variety of behaviors
in many different settings.

In general, the expectancy component of the model addresses the
question, ”Can I do this task?” This involves issues such as how well one is
likely to do the task, evaluations of one’s competence for the task, and one’s
ideas (attribution) about what it would take to do well on a task (Harter, 1981;
Bandura, 1986; Pintrich 8: DeGroot, 1990; Weiner, 1992). The value
component concerns the question, ”Why am I doing this task?” Investigators
have conceptualized this motivational component as one’s intrinsic interest
in the task, one’s evaluations and estimations of the task’s utility and
importance, and one’s goals or purposes for engaging in the task (Eccles, 1983;
Pintrich 8: DeGroot, 1990; Weiner, 1992; Wigfield, 1994).

A sizable body of research has demonstrated that motivation plays a
critical role in determining the level of an individual’s performance (Eccles,

1983; Pintrich 8: DeGroot, 1990; Weiner, 1992; Wigfield, 1994). Independent of

7
a person’s ability, one’s motivation has been shown to determine to what

extent, if at all, effort will be expended in a task applying whatever abilities
one may have. The expectancies and values held by the individual,
historically elaborated and operationalized as one’s perceptions of
competence, success attributions, interest in and value afforded the task, and
one’s long-range and short-range reasons for engaging in the task
(achievement goals), are all likely to be critical considerations in deciding how
to apply and expend the efforts, strategies, and knowledge one has with

respect to any considered task.

11.. ID!

As children grow and mature many Changes may be observed in a
variety of domains including their physical appearance, interests, values, and
behaviors. Any of these changes may be associated with development. But
change over time is not all that is typically meant by development.
Development is usually associated with a particular kind of change that
occurs over time; changes that result in an increased ability, capacity, or
competence to accomplish tasks, make decisions and distinctions, and to
understand and interpret various situations.

Harter (1983) presents a perspective on the individual’s developing self

concept as a social construct that emerges and differentiates. This

8
development proceeds on the basis of both increased competencies and

changing social contexts and interactions. Motivation is considered an
important aspect of one’s personality or self-concept (Harter, 1978). Many
different aspects of one’s self-concept may also be considered from a
motivational perspective such as one’s self-descriptions, likes, dislikes, values
and priorities as well as one’s knowledge about the self as an active agent —
the reasons and purposes leading to specific decisions, choices, and behaviors.

Harter (1983) reasons that, in so far as motivation is a function of the
self, we should expect to find developmental changes in the differentiation,
strength, and structure of various aspects of motivation as the self grows and
matures. A complete model of motivation must, therefore, be a
developmental model which includes some description of the Changes in
motivation over time.

The following section identifies several key aspects of students’
motivation and discusses the importance of considering motivation from a
developmental perspective and with respect to a specific context (i.e., subject

matter).

Interestunillalues

As children grow and develop their interests and activities change. A
four year old who is very interested in art and spends a great deal of time

engaging in various artistic endeavors may become a soccer fanatic by age 9

9
and completely engrossed in computers and mathematics by age 14. This sort

of scenario illustrates the common sense connection between one’s interests,
values, and behavior. One might reason that one would tend to value and
pursue through activities those endeavors that represent one’s interests.
Accordingly, with reference to particular school subjects, one would expect to
find a close relationship between student interest, perceived value of the
subject, and subject-matter-specific achievement behavior. It would appear
reasonable that students would invest themselves, their time, energy, and
cognitive efforts, in those subjects that they both valued and were interested
in.

Stipek (1984), for example, found that both students’ interest in and the
value afforded a particular subject, e.g., math or reading, decreased from
upper elementary through middle or junior high. However, this close
connection between interests and values has not always been found.
Wigfield (1994) reports that for another group of students, their interest in
mathematics did not decrease over a three year period, from fifth to eighth

grade, despite a decrease in the importance students’ assigned to it.

Competence

Closely related to one’s interest in and perceived value for a subject is
one’s self-evaluation of competence. Harter has documented the changing

nature of perceived competence, from preschool age through adolescence

10
(Harter, 1981 ; Harter, Whitesell, 8: Kowalski, 1992). Harter found that even

Children as young as four and five make a distinction between being
competent socially and being competent in sports. As children grow, their
competence beliefs become even more differentiated so that their self-
perception regarding mathematics is distinct from the competence beliefs
about reading, music, and other domains (Harter, 1983).

In addition, there is a developmental trend in the strength of students’
competence beliefs as they move through elementary school and into middle
school or junior high. Young children tend to maintain relatively high
competence beliefs even in the face of failure but these competency beliefs
tend to decline from early elementary into middle school or junior high
(Dweck, 1989; Stipek, 1984; Wigfield, 1994). This decrease in students’
perceived competence has been explained, in part, by their increased capacity
for considering information from several sources, i.e., their own performance
and the performance of others, and by their increased ability to form more
realistic evaluations of what they have done. The changing classroom
environment from early elementary to middle school has also been thought
to play a role in students’ decreasing evaluations of their competence. In
early elementary, students are often praised and rewarded for whatever effort
they may put forth without regard for the quality or product of that effort. As
the student advances through elementary school and into middle or junior
high, the quality and product of the student’s effort becomes more and more

the focus of reward and evaluation (Eccles 8: Midgley, 1989).

11
The corresponding decrease in students’ perceived competence and

their valuing of a specific subject matter has been explained by the idea that
what one is good at, one values. Thus, if a student is good at math, she will
place a high value on math but if she is not good at reading, she will not
highly value reading. Such Changes in the relationship among mean levels
of students’ subject-matter interest, importance afforded the subject, and their
subject-matter-specific perceived competence suggests that the role these
motivational aspects play in predicting subject-matter-specific behavior may
not be the same at every developmental level. If students do tend to value
what they are good at and choose those activities over others, it would follow
that the value aspects of motivation would become more predictive of

behavior as students are able to make Choices in their activities.

Eccles has also considered motivation within a developmental
framework. Referring specifically to the role attributions play in motivation
she hypothesized that their influence ”may well become an epiphenomenon
rather than a causal influence on subsequent expectations and performance”
once a stable self-concept has been formed (Eccles, et a1, 1983, p. 87). These
attributions have to do with how one interprets the causal connections
between one’s own effort, ability, and achievement performance (Eccles, 1983;

Gentile 8: Monaco, 1988; Schunk, 1991; Weiner, 1989; Weiner, 1992).

12
Recently, two different orientations have been linked with students’

achievement behavior that involves students’ attribution of success to either
effort or ability (Ames, 1992; Cobb, Wood, Yackel, Nichols, Wheatley, Trigatti,
8: Perlwitz, 1991; Dweck 8: Bempechat, 1983; Eccles 8: Midgley, 1989; Ginsburg
8: Asmussen, 1988; MCCaslin 8: Murdock, 1991 ; Nichols et al., 1990; Pintrich 8:
DeGroot, 1990). The defining Characteristic of one orientation, referred to as a
mastery goal (Ames, 1992), learning goal (Dweck 8: Bempechat, 1983) or task-
involved orientation (Nichols et al., 1990), is an attribution of success to
effort. The other orientation involved an attribution of success to ability.
This is one of the main Characteristics of those who endorse a performance
goal (Ames, 1992; Dweck 8: Bempechat, 1983) or an ego-involved task
orientation (Nichols et al., 1990).

Developmental differences in these types of attributions have also been
reported. For example, Stipek (1984) found that students in early elementary
school were more likely to attribute success to effort while older students
were more likely to attribute success to ability. These developmental changes
in success attributions parallel the developmental changes regarding a
student’s competence beliefs. The proposed reasons for why students’
competence beliefs decrease is that they become more aware of their relative
performance in the Classroom and that their efforts are more critically
evaluated. These developmental changes in students’ cognitive skills and in
the nature of their educational environments may also be the basis for the

shift in students’ success attributions from effort to ability. Part of the reason

13
may be that younger students do not readily differentiate between competence

beliefs and success attributions since both are based primarily upon the effort

they expend.

A fundamental assumption in career development theory is that
individuals desire to implement their self concept, that is their knowledge of
themselves, their interests, values, and competencies, in their vocation or
career in a congruent manner (Holland, 1973; Gottfredson, 1981; Super, 1990).
In other words, peOple desire to have specific positions and to develop careers
that explicitly or implicitly endorse, or at least are compatible with, their own
most prized interests, values, and abilities. Someone who loves to read, for
example, but despises working with numbers would be more likely to seek
employment as a writer, editor, or bookstore Clerk than as a bookkeeper, bank
teller, or engineer. Similarly, someone who enjoys science and highly values
the sanctity of human life would be more likely to pursue a career in
prosthetics research and design, hospice care, or environmental management
than one in weapons development and manufacture or with a health care
corporation known for a ”bottom line” orientation and seemingly little
regard for the people involved.

However, people do not typically wait until they are ready to look for

their first career-related employment position to ”implement” their self-

14
concept. In fact, one’s self-concept is a dynamic concept formed along the way

through life experiences. Some of these formative life experiences include
making decisions about which subjects to study, how much time and effort to
invest in schooling and academics, and which types of employment positions
are feasible to pursue. These issues of self-concept, identity and career, are
major developmental themes for adolescents and young adults (Erikson,
1963; Marcia, 1980). For example, Montemayor and Eisen (1977) found a
significant increase from age 10 to age eighteen in the number of subjects who
used some reference to an occupational role in responding to the question,
”Who am I?” In addition, one British study reported that 14 year-old students
rated ”usefulness for a jo ” as the single most important factor in
determining their school subject choices (Kelly, 1988).

One of the motivational questions examined in this study is, ”Why am
I doing this task?” One way this motivational component has been assessed
is by looking at the goals or reasons one has for engaging in specific behaviors
(Ames, 1992; Bereiter 8: Scardamalia, 1989; Carr, Borkowski, 8: Maxwell, 1991 ;
Cobb et al., 1991; Nichols et al., 1990; Schunk, 1991). Eccles’ (1983) identified
two types of achievement goals, long range and short range, associated with
this aspect of motivation. These achievement goals were conceptualized as
broad life goals, such as career plans or the desire to act in a particular manner
relative to specific gender-role considerations. These reflect the purposes one
has for learning and doing different activities. Considerations of gender role

stereotypes and sex differences in achievement have dominated the research

15
on these types of goals (Wigfield, 1994). In this study, students’ perception of a

specific subject’s relevance to their future career is assessed as an achievement
goaL

This type of achievement goal may be considerably more important for
older students than younger ones. Issues of vocational or occupational
concerns are more prominent and immediate in their thinking about
themselves and their future so that career relevance could be expected to
demonstrate a stronger relationship with their achievement in the relevant
subject matter than that for younger students. In addition, as career issues
become more salient as students move from elementary to high school, one
might expect students’ subject matter career relevance to demonstrate an
increasing relationship with other aspects of the motivation, most notably

indications of their interest in and value afford the relevant subject.

51' H S .f.

Earlier, motivation was defined as one’s adaptive response to specific
situations in which personal resources are flexibly applied. In contrast to a
trait theory of motivation where an individual has a certain level of
motivation that is brought to bear in all situations and domains, the flexible
and adaptive theory suggests that one’s motivation for mathematics and for
science would not necessarily look the same. Consistent with this flexible and

adaptive conception, Harter (1983), as mentioned previously, has found that

16
children’s perceived self-competence demonstrates an increasing

differentiation among domains with increasing age. Young children
discriminate between the academic and social areas while older children
begin to discriminate among academic subjects in their competence
assessments. Wigfield (1994) reports that in a series of studies conducted with
students as early as first grade, factor analyses revealed students’ competence
beliefs formed distinct factors for the domains of math, reading, music and
sports activities.

However, the implications of these studies for the differentiation of
students’ motivation with respect to mathematics and science remains
unclear. Mathematics and science may be more closely associated than, for
example, math, reading, music and sports. Mathematics and science are often
located within the same department or college in educational institutions
while reading (language arts, literature, English), music and sports are not.
The fact that the advanced sciences require a certain degree of facility with
advanced mathematics emphasizes the close relationship between the
academic pursuit of the two domains.

Given this Close association between mathematics and science it is
interesting to note that high school mathematics and science teachers have
significantly different views of their respective subjects. Mathematics
teachers View their subject as considerably more defined, sequential and static
(unchanging) than do science teachers (Stodolsky 8: Grossman, 1995).

Therefore, one might expect students to differentiate their motivation for

17
mathematics and science to the extent that these were Viewed as different

subjects. Older students who have had. more exposure to the two disciplines
may be more likely to have been socialized into their teachers’ academic
perspective and make a distinction in their motivation for the two subjects
than younger students.

In a longitudinal follow up to an earlier investigation of children’s
interest in and beliefs about the value of math, reading, instrumental music,
and sports, Eccles and her colleagues found that the children’s beliefs about
the usefulness and importance of all subjects decreased over 3 years.
However, only the children’s interest in reading and instrumental music
demonstrated the same decrease; Children’s interest in math and sports did
not decrease (Wigfield, 1994). Self-efficacy and perceived self-competence, two
measures of expectancy, also demonstrate differences as a function of
academic domain (Bandura, 1986; Harter, 1983). These results suggest that not
only may the different aspects of students’ motivation demonstrate different
developmental trends from one another, but the developmental trend may

not be the same with respect to the two domains of mathematics and science.

I .5]. n

Students take many different kinds of tests which serve a variety of
purposes. Resnick 8: Resnick (1992) identify three main classes of educational

assessments that serve different purposes: tests for public accountability and

18
program evaluation, tests for student selection and certification, and tests for

instructional management and monitoring. Students are probably most
familiar with this last type - quizzes and tests given in classrooms by teachers.
They are developed and administered by teachers to diagnose and monitor
student learning and to inform and guide teachers as they plan and evaluate
their instruction. These may also be used by teachers as a basis for informal
and formal evaluations and reports of students’ learning. This type of
assessment is commonly developed and evaluated at the discretion of the
individual teacher.

A second type of test students may take is one that is given to evaluate
students for selection into or out of particular educational programs and
opportunities. This type may also be administered by classroom teachers but
is probably less common in the overall experiences of students. Examples of
this type of assessment include assessments of student ”readiness” for
entrance into first grade, mastery of basic mathematics skills and ”readiness”
to study algebra, mastery of specific curricular content upon which specific
kinds of certification, recognition, or credit may be awarded. The items and
the recognition criteria for this type of assessment are not typically
determined at the classroom level by individual teachers but by some group
of educators who work to develop a commonly recognized standard for
student performance.

The third type involves tests that students take in order to obtain an

indicator of some aspect of the education system or process. These might

19
involve an indicator of the effectiveness of a particular instructional

approach or a particular curriculum. In some instances, this type of
assessment may be used to generate indicators to inform educators, policy
makers, and the public about the general state of the education system. The
items, scoring, and evaluation criteria for these assessments are always the
responsibility of a single organization that most likely has little if any
affiliation with individual teachers, classrooms, schools or school districts.
While this type of test may have a rather ”high profile” in the public arena
and may be spoken of in Classrooms as very important, these are probably
relatively infrequent for students. Since these assessments are given to
generate indicators for some level of the education system, such as the state,
school district or school, rather than indicators of individual student
achievement, the immediate effect and consequence for students is less clear
that with the other types. The assessment employed in the present study is of
this last type.

Recently there has been a great deal of discussion about the need for
”alternative” forms of assessment. At least one researcher has attributed this
dissatisfaction to the inappropriate use or misuse of the assessments that
have commonly been employed (Taylor, 1994). Dissatisfaction, confusion and
frustration have arisen when assessments of one type have been forced to
serve the purposes of another type of assessment. Discussions in everyday
language about the ”faimess” of a test often stem from such inappropriate

application of assessment results. Examples of the misuse of assessments

20
would be the attempt to use the results of a student selection or credential

exam as an evaluation of a general education program or the use of an
assessment designed to create a program evaluation indicator as an indicator
of individual student achievement.

Dissatisfaction with commonly employed assessments have stemmed
from a failure to interpret results appropriately and from overgeneralizations.
This form of misuse or misinterpretation is related more to the nature or
content of the test rather than the purpose or type of the test. The source of
dissatisfaction comes from the use of test results to draw conclusions about
constructs or issues not actually measured by the test (Resnick 8: Resnick,
1992). In such instances, there is often a mismatch between what the
assessment is measuring and what has been taught. This problem is not
necessarily inherent in the quality or type of the assessment tool employed
but has to do with what is valued within a system. In their discussion of this
phenomena Resnick and Resnick conclude that ”(t)he problem of assessment
is really a problem of curriculum and of educational goals” (pp. 59-60).

The achievement assessments employed in this study were designed as
a part of an international investigation of curriculum, educational goals, and
the teaching and learning of mathematics and the sciences. Assessment
topics and items were identified through international consensus regarding
what would be appropriate to include in measuring student achievement at
specific student levels. The assessments and the research have been designed

to create country level or regional indicators of student achievement but not

21
indicators of individual student performance.

While individual indicators of achievement and motivation are
generated and employed in analyses for this study, they are not interpreted at
this level; that is, scores are not reported for specific individuals. Indicators of
students’ motivation and achievement in the areas of mathematics and the
sciences are described, modeled and interpreted at an aggregate level
according to students’ grade level. This use is consistent with the nature and

purpose for which the assessment instruments have been designed.

“"1311! Al' |

As a general framework for understanding students’ achievement
motivation and behavior, Eccles’ (1983) comprehensive model of
achievement performance and choice includes the origins and the causal
relationships among students’ expectancies and values. Subsequent research
by Eccles and her colleagues has yielded empirical support for many parts of
the model. For example, using confirmatory factor analysis on data from first
through twelfth graders, they found that a two factor model involving
expectancy and value had significantly better fit indices than the single factor
model. They interpreted this to mean that even first graders made a
distinction between their beliefs about what they may be good at (expectancy)
and their ideas about what is important (value) with respect to the domains

of math, reading, and sport.

22
Much of the work by Eccles and her colleagues has examined the

relationships among aspects of students’ expectancies and values and how
these relate to students’ course selection and persistence in studying
mathematics. Other studies have examined the effect of specific aspects of
motivation, such as self-efficacy or self-concept and intrinsic value on
students’ achievement behavior as measured by classroom grades. As
previously noted, the relationship between students’ motivation and their
achievement behavior as assessed by an achievement test has rarely been
examined. In addition, the developmental Changes in the mean level and
structure of many aspects of students’ motivation suggests that the
relationship between students’ motivation and achievement would not be a
static one. The developmental Changes previously noted in students’
interests, competence, and career considerations suggest that the relationship
between these motivational aspects to their achievement would differ as well.
The current study examines the relationship between students’
motivation and their performance on an achievement test as a function of
their developmental level and the subject matter domain. This involves
examining the interrelationship among the same aspects of motivation at the
three developmental levels as well as the way these motivation factors relate
to subject-matter-specific achievement at the different levels. Figure 1
illustrates how the specific aspects of motivation measured relate to

achievement according to the generalized expectancy-value model.

23

Figure 1 - Aspects of Motivation Related to Achievement

 

59" envetenee Success ritutions

@ SUBJECT

MATTER
ACHIEVEMENT
PERFORMANCE

  

 

Subject lnporhnce

 

lswject nterest

Research Questions and Hypotheses

This study employs concepts associated with a general expectancy -
value model of motivation to explore students’ motivation and how these
aspects of motivation are related to their performance on a mathematics and
science achievement test. These are described and explored as a function of
students’ developmental level. In particular, this study addresses two main
questions:

1. How does students’ motivation differ as a function of their developmental
level and the relevant subject matter? More specifically, do students’
interest, importance, and perceived competence with respect to

mathematics and science decrease across the three developmental levels

2.

24

assessed? How do students’ success attributions differ at these three

developmental levels? How do students’ perception of subject matter

career relevance Change? Does the relationship between students’

motivation in mathematics and science Change as a function of students’

developmental level?

Hypothesis 1:

Hypothesis 2

Hypothesis 3

Hypothesis 4:

Hypothesis 5:

Students’ interest, importance, and perceived competence
for both mathematics and science will decrease across the
three developmental levels assessed.

Elementary students will attribute success in both
mathematics and science more to hard work than to talent
while older students will attribute success in both subjects
more to talent than hard work.

Perceived competence and success attributions (i.e., to
natural talent/ ability and to hard work/ effort) will not be
differentiated in elementary students but will be
differentiated in older students.

Students’ subject matter related career interest will show an
increasing relationship with other motivational concepts
from middle elementary to middle school to high school.

The relationship between students’ mathematics and
science motivation will decrease across the three

developmental levels, i.e., from middle elementary to
middle school to high school.

How does students’ motivation relate to their achievement test

performance?

Is this relationship the same at each developmental level

for both mathematics and science? More specifically, does the relationship

25
between students’ subject matter career relevance and their achievement

differ over the three developmental levels assessed?

Hypothesis 6: The relationship between students’ interest, importance,
and perceived competence with their achievement will
increase across the three developmental levels assessed.

Hypothesis 7: Subject matter career relevance will demonstrate a stronger
relationship with achievement for twelfth grade students

compared to younger students.

Hypothesis 8: The relationships between motivation and achievement
will be different in the two domains of mathematics and

science.

CHAPTER 2: NIETHODOLOGY

Research Design

This study represents a secondary analysis of data gathered as a part of
the Third International Mathematics and Science Study (TIMSS) in the
United States. Sponsored by the International Association for the Evaluation
of Educational Achievement (IEA), TIMSS is a comparative study of
education in mathematics and the sciences conducted in 50 educational
systems on five continents. The goal of TIMSS is to measure student
achievement in mathematics and science in participating countries and to
assess some of the curricular and classroom factors that influence student
learning in these subjects. TIMSS will provide educators and policy makers
with an unparalleled and multidimensional perspective on mathematics and
science curricula; their implementation; the nature of student performance in
mathematics and science; and the social, economic, and educational context
in which these occur. The study employs a cross-sectional design to assess
student motivation and background and a randomized block design to assess
student achievement.

The present study employs descriptive, correlational and structural
equation analyses to investigate student motivation and to evaluate the

usefulness of an expectancy-value model of motivation in explaining

26

27
students’ performance on a large scale, multinational achievement test. This

large-scale survey was designed to obtain measures of educational
achievement representative of students in the United States at three different
age levels. The descriptive part of the study involves characterizing students’
motivation as assessed in the TIMSS Student Background Questionnaire.
MANOVA and correlational analyses are employed to create a
description of the relationship among the motivational constructs as a
function of subject matter and students’ grade level. In these analyses, subject
matter is a within subjects variable while grade level is a between subjects
variable. Structural equations are employed to test the equivalence of the
expectancy-value model of motivation in predicting students’ achievement
test performance in the two different subject matters at each of the three
student grade levels. In the structural equation analyses, subject matter and
grade level are both between subjects variables. The exception to this is
subject matter for grade 12 students where all students took a single test that

assessed both mathematics and science.

Sample

The TIMSS involved obtaining measures of students’ mathematics and

science achievement at three different developmental levels. The

international definitions for these three student populations are the two

28
grade levels containing most 9-year-old students (population 1), the two grade

levels containing most 13-year-old students (population 2), and those in the
last year, i.e., the highest level offered, of secondary education (population 3).
In the United States, the grade levels associated with these student population
definitions are grades three and four for population one, grades seven and
eight for population two, and grade twelve for population three.

TIMSS examined students in two adjacent grade levels at the two
younger student populations to obtain a pseudo-longitudinal measure of
students’ learning in the upper of the two adjacent grade levels. In TIMSS,
the focus of all data collection and analyses is upon the upper grade of these
two student populations. The same test, intended to be appropriate for the
upper grades’ curriculum, is administered to students in the two adjacent
grades so that the lower grade students’ achievement may be used as a
pseudo-pretest for upper grade students’ achievement. However, since the
focus of this study is on investigating the relationship between students’
motivation and their achievement, rather than an investigation of any
curriculum effect, this study employs data only from the upper grades for the
younger two student populations.

This study focuses solely upon data collected from students in grades
four, eight, and twelve. Since the same test is used with the two adjacent
grades, this design avoids confounding the curriculum effect on students’
achievement due to the rather large differences in the learning opportunities

found in the curricula of the two adjacent grade levels with differences in

29
achievement that may be explained by their motivation. Focusing solely

upon the upper grades for the younger student populations also reduces
variation that may be due to developmental changes across the two adjacent
grades of populations one and two and increases the interpretability of
differences that may be found across the three different grade levels.

Since the goal of TIMSS is to obtain a nationally representative sample
of student achievement, geographical primary sampling units (PSUs) were
identified and a stratified random sampling of the PSUs was made to obtain a
sample representative of the US. Schools were selected from each
geographical PSU and mathematics classrooms were then randomly selected
from these schools for participation in the educational survey. Students in
the selected mathematics classrooms participated in the mathematics and
science assessments. In this way the student sample is considered to be
representative of the entire U. S. student population at the sampled grade
levels. For the two younger student populations, a total of 26 schools, twelve
schools for student population one and fourteen schools for population two,
were selected from seven states. This school sample consisted primarily of
public schools except for two private schools, one at each of the two student
populations. In addition, four of the student population two schools were
considered magnet schools with advanced placement programs. For student
population three, 18 schools were selected from eight states. Three states but
no schools or school districts were the same between the student populations

one and two sample and the student population three sample.

30
A total of 1510 students, 778 girls and 732 boys, in grades four, eight, and

twelve participated in the educational survey. There were 516 in grade four,
266 girls and 250 boys, 702 in grade eight, 374 girls and 228 boys, and 292 in
grade twelve, 154 girls and 138 boys. Because administration of the various
instruments could occur on two separate days, some students did not
complete all parts of both the achievement instrument and the background
questionnaire. In addition, only those grade twelve students currently taking
science courses completed all the questions pertaining to science on the
background questionnaire. Only those students who had valid responses to
all the motivation items and the relevant achievement items were included
in the analyses reported here. Exclusion of cases having missing or
incomplete data yielded a total of 377 grade four students, 603 grade eight
students and 114 grade twelve students. Descriptions of the student sample

are summarized and presented in Table 1.

31
Table 1 — Description of Student Sample by Grade

 

 

Variable Grade 4 Grade 8 Grade 12
Mean age in years 10.00 13.85 17.88
(SD = 0.42) (SD = 0.46) (SD = 0.53)
Sex of students
Female 49.3 °/o 55.9 % 59.3 °/o
Male 50.7 ‘70 44.1 o/o 40.7 ‘70
Books in the home
None 0.3 ‘70 - -
Very few (1-10) 2.4 % 1.0 % 1.8 °/o
One 8118“ (ll-25) 8.1 0/o 6.6 °/o 5.3 ‘70
One bookcase (26-100) 30.5 % 32.5 % 27.4 "/0
More than one bookcase (>100) 58.8 % 60.0 °/o 65.5 %
English spoken at home
almost never 1.6 % 0.5 % 2.7 %
some of the time 5.1 "/0 4.9 °/o 5.4 %
most of the time 12.2 % 14.0 °/o 6.3 %
always 81.1 % 80.5 % 85.6 %
Patents’ education level
Don’t know 61.3 "/0 31.2 °/o 14.9 ‘70
Some school 1.1 °/o 2.0 °/o 5.3 %
High school graduate 2.7 °/o 6.8 "/0 9.6 %
Some college 8.0 °/o 12.8 "/0 13.2 %
College graduate 27.1 % 47.3 "/0 57.0 %
Instruments
51 1 1 B l I Q I. .

 

 

The Student Background Questionnaire contained items providing
information about student’s general background, i.e., age, country of birth, the
frequency with which English is spoken at home, the family’s cultural and
economic capitol, student’s time use outside of school, student’s motivation

and interest in mathematics and the sciences, and an indication of the

32
frequency with which specific instructional activities occur during

mathematics and science lessons. Items that addressed these concepts were
either adopted from previous IEA studies or were crafted specifically for
T'IMSS through the activities of the Survey of Mathematics and Science
Opportunities (SMSO) project (see Survey of Mathematics and Science
Opportunities, 1993 for more detail).

Initially, all the items on the Student Background Questionnaire were
the same for all three student populations. However, during the
development phase of the questionnaire, many expressed concern over the
response burden this placed on the youngest students. Consequently, the
SMSO eliminated a few items from the population one student questionnaire
to shorten the length of the background questionnaire and the amount of
time it would take the younger students to complete it (Schmidt 8: Cogan, in
press).

Another difference between the versions of the background
questionnaire for students at the three different population levels was
necessitated by the differentiation of the sciences. While mathematics courses
have different titles and address different branches of mathematics, there is a
greater perceived consistency and relationship between branches of
mathematics than branches of science (see, for example, Stodolsky 8:
Grossman, 1995). At the college level, mathematics is usually a single major
while teachers and others who major in the sciences usually concentrate on a

single branch of science such as biology, chemistry, or physics. During the

33
development phase of the Student Background Questionnaire, SMSO found

strong evidence internationally that this greater differentiation among the
sciences is often established in students’ experiences and the curriculum as
early as the population two student level. For this reason, most of the science
motivation items were asked successively with respect to biology, earth
science, and physical science or biology, chemistry, earth science, and physics.

In the version of the Student Background Questionnaire employed in
the United States, multiple science versions of the motivation items were
asked only of grade twelve students. Since the achievement test contained
items from all areas of science (as is explained more fully in the next section),
students’ responses to the motivation items for multiple sciences were
combined for analyses. If items were asked four separate times, once each for
biology, chemistry, earth science, and physics, students were to respond only
to those items having to do with the sciences they were currently taking. The
mean of the multiple responses by grade twelve students to more than one
science was employed in analyses for comparability with the responses of
population one and two students. The specific items used to assess students’
science motivation along with the multiple science options for grade twelve
are listed in Appendix 2.

The motivation constructs employed in the analyses in this study
include students’ subject matter Interest, Importance, Career interest,
Perceived competence, and Success Attributions. Students responded to each

item that assessed these constructs using a 4-point Likert scale. Parallel items

34
were included concerning motivation in mathematics and science. Interest,

Importance, Career interest, and Perceived Competence for both mathematics
and science were assessed with more than one item. A single item assessed
students’ attribution of success to ability and another single item assessed
students’ attribution of success to hard work. Students’ Interest in the subject
matter (i.e., mathematics or science) and their rating of the subject matter’s
Importance were both measured by three items. Students’ subject-specific
Perceived Competence and subject-specific Career Interest were both
measured by two items. The respective reliabilities, calculated according to
Cronbach’s alpha, for the mathematics scales were .83 (Interest), .71
(Importance), .40 (Perceived competence), and .70 (Career Interest). The
corresponding science scales had reliabilities of .76 (Interest), .72 (Importance),
.32 (Perceived competence), and .82 (Career Interest). Due to the shortening of
the grade four Student Background Questionnaire, the Career Interest and
Importance scales had one less item each. This reduced the Career Interest
scale to a single item for students at this grade level and therefore, no
reliability is reported. The two item Importance scale for grade four students
had reliabilities of .63 and .62 for mathematics and science respectively.
Appendix 1 identifies all the items for mathematics motivation constructs
from the Student Background Questionnaire together with their associated
reliabilities. Appendix 2 contains the same information for all the science
constructs from the Student Background Questionnaire employed in the

analyses.

35

The work behind the development of the items included on the TTMSS
student assessments involves a number of individuals from different
countries and disciplines reflecting a genuine desire to create the most
appropriate and fair assessments that have yet been employed in a multi-
national comparative educational survey (Garden 8: Orpwood, in press). This
process began with the development of the curricular frameworks for
mathematics and the sciences. The frameworks were developed to provide a
language system that would accurately describe the mathematics and science
curricula across the many varied education systems internationally. Such a
language system makes possible meaningful comparisons across a system’s
intended (i.e., system-level curricular guides), implemented (i.e., topics
actually taught in classrooms) and attained (i.e., what students have learned)
curricula as well as comparisons of these curricular elements across education
systems.

The items finally selected to be included in the achievement tests were
chosen to meet specific curricular specifications and to address key curricular
topics of interest at each of the three grade levels. The tests were designed to
balance assessment of appropriate curricular breadth as well as in-depth
assessment of key focal topics for each of the three student levels. Discussions

were conducted with representatives from many different countries to obtain

36
a description of the range of topics that could be considered appropriate for

students at each level. The mathematics and science frameworks embody the
result of much of this discussion (Robitaille, et. al., 1993).

Item development began with the formation of an international item
bank. The bank originally contained items from two previous IEA studies,
the Second International Mathematics Study (SIMS) and the Second
International Science Study (8155), as well as from national assessments such
as the National Assessment of Educational Progress (NAEP) from the United
States. Specialists in mathematics and the sciences from a variety of countries
formed the TTMSS’ Subject Matter Advisory Committee (SMAC) who worked
together with educational measurement specialists to review, write, rewrite,
and select items for the achievement tests. Each item was critically reviewed
by subject matter experts from each of the TIMSS’ participating countries and
were piloted with students in a number of countries before being selected for
inclusion on the assessments (Garden 8: Orpwood, in press).

Additionally, three item types were included in the student
assessments: multiple choice, short answer, and extended response. The vast
majority of the items were traditional multiple Choice with four or five
options presented. Short answer questions were designed to be answered
with a few well chosen words, a phrase, or one or two sentences. Extended
response items were constructed to require a more detailed and descriptive
response that would require students to write a brief paragraph of three or

four sentences or present a problem solution and then briefly explain it.

37
The TIMSS Field Trial student assessment booklets, used in the

analyses reported here, consisted of a total of eight different booklets for
students in grades four and eight. Each booklet contained all three item types.
Four booklets assessed students’ learning in mathematics and four assessed
students’ learning in the sciences. Each of the grade four mathematics
booklets contained between 50 and 55 multiple choice items, 3-7 short answer
items, and between 4 and 8 extended response items. The grade four science
booklets contained between 39 and 44 multiple Choice items, 3-7 short answer
items, and between 4 and 8 extended response items. At the grade eight level,
mathematics booklets contained between 42 and 63 multiple choice items, 3-7
short answer items, and between 4 and 8 extended response items while the
science booklets contained between 33 and 43 multiple choice items, 3-7 short
answer items, and between 4 and 8 extended response items.

Grade four booklets addressed seven different mathematics topic areas:
whole numbers, fractions and decimals, estimation and number sense,
measurement, geometry, ratios and proportions, functions relations, and
patterns, and data representation, probability and statistics. Grade eight
booklets assessed all of these same topic areas except whole numbers which
was not considered an appropriate topic for students at this grade level. In
science, the grade four topic areas were earth science, life science, physical
science, and science and technology. Grade eight topic areas were earth

science, life science, chemistry, and physics.

38
There were three test booklets for students at the twelfth grade level.

Each booklet contained either 48 or 49 items assessing both mathematics and
the sciences. These booklets were designed for the general student population
at this grade level which includes both students who have little coursework
in either mathematics or the sciences as well as students who have advanced
coursework in either mathematics or the sciences at the secondary level. For
this reason, the items were designed to measure what experts considered an
acceptable ’literacy’ level in mathematics and the sciences (Survey of
Mathematics and Science Opportunities, 1993). Each of the three booklets
contained a mixture of mathematics and science items presented in the three
different formats, multiple choice, short answer, and extended response.
Between 20 and 25 items assessed the mathematics topics of fractions and
decimals, functions and relations, measurement, estimation and number
sense, and data representation, probability, and statistics. Science topics
addressed by between 23 and 25 items included earth sciences, life sciences,
physical sciences, and science and technology. Appendix 3 presents a table
that details the number of each type of item that addressed each topic for each
of the booklets used in the study.

Mathematics and science achievement scores were constructed in the
same manner. Two achievement scores, multiple choice and short answer,
were constructed for all students. Multiple choice items were scored either
right (’1”) or wrong (’0”). The mathematics or science multiple choice score

for each student was the mean of the student’s scores on all the mathematics

39
or science multiple choice items contained in the student’s booklet. Short

answer items were also scored either right (’1”) or wrong (’0”). International
coding rubrics had been developed for the extended response items
identifying between two and five levels of correct response for each item. For
the analyses reported here, the most correct response was assigned a value of
”1”, the second most correct response assigned a value of ”0.9”, the third most
correct response assigned a value of ”0.8”, fourth ”0.7”, and fifth ”0.6”.
Incorrect or unintelligible responses were assigned a value of ”0”. The
mathematics or science short answer score was the mean of all the scores
assigned to the mathematics or science short answer and extended response
items contained in each students’ test booklet. Finally, students’ mean scores
were standardized within each assessment booklet using the T-scale which
has a mean of 50 and a standard deviation of 10. Standardized scores define
an individual student’s score relative to the mean. The use of standard scores
permits the comparison and aggregation of covariation of students’
achievement scores with background variables across achievement booklets

that may have different raw mean scores.

Data Collection

Data were collected during March, April and May of 1994. Students in

grades four and eight completed assessment instruments during the later part

40
of March and the first part of April. Grade twelve students completed their

assessments during the early part of May. Test administrators had been
recruited and trained early in 1994 by a professional research corporation
retained by the United States government to conduct all data gathering and
data entry procedures for US. participation in TIMSS. These trained test
administrators conducted all the sessions in the selected schools and
classrooms in which students completed the assessment instruments.

At grades four and eight, students completed one of eight different
achievement test booklets. Each achievement test booklet contained only
mathematics problems or science problems and consisted of two parts, Part A
and Part B. Thus students in grades four and eight completed either a
mathematics test booklet or a science test booklet. No student in these grades
completed booklets for both mathematics and science. For students in these
grades, administration of parts A and B of the booklets was separated by a
break of at least 20 minutes. Grade four students were given 30 minutes to
complete each of the two parts of the test booklet. Grade eight students were
given 45 minutes to complete each of the two test booklet parts. Thus the
total achievement testing time was 60 minutes for grade four students and 90
minutes for grade eight students.

Twelfth grade students each completed one of three different
assessment booklets that contained both mathematics and science items.
Mathematics and science items were intermingled throughout the test

booklets which were not divided into sections or parts. Grade twelve

41
students were allotted one 90 minute session to complete the test booklet

with no break during the testing session. At all three grade levels,
achievement test booklets were randomly distributed to the students in the
mathematics Class that had been randomly selected within the school as
previously described above.

A Student Background Questionnaire was completed by students in all
three grades. Administration of the background questionnaire always
occurred in a separate and subsequent session to those in which students
completed the achievement assessment. In some instances, it was possible for
students to complete the background questionnaire later the same day as the
assessment instrument. In many instances, however, particularly for twelfth
grade students, it was necessary to hold the Student Background
Questionnaire session on the day following the achievement testing in order
to refrain from a gross disruption of schools’ schedules. This in part explains
the relatively large number of twelfth grade students that completed
assessment booklets but did not complete the Student Background
Questionnaire.

Students in all three grades were given at least 20 minutes to complete
the Student Background Questionnaire. The Student Background
Questionnaire contained items that assessed students’ motivation in both
mathematics and the sciences. For those students in grades four and eight,
students completed an achievement test for either mathematics or science

and then completed the Student Background Questionnaire that assessed

42
their motivation in both mathematics and science. Grade twelve students

completed one achievement instrument that assessed both mathematics and
the sciences. They then completed the Student Background Questionnaire

that assessed their motivation in both mathematics and the sciences.

CHAPTER 3: RESULTS

This study has two main components. The first component describes
students’ motivation in mathematics and science, how aspects of motivation
relate to one another, and how students’ motivation differs across grades
four, eight, and twelve. The second component relates students’ motivation
to their performance on a mathematics and / or science achievement test. The
first five hypotheses pertain to issues related to the descriptive component
while the last three hypotheses pertain to the relationship between students’
motivation and their achievement.

Three different types of analyses were carried out to address the specific
questions and hypotheses pertaining to the study’s two main components.
Multivariate analyses of variance and correlational analyses were employed
to address the questions and hypotheses of the descriptive component. Those
pertaining to the second main component, the relationship between
motivation and achievement, were examined through correlational analyses

and structural equation modeling.

Describing Student Motivation

The main objective of this component entails describing the
relationship among the mathematics and science motivation variables at

each developmental level assessed. Table 2 presents the means and standard
43

44
deviations for the six motivation variables for both subjects for students in

fourth, eighth, and twelfth grades.

Table 2 - Motivation Means (Std Dev) by Grade Level and Subject

 

 

 

 

 

 

 

 

 

 

Grade 4 Grade 8 Grade 12
n = 377 n = 603 n = 114

Math Science Math Science Math Science

Interest 3.2 3.1 2.8 2.8 2.8 2.9
(0.7) (0.7) (0.7) (0.7) (0.8) (0.6)

Importance 3.5 3.4 3.4 3.4 3.2 3.1
(0.6) (0.6) (0.5) (0.5) (0.6) (0.6)

Career 3.3 3.3 2.8 3.1 2.7 2.5
Relevance (0.8) (0.8) (0.7) (0.8) (0.9 (0.9)

Perceived 2.9 2.9 2.7 2.7 2.6 2.6
Competence (0.6) (0.6) (0.6) (0.6) (0.6) (0.5)

Talent 2.9 2.8 2.3 2.2 2.5 2.4
(0.9) Q9) (0.8) (0.9) (0.7) (0.7)

Hard Work 3.5 3.5 3.4 3.5 3.3 3.4
(0.7) (0.7) (0.6) (0.6) (0.6) (0.7)

 

 

 

Since the motivation variables measured are conceptually related, a
single two-factor multivariate analysis of variance (MANOVA) was used to
examine the effect of subject and grade level on students’ motivation.
MANOVA evaluates the effect of one or more independent factors on the
mean levels of two or more related dependent variables. The rationale for
employing a single MANOVA rather than a series of ANOVAs is analogous
to the rationale for using one ANOVA rather than a series of paired t-tests to
examine the effect of one or more independent factors upon a single
dependent measure. ANOVA enables a more precise control of the

probability of a type-I error than multiple t-tests reducing the likelihood that

45
the null hypothesis, that there is no difference between group(s) means, is

incorrectly rejected (Glass 8: Hopkins, 1984). Similarly, MANOVA more
precisely controls the probability of a type-I error than a series of ANOVAs
preventing the unwarranted identification of differences between the means
of two or more dependent measures across two or more groups.

A repeated measures two factor MANOVA was conducted using the
mathematics and science motivation variables as the dependent measures.
Subject matter (i.e., mathematics and science) was a within-subjects factor and
grade level was a between subjects factor. This analysis provided a test for the
main effect of grade level and subject matter as well as the interaction
between the two. MANOVA holds the effect of one factor constant to
examine the effect of another factor. Accordingly, the difference between
students’ mathematics and science motivation was employed to evaluate the
effect of subject matter while the mean of students’ mathematics and science
motivation was used to evaluate the grade level effect. Furthermore, the
effect of grade level was examined by partitioning the grade level effect into
the linear and quadratic components. The intent of this analysis was not to
test specific hypotheses about the type of grade level effect but rather to
provide a full description of the difference in students’ motivation across the
three grade levels. A complete summary of all the multivariate effects

together with the corresponding univariate results is presented in Table 3.

Table 3 - Summary of MANOVA on Students’ Motivation

Multivariate Effect

 

 

 

 

 

 

 

Univariate Effect for Motivation Variables F df Significance
Subject 12.87 6, 1086 .00
Interest 0.68 1, 1091 .41
Importance 33.13 1, 1091 .00
Career Relevance 6.06 1, 1091 .01
Perceived Competence 1.09 1, 1091 .30
Talent 12.33 1, 1091 .00
Hard Work 4.58 1, 1091 .03
Linear Grade 15.61 6, 1086 .00
Interest 25.83 1, 1091 .00
Importance 34.45 1, 1091 .00
Career Relevance 68.45 1, 1091 .00
Perceived Competence 24.38 1, 1091 .00
Talent 15.48 1, 1091 .00
Hard Work 5.15 1, 1091 .02
Quadratic Grade 24.66 6, 1086 .00
Interest 30.49 1, 1091 .00
Importance 9.80 1, 1091 .00
Career Relevance 0.43 1, 1091 .51
Perceived Competence 0.18 1, 1091 .67
Talent 51.68 1, 1091 .00
Hard Work 1.68 1, 1091 .20
Subject by Linear Grade 5.08 6, 1086 .00
Interest 5.16 1, 1091 .02
Importance 2.57 1, 1091 .11
Career Relevance 10.30 1, 1091 .00
Perceived Competence 1.02 1, 1091 .31
Talent 1.01 1, 1091 .31
Hard Work 2.00 1, 1091 .16
Subject by Quadratic Grade 24.66 6, 1086 .00
Interest 1.22 1, 1091 .27
Importance 0.52 1, 1091 .47
Career Relevance 140.47 1, 1091 .00
Perceived Competence 0.12 1, 1091 .73
Talent 1.02 1, 1091 .31
Hard Work 0.00 1, 1091 1.00

 

47
The two factor MANOVA on students’ motivation (i.e., Interest,

Importance, Career Relevance, Perceived Competence, success attributions to

natural Talent and Hard Work) revealed a significant linear grade level by

subject interaction, P (6, 1086) = 5.08, p < .001 as well as a significant quadratic

grade level by subject interaction, F (6, 1086) = 24.66, p < .001. Figure 2

graphically represents the interaction of subject matter and grade level by
showing the difi‘erence between mathematics and science motivation means

at each of the three grades.

Figure 2 - Differences Between Mathematics and Science Motivation Means

 

 

 

 

 

 

by Grade
E
°‘2 " +CAREER
+IMPOFITANCE
g 0.1 +
.2
8 +TALENT
ID
2 +W
.3
‘6
g - 0.2 ~ +HARDWORK
.C
E
—II—INTEREST
- 0.3 —+
- 0.4 L i

 

 

Grade 4 V Grade 8 Grade 12

48
As shown in Table 3, univariate tests of these subject by grade level

interactions revealed a significant linear grade level effect for the difference

between students’ mathematics and science motivation for two of the six

motivation variables: Interest, P (1, 1091) = 5.16, p < .05, and Career Relevance,

F (1, 1091) = 10.30, p < .01. Career relevance was also the only variable to
demonstrate a significant interaction of subject matter and quadratic grade
level effect: P (1, 1091) = 140.47, p < .001. These results mean that grade 4

students’ mean interest in mathematics was greater than their interest in
science but that students in grades 8 and 12 demonstrated a greater mean
interest in science than mathematics. Grade 4 students expressed no
difference in their perception of the career relevance of mathematics and
science but differences were observed among older students. Grade 8 students
perceived science to be more relevant to their future career than mathematics
but grade 12 students expressed the opposite.

In addition to the significant interactions, the MANOVA also yielded
significant main effects for grade level, P (6, 1086) = 15.61, p < .001 for the
linear effect and F (6, 1086) = 24.66, p < .001 for the quadratic effect, and subject

matter, P (6, 1086) = 12.87, p < .001. Univariate tests yielded a significant linear
grade level effect for each of the four motivation variables that did not

demonstrate a significant interaction: Importance, F (1, 1091) = 34.45, p < .001;

Perceived Competence, P (1, 1091) = 24.38, p < .001; and success attributions to

49

Talent, F (1, 1091) = 15.48, p < .001, and Hard Work, F (1, 1091) = 5.15, p < .05.

Univariate tests also yielded significant quadratic grade level effects for

students’ Importance, P (1, 1091) = 9.80, p < .001 and success attribution to

Talent, P (1, 1091) = 51.68, p < .001. These grade level effects are illustrated

graphically in Figure 3.

Figure 3 - Mean of Mathematics and Science Motivation Variables by Grade

3.6

Mean of Mathematics and Science Motivation

2.2

 

3.4 ~~

3.2 r

3.0 ..

2.8 v

2.6 ..

2.4 -.

 

 

 

 

 

 

 

 

 

 

t:
\ O
+ HARD WORK
-D-~ IMPORTANCE
+ W
+TALENT
Grade 4 Grade 8 Grade 12

As can be seen in Figure 3, the quadratic effects reveal that the mean

Importance of subject-matter is quite similar and relatively high for students

in grades 4 and 8 but drops for students in grade 12. Students’ mean

attribution to natural Talent for subject-matter success reveals a different

50
pattern: students in grades 4 and 12 endorse Talent as important for doing

well to a greater extent than do students in grade 8. The linear effect seen in
Figure 3 shows that students’ mean subject-matter Perceived Competence is
greater among grade 4 students than among grade 8 students and is even less
for students in grade 12. A similar pattern is observed with students’ mean
attribution of subject-matter success to Hard Work. Nonetheless, this mean is
consistently the largest among the six motivation variables measured in this

study.

Figure 4 -Motivation Means for Mathematics and Science

 

3.4 r 8::
a...” -¢-HARD WORK

«Kw-IMPORTANCE
3.0 ~~

2.8 “r

Mean Across Grade Levels

+TALENT

 

 

 

2.6 e

I

.§\-

Mathematics Science

 

 

Univariate tests of the subject matter effect revealed a significant

difference between students’ mathematics and science motivation for three of

51
the four motivation variables that did not demonstrate a significant

interaction: Importance, P (1,1091) = 33.13, p < .001 and success attributions to
natural Talent, P(1,1091) = 12.33, p < .001 as well as to Hard Work, P(1,1091) =

4.58, p < .05. These differences are graphically presented in Figure 4. As can

be seen from Figure 4, students in general endorsed Hard Work as a reason
for doing well in science more than in mathematics. However, they endorsed
natural Talent as a reason for doing well in mathematics to a greater extent
than they did with respect to science. Students’ mean subject-matter

Importance was also greater for mathematics than for science.

“1.1.12 'II"!!!

Hypothesis one predicted that students’ interest, importance, and
perceived competence in both mathematics and science would demonstrate a
decrease across the three developmental levels. The means presented in
Table 2 and graphically represented in Figure 3 are, for the most part,
consistent with this hypothesis. The significant interaction of grade level and
subject-matter for students’ interest suggests that the hypothesized decreasing
trend is dependent upon the specific subject-matter considered. The
hypothesized trend appears to hold for student interest in mathematics but
not for students’ interest in science. The significant multivariate effect of
grade together with the subsequent significant univariate grade level effects

reported from the two-factor MANOVA support the hypothesis of a

52
decreasing trend among students’ subject-matter Importance and Perceived

Competence.

II 1.2.! '1' 111151] 11:]

Hypothesis two predicted that only elementary students would
attribute success in both mathematics and science more to hard work than to
talent; older students would attribute success in both domains more to talent
that to hard work. As may be surmised from Table 2 and the representations
of students mathematics and science motivation in Figure 3, this hypothesis
is not supported by the data. A second MANOVA was performed with
students’ mathematics and science motivation measures to obtain specific
contrasts between their success attributions to Hard Work and Talent. The

MANOVA has a significant multivariate grade level effect, P (24, 2162) =

18.75, p < .001, together with significant univariate tests of the difference
between Hard Work and Talent both in mathematics, P (2, 1091) = 11.80, p <

.001, and science, F (2, 1091) = 35.27, p < .001, across grades 4, 8, and 12. This

means that, on average, students endorsed hard Work as a reason for doing
well in a subject to a greater extent than they did natural Talent. Contrary to
the hypothesis, this is true for students at all three grade levels and with
respect to both mathematics and science. In fact, at all three grade levels and
with respect to both mathematics and science, students’ mean level

attribution of success to Hard Work was either the highest or second highest

53
of the six motivation means while their mean level attribution of success to

natural Talent was the lowest.

3 1001‘ ' ‘ 1‘01 HU‘ '1 ‘ 1.10. ‘ sue-150-1.

Hypothesis 3 addresses the relationship between students’ perceived
competence and their success attributions (i.e., to either talent or hard work)
predicting that these would not be differentiated in elementary students but
would be differentiated in older students. Table 4 presents the correlations
among these variables in both mathematics and science at each of the three
grade levels.

Table 4 — Correlations Between Perceived Competence and Success
Attributions by Subject and Grade

 

Mathematics Science
Talent Hd er Comp Talent Hd er Comp

Grade 4

Talent 1.00 1.00

Hard Work .35" 1.00 .26“ 1.00

Competence .13" .17" 1.00 .03 .14" 1.00
Grade 8

Talent 1.00 1.00

Hard Work .04 1.00 .05 1.00

Competence - .03 - .04 1.00 - .05 - .02 1.00
Grade 12

Talent 1.00 1.00

Hard Work - .15 1.00 .01 1.00

Competence - .13 - .27" 1.00 - .03 .00 1.00

 

two-tailed significance " p < .01 “i p < .001

54
Students’ mathematics perceived competence and success attributions

(i.e., talent and effort) all significantly relate to each other at grade four. Grade
four students’ science attributions are similarly related except that the
correlation between their Perceived Competence in science and attribution of
success in science to natural Talent is not significant. In contrast, none of
these relationships is significant with grade eight students. Only one of these
relationship was significant among twelfth grade students —the correlation
between students’ perceived mathematics Perceived Competence and their
attribution of mathematics success to Hard Work.

This pattern of relationships among students’ Perceived Competence
and success attributions is consistent with hypothesis 3: these relationships
are positively and significantly related among grade four students but not
among students in grades eight or twelve. This means that these concepts are
not clearly differentiated in grade 4 students while they are differentiated

among grade 8 and grade 12 students.

‘ 1-1.. 01.1: a 0‘ . 0 HO! ;!0_I

[I
.L.
-

l_"'.l° ° 1 '1‘

The relationship between students’ subject-matter-specific career
relevance and other aspects of motivation is the substance of hypothesis four.
This hypothesis predicted that students’ subject-matter-specific career
relevance would demonstrate an increasing relationship with other

motivational concepts from middle elementary to middle school to high

55
school. These correlations are illustrated in Figure 5 and Figure 6 and

presented in Table 5. The relationships between students’ subject-specific
career relevance and other motivational aspects appear quite similar for both
mathematics and science. Not all of the correlations demonstrated the
straightforward increase with other motivational variables across ages as
predicted. Consistent with hypothesis four, students’ mathematics Interest,
Importance and Perceived Competence demonstrate an increasing
relationship with their perception of the subject’s Career Relevance across the
three grade levels.
Figure 5 — Correlation Between Mathematics Career Relevance and Other
Aspects of Mathematics Motivation by Grade

0.70

 

0.60 ~~

 

0.50 -» +MPOHTANCE
0.40 -» -o—HARDV\K)FK
0.30 ~~ +WTEREST
0.20 ,_ +TALENT

0 10 +oaw=EIENCE

 

 

 

 

1..

0.00 .,

 

 

 

Grade 4 Grade 3 Grade 12

56
The picture for students’ science motivation, illustrated in Figure 6,

appears slightly different: these relationships are greater at grade 12 than grade
4 but at grade 8 are less than at grade 4. In contrast, and contrary to what was
predicted in hypothesis four, the relationships between students’ Career
Relevance and their success attributions (i.e., Talent and Hard Work/ effort)
do not appear to increase but to decrease across the three grade levels.

Figure 6 - Correlation Between Science Career Relevance and Other Aspects
of Science Motivation by Grade

 

 

 

 

 

 

 

 

 

0.70
0.60 "
0.50 -» J—MPORTANCE
0.40 «P —u—INIEREST
0.30 -»
-o—HAFDWOFI<
0.20 ~-
+TALENT
0.10 .. "
0.00 «r W
0.10
'0.20 i + i l i
Grade 4 Grade 8 Grade 12

Table 5 summarizes the correlations across the three grade levels
between students’ career relevance and the other aspects of motivation for
mathematics and science. Marascuilo (1966) described a general method for
evaluating comparisons among statistics such as correlations and proportions

as well as means or medians. The ratio between the square of the contrast

 

 

57

and the contrast variance, has an approximate x2 distribution

x2=‘—”—

6"
with I - 1 degrees of freedom where I is the number of independent statistics
being compared. Table 4 contains the X2 values for the linear contrast across
the three grade levels for each motivational aspect and the associated

probability value of each X2 obtained. In each case, the contrast degrees of

freedom is 2.

Table 5 — Correlations Between Career Relevance and Other Motivation
Variables by Subject and Grade

Grade 4 Grade 8 Grade 12 Z: Wu“... X: p

 

 

value
Mathematics
Interest .23" .44" .63" 62.59 .000
Importance .45“ .49" .69" 21.85 .000
Competence .05 .28“ .37“ 46.50 .000
Talent .18" .04 .03 37.21 .000
Hard Work .33" .22“ .01 150.21 .000
Science
Interest .36" .15” .59" 18.45 .000
Importance .50" .35“ .65" 7.94 .019
Competence .14" .11 .29" 10.22 .006
Talent .16" .01 - .16 51.00 .000
Hard Work .32" .25" .08 48.74 .000
two-tailed significance " p < .01 “ p < .001

The results reveal that the linear trends illustrated in Figure 5 with
students’ mathematics motivation are statistically significant (p < .001). These
linear trends are also statistically significant for students’ science motivation

(p < .05). However, as Figure 6 would suggest, the quadratic trend for

58
students’ science Interest, Importance, and Perceived Competence across

grades 4, 8 and 12, are also significant and yield larger x2 values than the

linear contrasts (Interest, )5: unadratic = 114.72, p < .001; Importance, x: mm...

= 48.53, p < .001; and Perceived Competence, X: wquamfic = 14.98, p < .001).

These linear trends indicate that students’ perception of the relevance
of mathematics and science to their future careers is increasingly related to
their Interest in the subject, their perception of the subject’s Importance, and
their Perceived Competence in the subject. The opposite trend is observed
with students’ success attributions. These are positively related to students’
perception of the relevance of mathematics and science to their future career

among grade 4 students but not among students at grade 12.

.0 004‘ ' : ‘10 10 31‘s.“; 1_-.l'tIn‘-. 1-4..- 1‘1 ' tu'v'nio

Hypothesis 5 concerns the relationship between students’ mathematics
and science motivation. It predicted that this relationship would decrease
across the three grades for each aspect of motivation assessed. Figure 7 depicts
the declining relationship between the corresponding aspects of students

mathematics and science motivation from grade 4 to grade 8 to grade 12.

59

Figure 7 - Correlation Between Aspects of Mathematics and Science
Motivation by Grade

1.00

 

0.90 ..

 

0.80 ..

0.70 .-

 

0.60 4-

*HARDW
0.50 ..

+TALENT

0.40 **
+MPORTAICE

°-3° *’ +oo~l=ETBce

 

 

0-20 .. +mreaesr

 

0.10 <~

 

 

0.00 ; A - : .
Grade 4 Grade 8 Grade 12

 

Table 6 contains the correlations between these corresponding

motivational aspects at each grade level and the x2 value for the linear trend
across the three grades. A significant decreasing linear trend is demonstrated

for each motivational aspect except students’ success attribution to Hard

Work.

60

Table 6 - Correlations Between Corresponding Aspects of Mathematics and
Science Motivation by Grade

Grade 4 Grade 8 Grade 12 X3 Wm X; p

 

 

value
Interest .43“ .31" .10 70.98 .000
Importance .79“ .59“ .52" 26.51 .000
cm“ 1.00" .83" .20* 449.24 .000
Relevance
Competence .50" .36" .22" 34.66 .000
Talent .81“ .82" .71" 4.36 .113
Hard Work .83“ .74“ .68" 10.52 .005

two-tailed significance ' p < .01 “ p < .001

This decreasing relationship between corresponding aspects of
students’ mathematics and science motivation suggests that students’
motivation is more differentiated at grade 8 than grade 4 and even more so at
grade 12. Grade 12 students’ motivation in mathematics and science is much

less similar than is grade 4 students’ motivation in these two subjects.

Relating Motivation to Achievement

Hypotheses 6, 7, and 8 are concerned with the relationship between
students’ motivation and their achievement. Table 7 presents the
correlations between the aspects of students’ motivation and their
mathematics and science multiple choice and open-ended achievement
scores. These relationships are illustrated in Figures 8, 9, 10, and 11.
According to these figures, few of the relationships between the various
motivational aspects and achievement appear to be linear across the three

grades. Rather, most of the relationships appear curvilinear.

61

Table 7 — Correlations Between Motivation and Achievement Scores by
Subject, Score Type and Grade

. Grade 4 Grade 8 Grade 12 x2 Wm X2 p

 

value
Mathematics
Multiple Choice Score
Interest .22“ .17" .32" 3.37 .185
Importance .21“ .15‘ .22" 0.04 .982
career .15" .10: .26" 7.27 .026
Relevance
Competence .36" .26“ .27” 2.79 .247
Talent .01 .07 .14 14.85 .001
Hard Work .17” .02 - .14 44.78 .000
Mathematics Open
Ended Score
Interest .18" .19" .32" 7.13 .028
Importance .20" .14" .33" 6.14 .046
career .13 .12: 30* 11.61 .003
Relevance
Competence .26“ .23“ .16 4.46 .108
Talent - .04 .05 .11 20.77 .000
Hard Work .22" - .01 - .09 53.16 .000
Science Multiple
Choice Score
Interest .20" .14" .07 11.67 .003
Importance .22" .22" .01 43.47 .000
career .09 .00 .02 7.20 .027
Relevance
Competence .23" .34" .06 21.69 .000
Talent .00 - .05 .19" 27.54 .000
Hard Work .06 - .10 .07 0.06 .973
Science Open Ended
Score
Interest .12 .13" .12 0.00 .998
Importance .15" .21" .26" 4.91 .086
career .04 .03 .15 3.47 .014
Relevance
Competence .09 .30” .07 0.41 .814
Talent - .11 - .06 .13 35.08 .000
Hard Work .07 - .08 - .01 15.76 .000

 

two-tailed significance " p < .01 “ p < .001

62

.01-01‘ or .9100 1.! ' ‘ ‘ ‘0. our ' ‘ 2.1! a. 1' ‘ n

Hypothesis 6 stated that the relationship between students’ Interest,
Importance and Perceived Competence with their achievement would
increase across the three grade levels. Contrary to hypothesis 6, these
correlations do not appear to increase linearly across the three grades for any
of the four different achievement scores. Although all the correlations
between students’ mathematics multiple choice and open-ended scores with
Interest and Importance are significant, the only significant linear increases

across the three grades are the correlations between students’ Interest and

Importance with their mathematics open-ended achievement score ( I: Wan...

= 7.13, p < .05 and X22 vim” = 6.14, p < .05 respectively). Quite the opposite of

what was predicted in hypothesis 6, the correlations between students’

Interest and Importance with their science multiple choice achievement

scores demonstrate significant linear decreases ( I: when, = 11.67, p < .01 and

x: 01m, = 43.47, p < .001 respectively).

Although eight of the twelve correlations across the three grades
between students’ Perceived Competence and their achievement scores are

statistically significant, no discernible pattern seems immediately obvious.

Linear contrasts across the three grade levels yield non-significant X2 values

for both types of mathematics scores ( X: 01m,“ = 2.79, p = .247 for multiple

choice and X: when = 4.46, p = .108 for open-ended). Students’ perceived

63
Figure 8 — Correlations Between Mathematics Motivation and Multiple

 

 

 

 

 

 

 

 

 

Choice Score by Grade
0.40
0.30 4- /
+Interest
0.20 -.
+Importance
0-10 ” +Career
+Com etence
0.00 -. p
+Talent
-0.10 ~»
--O—Hard Work
-0.20 t 1 1.
0 4 8 12

Figure 9 —Correlations Between Mathematics Motivation and Open-Ended

 

 

 

 

 

 

Score by Grade
0.35
0.30 4-
0.25 ~~ +lnterest
0.2 «-
0 +lmportance
0.15 —»
H +Career
0.10 «~
0.05 1” +Competence
0.00 ~- +Talent
-0.05 ~- —o—Hard Work
—O.10 i 1

 

 

 

64
Figure 10 - Correlations Between Science Motivation and Multiple Choice

 

 

 

 

 

 

 

 

 

Score by Grade
0.35
0.30 ~-
0.25 1
+lnterest
0.20 ..
+Importance
0.15 -~
+Career
0.10 .. ‘
‘ +Competence
0.05 -.
A +Talent
0.00 ~-
—0-Hard Work
-0.05 ..
-0.10 .' .1
0 4 8 12

Figure 11 —Correlations Between Science Motivation and Open-Ended Score
by Grade

0.30

 

0.25 e~

 

0.20 -. +Interost

0.15 ~~ A +|mportance
0'10 ”b : +Career
0.05 -. : 5
+Competence
0.00 ~—
+Talent
-0.05 ~-
—0-Hard Work
-0.10 -*

-0.15 . . .
0 4 8 12

 

 

 

 

 

 

 

 

65
Perceived Competence demonstrates a curvilinear relationship with their

science achievement scores across the three grades with the highest

correlations occurring with grade 8 students ( xiwquadmfic = 35.40, p < .000 for

multiple choice and I: wquadmfic = 50.61, p < .000 for open-ended). In addition,

out of the 24 correlations across the three grade levels between students’
success attributions and their achievement scores, the only statistically

significant correlations occur with grade 4 students’ mathematics scores: r =
.17 (p < .05) for hard work and mathematics multiple Choice and r = .22 (p <

.05) for hard work and mathematics open-ended score.

Hypothesis 7 stated that subject-matter career relevance would
demonstrate a stronger relationship with achievement among grade 12
students compared to the younger students. As can be seen from the
correlations in Table 7, this hypothesis received mixed support. Across the
three grade levels, the only statistically significant correlations between
students’ Career Relevance and their achievement were in mathematics. For
both the multiple choice mathematics score and the open-ended mathematics

score, the correlation with career relevance demonstrated a linear increase
from grade 4 to grade 12 ( 1: WM = 7.27, p < .05 and x: 01m = 11.61, p < .01).

In science, there did not appear to be any relationship at all between either

66
students’ multiple choice score or their open-ended score and their perception

of the relevance of science to their future career. The only exception was the
significant positive correlation between students’ science multiple choice

science score and Career Relevance among grade 8 students.
a 1004' ' ' Hel‘": ' 1].. ‘r ‘ u. ' 1!.11’ ._ ‘0. e .‘._1' ‘11‘1

Hypothesis 8 stated that the relationship between motivation and
achievement would be different for the two domains of mathematics and
science. Structural equation modeling was used to compare the relationship
between students’ motivation and their achievement in mathematics and
science. At the same time, this modeling approach was used to evaluate the
usefulness of a general two-factor, expectancy-value model of motivation in
predicting students’ achievement. To accomplish this, a multi-sample
analysis procedure was used in which a single model is fitted to data from
several different groups simultaneously (JOreskog 8: SOrbom, 1989). Pooled-
within-school variance covariance matrices were obtained for the motivation
and achievement measures at each of the three grade levels for both
mathematics and science. This resulted in six matrices: grade 4 mathematics;
grade 4 science; grade 8 mathematics; grade 8 science; grade 12 mathematics;
and grade 12 science.

In the two-factor, expectancy-value model, Interest, Importance, and

Career Relevance were value components while Perceived Competence and

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the two success attributions, Talent and Hard Work, were expectancy

components. The two latent variables, Expectancy and Value, were allowed
to be correlated. These two latent variables in turn predicted a third latent
variable, Achievement, which was indicated by the two achievement

measures, a multiple-Choice score and an open-ended response score. This
model was simultaneously fit across the six groups. This yielded a X2 of 348.17

with 102 degrees of freedom, p = .000. Although the X2 may theoretically be
viewed as a statistic testing the significance of a model, it is more

appropriately viewed as a ”badness-of—fit" measure in that small values that
are not statistically significant signify that the model fits the data well while

large values that are statistically significant signify that the model does not fit

the data (JOreskog 8: SOrbom, 1989). This X2 test statistic is, however, overly
sensitive to large sample sizes leading to a rejection of a model on the basis of

relatively minor misspecifications (Gerbing 8: Anderson, 1993). This has led

to the test statistic-degrees of freedom ratio comparing the X2 test statistic with
its associated degrees of freedom. Criterion for an acceptable fit using this
ratio ranges from as low as two or three to as high as five (Bollen, 1989; Bollen
8: Long, 1993). This ratio for the two-factor model was 3.4 which would
indicate an acceptable fit.

Goodness-of-fit indices indicate the extent to which the matrices
estimated according to the specified model agree with those observed with the
sample data. For this reason, some have proposed that the best way to assess

models is to compare competing models rather than rely upon any single or

68
even a series of goodness-of—fit indices (Gerbing 8: Anderson, 1993).

Previously, Eccles (1989), using structural equation modeling, had reported
that a two-factor motivation model fit better than a single factor model.
Consequently, the multiple group approach was used to evaluate a single
factor motivation model for the purpose of comparing its fit to the data with
that of the two-factor model. In this model, all motivation variables were
components of a single latent variable, Motivation, which predicted a second

latent variable, Achievement, which, again, was indicated by the two

achievement measures. This model yielded a X2 of 416.98 with 144 degrees of

freedom, p = .000. A comparison of the two models can be done by comparing
the difference between the two X2 s (JOreskog 8: SOrbom, 1989). This resulted

in a X2 of 68.81 with 42 degrees of freedom, p = .006, confirming with these
data Eccles’ (1989) earlier finding that the two-factor model was a better fit
than a single-factor model.

A third, no factor or MIMIC (Multiple Indicators and Multiple Causes)
model was applied to the six groups. This model posits a single latent
variable that is measured by two different sets of variables. Thus, each
motivation variable directly predicts a latent variable, Achievement, which
is, again, indicated by the two achievement measures. This model
simultaneously estimates the relationships among the sets of motivation and

achievement variables and basically represents a canonical analysis. This

model yielded a X2 of 22.07 with 30 degrees of freedom, p = .851 which

represents a good fit to the data. Comparing this model with the two-factor

69
model yielded a X’ of 326.10 with 72 degrees of freedom, p = .000, confirming

that this model was a better fit than the two-factor model. However, if all the

measurement error terms in the two-factor model are freed for estimation,

the resulting X2 is identical to the MIMIC model. In addition, two other
goodness-of-fit indices are also identical but the coefficients of determination,
an indication of the total amount of variance explained by all the equations in
the model, are greater for each group according to the two-factor expectancy-
value model than for the MIMIC model. Although the MIMIC model
demonstrates favorable goodness-of-fit indices, the equating of motivation
and achievement implied by the model lacks theoretical and conceptual
support. Motivation has been theorized to affect or even determine
achievement but this is not the same as positing that the two concepts are
synonymous as implied by the MIMIC model. All of this considered together
suggests that the two-factor expectancy-value structural model represents a
satisfactory fit for the sample data and is a useful model for relating
motivation and achievement. Table 8 summarizes three different goodness-

of-fit measures for the two-factor and MIMIC models.

 

70

Table 8 — Goodness of Fit Measures for Two Models

 

E - V Model MIMIC Model
X26 = 22.07 p = .001 X230 = 22.07 p = .851
Coefficient Goodness of Root Mean Coefficient Goodness of Root Mean

of Deter- Fit Index Sq. of Deter- Fit Index Sq.

mination Residual mination Residual
4 Math 2.897 0.994 0.115 0.206 0.994 0.115
4 Science 3.165 0.995 0.114 0.110 0.995 0.113
8 Math 3.709 0.997 0.051 0.129 0.997 0.051
8 Science 3.567 1.000 0.031 0.194 1.000 0.031
12 Math 3.837 0.991 0.136 0.176 0.991 0.136
12 Science 12.537 0.990 0.142 0.243 0.990 0.142

 

Although the same general two-factor structural model relating
motivation to achievement appears acceptable across the three grade levels
and two subject-matter domains assessed, examining the path coefficients
together with their standard errors provides an evaluation of the consistency
with which these various aspects of motivation are related to achievement.
However, despite the relatively good fit of the two-factor expectancy-value
model, LISREL had difficulty estimating the error portion of the model
preventing the generation of standard errors for path coefficients. Although
the MIMIC model may not be the most appropriate for representing the
structural relationship between motivation and achievement, comparing the
path coefficients for mathematics and science across the groups can provide

some information relevant to hypothesis 8.

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Hypothesis eight stated that the relationship between motivation and

achievement would be different for mathematics and science. Unfortunately,
the size of the path coefficients and their associated standard errors did not
permit meaningful comparisons to adequately address this hypothesis. Table
9 presents a summary of all motivation path coefficients for each grade and
subject. Although differences in the path coefficients for each motivation
variable at each grade level appear different between mathematics and
science, few of these path coefficients are significant. At grade 4, Perceived
Competence is the only significant path coefficient. This is significant,
however, for mathematics but not for science. At grade 8, Perceived
Competence again has a significant path coefficient and for these students it is
significant for both mathematics and science. In addition, Importance also
has a significant coefficient for science. At grade 12, none of the motivation
variables had a significant path coefficient for either mathematics or science.
While these findings do not establish a complete picture of the relationship
pattern between aspects of motivation and achievement, they do suggest that
this relationship pattern is not identical for mathematics and science nor

identical for either subject across the three grade levels.

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Table 9 — Path Coefficients (Std. Error) for MIMIC Model by Subject and Grade

 

Career Perceived Hard

Interest Importance Relevance Competence Talent Work

Gfiiifiemafics -1.322 3.365 1.266 5.459 -0.777 0.261
(1.134) (1.726) (1.000) (1.093) (0.730) (1.326)

Science 0.520 2.061 0.721 1.595 0.593 -0.971
(1.011) (1.291) (0.841) (0.943) (0.610) (0.917)

Gfiiifemafics 0.682 1.493 -0.637 3.303 -0.118 —0.814
(0.704) (1.082) (0.642) (0.767) (0.475) (0.693)

Science -0.747 3.420 -0.099 3.492 -0.444 -1.698
(0.753) (1.070) (0.622) (0.821) (0.511) (0.753)

61%;: at. 5 -1.051 -0.380 1.023 2.557 1.683 0.199
a m ‘C (1.294) (1.692) (1.162) (1.472) (0.899) (1.127)
Science -1.256 1.438 0.168 1.671 0.332 0.538
(1.133) (1.190) (0.489) (1.222) (0.468) (0.575)

 

CHAPTER 4: DISCUSSION

The results of this study reveal a complex portrait of student
motivation and its relationship to their achievement in mathematics and
science at three different grade levels. The goal of the present chapter is to
better understand this portrait by examining it in relation to previous
research and the motivational theory on which the study is based. The first
section explores the meaning and some of the implications of the mean
differences and different patterns of interrelationships among the specific
aspects of motivation involved in this study. The next section looks at the
relationship between student motivation and achievement. The last section
examines some of the limitations of the present study and concludes with

some thoughts for further research.
Interpreting the Portrait of Student Motivation

One of the most important results of this study is the significant
interaction of subject matter and grade level on the mean level of students’
motivation. The significant linear grade level by subject-matter interaction
upon the mean level of students’ Interest and the significant quadratic grade
level by subject interaction upon the mean level of students’ Career
Relevance highlights the importance of both these factors in determining
students’ motivation. The significant main effects of subject-matter and grade
level on the mean level of virtually all the other motivational aspects
measured confirm the important role these factors play in students' academic

motivation.

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74
The interaction of these two factors signifies that there is a difference in

the relative evaluation of mathematics and science from one grade level to
another. What’s important in grade 4 may be less so in grade 8. The subject
that is most fascinating at grade 4 may, at grade 8, seem much less so
compared to another subject. The subject that appears to have great career
relevance in grade 8 may, at grade 12, appear less relevant to one’s future
career plans than another subject. All of this suggests that the meaning of
certain aspects of motivation does not remain constant. The meaning of
these aspects of motivation, and hence the implications of these for students’
behavior, is dependent upon the students’ development (i.e., grade level) and
the specific subject-matter being considered. In short, student motivation is
both specific to a subject and distinctive at different developmental levels.
Motivation is not unidimensional or general but must be examined in a
subject-specific manner. This understanding of student motivation calls into
question the assumption made by some that students' interests and academic

preferences are "cast in stone" rather early in students' academic career.

Interest

In this student sample, fourth graders expressed more interest in
mathematics than science. Eighth graders’ interest in the two subjects was
almost the same while twelfth graders expressed more interest in science than
mathematics. What explanations could be offered for this shift in the relative
evaluations of these two different subjects? One possible explanation may
have to do with the relative exposure students have had to these two subjects.

Students may simply be more interested in whichever subject is most salient

75
in their current experience. Mathematics is typically a fundamental and

highly visible part of the elementary curriculum and, hence, elementary
students’ experience. Science is typically not taught as frequently as
mathematics in elementary schools and may not be as familiar to grade 4
students. Eighth grade students typically spend an equal amount of time in
mathematics and science classrooms while all the grade 12 students surveyed
were enrolled in science classes but not all were enrolled in mathematics
classes. However, such an explanation seems rather superficial and at odds
with the flexible and adaptive nature of motivation as developed in the
introduction.

An alternative explanation may be found in the person-environment
fit theory of Eccles and her colleagues (Eccles 8: Midgley, 1989; Eccles, 1993).
According to their research and theory, the decline in students’ subject matter
interest from elementary school to middle school stems from the mismatch
between students’ cognitive and social needs and the cognitive and social
demands placed upon them at the middle school level. Developmentally,
middle school students have greater cognitive abilities and increased social
interests and skills than elementary students. However, as Eccles develops
the argument, middle school classrooms are often less personal than the
elementary classrooms students have experienced and, contrary to what one
might expect, the academic work in middle school is often less cognitively
demanding than that in elementary school. At a time when students are
ready for more interpersonal interaction, more demanding academic
activities, and more responsibility they actually encounter less of these in

their middle school classrooms than they did in their elementary classrooms.

76
Presumably, this mismatch could continue and be compounded through high

school.

Still, the person-environment fit theory only explains the decline in
students’ interest from elementary school to middle school and, perhaps, into
high school. The explanation for the developmental differences in students’
relative interest in mathematics and science and, particularly, the increased
interest in science demonstrated by the grade 12 students in this study may
also reside in the nature of these two academic disciplines as they are
encountered in schools. To the extent that students are socialized by their
teachers and come to share the disciplinary perspectives of their teachers,
students may find one subject a better ”fit” than another at different points in
their development. According to Stodolsky (1995), mathematics teachers
rated their subject as being more defined and static than did science teachers.
In addition, there is typically more diversity in the learning activities and
social interaction in science classes than in mathematics classes. Mathematics
classes typically involve little social interaction or discussion and students
usually work alone on exercises for a good portion of the class. In contrast,
science classes often involve experiments or other cooperative learning
activities that provide students an opportunity to talk and work together.

Thus, grade 4 students’ greater interest in mathematics might be a
reflection of the relatively more rigid and static nature of mathematics. The
relatively more structured approach to mathematics together with the
relatively less time devoted to science (Stodolsky & Grossman, 1995) might be
a better match with the cognitive and social needs of children at this age.
Grade 8 students might not yet fully appreciate the differences between the

two subjects in their classrooms. While these students are rapidly developing

77
new cognitive abilities, social awareness, and social needs, the composite

portrait in which students rate their interests in the two subject similarly may
not accurately represent any particular student at this age. The portrait
formed on the basis of mean levels may disguise the differences between
those more rapidly developing students with needs and ideas similar to older
students and those who are yet more like younger students. Thus, this may
be a period of transition that reflects both changes in students’ intellectual and
social functioning as well as changes in the curriculum. Grade 12 students’
greater interest in science could be explained by the relatively better fit science
classrooms have to their general social and cognitive needs — greater social
interaction, less structural rigidity while still presenting generally challenging

cognitive demands.

Career Relevance

The specificity of students’ motivation and the impact of their
developmental level on their motivation is particularly evident in their
indication of a subjects’ relevance to their future careers. Fourth graders rated
mathematics and science equally relevant; eighth graders rated science more
relevant than mathematics and twelfth graders rated mathematics more
relevant than science. The meaning of these differences in students’ ratings
of career relevance is made more difficult to interpret given that students at
each developmental level rated mathematics as more important than science.
In addition, students’ interest in the two subjects demonstrated yet a different

developmental pattern.

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As previously noted, fourth graders expressed more interest in

mathematics than science, eighth graders expressed only slightly more
interest in science than mathematics, and twelfth graders expressed a greater
interest in science. Thus, twelfth graders present the curious profile of rating
mathematics more important than science, more relevant to their future
careers yet expressing greater interest in science. This is all the more curious
given that in this student sample, all twelfth graders were currently taking at
least one science but not all were taking a mathematics class.

Given these patterns of students' interest and ratings of a subject's
important and career relevance for two different subject-matters across the
three grades, one might suppose that these motivational aspects were not
integrated into a coherent whole. Perhaps a student's interest in a subject is
essentially independent of evaluations of the subject's importance or
relevance to the student's personal future career. As reasonable as this may
seem, this interpretation would suggest that these aspects of motivation are
less integrated or coherent among twelfth graders than among fourth graders.
This contradicts one of the foundational concepts of career theory - that
individuals desire to implement their self-concepts in their career choice.
According to the career development theories of Super (1990) and Holland
(1973), to the extent possible, people choose careers that are consistent with
their interests, values and abilities. The more differentiated and developed
concept of self exhibited by twelfth graders (Harter, 1983), together with career
development theory, would lead one to expect twelfth graders to exhibit the
more coherent relationship among their interest in a subject, their evaluation
of the subject's important and their perceptions of the subject's relevance to

their future career. These curious patterns between motivational aspects for

79
two subjects across the three grade levels deserve further study but, at the

least, suggest that not only is the meaning of mathematics and science
different, as concluded in the previous discussion about students' interest, but
the meaning of the specific aspect of motivation, career relevance in this
example, may also be different.

An explanation of the developmental pattern exhibited by students'
evaluation of a subject's relevance to their future careers may be built upon
the person-subject matter fit explanation developed in reference to students’
interest. In addition to the differences in subject matter previously noted,
students at different developmental levels have quite different perspectives
on their future careers. For fourth graders, the idea of a future career is not
typically a particularly pressing issue. Children at this point do not have firm
occupational or career identities nor do they have particularly well informed
understandings of various occupations (Montemayor 6: Eisen, 1977). Thus,
any subject may conceivably be as relevant to their future career as any other.

The issue of careers becomes a more relevant issue for eighth graders.
More students have given serious thought to ”what I want to be when I grow
up” and have begun to make some decisions accordingly (Kelly, 1989). If
students perceive their science classes as being a better ”fit” with their
intellectual and cognitive needs, they may also decide that science is going to
be more relevant to their future careers. In addition, science may be
presented in classrooms in a manner that more saliently links science to
careers. Classroom discussions of science topics together with the use of
specific words may more readily link science to specific careers; e.g.,

meteorology — meteorologist; chemistry - chemist; physics -

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physicist/ engineer; biology - biologist / doctor / veterinary / nurse / emergency

medical technician.

By twelfth grade, students may have had enough exposure to the world
of work to better understand the requirements, duties, and skills associated
with various careers. On the basis of their knowledge of the world of work,
they may have come to the conclusion that, despite their greater interest in
science, the mathematics they’ve encountered is more relevant to a broader

range of viable career options than are the sciences they've studied.

Effert, Ability and Bereeived Cempetenee

Contrary to previous research and hypothesis two, students
consistently attributed success both in mathematics and science more to effort
than to ability. In addition, these attributions for success in mathematics and
science demonstrated the most consistent correlations between the two
subjects across the three grades. While the means for these attributions did
demonstrate a decrease across the three grades what is perhaps more
significant is the stability of their relative rank among the motivation means.
Students’ success attribution to ability was consistently the lowest of all the
means across the three grades and both subject-matter areas whereas their
effort attribution was consistently either the highest or second highest. It
appears that there were, in this student sample, very few, if any, at any of the
three grade levels who endorsed ability more than effort as a reason for
success. These findings deserve further exploration. Directly examining the

differences between each students’ success attributions and factors that affect

81
this difference may prove more enlightening than the consideration of the

two separately as has been done here.

The consistent attribution of success in a subject-matter to effort rather
than ability is all the more surprising given the theoretical explanation that
has been proposed for younger students' success attribution to effort and older
students' success attribution to ability. Stipek (1984) reasoned that success
attributions were based on the same evidence as were children's perceptions
of their competence. She reasoned that younger children based both their
perceived competence and their success attributions on the amount of effort
they expended with respect to a particular subject-matter. Older students,
given their increased cognitive abilities for self-evaluation and social
comparison, based both of these on their subject—matter-specific effort and
performance relative to that of their peers. While the results of the present
study did not confirm this differential attribution of success between younger
and older students, it did find evidence supporting Stipek's theoretically
reasoned link between younger students' success attributions and perceived
competence.

The relationship between success attributions and students’ perceived
competence were positively and significantly correlated at grade 4 but not at
the other two grades. These findings are also consistent with Nicholls’ (1990)
explanation of children’s levels of differentiation of ability and effort.
According to Nicholls, children fail to differentiate between effort and ability
and their effects until they are around six years old; effort and ability are 1
perceived to be similar leading to success. Between the ages of six and nine,
children begin to identify effort as the primary cause. Around the ages of

nine to twelve, children begin to differentiate effort and ability noting that

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variations in either may yield a change in outcome. Finally, children arrive

at the concept of ability as capacity, that is, the notion that an increase in effort
can increase a performance outcome but only up to a limit.

Inherent in the concept of ability as capacity is the notion that capacity
is relative to others. My perceived competence may not suffer, for example, if
I am unable to jump to the moon since no one has or can. However, my
perceived competence may suffer if I am unable to do something that most
everyone else is able to do such as hit a ball with a bat, whistle, or add up a
column of numbers. This notion may also explain the appearance of a
negative correlation between effort and perceived competence in
mathematics among twelfth graders. As Nicholls (1990) explains, ”the
concept of . . . capacity means that even tasks we are able to master as well as
others can -— if we expect others to need less time or effort — offer us no
prospect of a sense of accomplishment” (p. 26). This is true at least in part
because the lesser time or effort required by others implies that they have
greater ability. In this manner, the two concepts of effort and ability are
always inextricably linked but would only be positively correlated with one
another in young students who do not yet differentiate the two. Thus twelfth
graders who strongly endorse effort as a cause for success in mathematics may
also be aware that their own success requires more time than other successful
students resulting in a lower sense of perceived competence. The absence of a
similar correlation for twelfth graders in science may again be related to the
previously noted differences in mathematics and science classrooms. The
type of learning activities in science classrooms are more cooperative and
social and may present students with less opportunity to arrive at individual

evaluations of links between effort, time, and successful task completion

83
whereas activities in mathematics classrooms may make these types of

evaluations particularly salient. These explanations for a different pattern
with science are speculative but they highlight the need for further research.
Why is there a different pattern of relationship between success attributions
and perceived competence in mathematics and science? Is there something
about the way these two subjects are taught in school that could account for

this difference?

M an ub'e t-Matter e ifi i and D vel m nt

The specificity and developmental differences inherent in students’
motivation is also demonstrated by the differences in the correlations
between students’ mathematics and science motivation across the three grade
levels. The decrease in the correlations between students’ mathematics and
science motivation suggests that an individual student’s motivation is
increasingly specific and differentiated. In particular, the dramatic difference
in the correlation between students’ perceptions of the career relevance of
mathematics and science, which was perfectly correlated among grade 4
students but one of the lowest correlations observed between corresponding
aspects of grade 12 students’ mathematics and science motivation, lends
support to the notion that the meaning of these subjects changes over time
for students. The correlations between corresponding aspects of students'
motivation in mathematics and science decreased from grade 4 to grade 8 and
again from grade 8 to grade 12. The basis for these differences among students
at these three grade levels may lie in the different degrees to which these

students differentiate one subject from another. Younger students'

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motivation for mathematics appears practically identical to their motivation

for science. The relationship between mathematics and science motivation is
less similar among eighth grade students and is clearly differentiated among
twelfth graders.

Consistent with hypothesis one, the mean levels of students’ Interest,
Importance, and Perceived Competence decreased from grade 4 to grade 8 to
grade 12. This provides clear evidence in support of the deveIOpmental trend
noted by Eccles (1993), Harter, Whitesell, and Kowalski (1992) and others.
However, the practical implications of these decreases are not entirely clear.
While these declines are statistically significant this does not, and cannot,
settle the issue of the practical importance of the observed decline in students'
mean motivation levels. Does the observed decline in students' mean level
of motivation signify a decreased interest in and willingness to learn from
school? Or are these decreases simply a result of a more accurate reporting by
students — the result of older students increased self-knowledge and the
ability to communicate this knowledge. One wonders, how interested in
mathematics or science should a student be? The fact is that, according to
theories of the deve10ping self and self concept (Harter, 1983), decreases in the
mean levels of various aspects of motivation is exactly what one would
expect as students mature and develop ever more distinct personalities and
preferences.

Whatever the impact of an increasing differentiation of interests and
self may be, the issue of the practical significance of the observed decline in
students’ motivational means is even more problematic in the light of the
much greater mean differences noted among schools. In the process of

creating the pooled-within schools variance-covariance matrix for use in the

85
structural equation modeling analyses, mean differences between schools as

corresponding grade levels two to five times as great as the mean differences
due to grade level or subject-matter were discovered. This suggests that
differences in the characteristics or schools, classrooms, or perhaps even
home environments (assuming homes represented by a single school share a
certain degree of homogeneity) should also be considered in developing a
complete portrait of students’ achievement motivation. Previous research
suggests that these factors do play a significant role in students’ learning and
motivation (Ames, 1992; Cogan & Oka, 1992; McGillicuddy-DeLisi, 1985).

While the statistically significant differences between mean motivation
levels according to grade level and subject matter cannot settle the issue of the
practical importance of these differences, neither can a discussion of mean
differences alone contribute to an understanding of what an optimal level of
motivation may be. Both of these issues require some analysis that links
motivation to specific behaviors of interest. The next section explores some
of the issues involved in linking motivation to achievement through the

correlational and structural analyses employed in this study.

Conceptual and Structural Links Between Student Motivation and

Achievement

The preceding discussion has highlighted the specificity of motivation
with respect to mathematics and science. It has also been posited that
characteristic differences in these subjects and the way they are treated in
schools is a partial explanation for the observed differences. This specificity is

now extended to how motivation relates to achievement in the two domains.

86
For mathematics, hypotheses six and seven were generally supported:

the relationship between aspects of students’ motivation and their
achievement increased across the three grade levels. This picture was much
less clear for science. Many of the same aspects of motivation did
demonstrate an increased relationship to achievement from grade 4 to grade 8
but almost none of the relationships between motivation and achievement
were significant at grade 12.

The pattern of relationships between aspects of motivation and
achievement were not entirely parallel with respect to the two domains of
mathematics and science. Students' rating of the relevance of mathematics to
their future career was consistently and significantly related to the
mathematics achievement at all three grades levels. None of these six
correlations were significant for science. As suggested in the discussion of the
motivational means, this differential pattern suggests that motivation is not
only subject-matter specific but that how motivation for a specific subject
relates to achievement within that subject is also specific.

The explanation for these differential patterns may, once again, lie in
the distinct natures of mathematics and science. Although mathematics
courses may bear the names of different branches of mathematics such as
geometry, algebra, trigonometry, or calculus, there is greater perceived, if not
real, coherence among these than among the various branches of science. At
the college level, mathematics is a single major while science becomes ever
more specialized -— chemistry, chemical engineering, botany, zoology,
microbiology, and geology for example. In fourth and eighth grade, students
in the United States typically follow a general science course that provides

some exposure to all the different branches of science. However, at the high

87
school level, schools begin to offer and students begin to choose courses that

concentrate on a particular area within science. The differences among these
various branches of science are potentially as great as the differences between
any two other subjects or courses. The achievement measure for twelfth
graders was very similar to the general science measure employed at grades 4
and 8. This general science approach is more consonant with the school
experiences of students at the lower two grades and may not have been
consistent at all with the conception of science held by twelfth graders or the
more focused science classes they were taking (e.g., biology, chemistry,
physiology, physics). This general science approach may also begin to explain
why motivation demonstrated so few relationships with students science
achievement at grade 12.

Structural equation modeling revealed that motivation could be useful
in understanding students’ achievement. The specific approach employed a
single model that simultaneously estimated the relationship between
motivation and achievement at all three grades and in both subjects. The
idea that a single model could represent the relationship between motivation
and achievement for two different subjects at three different grade levels may,
at first, seem to contradict the preceding discussion stressing the specificity of
motivation. However, motivation specificity can refer to differences in an
individual’s motivation in two areas. A single model may represent the
structural relationships but the relative strength or value of these
relationships could differ. An entirely subject-specific model would
necessarily require that the number of factors in the model and the structural

relationships among them would be different as well.

88
The structural modeling analyses in this study did not attempt to

address the issue of an entirely subject-specific model, i.e., one relating
motivation to achievement for mathematics and another one relating these
two for science. The analyses in this study simultaneously fit a single
structural model to data representing the relationship between motivation
and achievement for two different subjects at three different grade levels.

The results of this analysis suggest that the same two factor, expectancy-value
model, could represent this relationship both for mathematics and science
across grade 4, 8, and 12. Although the strength of these relationships looked
different in each of the six sub-samples, problems in the estimation procedure
prevented a thorough analysis and confirmation of these differences.

One of the strengths of structural equation modeling is that a number
of models regarding the relationships among a set of variables may be
proposed and empirically evaluated against data gathered from a relevant
sample population. The three different models evaluated represent different
ways of thinking about motivation. The MIMIC, or no factor, model implies
that motivation and achievement are the same; the achievement measures
simply provide alternative measures of the motivation indices. While many
have argued for a close connection between motivation and achievement
with motivation playing a pivotal role in determining the level of one's
achievement, the two constructs are not synonymous or equivalent.
Motivation refers to the personal resources, constructs, and ideas a person
brings to bear in a particular situation. Achievement refers to a specific type
of behavior one has accomplished at a given time within a given setting or
accumulated over a series of times. However, many factors beyond one's

motivation may affect one's level of achievement. Indeed, as Weiner (1990)

89
has noted, academic achievement is an "overdetermined" phenomena — it

can be related to a wide variety of psychological and sociological factors.

The preference for a two-factor motivation model over a single factor
suggests that students do consider two different types of issues involving
their academic behavior: their expectancies or how they think about their
performance and their values, the various reasons why they would engage in
the behavior under consideration. However, positing the important role of
motivation in determining academic achievement and modeling this
relationship is not to suggest that motivation tells the whole story about
achievement. Motivation may be a necessary but not sufficient condition for
determining a specific level of academic achievement. In relation to
students' academic achievement, motivation may function similarly to the
electrical system of a vehicle - it is necessary for proper functioning but the
entire performance of the vehicle is determined by the specifications of other
systems as well such as the engine, transmission, body shape and style. In this
sense, all aspects of motivation together may function in a manner similar to
Nicholl's (1990) concept of ability as capacity - that is, motivation is important
but its effect on actual performance in any given situation may be
circumscribed by a variety of other factors. Indeed, motivational indices may
well serve as indicators of a person's general readiness and capacity to
perform. More specifically, a student may place a high value upon
mathematics or science and have reasonably high expectations about doing
well in these subject areas. The student's ability to learn either of these
subjects and perform well on an achievement measure, however, can be
affected by a number of other factors. These may include a variety of

classroom issues affecting the quality of learning such as adequate lighting,

90
temperature control, and air quality conducive to learning, the quality of

learning activities and instruction, and the opportunity to learn the specific
topics included on the achievement assessment.

The discussion throughout this study has often referred to motivation
and achievement as an abbreviated way of referring to a particular set of
concepts. It is not assumed that the measures employed in these analyses
exhaust or fully capture either of these constructs. Other ways of assessing
both of these constructs are possible and may be desirable for future
investigations. Nonetheless, the portrait of motivation that emerges from
the present analysis suggests that students’ academic or achievement
motivation is not a stable or unitary concept. This is an important insight for
parents, classroom teachers, administrators, and test constructors among
others to maintain. As the student quoted at the beginning of this paper
noted, students do change. What motivates, excites, interests, and activates
students’ energies and personal resources for learning are not likely to be
identical across all subjects nor across the entire stretch of schooling. The
specific aspects of motivation that are strongly related to achievement in
elementary schools, such as the perceived importance of a subject, may be
joined by other motivational aspects, such as the perceived relevance for a
subject to a future career, in relating strongly to achievement later in

students’ schooling.
Limitations and Future Considerations

Several aspects of the present study contain limitations that affect the

interpretation of results. Some of these same issues suggest directions for

91
future research. This study employed a cross-sectional design to explore

. developmental issues. Students' grade level was employed as a way of
investigating age-related differences. While there is a substantial overlap
between grade level and age level the two are not identical and, while the
difference between any two students in two different grades would be
constant, there would be considerable variation in the age differences of
individuals in different grades. This would not be case if the same students
had been involved in the study at three different time periods when they
were in the three grades employed in this study. While there is nothing in
the data to suggest a particular cohort effect upon the factors considered here,
the conclusions suggesting developmental differences require confirmation
with longitudinal data.

The present study examined the effect of grade level and subject-matter
on students’ motivation. A number of previous studies have also found
motivational differences between boys and girls (e.g., Post-Kammer & Smith,
1985; Eccles & Jacobs, 1986; Hackett 8r Betz, 1989). The extent to which a
portrait of boys’ and girls’ motivation would differ from the motivation
portrait constructed in the present study is unknown. It may well be that no
significant changes would be necessary. Early analyses of item level responses
seemed to indicate few if any differences in the responses of boys and girls.
However, simple comparisons of means may mask more dramatic differences
in the way in which factors relate to one another. If this were the case, the
modeling approach employed in this study treating all students the same
would mask the differences between boys and girls. It may well be, for
example, that the relevance of a subject is more related to other aspects of

motivation for boys than for girls or that girls’ interest in science is more

related to their perception of the impocffance of science than is the
corresponding relationship in mathematics. These relationships might also
differ for boys and girls at different grade levels — the relationships may be
more similar among younger students, for instance. Separately modeling the
relationships between the aspects of motivation and achievement for boys
and girls would contribute to a more complete portrait of motivation.

Although the sample in this study is representative of students in the
United States, the twelfth grade sample is admittedly biased. Unlike the
general population of twelfth graders, the students in this study were all
currently taking at least one science class with some taking two or even three.
The extent to which this has affected the means and relationships reported
here is unknown. Particularly in those analyses involving science
achievement, much of the difficulty in finding the same patterns observed in
the lower grades could be due to a more restricted range. A more general
sample of twelfth graders that included many who were not currently taking
a science would probably yield more students having less science motivation
and lower science achievement scores. Given the general nature of the
science test, however, this is by no means a certainty.

In addition, the instrumentation for science may not be as sensitive to
subject specific motivation as were the mathematics items despite their
parallel construction. As noted, science is a more diverse domain than
mathematics. Consequently, while items were asked once about
mathematics, at grade 12 some science items were asked three or four times
each in reference to a specific science. In order to parallel the general science
format in grades 4 and 8, the responses of students taking more than one

science were averaged to obtain an indicator of ”general” science motivation.

93
Furthermore, the specific manner in which science motivation was assessed

at grade 12, i.e., with respect to biology, earth science, chemistry, and physics,
might not relate well to the general science nature of the grade 12
achievement measure. The grade 12 science assessment was created to
measure a literacy level of scientific knowledge - a level not much more
advanced or in-depth than what was expected of grade 8 students. Phrasing
the motivation questions either broadly in terms of ”science” for some items
and more specifically in terms of the four broad branches of science for other
items probably did not tap the type of science motivation that would related
well to the performance of these advanced science students on a general
science literacy assessment.

All of the motivation items have good face validity - teams of
researchers worked to word and construct items to address the specific aspects
of motivation and constructs of interest. Nonetheless, ambiguities in the
meaning and interpretation of some items remain. More specifically, the way
in which the success attribution items are worded it would be possible for
students to respond either on the basis of their belief about what is generally
necessary for someone to do well or on the basis of their belief about what is
necessary for their own personal. success. In addition, some constructs, such
as success attributions and perceived competence, were measured with fewer
than three items. Three items are often recommended for obtaining reliable
measures (McArdle, 1996). The lower reliabilities of the two-item fourth
grade Importance scales compared to the three-item scales for older students
illustrates the effect that fewer items have on obtaining reliable measures.
These measurement issues do not necessarily negate the specific and

multidimensional portrait of motivation constructed in this study but they

94
do highlight the need for further confirmatory research with more refined

motivation measures.

Because a few of the motivation items were not presented to grade 4
students but only to students in grades 8 and 12, motivational analyses were
conducted with scales of two or three items where possible rather than with
individual items. The consequence of this is that the structural equation
modeling amounted to a second order confirmatory factor analysis. The
reliability of the scales would affect the quality of the modeling analyses.
Some of the problems encountered in estimating the error portion of some of
the models may well be related to this issue. Evaluation of the various
structural models might be improved if the analyses were conducted with all
the corresponding motivation items rather than using the motivation scales.

As previously mentioned, structural equation modeling is a powerful
tool for examining and evaluating theoretical models. However as with
other statistical procedures, these evaluations require that a number of
assumptions about the data be made. Consequently, the results of analyses
are always dependent on the quality of the data that inform them. Restriction
of range and the degree to which data deviate from the assumed normal
distribution are two important factors that affect the quality of structural
modeling analyses (McArdle, 1996). The biased twelfth grade student sample
probably restricted the range of both the motivation and achievement
measures. In addition, the distributions for almost every item were skewed at
all three grade levels. Out of four possible categorical responses, students
consistently responded to either the two upper or the two lower categories,
depending on the item, much more frequently than the two remaining

categories. This skew in the raw data is retained in the later summaries and

95
scales which probably contributed to the estimation problems encountered in

the modeling analyses. The problem of skewed data is especially common
with the type of categorical data employed here. Although not a complete
solution to this problem, some have recommended the use of tetrachoric or
polychoric correlations rather than covariances in structural modeling with
categorical variables (Muthén, 1993). The modeling analyses employed in this
study were conducted with the pooled-within schools variance covariance

matrix and might be improved if conducted with polychoric correlations.
Summary

The current study has drawn upon concepts associated with a general
expectancy-value model of motivation to examine issues of specificity and
developmental differences in students’ motivation. These issues have been
explored by: 1) examining specific aspects of students’ motivation, i.e., subject
matter interest, importance, career relevance, perceived competence, and
success attributions, and their interrelationships, and 2) evaluating the
usefulness of these aspects of motivation in predicting students’ performance
on an achievement test. Students’ motivation in two different subjects,
mathematics and science, and at three different developmental levels, grades
4, 8, and 12, was assessed to examine these issues.

Analyses of means and correlations demonstrated both the specificity
and developmental differences in students’ motivation. Achievement
motivation is not a stable or unitary construct. In general, motivation
becomes more specific and differentiated across the three grade levels.

Decreases in the mean levels of students’ indication of their interest in a

96
subject, the importance of a subject, and their subject-specific perceived

competence were observed. In addition, these aspects of motivation together
with students’ perception of a subject’s career relevance were correlated to two
different measures of achievement. These relationships between motivation

and achievement appeared greater for mathematics than for science.

APPENDIX A

Items used to assess Students’ Mathematics Motivation

EXPECT ANCY
Bemeixedfiomnejence — a = .40

I usually do well in mathematics.
Mathematics is a hard subject. (Reversed scored.)
5 5 i] .
To do well in mathematics you need lots of natural talent.
To do well in mathematics you need lots of hard work studying the

subject.

VALUE
humst - a = .83

How much do you like mathematics?
I enjoy studying mathematics.

Mathematics is boring. (Reversed scored.)

W- on = .71, a = .63 for grade 4.
I think it is important to do well in mathematics lessons.
I think the study of mathematics is important.

*Mathematics is important to everyone’s life.

CareeLRelmnce - a = .70
I would like a job that involved using mathematics.

*I need to do well in mathematics to get the job I want.

*Items not included in the grade four version of the Student Background

Questionnaire.

97

APPENDIX B

Items used to assess Students’ Science Motivation
Multiple science options for grade twelve students in brackets [].

EXPECT AN CY

Berseiyedfiomnetence - a = .32
I usually do well in science. [biology/ earth science / physical science]
Science is a hard subject. [biology/ earth science/ chemistry/ physics]

(Reversed scored.)

5 5 || .1 I'
To do well in science you need lots of natural talent.

To do well in science you need lots of hard work studying the subject.

VALUE

Interest - a = .76
How much do you like science? [biology/ earth science / physical science]
I enjoy studying science. [biology / earth science / chemistry / physics]
Science is boring. [Biology/ earth science/ chemistry / physics] (Reversed

scored.)

Impedance — a = .72, a = .62 for grade 4.
I think it is important to do well in science lessons.
I think the study of science is important. [biology/ earth
science / chemistry / physics]
*Science is important to everyone’s life. [biology/ earth

science / chemistry / physics]

98

CareeLRelexancc — a = .82
I would like a job that involved using science.

[biology / earth science / chemistry / physics]

*1 need to do well in science to get the job I want.

[biology / earth science / chemistry / physics]

*Items not included in the grade four version of the Student Background

Questionnaire.

99

APPENDIX C

Item Content Categories and Type by Book and Population

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Mathematics
TOPIC BOOK 3 BOOK 5 BOOK 6 BOOK 8
MC OE MC OE MC OE MC OE
WholeNumbers 19% 5% 23% 6% 8% 0% 11% 2%
Fractions & Decimals 10 % 2 % 2 % 0 % 6 % 0 % 33 % 8 %
Integers, Real Numbers, & Number 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 %
Concepts
Estimation & Number Sense 5 % 2 % 6 % 2 % 18 % 3 % 2 % 0 %
Measurement 8% 0% 10% 0% 9% 8% 3% 2%
Geometry 21% 5% 6% 0% 9% 0% 11% 0%
Ratios&Proportions 6% 0% 16% 6% 3 % 0% 5 % 2%
Functions, Relations, & Patterns 6 % 0 % 0 % 0 % 18 % 3 % 5 % 0 %
Data Representation, Probability, & 6 % 6 % 18 % 5 % 12 % 2 % 16 % 0 %
Statistics
TYPETOTALS 81% 19% 81% 19% 85% 15% 87% 13%
BOOK TOTALS 100 % 100 % 100 % 100 %
Population 2 Mathematics
TOPIC BOOK 3 BOOK 5 BOOK 6 BOOK 8
MC OE MC OE MC OE MC OE
WholeNumbers 2% 0% 1% 0% 1% 0% 2% 0%
Fractions & Decimals l9 % 6 % 14 % 0 % 15 % 5 % 21 % 5 %
Integers, Real Numbers, & Number 2 % 0 % 1 % l % 0 % 0 % 2 % 0 %
Concepts
Estimation & Number Sense 3 % 5 % l8 % 3 % 3 % 0 % 3 % 0 %
Measurement 6% 0% 5% 0% 3% 0% 16% 8%
Geometry 21% 3% 20% 4% 11% 1% 6% 0%
Ratios & Proportions 0 % 0 % 0 % 0 % 19 % 4 % 2 % 0 %
Functions, Relations, & Patterns 13 % 3 % 8 % 1 % 27 % 1 % 17 % 6 %
Data Representation, Probability, & ll % 6 % 20 % 3 % 8 % 1 % 11 % 2 %
Statistics
TYPE TOTALS 76 % 24 % 88 % 12 % 86 % 14 % 79 % 21 %
BOOK TOTALS 100 % 100 % 100 % 100 %

 

 

 

 

 

 

 

100

101

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 3 Mathematics
BOOK 1 BOOK 2 BOOK 3
MC OE MC OE MC OE

Whole Numbers 0 % 4 % 0 % 2 % 0 % 0 %
Fractions & Decimals 12 % 2 % 10 % 2 % 14 % 0 %
Integers, Real Numbers, & Number 2 % 0 % 0 % 0 % 0 % O %
Concepts

Estimation & Number Sense 2 % 6 % 8 % 0 % 8 % 2 %
Measurement 10 % 6 % 15 % 2 % 12 % 4 %
Geometry 0 % 4 % 0 % 2 % 0 % 0 %
Ratios & Proportions 12 % 2 % 4 % 2 % 6 % 2 %
Functions, Relations, & Patterns 8 % 2 % 6 % 2 % 2 % 4 %
Data Representation, Probability, & 4 % 2 % 6 % 4 % 0 % 6 %
Statistics

TYPE TOTALS 37 % 18 % 38 % l3 % 37 % 20 %
BOOK TOTALS 55 % 50 % 57 %

Population 3 Science
BOOK 1 BOOK 2 BOOK 3
MC OE MC OE MC OE

EarthSciences 0% 2% 4% 4% 2% 4%
Life Sciences 6 % 6 % 4 % 8 % 10 % 8 %
Chemistry 4% 2% 2% 0% 2% 4%
Physics 12 % 4 % 6 % 10 % 4 % 4 %
Environment, Technology, & Science 6 % 4 % 10 % 13 % 4 % 0 %
TYPE TOTALS 27 % 24 % 25 % 27 % 22 % 22 %
BOOKTOTALS 51% 51% 51%

 

 

 

 

 

 

 

102

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 2 Science
TOPIC BOOK 1 BOOK 2 BOOK 4 BOOK 7
MC OE MC OE MC OE MC OE
EarthSciences 0% 0% 23 % 6% 14% 4% 16 % 4%
Life Sciences 31% 13 % 21 % 4% 25 % 7% 13 % 2%
Physical Sciences 33 % 12 % 29 % 15 % 38 % 9 % 34 % 13 %
Environment, Technology, & Science 10 % 2 % 0 % 2 % 0 % 4 % 14 % 5 %
TYPE TOTALS 73 % 27 % 73 % 27 % 77 % 23 % 77 % 23 %
BOOK TOTALS 100 % 100 % 100 % 100 %
Population 1 Science
TOPIC BOOK 1 BOOK 2 BOOK 4 BOOK 7
MC OE MC OE MC OE MC OE
EarthSciences 0% 0% 14% 14% 21 % 3 % 21 % 7%
Life Sciences 48 % 16 % 23 % 7 % 33 % 7 % 21 % 2 %
Physical Sciences 16 % 13 % 25 % 7 % 16 % 9 % 21 % 7 %
Environment, Technology, & Science 5 % 2 % 7 % 2 % 7 % 5 % 7 % 13 %
TYPE TOTALS 70 % 30 % 70 % 30 % 76 % 24 % 71 % 29 %
BOOK TOTALS 100 % 100 % 100 % 100 %

 

 

 

 

 

 

 

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