Download - Goals, Values, and Beliefs as Predictors of Achievement and Effort in High School Mathematics Classes

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].

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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


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.


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.


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


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


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


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)


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


(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

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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

eiv

ed

ab

ilit

y;

MD

5m

ath

dif

®cu

lty;S

T5

stere

oty

pin

go

fm

ath

as

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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


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


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


Fig

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448 Greene et al.

Fig

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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

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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


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-


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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