differences in expectancy-attribution patterns of cognitive components in male and female math...

CONTEMPORARY EDUCATIONAL PSYCHOLOGY 15, 284-298 (1990)

Differences in Expectancy-Attribution Patterns of Cognitive Components in Male and Female

Math Performance

RENBE C. TAPASAK Syracuse Universi@

The “relative math expectancies” and math performance attributions of male and female eighth-grade students were examined in relation to a proposed Expec- tancy-Attribution (E-A) process model of performance. Results showed relative math expectancy (RME) to be related to attributional style along the stability dimension of the model. Students in the Low RME group exhibited a “negative” Expectancy-Attribution (E-A) pattern, attributing math success more to variable than stable factors and failure more to stable than variable factors. High RME group students exhibited a “positive” pattern in part, attributing math success more to stable than variable factors. A greater percentage of females than males, and a greater percentage of females than expected from Math GPA level, composed the Low RME group. A greater percentage of males than females and greater percentage of males than expected composed the High RME group. The results were seen as supporting the proposed E-A model and as providing further evidence of gender differences in cognitive patterns in mathematics. 0 1990 Academic press, hc.

Past studies of female math performance have found that females do as well or better than males from the elementary through the middle school grades and that it is at the high school level at which males begin to excel (e.g., Maccoby & Jacklin, 1974; Sherman, 1980). More recent studies show similar results with the turning point at an earlier level. For example, a longitudinal study which examined sex differences in math learning found that third-grade girls obtained higher scores on the Surveys of Basic Skills in all but one of the six math areas measured. By the sixth grade, girls’ performance had declined. They had fallen further behind boys in two areas and only surpassed them on two of the six areas (Marshall & Smith, 1987). Similarly, Feingold’s (1988) examination of gender differences in cognitive abilities using standardization norms of the Preliminary Scholastic Aptitude and Scholastic Aptitude Tests showed that although the magnitude of the difference tended to decline across 1960 to 1983 norms, males at junior and senior high school grade levels consistently

This research is based upon the author’s master’s thesis while a graduate student at Syracuse University. Requests for reprints should be sent to the author, who is presently an NIMH Postdoctoral Fellow at Yale University, Department of Psychology, P.O. Box 1 IA Yale Station, New Haven, CT 06520.

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0361-476X&O $3.00 Copyright 8 1990 by Academic Press, Inc. AU rights of reproduction in any form reserved.

COGNITIVE COMPONENTS IN MATH 285

obtained significantly higher math subtest scores than their female grade equivalent peers.

Paired with achievement differences are the differences in numbers of male and female students who elect to study math in high school and beyond. While sex-related differences in math elective study continue to exist in high school, they are less dramatic than noted in the past (e.g., Brush, 1980; Fennema, 1984). After high school, however, the majority of those females who go on to college continue to enroll in programs in allied health professions and education; those who enroll in vocational/technical schools elect traditional female occupational programs (Astin & Snyder, 1984).

A number of empirical and theoretical approaches have been used to examine what appear to be progressive differences in male-female math achievement-related behavior. Several models have been proposed to examine how such covert cognitive variables as attitudes, perceptions, or beliefs might relate to observable math achievement-related behavior such as task performance and persistence (e.g., Eccles, Adler, Futter- man, Goff, Kaczala, Meece, & Midgley, 1983; Fennema & Peterson, 1983). The math expectancy-attribution model proposed in the present study draws upon theory and research on gender differences in achievement attributions and expectancies. In spite of consistent findings that females do as well or better than males in math grades and standardized achievement test scores through the middle school grades (e.g., Maccoby & Jacklin, 1974; Marshall & Smith, 1987; Sherman, 1980), females “underestimate” their future performance capabilities and have lower expectancies than males for future, unfamiliar general tasks (e.g., Calsyn & Kenney, 1977; Dweck, Goetz, & Strauss, 1980; Frieze, Fisher, Ha- nusa, McHugh, & Valle, 1978) as well as for future, unfamiliar math- related tasks (e.g., Fennema & Sherman, 1977; Heller & Parsons, 1981; Lantz & Smith, 1981). They tend to attribute success outcomes to variable factors and failure outcomes to stable factors, both in general (e.g., Bar-Tal & Darom, 1979; Cooper, Burger, & Good, 1981; Deaux, 1976), and specifically, in mathematics (e.g., Fennema, Wolleat, Pedro, & Becker, 1981; Pedro, Wolleat, Fennema, & Becker, 1981). Males differ from females in that they tend to “overestimate” their future performance capabilities and have expectancies for future, unfamiliar tasks which, on the average, are higher than those of females. They attribute success outcomes to stable (i.e., unchangeable) factors and failure outcomes to variable (i.e., changeable) factors.

The present study proposes that individuals’ perceptions of themselves and their performance in achievement situations can be represented within an “Expectancy-Attribution” (E-A) process model. Components of the model were based upon the achievement attribution theory of

286 RENfiE C. TAPASAK

Weiner (e.g., Weiner, 1974), supportive attribution and expectancy research (e.g., Dweck & Bush, 1976; Valle & Frieze, 1976), Frieze’s “multistage” achievement model (Frieze, 1981), and Nicholls’ theory and research on self-concept of attainment (e.g., Nicholls, 1976, 1978). In the proposed model, cognitive factors are integrated in pairs (i.e., expectancies and attributions) which may influence or be influenced by behavior in success and failure situations. The present study focused on obtaining performance attributions (i.e., what an individual believes causes or caused his or her performance outcome) based on Weiner’s 2 x 2 model (e.g., Weiner, 1974). Focus was placed on the Stability (stable-variable) as opposed to the Locus dimension (internal-external) since the former appears, theoretically and empirically, to be related to expectancies for future performance (e.g., Fontaine, 1974; Valle & Frieze, 1976; Weiner, 1979). Within the Stability dimension, outcomes may be attributed to stable or unchangeable causes (e.g., ability, task difficulty) or to unstable or changeable causes (e.g., effort, luck). The present model differs from Weiner’s work in that performance is defined as academic or school- related performance, and expectancies are reciprocally tied to performance attributions as part of an individual’s “cognitive style” in a specific performance area. In addition, the model recognizes the importance of “relative expectancy”: one’s idea about how well he or she will perform relative to others in a specific performance situation. Relative expectancy is determined by an individual’s situation or task-specific: (1) self-perception of his or her ability, (2) perception of the ability of a comparison group, (3) expectancy of how well comparison group mem- bers will perform, and (4) past experiences with the same or similar reference groups in similar performance situations. The greater the perceived similarity between oneself and a reference group, the greater the influence the expectations for the reference group’s performance will have on one’s relative expectancy. An individual’s E-A patterns may vary according to the particular performance domain being measured or the perceived similarity of the reference group.

Within the E-A model, “positive” and “negative” patterns are proposed. The “positive” (or optimistic) pattern is hypothesized to be characteristic of individuals who maintain high expectancies for future performance, in addition to an attributional style in which they explain their successful performance as being determined by stable factors such as high ability or the ease of the type of achievement task being measured. They explain their failures as being determined by variable (i.e., changeable) factors such as low effort, test format, or teacher instructional style. Because these individuals explain their failures as being due to changeable factors and view their own innate ability as causing their successes, they continue to have high expectancies for success. Consequently, they


continue to seek out and persist at tasks in a particular performance domain. In contrast, the “negative” (or pessimistic) pattern is hypothesized to be characteristic of individuals who maintain low expectancies for future performance paired with an attributional style in which they explain their successful performance as being determined by variable factors such as high effort, test format, or teacher instructional style. They explain their failures as being determined by stable factors such as low ability or the difficulty of the type of achievement task being measured. Because of the way in which these individuals explain their failures as being due to stable factors, their expectancies for successful performance on tasks within a particular performance domain remain low. These individuals, thus, will be unlikely to seek out and persist at such domain-specific tasks. The E-A model is shown in Fig. 1.

Taking into consideration the above-mentioned results of research on male-female differences in expectancies and performance attributions in general, and specific to mathematics, the intent of the present study was to discover whether the proposed cognitive patterns would differentiate

Relative

t +

--_-

Positive E-A Style Expectancy Negaciw E-A Style / i

1 High E of success Low E of Su!cess

1 I , I

1 Performance 0ucc0me

1 PerformancP outcome

r---- S” cess Failfrr Suctc’cess f

Failure , 4 I

I 1 I , I

,Causal Attributions madei ’ Causal Attributions made 8

t Stable

t Variable Va!iablr +b sta le

(e.g., high ability) (e.g., low effort) (e.g., high e-ffort) (e.g., low

ability)

t High E of SUCCESS

‘.I L r

E = rxpcctancy

A = attribution

FIG. 1. Expectancy-attribution model of performance.

288 KENfiE C. TAPASAK

between male and female student groups such that males would exhibit the “positive” expectancy-attribution pattern more than would females, and females would exhibit the “negative” pattern more than would males. Specifically, it was predicted that:

1. Relative to their math grade point average, females’ self-ratings of their future math performance would be lower than males’.

2. When students were categorized into high, middle, and low self- rating groups, females (in general, and relative to math level group) would comprise a higher percentage of subjects in the low group; males would comprise a higher percentage of subjects in the high group.

3. For math successes, students in the low self-rating group (of which a greater percentage would be female) would cite the contribution of variable factors (e.g., effort) as high and stable factors (e.g., ability) as low. High self-rating group students (of which a greater percentage would be male) would cite the contribution of stable factors as high and variable factors as low. For math failures, students in the low self-rating group would cite the contribution of stable factors as high and variable factors as low. In contrast, high self-rating group students would cite the contribution of variable factors as high and stable factors as low.

By examining patterns of expectancies and attributions related to the math achievement process within the proposed Expectancy-Attribution model, the present study hoped to discover differences in cognitive styles which might relate to students’ progressive math behavior through school, college, and later careers.

METHOD

Subjects The subjects in this study were eighth-grade mathematics students from a Northeastern

suburban school district. The majority of students were from white, middle-class back- grounds. Six teachers, five male and one female, participated in the study by distributing the measures and collecting answer sheets from students in their classes. The original sample contained 304 students, of which 65 were tracked into either remedial (11 students) or advanced classes (54 students). To prevent any tracking effects, only students enrolled in Math 8 classes (typical math class for this grade level) were included. This resulted in the final sample of 239 students (122 mate, 177 female).

Math letter grades from grade reports from the first three quarters of the school year were collected for all students. Grades were converted to numeric form and averaged for each student. These conversions were similar to those used by schools to determine grade point average (GPA) from letter grades. Students were assigned to either High (3.2 to 4.3), Av- erage (2.0 to 3.1), or Low (0 to 1.9) Math Level Groups on the basis of their mean math grade (GPA). Math GPA was used since grades and GPA provided to students several times a year serve as ongoing sources of curriculum-relevant performance information by which they may compare themselves to their classroom peers.


Measures

Two kinds of information were obtained: individuals’ attributions for their math performance and their relative performance expectancies for the following grade level. All students were asked to complete the Mathematics Attribution Scale (MAS) (Fennema, Wolleat, 8t Pedro, 1979) and a rating scale of relative math expectancy (RME). The MAS measures students’ perceptions of the causes for their performance in mathematics. Based on Wein- er’s model of achievement attributions (e.g., Weiner, 1976), each of four failure and four success event stems are followed by attribution statements which correspond to four causal factors (effort, ability, task difficulty, environment). Students rate 32 statements presented in Likert-type format (range from 1 to 5) on how each contributes as a cause of a math event. The MAS contains eight subscales (combinations of success and failure events and the four causal factors), each of which is represented by four statements. Subscales are scored by summing the values assigned to the four statements (possible range: 4 to 20). In the present study, the separate causal factors were combined into stable (ability, task difficulty) and variable (effort, environment) attribution dimensions. This resulted in four subscale scores per student: Success-stable, Success-variable, Failure-stable, and Failure-variable (possible range per subscale: 8 to 40). The MAS was modified for use with eighth-grade classes by replacing the word “algebra” in scale items by the general term “mathematics.” Reading level for the scale is reported by the authors to be below Grade 9. All subjects in the study were identified by their teachers as either at or above grade level in reading achievement. Therefore, only minor word changes were made in the scale. Internal consistency reliabilities are reported as .77 and .79, respectively, for Success-ability and Success-effort subscales. For Failure-ability and Failure-effort, reliabilities are .67 and 66, respectively. Re- liability coefftcients of .39, .48, .48, and .48 were obtained for Success-task, Success- environment, Failure-task, and Failure-environment subscales. The authors of the MAS attribute the low reliability of these subscales to the variations in the kinds of tasks and environments included in the items.

The second measure was a one-item, 9-point rating scale which was developed for use in the present study. The scale was modeled after similar measures used by Nicholls to assess “selfconcept of attainment” (e.g., Nicholls, 1978), and Licht and Dweck (1984) to measure children’s perceptions of their ability relative to that of their classmates. The scale in the present study was divided into nine (unnumbered) sections with the words “bottom,” “middle,” and “top” printed at equidistant points underneath. Students were given directions which asked them to imagine that all math classes had students who performed at the bottom, middle, and top ranges. They were asked to think about their next (ninth grade) math class and check off where they felt they would belong on the scale relative to their (hypothetical) ninth-grade classmates. This self-rating resulted in each student’s “relative math expectancy.” The test-retest reliability of the scale over a 5-week period was .79. Scores obtained from the first administration were used in all primary analyses.

Procedures

Testing occurred in the last quarter of the school year after students had received math grades for the first three quarters. A brief meeting was held prior to testing to inform participating teachers of procedures to follow. At the beginning of the testing session, students were told that the intent of the study was to “find out how eighth graders feel about their math classes and about how well they think they’ll do in math.” Directions and items for measures were provided in written form. After teachers read directions aloud, students completed each measure independently. Teachers answered only questions pertaining to procedures or vocabulary usage. The rating scale and MAS were administered in consecu-


tive order in one 30-min session. Five weeks later, the rating scale was readministered to students to obtain test-retest reliability data.

RESULTS

Females obtained significantly higher mean math GPAs than males: 2.60 (SD = .91) and 2.30 (SD = .93), respectively, [t(237) = 2.54, p < .Ol].

Relative Math Expectancy (RME)

To examine the prediction that females would rate themselves lower than males would on the self-rating scale, Relative Math Expectancy (RME) scores were analyzed by means of a 2 (Gender) x 3 (Math GPA Level) analysis of variance. A highly significant main effect of Math Level resulted [F(2,233) = 38.32, p = .OOOl]. Mean RME ratings for High, Average, and Low groups, respectively, were 6.86 (SD = 1.21), 5.93 (SD = 1.16), and 4.99 (SD = 1.17). The predicted Gender main effect approached significance [F(1,233) = 3.38, p = .07]. Mean RME ratings were 5.78 (SD = 1.18) for females and 6.07 (SD = 1.30) for males.

Next, students were rank ordered according to their RME self-ratings and sorted into three groups by division of the sample into top, middle, and bottom thirds according to rating scores. High (ratings of 7-9), Middle (ratings of 6) and Low (ratings of 1-5) groups contained 80, 66, and 93 subjects, respectively (unequal group sizes resulted since tied scores were similarly grouped). Pearson chi-squares were computed to determine whether: (a) males and females were distributed in RME groups as would be expected by Math Level group and (b) student Gender was related to RME group. The “Expected distribution” of male and female students in each of the three RME groups was determined by the resultant frequency distribution of males and females in the three Math Level groups. The “Observed distribution” was the number of males and females who had been sorted into each of the three RME groups based upon self-rating scale scores. Results were highly significant for both male [x2 (2, n = 122) = 60.74, p < .Ol] and female [x2 (2, n = 117) = 18.80, p < .Ol] groups. The observed distribution for males deviated significantly from the expected distribution. A greater number of males than expected (by Math Level) was distributed in the High RME group; a smaller number than expected was distributed in the Middle RME group. Similarly, the observed distribution of females deviated significantly from the expected distribution. A greater number of females than expected was distributed in the low RME group; a smaller number than expected was distributed in the Middle RME group.


The greater x2 value obtained for males, considered along with the observed and expected frequency distributions of students (shown in Ta- ble I), suggests that the male distribution of actual RME ratings was more discrepant from expected ratings than was the female distribution. The x2 value which resulted for the Gender and RME association was highly significant [x2(2, 12 = 239) = 64.54, p < .Ol]. A Cramer’s statistic indi- cated a moderate strength of association between these two variables (5’ = .52).

Relative Math Expectancy (RME) and MAS Attributions

A split-plot factorial design (SPF 23 . 2) with Gender (2), RME (3), and Attribution Dimension (2) as independent variables and MAS scores as the dependent variable was used in two separate analyses for MAS Suc- cess and Failure events. Gender and RME were between-subjects factors, with Dimension a within-subjects factor.

Success events. The Success event analysis resulted in a Main Effect of RME [F(2,233) = 7.73, p < .Ol] and significant interactions of RME x

TABLE 1 MATH LEVEL AND RME GROUP FREQUENCY DISTRIBUTIONS

Math level group (Expected x2 frequencies)

High Average Low

GPA range No. of subjects Math level group

composition #M/#F %M/%F

Percent distribution of total subjects: all Subjs.

all MS/all Fs

3.2-4.3 2.0-3.1 0.0-1.9 55 114 70

19136 6315 1 40/30 34.55165.45 55.26144.74 57.14142.86

23.01 47.70 29.29 15.57130.77 51.64l43.59 32.7912564

RME Group (Observed x2 Frequencies)

Self-rating score No. of subjects Self-rating group

composition: #M/#F %M/%F

Percent distribution of total subjects: all subjs.

all MS/all Fs N = 239

7-9 6 l-5 80 66 93

48132 31135 43150 60.00/40.00 46.97153.03 46.24153.76

36.46 27.62 38.92 39.34127.35 25.41129.91 35.25142.74

122 M 51.05% 117 F 48.95%

292 KENtiE C. TAPASAK

Dimension [F(2,233) = 10.72, p < .Ol] and Gender x Dimension [F(1,233) = 6.56, p < .05]. Randomized block designs were used to test simple effects for the predicted RME x Dimension and the unpredicted Gender x Dimension interactions which resulted. Dunn’s (1961) procedure was used to control for overall simultaneous error rates of .Ol and .05. For the RME x Dimension interaction, significant effects were obtained for High [F(1,233) = 15.02, p < .Ol] and Low [F(1,233) = 7.56, p < .05] groups: students in the High RME group made significantly higher stable (z = 27.45) than variable (x = 24.95) attributions; students in the Low group made significantly higher variable (x = 24.66) than stable (x = 23.16) attributions.

A Gender x Dimension interaction not directly predicted as part of the major hypotheses, but not surprising in light of past research findings, resulted for success events. Females made significantly higher variable (x = 25.67) than stable (x = 24.81) attributions [F(1,233) = 5.70, p < .05]. Males made significantly higher stable (x = 24.97) than variable (x = 23.88) attributions [F(1,233) = 5.47, p < .05].

Failure events. A significant Main effect of RME [F(2,233) = 14.15, p < .Ol] and the RME x Dimension interaction [F(2,223) = 7.23, p < .Ol] again resulted. A significant Main Effect of Dimension, not found for Success events, resulted for Failure events. Randomized block designs used to test Simple Effects for the RME x Dimension interaction were significant only for the Low RME group [F(1,233) = 29.60, p < .Oll. Students in the low RME group made higher stable (x = 25.89) than variable (X = 23.21) attributions for Failure events. Results for the High RME group were in the predicted direction (i.e., higher variable than stable) yet failed to reach significance. Dunn’s (1961) procedure was used to control for overall simultaneous error rates of .Ol and .05. Group means and standard deviations for MAS Dimensions are presented in Table 2.

Additional Analyses

After initial analyses of the data were completed, correlation and regression analyses were used to examine further results of the x2 procedures. A significant positive correlation resulted for Math GPA and RME (r = .55 for females, r = .62 for males, p = .OOOl). Next, a multiple regression with Math GPA as criterion, and RME and Gender as predictor variables was performed (gender coded as 0 and 1 for male and female groups, respectively). RME, Gender, and the RME X Gender interaction were entered in order in the equation. The interaction was not significant and was dropped from the model. Significantly different [t(236) = 3.35, p


TABLE 2 GROUPMEANS AND STANDARDDEVIATIONSFOR MAS STABLE AND VARIABLE

DIMENSION SCORES

A. Success events RME Group Stable Variable

High Middle Low

Sex Males Females

B. Failure events RME Group

High Middle Low

Sex Males Females

MAS mean score (SD) 27.45 (4.96)** 24.05 (4.86) 23.16 (4.87)’

24.97 (4.94)* 24.81 (4.95)*

21.10 (4.94) 22.80 (3.74) 25.89 (4.85)**

22.53 (4.92) 23.99 (4.93)

MAS mean score (SO) 24.95 (4.%) 24.71 (4.86) 24.66 (4.87)

23.88 (4.94) 25.67 (4.95)

21.25 (4.94) 21.75 (3.74) 23.21 (4.85)

21.90 (4.92) 22.25 (4.93)

Note. Dunn’s (1961) procedure was used to control for overall simultaneous error rates of .Ol and .05. Significant differences between stable and variable mean scores, * = p < .05; ** = p < .Ol.

= .OOOS] and parallel regression lines were obtained for male and female groups.

SUMMARY AND DISCUSSION

The results of the present study are seen as providing support for the major hypothesis (hypothesis 3) concerning the existence of a relationship between gender and cognitive components of the math performance process. Expectancy-attribution patterns differentiated students in High and Low Relative Math Expectancy (RME) groups. The majority of students in the High group exhibited the hypothesized “positive” cognitive pattern which would contribute to the likelihood that they would be motivated to continue to persist at tasks and courses in the area of mathematics. The majority of students in the Low group exhibited the hypothesized “negative” cognitive pattern which would contribute to the likelihood that they would not be motivated to continue to persist at tasks and courses in mathematics. The hypothesized pattern strongly differentiated the Low RME group for both Success and Failure events, whereas predicted High RME group attributions significantly differed only for Suc- cess events (although Failure attributions were in the predicted direction). As predicted, (hypothesis 2) a significantly greater percentage of the High


RME group was male and a significantly greater percentage of the Low RME group was female. This suggests that more females than males might follow the “negative” pattern while more males than females might follow the “positive” pattern in mathematics. The results suggest that male and female eighth-grade students tend to interpret their own math performance differently when making future performance predictions. Furthermore, in general, and in spite of their ability level, they also explain their math successes and failures differently. Despite the fact that eighth-grade girls generally obtained higher math grade point averages than boys (a finding which supports prior research; e.g., Maccoby & Jacklin, 1974; Sherman, 1980), they did not view their math competence as highly relative to other students as one would have expected given their GPA levels. They felt that their effort, rather than their ability, was the main cause of their successes, but viewed their ability as the main cause of their math failures.

Some of the results need further clarification. The predicted attributional style for the Low RME group (majority female) was significant for both Success and Failure events and supportive of past research which has found such differences in female causal attributions (e.g., Fennema et al., 1981; Heller & Parsons, 1981). For the High RME group (majority male), although the predicted attributional style resulted, it reached significance only for Success events. One explanation for this result is that High RME group individuals recognize that either stable or variable causal factors may be involved, depending upon the conditions under which they experience failure. Or, they may define failure differently than Low RME group individuals and thus may have interpreted MAS failure items differently (e.g., perhaps as neither successes or failures, but neu- tral events). Future research might examine these possible explanations.

A unique aspect of the present study was that students were asked to predict their math performance relative to a class of their peers for the following school year. The predicted difference in hypothesis 1 of female lower than male mean relative math expectancies only approached significance. This result may be due to the fact that most students chose expectancy ratings around the scale midpoint and did not use the ex- tremes. Students at this age level could have been responding to the social desirability of being similar to their peers (i.e., near average-not too far above or below everyone else) rather than predicting their class status based upon their performance relative to that of their peers. A study which includes a measure composed of several expectancy questions, some of which relate to the social desirability of certain attitudes and behaviors in reference to age- and gender-equivalent peer groups might address this possible explanation.

The x2 distribution of males and females in Low and High RME groups


revealed gender differences in support of past math expectancy research (e.g., Fennema & Sherman, 1977; Lantz & Smith, 1981). Males tended to overestimate, while females tended to underestimate, their future math performance in relation to their present math GPA level. The significantly different and parallel regression lines for male and female groups made this clear: when linear plots of individuals with the same RME were examined, females had higher GPAs than males. How expectations and attributions are formed was not examined in the present study. The results deserve speculation, however. One possible explanation is that males and females interpret their math grades differently when making judgments about their future math performance. Another possible explanation is that present performance alone may not be a strong predictor of future performance expectations. Males and females may have been using several kinds of information when reporting expectancies and attributions. Future research might address, for example:

1. whether tangible (e.g., grades, exam scores) and social (e.g., praise, extra attention) variables specific to a subject area have differential reinforcement value for males and females;

2. whether the sources of social reinforcement (e.g., male vs. female teachers, fathers vs. mothers), and the relationship between reinforcement sources and reinforcement value vary for males and females; and

3. how the subject area-specific reinforcement value of these variables might relate to the development of expectancy-attribution patterns and, subsequently, area-specific task persistence and motivation.

Since the present study limited exploration of E-A patterns to mathematics performance, further research is needed to examine the general- izability of the model to other subject areas. Do male-female E-A patterns vary in performance areas such as reading, in which females are typically viewed as doing better? Another limitation of the present study was that it was not longitudinal. Additional research which would provide valida- tion for expectancies through examining actual future grades would be an important contribution to the literature.

In conclusion, the present study provided support for the existence of individual differences in cognitive styles in mathematics. The proposed Expectancy-Attribution model was largely supported. Furthermore, males and females, respectively, comprised significant numbers within groups which followed two distinct paths within the model. “Positive” and “negative” cognitive styles do exist and are likely to contribute to students’ progressive math behavior through school, college and career. As suggested by the E-A model, individuals who continue to have high performance expectancies and attributional styles in which they attribute their successful performance to unchangeable factors (i.e., ability), and

296 RENkE C. TAPASAK

unsuccessful performance to changeable factors (i.e., effort), would seem likely to be motivated to seek out further opportunities in math-related coursework and careers. They continue to expect to do well because they are confident in their ability to do well-possibly because their positive cognitive styles have been reinforced by the behavior of others in their environment (e.g., teachers telling them they have the ability to do well in math). The reciprocal process may lead females in the opposite direction-away from math-related fields. Their negative cognitive styles in math (which include low performance expectancies and effort, rather than ability, as the determinant of success) are also reinforced by others. It does not seem unlikely that females would choose to enter a field in which they felt that the more stable factor of ability was responsible for their success.

Further research is needed on the specific determinants of cognitive style, the long-term effects of cognitive style on math behavior, and the differential contribution of person (e.g., cognitive) and environment (e.g., performance feedback such as grades) factors to the formation of male- female expectancies and attributions.

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