goals, values, and beliefs as predictors of achievement and effort in high school mathematics...
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Sex Roles, Vol. 40, Nos. 5/6, 1999
Goals, Values, and Beliefs as Predictors ofA chievement and Effort in High School
Mathematics Classes1
Barbara A . Greene,2 Teresa K. DeBacker, Bhuvaneswari Rav indran, andA . Jean KrowsUniversity of Oklahom a
G ender and motivation in high school mathematics class were examined byusing an expectancy-value fram ework. There were 366 students (146 males,212 females)from a school with an enrollment of approxim ately 1900 students(81% Caucasian , 8% Native American , 5% Hispanic, 4% African American ,and 2% Asian). These students completed a questionnaire consisting of 92items which measured students’ situation-speci® c goals (4 subscales), task-speci® c values (3 subscales), task-speci® c beliefs (3 subscales), and genderself-schemata (2 subscales). Students’ percentage grade in math and self-reported effort in math class were the dependent variab les. The three sets oftask-speci® c variab les each accounted for between 11% and 14% of variancein achievement, while the gender self-schemata variab les contributed another2%. Task-speci® c goals were much stronger predictors of effort than anyother set of variab les. An unexpected ® nding was that, for both males andfemales, endorsing the stereotype that mathematics is a male domain wasnegatively related to reported effort. There were also differences in the predic-tion of achievement and effort based on gender and math class type (requiredor elective). Several path models supported these results.
Important questions concerning the role of gender in explaining mathemati-
cal achievement and achievement-re lated behaviors remain unanswered
despite ongoing research efforts. As Meece, Wig® eld, and Eccles noted
1A version of this paper was presented at the 1997 annual mee ting of the American EducationalAssociation in Chicago. We would like to thank the teache rs who allowed us into their
classroom and the colleague s who provided us with helpful comme nts.2To whom corre spondence should be addresse d at Departme nt of Educational Psychology,
University of Oklahoma, 820 Van Vleet Oval, Norman, OK 73019 ± 2041; e-mail:[email protected].
421
0360-0025/99/0300 ± 0421$16.00/0 Ó 1999 Plenum Publishing Corporation
422 Greene et al.
(1990) , although there is evidence that achievement diffe rences between
male s and female s are disappe aring, differences in choice s related to mathe -
matics seem to persist. Of concern is the related ® nding that females are
less like ly than male s to choose high school coursework that requires highe r
level mathematics (Meece et al., 1990) . This is a concern because choice s
made in high school can limit the choice s available in college and for
career decisions. Therefore, the purpose of this study is to furthe r our
understanding of the psychologic al variable s that in¯ uence achievement-
related behaviors and choice s made by boys and girls in regard to high
school mathematics by building upon the work of Eccles and her colleague s.
There have been conside rable efforts focusing on motivational expla-
nations for gender diffe rences in both achievement and choices related to
mathematics (Eccles, 1984; Eccles, 1987; Eccles, Adler, & Meece, 1984;
Fennema & Sherman, 1977; Fennema, 1994; Licht & Dweck, 1983; Mills,
Ablard & Stumpf 1993) . Much of this work has been in response to consis-
tent evidence that female s, when compared to male s, have lower con® dence
in the ir math ability and are less like ly to enroll in advance d coursework
in mathematics. These diffe rences seem to persist even when there is no
evidence of actual achievement diffe rences.
Several researchers have sought an explanation for differences in math-
ematics achievement and choice through the linking of low perceived ability
in mathematics with ability attributions . For example , Licht and Dweck
(1983) argued that girls exhibit a maladaptive motivational patte rn in math-
ematics (i.e ., they have low perceived ability and they attribute the ir failure s
to ability) that leads to a helpless motivational stance since they convince
themselves that they cannot be successful. However, Eccles and her col-
league s tested the gender and learned helple ssness in mathematics hypothe -
sis and failed to ® nd support for the he lple ss patte rn ® tting female s more
than male s (Eccles, Adle r, and Meece, 1984; Parson, Meece, Adle r, &
Kaczala, 1982) .
Fennema and Peterson (1985) also argued for the importance of
con® dence in one ’s ability to learn math and the role of causal attributions
for achievement (successes or failure s) in math. Their notion was that
high-le vel achievement in mathematics require s Autonomous Learning
Behaviors that deve lop when childre n have high perception of ability; when
they attribute success to ability and effort, and failure to lack of effort;
and when they perceive the utility of mathematics. Although these three
facets of motivation have been supporte d in the lite rature as fostering an
adaptive stance toward learning (e.g., Schunk, 1989; Eccles et al.,
1983; Mille r et al., 1996) , there is no direct, empirical evidence that
proble ms associated with Autonomous Learning Behaviors (Fennema &
Peterson, 1985) offer explanations for gender diffe rences in motivation to
Goals, Values, and Beliefs 423
learn mathematics. However, a recent longitudinal study found differences
in the strategies reported by male s and female s in solving mathematics
proble ms (Fennema, Carpenter, Jacobs, Franke , Levi, 1998) . Fennema et
al. (1998) found that male s were more like ly to report abstract strategies
that re¯ ected a deep understanding of mathematics than female s who were
more like ly to report concre te strategie s. This ® nding could be inte rpreted
as supporting the Autonomous Learning Behaviors hypothe sis.
Eccles (1984) has argued, and we agree, that an expectancy-value
framework offers an alternative to the traditional approach of studying
gender diffe rences in mathematics through attempts to identify the de ® cits
shown by female s. In addition to having a philosophica l problem with using
a medical mode l approach that focuse s on discove ring the female defect
that impedes motivation to learn mathematics, we be lieve that such an
approach limits our unde rstanding of the diffe rent factors that in¯ uence
the motivation of both male s and female s in mathematics.
The purpose of this study was to use a variation of the expectancy-
value framework propose d by Eccles and her colle ague s (Eccles et al., 1983;
Eccles, 1984; Eccles, Wig® e ld, Harold, and Blumenfe ld, 1993; Eccles and
Wig® e ld, 1995; Wig® eld, 1994; Wig® e ld and Eccles, 1992) to explore diffe r-
ent aspects of gender and motivation that may help explain motivation
and performance in mathematics. An overview of the model, and our
modi® cations of it, is described below and shown in Fig. 1. The only major
modi® cation, from the earlie r mode l propose d by Eccles et al., (1983) , was
the inclusion of task-speci® c goals as direct in¯ uences on achievement and
achievement-re lated behaviors. A lthough short term goals were include d
in the original version of the Expectancy-V alue Mode l (Eccles et al., 1983)
only long term goals were actually tested in the research conducte d on the
mode l (Wig® e ld, 1994) . Additionally, goals in the original model were
Fig. 1. Rev ised Expectancy Ð Value Mode l.
424 Greene et al.
conceptualize d as aspects of a child’ s self that existed prior to encounte ring
an achievement situation (Eccles et al., 1983) , whereas in our formulation
the goals are part of the child’ s inte rpretation of the current achievement
situation (Maehr, 1984) . In this sense, we have borrowed from Maehr’ s
(1984) notion of goals as part of a student’ s Components of Meaning (i.e .,
the student’ s interpretation of an achievement situation) and added them
to the Expectancy-Value Mode l. We believe the addition of task-speci® c
goals will add to the power of the model to explain achievement and
achievement-re lated behaviors and think they might act as mediators be-
tween task-spe ci® c value s and achievement and achievement-re lated behav-
iors. We also agreed with Meece et al., (1990) that choosing to take course s
in mathematics is an important indicator of motivation, and thought that
comparing motivational constructs for male and female students in required
course s (situations without choice ) and elective course s (situations with
choice ) would be an informative approach to the issue of choice .
An Expectancy-Value Model and G ender Differences
The Eccles et al. (1983) mode l propose s that an individual’ s achieve-
ment-related behaviors (persistence, choice , and performance ) can be pre-
dicted by subje ctive task value s and expectancie s for success; which in turn
can be predicted by task be lie fs, broad goals, and general self-schemata.
Task be liefs, broad goals, and general self-schemata are seen as predicted
by an individual’ s perception of the attitude s and expectancie s of her/his
socialize rs and her/his inte rpretations of past experiences. The research
done using the mode l has provided evidence that different patte rns of
behaviors are predicted by diffe rent patte rns of task values and outcomes
expectancies (Eccles et al., 1983; Wig® e ld and Eccles, 1992; Wig® e ld, 1994) .
In our study we have focused only on the inte rnal factors associate d with
task values, expectancie s, task be lie fs, goals, and self-schemata as predictors
of achievement-re lated behaviors and performance .
The Role of Subjective Task Values. There are three subjective task
values proposed in the model that are concerned with how a task meets
the diffe rent needs of an individual (Wig® e ld and Eccles, 1992; Wig® e ld,
1994) . Attainment value is the importance of doing well on a particular
task. High attainme nt value is seen when an individual needs to prove to
herself/himse lf that she /he can be successful at some task. Intrinsic value
is the enjoyment an individual experiences while engage d in the task. Utility
value is the perceived usefulness of completing the task. A task can be
valued for the options available once the task is comple ted (e.g, knowle dge
or a requirement needed for some other goal) , even though it satis® es no
Goals, Values, and Beliefs 425
inhe rent need. In the Eccles model, these task value s are in¯ uenced by
task speci® c be liefs and a student’ s general goals and general self-schemata.
Evidence for gender diffe rences in subjective value s toward mathemat-
ics has been mixed (Wig® e ld & Eccles, 1994) . For example , evidence that
male s valued mathematics more than females was found in some of the
earlie r studie s (Eccles, 1984; Eccles et al., 1983; Eccles, Adle r, & Meece,
1984; Wig® e ld, 1984) , but not in the more recent studie s (e.g., Eccles,
Wig® e ld, Harold, & Blumenfe ld, 1993; Wig® e ld & Eccles, 1994) . Eccles et
al. (1993) did ® nd, though, that boys and girls in the ir elementary school
sample showed diffe rent orderings of value s placed on diffe rent subje cts
(math, reading, music, sports, and sports-re lated activitie s) , and girls had
math valued at the bottom while boys had it near the top. So although
males and female s showed the same leve l of value on mathematics, when
subje cts were rank ordered in terms of valuing, mathematics was lower in
the ordering for female s. It should be noted however, that the more recent
studie s also had younge r, pre-high school participants . As Wig® e ld and
Eccles (1992) noted, the ir work sugge sts that gender differences in the
valuing of mathematics become increasingly pronounce d in the high
school years.
The Role of Task-Speci® c Beliefs. Like task value s, expectancie s for
success are shown to be direct predictors of achievement-re lated choice s
(e.g., enrollme nt in course s) in the Eccles et al. model. Expectancie s for
success are an individual’ s belie fs about whether she /he will be successful
on a future task. In their earlier work, Eccles et al. (1983) showed expectan-
cies and ability perceptions as separate constructs, but they have since
acknowle dged that competence be lie fs and expectancie s are often not em-
pirically separate (Wig® e ld and Eccles, 1992; Wig® e ld, 1994; Eccles and
Wig® e ld, 1995) . As others have also found the two constructs indistinguish -
able in the ir research (e.g., Mille r, Behrens, Greene and Newman, 1993;
Greene and Mille r, 1996) , we chose to modify the Eccles et al., mode l and
have a single perception of ability construct that include s both task-speci® c
competency and expectancy be lie fs (see Fig. 1).
Gender differences in competence be lie fs have consistently been found
with female participants reporting lower competence be liefs than males in
mathematics (Eccles, 1984; Eccles et al., 1983; Eccles, Wig® e ld, Harold, &
Blumenfe ld, 1993; Wig® eld,1984; Wig® e ld & Eccles, 1994) . There are three
other common ® ndings from this body of work that make the lower compe-
tence belie fs for female s worthy of concern. First, as noted earlier, the lower
competence be liefs are found when there is no evidence of achievement
differences. Second, the differences show up as early as the ® rst grade
(Eccles et al., 1993 & Wig® eld & Eccles, 1994) . Third, while value s are
found to predict choice in mathematics enrollme nt, competence belie fs are
426 Greene et al.
found to predict performance . A similar patte rn of gender diffe rences
has also been found by other researchers studying mathematics self-
ef® cacy (e.g., Lent, Lopez, & Bieschke , 1991; Mille r et al., 1996; Pajare s,
1996) .
Following the Eccles et al. mode l, we also include d perceptions of
mathematics dif® culty as a task-spe ci® c be lie f. According to Eccles and
Wig® e ld (1995) , perceptions of task dif® culty should be negative ly related
to perception of ability and task value s. If a task is viewed as very dif® cult,
an individual should be less con® dent in her/his ability to succeed with the
task, which should decrease the valuing of that task. The idea here is that
protection of one ’ s ego or self-esteem is the over-arching goal.
In a minor modi® cation of the Eccles et al. (1983) mode l we include d,
as a third task-spe ci® c be lief, a measure of the extent to which an individual
believes that mathematics is a male domain. According to sample items
provide d by Wig® eld (1994) , the measure of domain stereotyping include d
in the work of Eccles and her colle ague s was conceived of as an aspect of the
individual’ s general self-schemata and achievement-re lated goals. Eccles et
al. (1983) argue d that domain stereotype s are only germane when gender
identity is also stereotyped and we suspect that that is why the domain
stereotype variable was placed with general goals in their model. We have
chosen to conceptualize it in terms of a task-spe ci® c belief to be consistent
with evidence supporting the value of task-spe ci® c measure s (e.g., Maehr,
1984; Marsh, 1992; Greene and Mille r, 1996) .
There were two studie s from the Eccles et al. group (Eccles, 1984 &
Eccles et al., 1983) that seemed particularly important for our work because
they include d both gender-role identity variable s and a stereotyping of
mathematics variable . Additionally, they had high school students as partici-
pants and this was the leve l that we were targe ting. The study reported in
Eccles et al. (1983) actually involve d students in grade s ® ve through twelve .
They found gender diffe rences in perceptions of the value of mathematics,
the dif® culty of mathematics, and the effort required for success in mathe -
matics. Females showed lower valuing of mathematics and highe r percep-
tions of dif® culty and of required effort. Eccles et al. (1983) used a form
of the Personality Attributes Questionnaire (PAQ) to measure students
on Femininity/ Expressivity and Masculinity/In strumentality scale s. They
found that the Femininity scores were not related to attitude s or the achieve-
ment-related variable s, but the Masculinity scores, for male s and females,
were positive ly related to both the expectancy and math self-concept scale s.
When they examined gender-role classi® cation and stereotyping of mathe -
matics as a male domain as predictors of the variable s related to values
and beliefs, they did not ® nd any predictive power from eithe r classi® cation
or stereotyping for male s or females.
Goals, Values, and Beliefs 427
Similar results were reported by Eccles (1984) with male s and females
in high school who were compared on reading and mathematics. Eccles
found that, when compared to females, high school-age d male s reported
highe r perceptions of ability, highe r expectancie s for success, and lower
requirements for effort in order to succeed in mathematics. Both male s
and female s rated math as more useful than reading for males and female s.
Additionally, the attitude s the females had toward math became more
negative over time, while the male s’ attitudes remained fairly constant. She
again used the PAQ to measure students on Expressivity/Fe mininity and
Instrumentality/Mascul inity. She found the same patte rn of relationships
reported by Eccles et al. (1983) . However, Eccles (1984) also found that
both male s and females in high school rated math as more useful for males
than female s. Additionally, there was a positive relationship found, for
both male s and female s, between the perception of math as useful for males
and subjective valuing of math. No such relationship was found for the
perception of mathematics as useful for female s. Eccles noted that an
inte rpretation of these ® ndings is proble matic. We agree.
Several other researchers have examined stereotyping of mathematics
as a male domain. For example , Hande l (1986) used an expectancy-value
framework to study correlations between future intentions for mathematics
coursework and the expectancie s and task perceptions of students in grade s
seven and eight who were at or above the 95th percentile on a mathematics
achievement test. These high achieving male and female students did not
differ in their perceptions of the usefulne ss of studying mathematics. How-
ever, both male s and female s rated males as more mathematically able
than female s and both indicated that mathematics was more useful for
adult male s than for adult female s. Rathbone (1989) examine d diffe rences
in attitude s toward mathematics between high- and low-achie ving, male
and female students in the ® fth grade . She found evidence that the be lie f
that mathematics is a male domain was more pronounce d among high-
achieving students, and more pronounce d among female s in both the high
and low-achie ving sample s.
The Role of G oals. Wig® e ld (1994) pointed out that the goals tested
in the ir mode l were broad goals tied to general self-schemata, rathe r than
task-spe ci® c goals. We chose not to include those broad goals described
by Wig® eld (1994) because they focused on gender-role identity and gender
stereotyping and were captured elsewhere in our modi® cation of the model.
As noted above , we have include d a variable for math stereotyping as
a task-speci® c belie f. We also included gender-role identity measure s of
masculinity and femininity as non-task-speci® c variable s since two of the
earlie r studie s conducted by Eccles (1984) and Eccles et al. (1983) included
such measure s. In other words, we have simply redistribute d the variable s
428 Greene et al.
in the component of their mode l labe led Child ’ s G oals and G eneral Self-
Schemata.
It should be noted that although task-spe ci® c goals do not seem to have
been tested in the Eccles et al. mode l, the model does contain immediate or
short-te rm goals in the compone nt labe led Child ’ s G oals and G eneral Self-
Schemata (e.g., Eccles et al., 1983, Eccles, 1987, Wig® e ld, 1994) . Given the
extensive evidence supporting the importance of task-speci® c goals for
understanding achievement motivation (e.g., Ames & Archer, 1988; Dweck,
1986; Mille r et al., 1996; Schutz, 1992; 1993) , we decided to include such
measure s. We thought an important extension of the work on the Eccles
et al. mode l was to test the inclusion of such goals. We also thought that
task-spe ci® c goals should theoretically follow task-spe ci® c value s. We ex-
plain this point following a brie f summary of research on task-spe ci® c goals.
Task-spe ci® c goals are the reasons students report for doing the work
in a particular achie vement setting (Mille r et al., 1996) . A lthough the level
of task speci® city varie s in the research on goals, it is often de ® ned in terms
of the tasks in a speci® c classroom situation (e.g., Ames & Archer, 1988;
Meece et al., 1988; Mille r et al., 1996; Nolen, 1988; Pintrich & Garcia, 1991) .
There is a large body of research that has focused on the distinction between
learning goals (also called mastery or task-orie nted goals) , which are related
to the desire to increase one ’s understanding or skill leve l, and performance
goals (also called ego-orie nted goals) , which are related to the desire to
perform better than others and protect one ’s ego. This research has consis-
tently found evidence for the positive relationship between learning goals
and productive achievement behaviors such as self-regulation and strategy
use (e.g., Ames & Archer, 1988; Greene and Mille r, 1996; Maehr, 1984;
Meece, Blumenfeld & Hoyle , 1988; Mille r, Behrens, Greene & Newman,
1993; Nolen, 1988; Pintrich & Garcia, 1991) and has sometimes found a
negative relationship between performance goals and productive achieve-
ment behaviors (Greene and Mille r, 1996; Zimmerman and Martine z-
Pons, 1990) .
There is a much smalle r, ye t emerging, literature that expands the
range of goals beyond learning and performance goals to include future
goals and pleasing the teacher (e.g., Mille r et al., 1996; Schutz,1992; 1993;
Wentzl, 1991) . Future goals refer to distant goals (e.g., e ligibility for extra-
curricular activitie s, colle ge admission, & career opportunitie s) that to some
extent are continge nt on current task performance but not inhe rent in the
performance itself. Pleasing the teacher is an example of a social responsibil-
ity goal that has been found, in Wentze l’ s (1989; 1991) research, to have a
positive in¯ uence on achievement. Mille r et al.( 1996) provide d evidence
for positive relationships between both future goals and wanting to please
the teacher and self-regulation, which was positive ly linked to achievement.
Goals, Values, and Beliefs 429
Given the weight of the empirical evidence supporting the in¯ uence
of task-spe ci® c goals on achievement-related behaviors and achievement
(e.g., Ames & Archer, 1988; Greene and Mille r, 1996; Meece, Blumenfeld &
Hoyle , 1988; Mille r et al., 1993; Mille r et al., 1996; Nolen, 1988; Pintrich &
Garcia, 1991; Schutz,1992; 1993; Wentzl, 1991) , we include d four task-
speci® c goals ( learning, performance , future goals, and wanting to please
the teacher) in our model. Wig® e ld (1994) noted that the logic of the ir mode l
sugge sts that task-speci® c goals should be depicted as be ing in¯ uenced
by task-spe ci® c belie fs and task value s, and also directly linke d to the
achievement variable s. We agree with Wig® eld’ s view for both theoretical
and methodological reasons.
One way to conceptualize the role of personal value s is that they
in¯ uence how a person inte rprets a speci® c achievement situation (Feathe r,
1988) . As Feathe r argued (1988) , subje ctive task value s can be seen as
sensitizing people toward eithe r a positive or negative interpretation of the
bene ® ts associate d with engaging in a particular academic activity. Task-
speci® c goals are thought to represent how people inte rpret their reasons
for engaging in a particular academic activity (e.g., Maehr, 1984) . Goals
are a way in which people expre ss the meaning they bring to an academic
setting, so it follows, theoretically, that goals are in¯ uenced by the personal
value s he ld.
Additionally, there is a methodological reason for value s to precede
goals in the mode l. The labe l ` t̀ask’ ’ differs in terms of speci® city when
used to describe the value s and goals in the mode l. Personal task value s
tend to be operationalize d in terms of a speci® c domain such as Math or
English (Eccles et al.,1983; Wig® e ld, 1994) . Task-spe ci® c goals, on the other
hand, have been operationalize d in terms of a speci® c achie vement setting
with items that ask students to respond based on ` t̀his class’ ’ (e.g., Greene
and Mille r, 1996; Mille r et al., 1993; Mille r et al., 1996) . Since personal task
values measure valuing about domains and goals measure reasons for doing
the work in a speci® c class in that domain, the goals logically follow valuing
of the general domain. It should be noted that the theoretical and method-
ological arguments are not independent. We conceptualize domain valuing
as a factor that in¯ uences the more concre te goals for working in that
particular domain.
Current Study
Given that the evidence , described above , for gender diffe rences based
on the expectancy-value framework was inconsiste nt and somewhat con-
fusing, we thought an examination of a modi® ed expectancy-value frame-
430 Greene et al.
work (see Fig. 1) for exploring gender differences in motivation towards
mathematics was warranted. We were interested in examining whether the
inclusion of task-spe ci® c goals would provide a clearer view of gender
differences. We liked the distinction between performance and achieve-
ment-related behaviors found in the work of Eccles and her colle ague s
(Eccles et al., 1983; Eccles, 1984; Eccles, Wig® eld, Harold, and Blumenfe ld,
1993; Eccles and Wig® e ld, 1995; Wig® eld, 1994; Wig® e ld and Eccles, 1992) ,
and decided to operationalize behavior in terms of reported use of effort.
We chose to take a different approach to the examination of gender diffe r-
ences and choice . Rather than predict choice to enroll in furthe r classe s in
mathematics, we examined the issue of choice in terms of diffe rences in the
prediction of effort and performance for students in required and elective
classe s. This allowe d us to examine diffe rences in motivational constructs
between students who are currently taking a required class, a situation
without choice , and students who are in an elective class, a situation
with choice .
METHOD
Participants
Participants were 366 student volunte ers from a large Midwestern
high school in a middle -class suburban city. The population consisted of
approximate ly 1900 students with the following ethnic/racial composition:
Caucasian 81%; Native American 8%; Hispanic 5%; African American 4%;
and Asian 2%. The sample consisted of students in grade s 10 through 12.
There were 146 male s, 212 females, and eight students who did not report
the ir gender. Students were enrolle d in one of the following math classe s:
Pre-Algebra, Algebra I, Geometry, A lgebra II, Honors Algebra II, Math
Analysis, Honors Math Analysis, and Advanced Placement Calculus. There
were 83 male s and 108 females in the required mathematics classe s (i.e .,
Pre-Algebra, A lgebra I, Geometry, A lgebra II, and Math Analysis) , and
63 male s and 104 females in the elective classe s ( i.e ., Honor’ s Algebra II,
Honors Math Analysis, and Advance d Placement Calculus) . Ten female
teachers and one male teacher were involve d in teaching these course s.
Instruments
A 92 item survey instrument was constructed with ® ve sets of variable s
measuring the subscale s in the revised Expectancy-Value model. The survey
Goals, Values, and Beliefs 431
Tab le I. Means, Stand ard Dev iations, and Cronbach A lpha Reliabilities for the Goals, Value s,and Beliefs Subscale sa
Variable Set Name and Subscale s Mean SD Alpha
Task-speci® c goals
I do the work in this class because . . .Learning goal 3.76 .74 .86
I want to understand the concepts.Performance goal 2.90 .90 .82
I like to perform better than other students.
Pleasing the teache r 3.03 .99 .85I want the teacher to be happy with me.
Future goals 4.61 .62 .75
Good grades lead to other things that I want (e.g.,money, graduation, good job, certi ® cation).
Task-speci® c valuesIntrinsic value 3.02 1.00 .73
I think working with mathematics is personally satisfying.Utility value 3.62 .85 .87
I can see the importance of math in my everyday experi-
ences.Attainment value 3.47 .97 .76
It is important for me to maste r mathematics.
Task-speci® c be liefsPerce ived ability 3.60 .80 .91
I understand the ideas being taught in this course .Stereotyped perception of mathematics as a male domain 1.83 .85 .81
In general, boys /men are better at math than girls/
women.Perception of task dif® culty 2.94 1.00 .88
In general, how easy or hard is learning math for you?
a. Very easyb. Somewhat easy
c. Ne ither easy nor hardd. Somewhat harde. Very hard
aItems pertaining to Perception of task dif® culty were asse ssed with multiple choice items
while all other items on the motivation survey used Likert-type items.
was organize d starting with goal items, followe d by value , be lie f, and effort
items; and conclude d with the Bem Sex Role Inventory. With the exception
of four multiple choice items for measuring perception of math dif® culty,
the 74 items used in the study (there were additional subscale s on the
survey not used in this study) were on a ® ve -point Likert-type scale with 1
representing Strongly Disagre e and 5 representing Strongly Agree. Sample
items and descriptive statistics are shown in Table I.
The task-spe ci® c goal items were adapted from Mille r et al.(1996) , and
based on approxim ate ly 15 years of goal research (e.g., Ames & Archer,
1988; Maehr, 1984; Meece, et al., 1988; Nolen, 1988; Pintrich & Garcia,
432 Greene et al.
1991) . The set include d four scale s measuring learning goals (5 items),
performance goals (4 items), pleasing the teacher (4 items) and future goals
(2 items). The task-spe ci® c value s set include d scale s measuring intrinsic
value (3 items), utility value (4 items), and attainment value (2 items).
These scale s were composed of items adapte d from Eccles (1983) and
Wig® e ld (1994) , and additional items created by the authors for this study.
The Task-Spe ci® c Belie fs set was made up of three scale s. The percep-
tion of ability scale (8 items) was adapte d from Greene and Mille r (1996) .
The perception of task dif® culty scale (4 items) and the perceptions of
math as a male domain scale (6 items) were created by the authors for
this study.
The Self-Schemata set was conceptualize d here as gender identity and
measured using the Bem Sex Role Inventory: Short form (Bem, 1977; Bem,
1981; Santrock, 1994) . Both masculinity scores and femininity scores were
calculated for all students.
There were two achievement-re lated outcome variable s. There was a
self-report measure of effort in math class (two effort items with a Cronbach
Alpha coef® cient of .82) . The achievement measure was percentage of
course points earned in the mathematics class where the survey was taken
and reported by the teacher.
Procedure
Math teachers administe red the survey to student volunte ers during
one math class in March. All students had parental permission to participate ,
and provide d personal informed consent as well. Teachers gave students
instructions for comple ting the survey, then students worked at the ir own
pace. In May, teachers reported ® nal percentage grades in math for each
participant.
RESULTS A ND DISCUSSION
We begin by reporting a series of analyse s based on the whole sample .
We ® rst report reliability analyse s and a factor analysis as evidence for the
inte rnal validity of the scales that form the sets of variable s in our version
of the expectancy-value mode l. We then conduct a series of Multivariate
Analyse s of Variance (MANOVA) in order to examine mean differences
due to gender (male , females) and math class type (required, elective ) on
the variable s in the model. Then we present regression analyse s for both
achievement and effort. We examine the prediction of achie vement and
Goals, Values, and Beliefs 433
effort for the subgroups formed by crossing gender and math class type .
Finally, we tested a series of path mode ls.
Subscale Reliab ilities
For each of the subscale s within the three sets of variable s measured
by our instrument, Cronbach alpha reliability coef® cients were computed.
As shown in Table I, the coef® cients for the goals, value s, and belie fs
subscale s ranged from .73 to .91. These coef® cients are suf® ciently high to
provide evidence for the internal consistency of our subscale s. For the
femininity and masculinity scale s, we found reliability coef® cients with our
sample to be .90 and .81, respective ly.
Facto r Analysis
To assess the coherence and independence of the scale s used in this
inve stigation a Principal Axis factor analysis with varimax rotation was
conducte d on the full sample . Nine factors were extracted with Eigenvalue s
ranging from 1.05 to 11.47, eight of which were inte rpretable (see Table II
for item factor loadings for these eight factors) . These eight factors repre-
sented all of the scale s used in the study except for Math Dif® culty. Items
measuring Math Dif® culty were not include d in factor analysis because
they were of a slightly different format than the remainde r of the items on
the questionnaire .
Results indicated the presence of six very clean factors, and two more
inte rpretable factors. Perception of ability, math stereotyping, learning
goals, performance goals, pleasing the teacher, and future goals were cleanly
represented as separate factors. The one exception was a performance goal
item that cross loade d with the perception of ability scale . Items related
to intrinsic value , utility value , and attainme nt value were split across two
factors. One factor consisted of items measuring utility and attainment
value s with loadings ranging from .46 to .83. The second factor consisted
of intrinsic value items with loadings ranging from .44 to .71. Several of
the value items cross loade d on both factors. In addition, some intrinsic
value items and one attainment value item tended to cross load on the
perception of ability factor. One intrinsic value item also cross loaded with
learning goals. No items had loadings greater than .25 on factor nine .
These results indicate good internal validity of our measures except
in the case of the value s variable s. Faced with a decision regarding treatment
of the values variable s in the remaining analyse s, we conside red the results
434 Greene et al.
Tab
leII
.It
em
Fact
or
Lo
ad
ings
fro
ma
Pri
ncip
al
Axis
Facto
rA
naly
sis
wit
hV
ari
max
Ro
tati
on
Item
Fact
or
1F
act
or
2F
act
or
3F
act
or
4F
act
or
5F
act
or
6F
act
or
7F
act
or
8
i25
(PA
).8
2151
.13353
2.0
0972
.03115
.04481
.02426
.12066
.16993
i34
(PA
).7
7983
.15705
2.0
5509
.09025
.00959
.05023
.09799
.07976
i36
(PA
).7
5607
.13412
2.1
0769
.13496
.01015
2.0
0537
.06931
2.0
8348
i21
(PA
).7
5001
.09080
.05346
.14570
.06406
2.0
1388
.17585
.01769
i37
(PA
).7
2152
.21778
2.0
2108
.12885
.02100
.07766
.14524
.16767
i17
(PA
).7
1119
.10864
2.0
9712
.10583
.00861
2.0
4415
.01385
.01207
i28
(PA
).6
4319
.12411
.11844
.05004
.08951
.06735
.12289
.11034
i31
(PA
).5
8939
.16499
2.0
1076
.21273
.10687
.07471
.08698
.10488
i33
(PA
).4
5946
.11850
2.1
3374
.07147
.00810
.00254
.17793
2.1
2934
i48
(UT
).1
6736
.82635
2.1
7271
.12747
.01656
2.0
3512
.05517
.03671
i39
(UT
).0
8871
.76791
213681
.08387
.03861
2.0
4221
.07585
.08606
i49
(UT
).1
7672
.76781
2.0
2365
.15548
.02862
2.0
1400
.10830
.05425
i23
(UT
).1
8194
.76614
.00323
.12679
2.0
4688
.09015
.11032
2.0
2193
i40
(AT
).2
7202
.54368
2.0
8730
.21526
.03974
.00753
.23317
.16804
i27
(AT
).3
0657
.52116
2.0
2037
.26883
.03878
.04259
.33600
.20680
i46
(UT
).1
8425
.46610
2.0
3664
.14574
2.0
3317
.05399
.34822
.04771
i45
(UT
).1
4532
.46442
2.1
2535
.12268
2.0
4485
.06834
.32605
.07718
i43
(ST
) 2.0
4163
2.0
5334
.79866
.00030
.07336
2.0
3118
.06430
2.0
6257
i24
(ST
) 2.0
2654
2.0
3354
.73943
.05316
.10644
2.0
4390
2.0
3018
2.0
1091
i50
(ST
).0
0934
.02438
.69888
2.0
3287
.06825
.00718
2.0
0014
.04381
i32
(ST
) 2.0
2287
2.1
2978
.68339
2.0
6622
2.0
0747
.01114
.05059
2.0
3168
i19
(ST
).0
8390
.01651
.64378
.03907
.10770
2.0
2338
2.1
1776
2.0
1325
i35
(ST
) 2.0
2471
2.0
4940
.61338
2.0
9217
.04654
2.0
7754
2.0
9785
2.0
4252
i51
(ST
) 2.0
3966
2.0
0385
.56971
2.1
1221
2.0
0878
.12213
.11423
.00970
i47
(ST
).0
0711
2.1
0914
.45154
2.0
8765
2.0
7465
2.0
1951
2.0
5909
2.1
1542
Goals, Values, and Beliefs 435
Tab
leII
.(C
on
tin
ued
)
Item
Fact
or
1F
act
or
2F
act
or
3F
act
or
4F
act
or
5F
act
or
6F
act
or
7F
act
or
8
i38
(ST
) 2.0
6218
2.0
4458
.43301
2.1
4041
.02086
.11433
.24588
.02429
i30
(ST
) 2.0
4055
2.0
1512
.40117
21.5
976
.16333
.05316
.12657
.03700
i20
(ST
) 2.1
3917
2.1
9210
.30273
2.1
1179
.10851
.04023
.08609
2.0
3626
i3(L
G)
.25659
.21173
2.0
5604
.72530
.05575
.03535
.19591
.02424
i11
(LG
).1
4088
.20684
2.2
3638
.67216
.08202
.09211
.16887
.15591
i6(L
G)
.25423
.24431
2.0
7570
.66669
.05550
.00184
.22779
.09879
i9(L
G)
.24666
.25902
2.2
1039
.52942
.01568
.13975
.08760
.16393
i1(L
G)
.24582
.24524
2.2
0512
.51923
.01739
.05899
.07893
.14262
i5(P
G)
.07379
2.0
0216
.06170
2.0
4238
.78049
.15392
2.0
3727
.07691
i16
(PG
).0
8502
2.0
4440
.14416
.12324
.74946
.17103
.04959
.05828
i12
(PG
).0
2968
2.0
0276
.04029
2.0
2847
.71498
.27962
.00974
.00951
i8(P
G)
.09483
.05297
.14494
.09741
.69090
.21489
.06438
.09343
i2(P
G)
.43724
.06321
.08014
.17438
.30844
.15325
.04187
.06574
i15
(PT
).0
3783
2.0
0955
.09477
.05683
.25454
.81762
.07180
2.0
0334
i10
(PT
).0
3756
.02403
2.0
4760
.02044
.25477
.80572
.02863
2.0
0841
i4(P
T)
.05270
.01198
2.0
0644
.07605
.24786
.79397
.08554
.04438
i13
(PT
).0
4223
.03814
2.0
2572
.04948
.11292
.50244
.12671
.15543
i44
(IV
).2
6780
.27405
.04794
.18406
.01299
.06410
.70707
2.0
1247
i18
(IV
).3
2440
.23976
.03804
.19792
.02089
.10803
.60955
.05392
i42
(IV
).3
6531
.40830
2.0
5003
.30300
.04359
.04411
.49283
.04096
i29
(IV
).1
3745
.16547
.11216
.08659
.07651
.16315
.45857
.03587
i26
(IV
).4
1441
.23965
.07291
.21504
.00261
.02651
.44089
2.0
3105
i14
(FG
).1
0305
.13261
2.1
5718
.15107
.08665
.07815
.0036
.72302
i7(F
G)
.12676
.14728
2.0
1618
.17132
.14023
.08064
.06391
.66266
436 Greene et al.
Tab le III. Means, Standard Deviations, Range s, and Numbers of Male s and Females inRequired and Elective Mathematics Classes for each Variable a
Required Courses Elective Courses
Variable Males Female s Males Females
Achievement 76.18 76.93 79.11 81.3315.00 15.13 13.62 13.29
25.00± 97.00 24.00± 99.00 32.00± 100. 32.00± 100.
(83) (107) (61) (104)Effort 3.37 3.68b 3.45 3.90b
.77 1.03 1.13 1.101.00± 5.00 1.00± 5.00 1.00± 5.00 1.00± 5.00
(83) (108) (63) (104)
Learning Goal 3.72 3.78 3.57 3.90.79 .70 .83 .65
2.00± 5.00 1.60± 5.00 1.00± 5.00 2.00± 5.00
(83) (108) (63) (104)Performance Goal 3.18 2.75 2.82 2.85
.98 .87 .83 .87
1.20± 5.00 1.00± 5.00 1.00± 4.60 1.20± 5.00(83) (107) (63) (104)
Pleasing Teache r 3.17c 3.12c 2.79 2.94.95 .97 1.02 1.01
1.00± 5.00 1.00± 5.00 1.00± 5.00 1.00± 5.00
(83) (108) (63) (104)Future Conse- 4.51 4.67b 4.46 4.71b
quence s .77 .60 .64 .46
1.00± 5.00 2.00± 5.00 2.50± 5.00 3.00± 5.00(83) (108) (63) (104)
Utility Value 3.71 3.60 3.53 3.63.77 .80 1.04 .84
1.67± 5.00 1.50± 5.00 1.00± 5.00 1.33± 5.00
(83) (107) (63) (104)Attainment Value 3.55 3.41 3.32 3.55
1.02 .90 1.01 .97
1.50± 5.00 1.00± 5.00 1.00± 5.00 1.00± 5.00(83) (108) (63) (104)
Intrinsic Value 3.16 2.98 2.69 3.02
1.02 .94 1.09 .941.00± 5.00 1.00± 5.00 1.00± 5.00 1.00± 5.00
(83) (108) (63) (104)Perce ived Ability 3.81d 3.44d 3.54 3.64
.72 .81 .82 .80
1.67± 5.00 1.00± 5.00 1.00± 5.00 1.33± 5.00(83) (108) (63) (103)
Stereotyping Math 2.26b,c 1.60c 2.17b 1.54
.73 .61 .84 .591.00± 4.67 1.00± 3.67 1.00± 4.33 1.00± 3.33
(83) (108) (63) (104)Math Dif® culty 2.77 3.25 2.72 2.87
.92 1.03 .90 1.01
1.25± 4.75 1.25± 5.00 1.00± 4.75 1.00± 5.00(83) (108) (63) (104)
Goals, Values, and Beliefs 437
Table III. (Continued )
Required Courses Elective Courses
Variable Males Female s Males Females
Masculinity Score 3.84 3.71 3.61 3.74
.55 .67 .53 .592.50± 5.00 1.00± 5.00 2.50± 4.70 2.2± 4.90
(82) (107) (62) (103)
Femininity Score 3.68 4.07a 3.63 4.21b
.64 .70 .68 .63
2.10± 5.00 1.00± 5.00 2.40± 5.00 2.00± 5.00(82) (107) (63) (103)
aMA NOVA procedures were used to test mean differences within sets; p , .01.bGender difference .cMath class type differencedInteraction.
of factor analysis in light of the acceptably strong Cronbach alpha coef® -
cients for each of the value s variable s (shown in Table I), and in light of
our initial intent for this study, which did not include a reformulation of
the value s set. We decided to conduct the regression analyse s including all
three value s scale s.
Descriptive Statistics for Males and Females in Required
or Elective Classes
Groups were formed in this study on the basis of two variable s: math
class type (required math and elective math) and gender (male and female ).
Means, standard deviations, and range s for all variable s, broken down by
group, can be found in Table III. It is important to note that restriction of
range was found for some variable s in some groups. For example , the full
range of value s for learning goals (1.00 to 5.00) was found only for male s
in elective classes. The other groups had minimum scores of 1.6 or 2.00.
For future goals, only male s in required classe s showed the full range . The
other groups had minimum scores of 2.00 or higher. Except for females in
the required classes, both of the gender self-schemata variable s had re-
stricted range s, in that minimum scores of 2.00 or highe r were found. We
point out these cases of restriction in range because they may help to
explain some of the corre lations and regression ® ndings.
Analyses of Mean Differences
We examined mean diffe rences for statistical signi® cance using Multi-
variate Analyse s of Variance (MANOVA) for each of the ® ve sets of
438 Greene et al.
variable s. We used an alpha leve l of .01 for both the multivariate and
univariate tests. The ® rst MANOVA, for achievement and effort, revealed
a multivariate effect for gender (Wilk’ s approxim ate F 5 4.90, p 5 .008,
D square 5 .027) . The univariate tests demonstrated a main effect of gender
on effort, F 5 9.58, p 5 .002, Eta square 5 .027) . Regardle ss of math class
type , greater effort was reported by female s than by male s. There were no
effects found for math class type or the inte raction of gender and math
class type.
The MANOVA computed for the goal variable s also showed a
multivariate effect for gender (Wilk’ s approximate F 5 5.68, p , .001, D
square 5 .047) . A signi® cant univariate effect for gender on future goals
was found (Wilk’ s approxim ate F 5 9.16, p 5 .003, Eta square 5 .025) .
Female s had higher scores on the future goals variable regardle ss of math
class type . There was also a univariate effect for math class type on pleasing
the teacher (Wilk’ s approximate F 5 7.21, p , .001, Eta square 5 .020) .
Both male and female students enrolled in required math had highe r means
on the pleasing the teacher goal variable than the students in elective
math classe s.
The MANOVA for the values set revealed no effects of gender, math
class type or their inte raction. However, the MANOVA for the set of be lie f
variable s showed several effects. The univariate tests for the inte raction of
gender and math class type demonstrate d that a statistically signi® cant
inte raction was present for perceived ability only, F (1,350) 5 7.32, p 5.007, Eta square 5 .020) . In looking at the means for perceived ability
shown in Table III, it seems that diffe rences between males and female s
are found in required math classes where male s show the ir highe st mean
and females show their lowest mean. In the elective math class group, the
female s actually show a slightly highe r mean on perceived ability than
male s. The multivariate test for a gender main effect was also signi® cant
(Wilk’ s approximate F 5 29.79, p , .001, D square 5 .203) . The univariate
test for the stereotyping variable showed a main effect of gender on stereo-
typing (Wilk’ s approximate F 5 76.39, p , .001, Eta square 5 .178) and
a main effect of gender on perception of math dif® culty (Wilk’ s approxim ate
F 5 76.93, p 5 .003, Eta square 5 .024) . From the means shown in Table
III, it seems that male s had higher scores on the stereotyping of math
variable and female s were highe r on the math dif® culty scale . Finally, the
multivariate test of math class was signi® cant (Wilk’ s approxim ate F 5 4.24,
p 5 .006, D square 5 .035) , but there were no signi® cant univariate effects.
The last MANOVA examine d mean diffe rences related to the two
scores on the BSRI. The multivariate test for gender was signi® cant (Wilk’ s
approximate F 5 25.94, p , .001, D square 5 .129) . The univariate test
for the femininity variable showed a main effect of gender on femininity
Goals, Values, and Beliefs 439
(Wilk’ s approximate F 5 20.77, p , .001, Eta square 5 .121) . Although
that is not a very inte resting ® nding, it is somewhat inte resting to note that
there were no differences based on gender on the masculinity variable .
Zero-Order Correlations and Regression Analyses
Zero-Order Correlations. We examined the interrelationships among
variable s using Pearson product-moment correlations to see if theoretical
predictions were supporte d. The corre lation matrix is presented in Table
IV. All of the patte rns expected based on theory and earlie r empirical work
were found. For example, achievement, effort, learning goals, perceived
ability, and the three task value variable s all showed positive inte rcorre la-
tions. The math dif® culty variable had negative corre lations with the goal
variable s, perceived ability, and the task value variable s. Interestingly, the
stereotyping of mathematics as a male domain showed negative relation-
ships with both gender self-schemata variable s. In fact, the masculinity
score was not related to any score othe r than the negative relationship with
stereotyping. Femininity scores, however, were positive ly related to effort,
learning goals, future goals, and masculinity scores. These relationships
were not expected. It is important to note here that multicolline arity among
the value items and between the intrinsic and learning goal items will
like ly render the Beta weights for those scale s in the regression equations
uninte rpretable (Cohen & Cohen, 1983, p. 115) .
Multiple regression analyse s were used to predict reported effort and
achievement for the whole sample and then for each of the four subgroups.
For all statistical tests using the whole sample we used p , .01 as the
minimum alpha leve l, while for the subgroups we used p , .05 as the
minimum criterion for statistical signi® cance . We recognize that Type I
errors are a threat and provide the obse rved alpha levels to provide some
furthe r information about the like lihood of Type I errors. The regression
analyse s for the whole sample are summarized in Table V. In Table VI,
the percentages of variance accounte d for by each set of variable s, and the
Beta weights from the ® nal regression equation are shown for each of the
four subgroups.
Regression Analyses with the Whole Sam ple
Predicting Achievement. Hierarchical regression was conducted by en-
tering: gender, mathematics class type, grade leve l, the four goals scores,
the three value s scores, the three be lie fs scores, and the two gender self-
440 Greene et al.
Tab
leIV
.P
ears
on
Pro
du
ct-
Mo
men
tC
orr
ela
tio
ns
Am
on
gth
eV
ari
ab
les
for
the
Wh
ole
Sam
ple
a
Ach
Eff
LG
PG
PT
FG
PA
MD
ST
UT
AT
INM
as
Fem
Ach
Ð.4
6.2
8.0
9.0
6.2
6.5
62
.51
2.0
6.2
5.3
8.4
22
.09
.03
Eff
Ð.4
9.0
6.0
9.3
7.4
92
.38
2.2
8.3
7.4
8.4
9.0
4.2
0L
GÐ
.12
.16
.38
.47
2.3
22
.23
.48
.59
.58
.06
.29
PG
Ð.4
7.1
9.1
42
.05
.18
.02
.09
.11
2.0
2.0
3P
TÐ
.17
.12
2.0
3.0
0.0
5.1
2.1
8.0
0.1
3F
GÐ
.24
2.1
02
.12
.26
.37
.25
.07
.27
PA
Ð2
.73
2.0
7.3
8.5
1.5
6.0
3.1
1M
DÐ
.00
2.3
42
.44
2.5
92
.05
.01
ST
Ð2
.16
2.1
22
.05
2.0
92
.28
UT
Ð.6
6.5
2.0
1.1
1A
TÐ
.66
.10
.17
INÐ
.05
.19
Mas
Ð.2
6F
em
Ð
aA
ch5
ach
ievem
en
t;E
ff5
eff
ort
;L
G5
learn
ing
go
als
;P
G5
perf
orm
an
cego
als
;P
T5
ple
asi
ng
the
teach
er;
FG
5fu
ture
go
als
;P
A
5p
erc
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Goals, Values, and Beliefs 441
Tab le V. Percentage of Variance Explained (R 2 Change ) and Regre ssion Weights from Analy-ses with the Whole Sample Predicting Achievement and Efforta
Achievement Effort
Model No. Ð Set R2 R2
Variable Cha B SE B Beta Cha B SE B Beta
1Ð Sex 0% 3%
2 1.63 1.58 2 .06 2 .40 .12 2 .18b
2Ð Class Type 2% 0%Sex 2 1.35 1.56 2 .05 2 .39 .12 2 .17b
Class Type 2 3.97 1.54 2 .14b 2 .13 .12 2 .063Ð Grade Leve l 6% b 0%
Sex 2 1.34 1.52 2 .05 2 .39 .12 2 .17b
Class Type 2 7.92 1.78 2 .27b 2 .21 .14 2 .09Grade Leve l Ð Ð Ð Ð Ð Ð
4 Ð Goals 12% b 26%
Sex .49 1.46 .02 2 .19 .10 2 .08Class Type 2 7.87 1.68 2 .27b 2 .20 .12 2 .09Grade Leve l Ð Ð Ð Ð Ð Ð
Learning Goals 4.45 1.06 .22b .62 .07 .40b
Performance Goals 2 .17 .83 2 .01 .00 .06 2 .02
Please Teach 2 .006 .83 .00 .00 .06 .00Future Goals 4.71 1.25 .20b .38 .09 .21b
5-Values 11% 7%
Sex 2 .19 1.38 .00 2 .23 .10 2 .10Class Type 2 7.73 1.57 2 .27b 2 .20 .11 2 .09Grade Leve l Ð Ð Ð Ð Ð Ð
Learning Goals 2 .69 1.22 2 .03 ,29 .09 .19b
Performance Goals 2 .13 .78 2 .01 .001 .06 2 .01
Please Teach 2 .41 .78 2 .03 .002 .06 2 .02Future Goals 3.67 1.20 .16b .31 .09 .17b
Utility 2 .24 .94 2 .02 .004 .07 .03b
Attainment 3.02 1.09 .20b .16 .08 .14Intrinsic 4.17 .96 .27b .26 .07 .23b
6-Beliefs 13% b 6%
Sex 2 2.60 1.42 2 .09 2 .15 .11 2 .07Class Type 2 6.32 1.46 2 .22b 2 .16 .11 2 .07Grade Leve l Ð Ð Ð Ð Ð Ð
Learning Goals 2 1.62 1.16 2 .08 .18 .09 .12Performance Goals 2 .42 .71 2 .03 .01 .06 .01
Pleasing Teach 2 .17 .70 2 .01 2 .002 .05 2 .02Future Goals 3.30 1.09 .14b .29 .08 .16b
Utility 2 .15 .86 2 .01 .001 .07 .01
Attainment 1.81 .99 .12 .11 .08 .09Intrinsic 1.01 1.00 .07 .20 .08 .18b
Perc Ability 6.79 1.22 .37b .33 .09 .23b
Stereotyping .27 .96 .01 2 .24 .07 2 .18b
Dif® culty 2 2.00 .98 2 .14 .00001 .08 .00
7Ð BSRI 2% b 0%Sex 2 2.50 1.44 2 .08 2 .15 .11 2 .07Class Type 2 5.92 1.50 2 .20b 2 .15 .11 2 .07
Grade Leve l Ð Ð Ð Ð Ð ÐLearning Goals 2 1.57 1.15 2 .08 .18 .09 .12Performance Goals 2 .51 .71 2 .03 .01 .05 .01
442 Greene et al.
Table V. (Continued )
Achievement Effort
Model No. Ð Set R2 R2
Variable Cha B SE B Beta Cha B SE B Beta
Pleasing Teach 2 .15 .70 2 .01 2 .02 .05 2 .02Future Goals 3.35 1.09 .15b .29 .09 .16b
Utility 2 .42 .86 2 .03 .01 .07 .01
Attainment 2.16 .98 .14 .11 .08 .10Intrinsic 1.03 .99 .07 .20 .08 .17b
Perc Ability 6.77 1.21 .37b .33 .09 .23b
Stereotyping 2 .09 .96 .00 2 .25 .07 2 .17Dif® culty 2 2.04 .97 2 .14 2 .001 .08 .00
Masculinity 2 3.06 1.03 2 .02 2 .04 .08 2 .02Femininity 2 .50 .98 .13b .0001 .08 .00
Total R2 46% 42%
Adjusted R2 43% 40%
aGrade refers to Grade Leve l that was dummy coded for use as a control variable ; thereforereporting Bs and Betas for the two dummy variables for grade level is inappropriate.
bp # .01.
schemata scores, in that order, as predictor variable s for achievement. The
results are summarized in Table V. As expected, grade leve l, mathematics
class and gender each only accounted for a small amount of variance . Goals,
value s and beliefs all explaine d signi® cant percentage s of variance that
were similar in magnitude . The gender self-schemata set accounte d for a
small, but statistically signi® cant amount of variance . The ® nal regression
equation accounte d for 42% of the variance in achievement scores (F
(16,334) 5 17.39, p , .0001) .
The statistically signi® cant Beta weights from that ® nal equation were
for grade leve l (p , .0001) mathematics class (p 5 .0001) , future goals
(p 5 .001) , perceived ability (p , .0001) , and the masculinity variable
(p 5 .003) . The negative Beta weight associate d with the masculinity vari-
able means that high scores on masculinity were associate d with lower
achievement scores. That no individual variable in the values set had a
signi® cant Beta weight in the ® nal regression equation may be an artifact
of the multicolline arity proble m noted above .
Predicting Effort. The same hie rarchical regression analysis was used
to examine the prediction of effort. As can be seen from Table V, the goals
set accounte d for the greatest percentage of variance in effort scores. Once
again, future goals was the only goal variable to have a statistically signi® -
cant Beta weight in the ® nal equation (p 5 .001) . The overlap between the
learning goals and the intrinsic value variable s may be suppressing the
contribution of learning goals. The Beta weight for the intrinsic value
variable was marginally signi® cant in the ® nal equation (p 5 .012) . Two
Goals, Values, and Beliefs 443
Tab le VI. Perce ntage s of Variance Explained (R 2 Change ) and Beta Weights from HierarchicalRegre ssion Analyse s Predicting Achievement for Male s and Female s in Required and Elective
Mathematics Classes
Achievement Effort
Required Elective Required ElectiveEquation No. Ð Se t
Variable Male s Females Males Females Males Females Males Females
1 Ð Grade Level 10% a 10% a 2% 10% a 2% 0% 2% 2%
2Ð Goals 15% a 17% b 26% a 6% 26% b 32% b 43% b 23% b
Grade level
Learning .16 .25a 30a .23a .31b .36b .60b .41b
Performance 2 .15 .18 2 .06 2 .04 .17 .14 2 .02 2 .22a
Future Goal .30b .17 .32a .04 .28a .26b .17 .16
3 Ð Values 9% 10% a 15% a 18% b 4% 4% 12% a 15% b
Grade level
Learning 2 .09 .05 2 .18 2 .03 .17 .22 .17 .18
Performance .01 2 .09 .16 2 .00 2 .15 2 .13 .09 .15
Please teach 2 .17 .13 2 .13 2 .04 .16 .12 2 .07 2 .24a
Future Goal .32a .13 .18 .02 .30a .22a .05 .15
Utility 2 .09 2 .13 .17 .03 2 .12 .02 .16 2 .01
Attainment .12 .14 .28 .26 .09 .04 .28 .20
Intrinsic .36a .35a .27 .29b 21 .23 .21 .33b
4Ð Be liefs 10% a 20% b 6% 7% 9% 5% 6% 6%
Learning 2 .17 2 .01 2 .17 2 .08 .11 .10 .13 .10
Performance 2 .05 2 .09 .14 .01 2 .18 2 .04 .10 .14
Please teach 2 .13 .14 2 .11 2 .02 .19 .08 2 .06 2 .21a
Future Goal .29a .10 .18 .02 .34b .21a .07 .10
Utility 2 .12 .03 .09 .03 2 .16 .02 .03 .00
Attainment .06 .03 .26 .18 .05 .01 .26 .11
Intrinsic .25 .01 .11 .10 .20 .23 .08 .24
Perc ability .43a .46b .12 .29a .06 .21 .32 .35a
Stereotyping .04 .02 2 .02 2 .01 2 .25a 2 .21a 2 .14 2 .06
Dif® culty .02 2 .20 2 .22 2 .13 2 .13 .05 2 .03 .06
5 Ð Gende r (BSRI) 1% 1% 6% % 1% 1% 2% 2%
Grade level
Learning 2 .20 2 .01 2 .13 2 .05 .11 .09 .12 .14
Performance 2 .05 2 .10 .08- .01 2 .17 2 .03 .12 .14
Please reach 2 .13 .14 2 .09 .00 .17 .08 2 .08 2 .19a
Future Goal .28a .11 .27a .00 .34a .21a .06 .12
Utility 2 .14 .04 2 .04 2 .03 2 .16 .02 .05 2 .04
Attainment .12 .03 .26 .22 .03 .01 .26 .14
Intrinsic .25 .01 .26 .07 .19 .23 .07 .21
Perc ability .45b .46b .10 .31a .06 .21 .37 .35a
Stereotyping .03 .03 2 .14 2 .06 2 .24a 2 .23a 2 .13 2 .10
Dif® culty .02 2 .21 2 .17 2 .10 2 .14 .06 .01 .08
Masculinity 2 .11 2 .07 2 .20 2 .19a .01 .05 .16 2 .15
Feminity 2 .01 2 .02 2 .17 2 .00 .09 .05 2 .03- .02
Total R2 45% 57% 54% 44% 42% 42% 65% 48%
ap , .05.bp , .01.
444 Greene et al.
variable s from the belie fs set were signi® cant, perceived ability (p 5 .001)
and the stereotyping variable (p 5 .001) . The negative Beta weight
associate d with the stereotyping variable means that high scores on stereo-
typing were associate d with lower effort scores. The ® nal equation ac-
counted for 44% of the variance in effort scores (F (14,334) 5 21.54,
p , .0001) .
Regression Analyses for the Four Subgroups
Predicting Achievement. Hierarchical regression was conducted by en-
tering grade leve l, the four goals scores, the three value s scores, the three
belie fs scores, and the two gender self-schemata scores, in that order, as
predictor variable s for achievement. These analyse s are summarized in
Table VI. For male s in required math the patte rn of prediction was that
goals accounte d for 15% (p , .05) , value s 9% (p , .05) and belie fs 10%
(p , .01) of variance in the ® nal equation. Gender self-schemata accounted
for only 1% of variance . The ® nal regression equation accounte d for 45%
of the variance in achievement ( F (14, 67) 5 3.88406, p , .001) , with
perceived ability (p 5 .002) and future goals (p 5 .017) be ing the only
individual variable s to contribute signi® cantly to the ® nal equation.
For female s in required math, goals, value s and beliefs all accounte d
for signi® cant proportions of variance (p , .01) ; 17%, 10%, and 20%, respec-
tively. Gender self-schemata accounted for only 1% additional variance .
Perceived ability (p , .001) was the only variable that reached signi® cance in
the ® nal equation, which accounte d for 57% of total variance in achievement
scores (F (14, 90) 5 8.55656, p , .0001) .
For male s in elective math, goals (26%) and value s (15%) each ac-
counted for signi® cant proportions of variance (p , .01) in achie vement.
Neithe r the beliefs (6%) nor gender self-schemata (6%) contribute d to
explaining signi® cant proportions of variance . The ® nal regression equation
accounte d for 54% of the variance in achievement (F (14, 45) 5 3.81918,
p , .001) . Only future goals (p 5 .047) reached signi® cance in the ® nal
equation. This is like ly due to the multicolline arity among the goal and
value variable s.
A different patte rn was found for female s in elective math, in that
value s (18%, p , .01) and belie fs (7%, p , .01) accounte d for signi® cant
proportions of variance in achievement, but goals (6%) did not. The ® nal
regression equation accounted for 44% of the variance in achievement
(F (14, 87) 5 4.86292, p , .0001) , with perceived ability (p 5 .032) and
masculinity (p 5 .046) making signi® cant contributions to the ® nal equation.
The negative Beta weight associate d with the masculinity variable shows
Goals, Values, and Beliefs 445
that high scores on masculinity were associate d with lower achievement
scores.
Predicting Effort. Once again, hie rarchical regression was conducted
by entering grade leve l, the four goals scores, the three value s scores, the
three be lie fs scores, and the two gender self-schemata scores, in that order,
as predictor variable s for effort. These analyse s are also summarized in
Table VI. For male s in required math, goals explaine d the greatest percent-
age of variance in effort scores, 26% (p , .01) ; although beliefs (9%, p ,.05) also made a signi® cant contribution . The ® nal regression equation
accounte d for 42% of the variance in effort (F (14, 67) 5 3.39500,
p , .001) , with future goals (p 5 .006) and stereotyping (p 5 .022) contribut-
ing signi® cantly to the equation. The negative Beta weight for stereotyping
indicate s that high stereotyping was associate d with lower effort.
The patte rn for female s in required math was very similar to that found
for male s in that goals explaine d the most variance in effort and both future
goals (p 5 .038) and stereotyping (p 5 .029) reached signi® cance in the
® nal equation, which accounted for 42% of the variance in effort (F (14,
91) 5 4.70692, p , .0001) . Stereotyping again had a negative Beta weight.
The equation for male s in elective classes showed that goals (43%)
and value s (12%) each accounte d for signi® cant proportions of variance .
In the ® nal equation (F (14,47) 5 6.26220, p , .0001) , which accounte d for
65% of variance in effort, no individual variable reached signi® cance.
For female s the pattern was similar. Goals (23%, p , .01) , value s
(15%, p , .01) , and belie fs (6%, p , .05) were all signi® cant contributors
to a ® nal equation that accounted for 48% of the variance in effort (F (14,
86) 5 5.69047, p , .0001) . Perceived ability (p 5 .012) and pleasing the
teacher (p 5 .049) were each signi® cant in the ® nal equation.
Path Models to Test the G ender Differences
We conducted two multiple -sample path analyse s, one for effort and
one for achievement, in order to test gender differences by class type. Given
the combination of small numbe rs and the complex design, we decided to
simplify the mode l by dropping variable s that were eithe r uncorre lated
with the two outcome variable s (performance goals, pleasing the teacher,
masculinity and femininity) or unimportant theoretically (math dif® culty
due to its redundancy with perceived ability) . We also eliminated the attain-
ment value scale due to its high corre lation with utility value . Finally, we
applie d an arcsine distributiona l transformation to the stereotyping variable
to reduce the skewness in that distribution .
Using EQS to analyze our data, we applie d the theoretically-de rived
446 Greene et al.
path mode l for achie vement (Fig. 2) to our four subsample s simultaneously,
initially imposing equality constraints on all parameters. Equality con-
straints that were proble matic for the overall ® t of the mode l were
then released one by one until we had arrived at the best ® tting
mode l for the multiple subsample s. Those equality constraints that were
released to achieve better ® t indicate areas in the path mode l where gender
and/or class type diffe rences exist. These diffe rences are presented be low.
The same procedure was repeated for the path mode l for effort
(Fig. 3).
Two ® t statistics were examine d for each path mode l: (a) the Bentle r-
Bonett Normed Fit Index (NFI), which compare s the ® t function used to
a base line mode l of uncorre lated variable s, and (b) the Comparative Fit
Index (CFI), which is a similar test with the additional advantage of be ing
less effected by sample size than the NFI. Fit statistics for the path mode l
predicting achievement were NFI 5 .69 and CFI 5 .73. For effort the ® t
statistics were NFI 5 .71 and CFI 5 .75. These relative ly low value s are ,
at least partially, an artifact of conducting a multi-sample comparison, as
is borne out by comparing them to the ® t statistics reported be low for the
whole sample .
In inspe cting path parameters (non-standard ized coef® cients are re-
ported) across the four subsample s the following differences were noted.
For female s in elective classe s, the links from the two value s variable s to
the two goals variable s were not statistically signi® cant although they were
for the other three groups. In the prediction of achie vement, the direct link
from perceived ability was statistically signi® cant for all four groups, but
within both males and female s the coef® cient is large r for students in
required classe s than students in elective classes. Interestingly, for the pre-
diction of effort (see Fig. 3), the males in required classe s had no statistically
signi® cant direct path from perceived ability to the dependent variable ,
while the othe r three groups had such a direct path. Finally, the corre lation
between learning goal and future goal was signi® cant for all subgroups
except female s in required classe s. Looking at relative magnitude of the
corre lations it can be seen that the relationship between learning goals and
future goals is stronge st for females in elective math (.54) , and weakest for
female s in required math (.16) , with males in required (.38) and elective
math (.35) falling in between.
Other parame ters in the path mode ls were equal across subgroups,
although there were diffe rences in the relationships between the indepen-
dent variable s and each dependent variable . For both effort and achieve-
ment there was a statistically signi® cant link from future goal; although,
the link from learning goal was only signi® cant for achievement. There was
also a signi® cant direct link from stereotyping to effort with a negative
Goals, Values, and Beliefs 447
Fig
.2.
Path
mo
del
for
gen
der
an
dm
ath
em
ati
cs
cla
ssty
pe
in¯
uen
ces
on
ach
ievem
en
t.
448 Greene et al.
Fig
.3.
Path
mo
del
for
gen
der
an
dm
ath
em
ati
cs
cla
ssty
pe
in¯
uen
ces
on
eff
ort
.
Goals, Values, and Beliefs 449
value indicating that highe r stereotyping was related to less reported effort.
No such direct link to achievement was hypothe sized to exist.
We ® nd the magnitude of path coef® cients for the relationships among
utility, intrinsic, learning goal, achievement, and effort somewhat puzzling
in that the low value s and negative relationships between some of these
pairs are not consistent with the zero-orde r corre lations among these vari-
able s. We conclude that a suppressor effect, resulting from relative ly high
zero-orde r corre lations among value s variable s and learning goal, is inte rfer-
ing with straightforward inte rpretation of these coef® cients.
Path Models to Test the Placement of Task-Speci® c G oals
One of the main diffe rences between our mode l and the Eccles et
al.(1983) mode l is the placement of task-speci® c goals as directly linke d to
both achievement and effort. Therefore , our ® nal analyse s were to test the
® t of path mode ls in which goals mediated between value s and outcomes.
We decided that the multicolline arity between learning goals and the
values would prevent an inte rpretation of the path coef® cients, as the large
negative path coef® cient found in the previous path model for achie vement
sugge sted, so we droppe d learning goals to examine this question. In addi-
tion we collapse d utility and intrinsic value s into a single value s measure .
We acknowledge that this is not an optimal test of our model given the
unresolved multicolline arity proble ms that necessitated removal of poten-
tially inte resting variable s. However, ® t statistics for the path mode ls shown
in Fig. 4 give a pre liminary indication that placing task-speci® c goals into
the model as moderating between value s and outcomes is a good ® t of the
data. For both the achievement and effort models NFI 5 .98 and CFI 5 .99.
Comparing mode ls across the two dependent variable s, we note that
the path coef® cients are of greater magnitude in the model for achievement
than for effort.
GENERA L DISCUSSION
The results of this study clearly support the usefulne ss of the modi® ed
Expectancy-V alue model for explaining substantial amounts of variance in
measure s of student achievement and effort in mathematics. The inclusion
of future goals as a predictor of both effort and achievement was strongly
supporte d. However,the results also suggest that furthe r work is needed
before the relationships between goals and value s are clear, and before the
gender self-schemata construct is clearly articulate d. We believe this work
450 Greene et al.
Fig
.4.
Path
mo
del
tote
sta
sim
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®ed
vers
ion
of
the
revis
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exp
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an
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ÐV
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od
el.
Goals, Values, and Beliefs 451
will require modi® cations that re¯ ect a con¯ uence of theoretical and mea-
surement issues. The current results also revealed differences based on
gender and math class type in the prediction of achievement and effort. The
® ndings concerning differences in patterns of prediction will be discussed
following a summary of what the data sugge st about the mode l itself.
Evidence for the Revised Model
Factor analysis offered support for the coherence and independence
of variable s within the goals and belie fs sets, but weaker support for the
separate ness of the variable s within the value s set (intrinsic value , utility
value , attainment value ). We noticed that Eccles (1984) has also collapse d
the value s into one construct in some of her work. We admit that our
modi® cations of the items presented by Eccles and Wig® e ld (1995) may
account for our failure to ® nd distinct factors.
It is obvious that the value s set contribute d signi® cantly to the predic-
tion of both achievement and effort, though the unique contributions of
the three value s is unclear. We think that the abstract nature of the notion
of value s makes it dif® cult to write items that ask about diffe rent value s
in ways that are concrete enough to be recognizably diffe rent. Although
conceptually these aspects of valuing seem distinct, we believe the distinc-
tiveness is at a highe r leve l of abstraction than what students normally use
for re¯ ecting on their learning. Framed this way, we are less surprised that
a sample of high school students would respond as though the value items
were not so different from one anothe r. This is a matter for furthe r study.
That the goal variable s were useful additions to the mode l is supporte d
by the fact that goals accounte d for signi® cant proportions of variance in
both achievement and effort scores, and future goals was a variable that
reliably made a unique contribution to the explanation of variance in both
scores. From Table V it can be seen that goals accounte d for twice as much
variance in effort scores than in achievement scores. The positive role of
future goals is consistent with other work we have done with a similar
population of high school students (Mille r et al., 1996) . Furthe r work is
needed to clarify the role s of the other goal variable s within such a mode l.
The ® ndings regarding the belie f variable s generally followed the same
patte rn as found in other work by Eccles et al.(e .g., Eccles and Wig® eld,
1995) , in that be lie fs have typically made a large r impact on the prediction
of achie vement than effort. In fact, the R2 for be liefs in predicting achieve-
ment was twice that found in the prediction of effort. Perceived ability
consistently playe d a signi® cant role in the prediction of achie vement and
effort, though, some group differences were found. Our data did not
452 Greene et al.
strongly support the usefulne ss of the be liefs about math dif® culty variable .
It’ s very high, negative corre lation with perceived ability sugge sts that both
might not be needed in the mode l.
Including the stereotyping of mathematics as a male domain variable
proved useful in the prediction of effort. The stereotyping variable had a
negative relationship with effort, for both male s and females. This ® nding
is in contrast to the ® ndings of Eccles (1984) who found that stereotyping
of mathematics as a male domain was positive ly related, for both males
and females, to the subje ctive valuing of math. We think that our ® nding
probably re¯ ects more current sociological perspective s on gender and
mathematics learning.
It is inte resting to speculate how the stereotype might be inte rpreted
differently by male s and female s. It is like ly that the association of stereo-
typed views with lower reported effort is due to diffe rent attributional
in¯ uences for male s and female s. For the young women, struggle s with
math when math is considered more of a male domain means that effort
should not pay off as ability related to gender is probably the reason for
the struggle s. For the young men holding the stereotype d notion, however,
the reason for lower effort in math might be that effort should not be
needed for a male in a male domain. It should come easy to male s. Further-
more , needing to exert effort might signal a low ability attribution since
male s are thought to be more able . So, while a stereotype d view of math
as a male domain may provide female s with a reason for not exerting extra
effort, for male s it might deter their initial attempts to put forth effort.
Regardle ss of the reasons, having a stereotyped view of mathematics is a
detriment to mathematics learning, for both male s and female s, whenever
effort will be needed. Since the learning and enjoyment of highe r-leve l
mathematic require s conside rable effort from typical male s and female s,
the stereotype is clearly proble matic.
The gender self-schemata variable s were not very useful in predicting
achievement or effort, though, the set did contribute a statistically signi® cant
2% to the prediction of achievement. Interestingly, the masculinity scores
had a statistically signi® cant, negative Beta weight demonstrating that
highe r masculinity scores were related to lower achievement scores. This
® nding is contrary to the stereotype that mathematics is a masculine domain.
We are reluctant to inte rpret the ® nding, however, because we now suspect
that the BSRI is not a valid measure of gender self-schemata for our pur-
poses.
We chose the BSRI because of its continued popularity in gender
research (Archer, 1989; Handal & Salit, 1988) and because it is so similar
to the measure used in the Eccles et al. (e .g., 1983) research. In retrospect,
we think that such a global measure of gender identity, that is additionally
Goals, Values, and Beliefs 453
not tied to conscious perceptions of gender identity, is probably not congru-
ent with our revisions to the mode l. The other variable s in the model are
speci® c to the context of learning mathematics and require conscious or
self-re¯ ective statements of value s, goals, and belie fs. The BSRI is suppose d
to measure general, culturally accepted attribute s of femaleness and male -
ness. Responde nts indicate the extent to which an attribute is like them
NOT whether they view that attribute as an aspect of their femaleness
and maleness. So, it does not require any conscious re¯ ection on their
gender identity.
We have also looke d more carefully at several critiques of the BSRI
(e.g., Archer, 1989; Ballard-Re isch & Elton study, 1992; and Gill, Stockard,
Johnson, Williams, 1987) . We thought that Ballard-Re isch and Elton (1992)
provide d strong evidence that the items on the BSRI did not correspond
to current conceptions of femaleness and maleness. We have , therefore ,
been persuaded that the validity evidence for the instrument is not suf® -
ciently strong to warrant use for our purpose s. An obvious need for future
research is the deve lopment of current measure s of gender self-schemata.
As a ® nal piece of evidence regarding the revised mode l, path analyse s
of the whole group indicated that placement of the goals variable s following
values and linke d directly to achievement and effort was a reasonable ® t
of the data. However, this does not preclude that othe r con® gurations of the
variable s would not yie ld equally good ® t statistics. Additional psychome tric
work is needed to addre ss this question.
Evidence for Differences Based on G ender and/or Math Class Type in the
Pred iction of Achievement and Effort
The regression equations summarized in Table VI demonstrate d the
additive contributions of variable sets in the revised expectancy-value mode l
to the prediction of achievement and effort by subgroups. These analyse s
revealed complex patte rns of differences. The two multi-sample path analy-
ses were able to provide support for some of these diffe rences. Our discus-
sion of these diffe rences will be organized around the variable sets for
goals, value s, and belie fs.
The set of task-speci® c goals accounted for more variance in achieve-
ment scores among male s in elective math classe s (25%), and less variance
among female s in elective math classes (6%), compared to other groups.
A like ly, partial explanation for the lack of relationship between goals and
achievement for female s in elective math is the lack of variability found in
two of the four goal scores (see Table III). These female s had very high
mean scores on learning goals and future goals with very small range s
454 Greene et al.
within these scores. Such restriction in range will attenuate the statistical
relationships with these scores and other variable s. That may explain why
the regression analysis demonstrate d that future goals were signi® cant for
predicting achievement in male s, but not in females. This gender diffe rence
was not supporte d by the path mode l. The path ® ndings are more consistent
with theoretical predictions.
This attenuation proble m was less obvious with the prediction of effort
scores. Female s in elective math were similar to the other groups in that
the goals set accounted for substantial amounts of variance and accounte d
for the most variance relative to the other sets.
As can be seen from Table VI, there were two group diffe rences found
in the goal set with the prediction of effort scores. Females in elective math
had a signi® cant negative Beta weight associate d with the pleasing the
teacher variable . This means that female s who reported wanting to please
the teacher as a reason for doing the work in elective math also reported
lower effort relative to their peers who did not have high scores on the
pleasing the teacher variable . A lthough it is inte resting to note that this
® nding is consistent with Fennema & Peterson’ s ( 1985) notion of Autono-
mous Learning Behaviors, we think it best to replicate this ® nding before
we commit to an interpretation.
The other group diffe rence found in the goal set with the prediction
of effort scores was that the male s and female s in required math had
signi® cant positive Beta weights associate d with the future goals variable ,
while the elective math class groups did not show such a relationship. It
should be noted that males in elective math also had very high mean scores
on future goals and a restricted range within these scores (see Table III).
So the absence of a relationship between future goals and effort scores for
the elective groups might be explaine d by the range restriction proble m.
In path analysis a statistically signi® cant link between future goals and
effort was found to ® t all four sub-sample s adequate ly.
The addition of the value s set accounte d for more additional variance
among students in elective math classes than in required math classe s. As
can be seen from Table VI, this was most pronounce d for the prediction
of effort scores. We offer a possible explanation, for the greater role of
value s for students in elective classe s, that is consistent with the argument
we made earlie r about the abstract nature of the value items. We suspect
that students who choose to take additional mathematics classe s have identi-
® ed some personal relevance (though not necessarily intrinsic) related to
math learning that goes beyond the concrete reasons for studying for a
particular class. Such personal relevance might support the perseverance
required for success in challe nging domains. Clearly this is speculation that
should be examine d in future inve stigations. We also note that the multi-
Goals, Values, and Beliefs 455
sample path analyse s indicate d signi® cant path coef® cients from utility to
future goals, and from intrinsic value to learning goal for all groups except
female s in elective classe s. The lack of a direct relationship is consistent
with the greater unique contribution of value s seen for female s in elective
when predicting achievement.
The most complex of the group diffe rences were found among the
set of task-spe ci® c be lie fs. When predicting mathematics achie vement, the
belie f set accounted for more additional variance among students in re-
quired math classe s, especially female students, than for students in elective
math, with perception of ability making the greatest contribution . The
multi-sample path analyse s revealed a similar diffe rence .
There was also a gender diffe rence obse rved among students in elective
math. For female s, the R2 change associate d with the be lie f set was statisti-
cally signi® cant as was the positive Beta weight for the perception of ability
variable . None of the be lie f variable s contribute d to the prediction of
achievement for males in elective math.
A different patte rn of diffe rences was found for the belie f set when
effort scores were be ing predicted. Across the four groups the R2 change
values were statistically signi® cant for male s in required math and females
in elective mathematics. For male s and female s in required math future
goals and stereotyping had signi® cant Beta weights, with the Beta for
stereotyping be ing negative . The multi-sample path analyse s did not reveal
a subgroup diffe rence in the links between perceived ability and effort
or between future goals and effort. Additionally, statistically signi® cant,
negative Beta weights associate d with the variable measuring the be lie f
that math is a male domain was found for both male s and female s in
required math. However, the path analysis demonstrated that the negative
relationship was found for all four groups.
Conclusions and Implications
The results of this study provide strong evidence for the importance
of the goals, value s, and belie fs that students bring to the context of learning
mathematics, in that large proportions of variance were accounte d for
when predicting both achievement and effort. Although furthe r research
is needed to clarify the contributions of some of the speci® c goals measured
here, we be lieve there is suf® cient evidence to support inte rvention research
on encouraging students to recognize the future goals of the ir current
coursework. We also think that the ® nding that value s were more important
for students in elective classes has important implications for theory and,
therefore , warrants furthe r investigation.
456 Greene et al.
Belie fs about one ’s ability to master a task were especially important
in the prediction of achievement for students taking required classe s. Future
research should examine whether maintaining high perceptions of ability
during the required course work in mathematics is prerequisite to students
choosing to take math elective s.
Our results also demonstrated that the goal, value , and belie f variable s
were important for both male s and female s. However,there were several
gender diffe rences noted. Perhaps the most noteworthy gender diffe rence
was that the be lie fs set was more important for female s when predicting
the achievement outcome than for male s. This means that female s might
be more vulne rable when high ability be liefs are challe nged or dif® cult to
establish. In general, these ® ndings on belie fs and achievement strongly
support the need for strategie s that teachers can apply in the ir classrooms
to support high ability perceptions for male s and females.
Our ® nal point is that we hope teachers and researchers will take note
of our ® nding on the negative in¯ uence of the ``math is a male domain’ ’
stereotype on the reported effort of male s and females in high school math
classe s. We have noticed that for some researchers the notion that girls are
not good at math is be ing renewed in terms of a feminist critique of tradi-
tional ways of teaching mathematics (Fennema, 1994) or of society’ s exalta-
tion of competence in mathematics (Noddings, 1998) . A lthough we agree
that the teaching and learning of mathematics should be debated in terms
of the large r, social structure issues, we are also concerned that some of
these perspective s may simply dress the old stereotype up for a post-modern
audie nce . Our data indicate that be lie fs that mathematics is a male domain
should be discourage d since these be lie fs discourage the motivation to learn
mathematics in both male s and female s.
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