Predicting Mathematics Performance: A Structural Equation Model

The relationships among personality and socialization factors that may contribute to mathematics performance were investigated using structural equation modeling . Five nested models were examined: a full model, a mediational model, a model eliminating the mediator , a regression model, and a model combining the significant paths from other models. Preliminary analyses (i.e., MANOVAS , follow-up univariate ANOVAS) revealed that men reported significantly higher math self-efficacy than women . Evaluation of the structural models identified the full model as the best representation of the data . This model examined the relationships among gender , gender schema, math anxiety, math selfefficacy, math attitude, math experience, math socialization, cognitive mediation, and math performance . Its hypothesis that direct paths from independent constructs to math performance would not be significant and that the direct paths to and from general ability would be crucial was supported. The full model accounted for 57% of the variance in math performance and 30% of the variance in general ability. These results suggest that the relationships among these variables function through the mediation of general ability. Interviews conducted with a small sub-set of the college-aged participants emphasized the role of elementary through high school teachers . This research clarifies conflicting findings concerning the predictors of math performance ; specifically refuting the often made claim that men are inherently better at math; suggesting that teachers ' and parents ' attitudes about children's math abilities may contribute to the development of strong math self-efficacy and a lessening of math anxiety, particularly pointing to the need for teachers to express equal math expectations for both boys and girls.

. 43 Table 1   Table 2   Table 3   Table 4 Table 5 Table 6 LIST The notion that men are simply superior to women in mathematical ability has been both supported and refuted . Some studies have shown that merely being male can predict better math achievement scores (Hackett, 1985~ Lent , Lopez , & Bieschke, 1991 and the likelihood of choosing science-based college majors (Betz & Hackett , 1983). Hallinan and Sorensen (1987) demonstrated that sex was a factor in the assignment of fourth through seventh grade students to mathematics ability groups : boys were more likely than girls to be assigned to the high-ability group. Others do not find such clear differences. Fennema and Sherman ( 1977) uncovered sex differences favoring men at only two of the four high schools they studied . Midkiff , Burke , and Helmstadte r' s (1989) path analytic study of adolescents uncovered no differences in math performance for boys and girls . In an extensive review of the literature , Meece, Parsons , Kaczala, Goff, and Futterman ( 1982) found that sex differences on tests of quantitative skills did not appear with any consistency before the 10th grade . Similarly, when Selkow ( 1985) accounted for the number of math courses taken beyond basic college arithmetic, she did not find sex differences in math ability either. Cooper and Robinson (I 989) were also unable to uncover any significant sex differences in math ability for a large sample of math-talented college men and women . Yet, Stanley (1980, 1983) showed that gifted seventh grade boys performed better than their female counterparts on mathematics reasoning ability tasks . Although aspects of Benbow and Stanley's studies have been criticized , this finding is important because at the seventh grade level, there would have been no substantive differences in the type and/or number of math courses taken by girls and boys.
2 However , gender differences (i.e., those based on socialization processes rather than biological sex) have been identified in several variables that relate to math performance . For example, one's attitudes toward math have been found to correlate positively with math performance , with men reporting more favorable attitudes concerning mathematics than those reported by women (Aiken, 1979;Rounds & Hendel , 1980a).
In college students , the amount of experience one has had with math has been shown to influence the selection of science-based (Betz & Hackett, 1983) and mathrelated college majors (Hackett , 1985), the adoption of math-related career goals (Singer & Stake , 1986), and one's level of mathematics achievement (Hackett , 1985). Experience with mathematics has also been found to correlate negatively with math anxiety (Betz , 1978) and positively with math self-efficacy (Hackett , 1985). Therefore , in addition to mathematics experience, math anxiety and math self-efficacy must be accounted for when predicting math performance .
3 In doing so, math self-efficacy has been shown to be positively related to both math achievement and math attitude (Hackett & Betz , 1989;Rounds & Hendel , 1980a;Randhawa , Beamer , & Lundberg , 1993), with men reporting higher levels of mathematics self-efficacy than women (Lent et al., 1991;Lent , Lopez , & Bieschke , 1993;Matsui , Matsui, & Ohnishi, 1990, Pajares & Miller, 1994Randhawa et al., 1993). Campbell and Hackett ( 1986) found that even women who performed well in math attributed their success to luck rather than ability. Betz and Hackett (1983) studied the relationship between math self-efficacy and math anxiety and found them to be inversely related.
Furthermore, it has been demonstrated that mathematics self-efficacy explains a significant portion of the variance in math performance , over and above what is accounted for by math skills (Siegel, Galassi, & Ware , 1985) and that mathematics self-efficacy alone can predict mathematics achievement (Lent et al., 1993;Randhawa et al., 1993). Mathematics self-efficacy has also been shown to predict science-based preferences in career choices (Lent et al., 1991) and college majors (Betz & Hackett , 1983), as well as lowered math anxiety (Hackett , 1985).
Considerable research has been conducted in the area of math anxiety, most of which has found that women report higher levels of math anxiety than men (Bander & Betz, 1981;Llabre & Suarez, 1985;Pajares & Miller, 1994;Richardson & Suinn, 1972;Shiomi, 1992;Tobias, 1987). Betz (1978) found that in lower level math courses , college women reported higher math anxiety than college men, but that upper level male and female students displayed no significant differences in math anxiety. Cooper and Robinson (1989) also found no gender differences in math anxiety in a math-talented college sample with similar ability; however , math anxiety did have an influence on math performance . In contrast, Llabre and Suarez ( 1985) demonstrated that when Scholastic Aptitude Test Math scores were introduced as a control for math aptitude , math anxiety did not predict performance .
Another viable explanation for the diverse findings on gender differences in math performance is that the women in upper level college math courses may not be stereotypically feminine gender-typed . Androgynous women have been reported to attain higher academic achievement than non-androgynous women (Heilbrun & Han, 1984). In fact, masculine and undifferentiatied gender schematic individuals, regardless of sex, have also been shown to achieve significantly higher math scores than feminine sex-types (Olds & Shaver, 1980;Selkow, 1985) . Generally, those who describe themselves as more masculine and less feminine have had better math performances (Signorella & Jamison, 1986). Gender schema has also been shown to relate to math anxiety . Masculine gendertyped women have displayed lower levels of math anxiety than any other gender schematic women (Bander & Betz , 1981;Heilbrun & Han, 1984); whereas feminine gender-typed men have tended to report higher levels of anxiety than other gender schematic men (Bander & Betz , 1981) . Those with masculine gender schemas also appear to have higher math self-efficacy (Betz & Hackett , 1983;Hackett, 1985;Hackett & Betz, 1989) which has accounted for a significant amount of variance in math performance over and above what is accounted for by math skills (Siegel et al., 1985).
It has also been proposed that stereotypical gender-typed attitudes toward math expressed by significant others may influence one ' s own attitude and subsequent math performance (Eccles & Jacobs, 1986). Tobias and Weissbrod (1980) argued that socialization processes discouraged girls and women from excelling in mathematics . Fennema and Sherman (1978) confirmed this when they found that boys perceived their parents and teachers as more positive toward their learning mathematics than did girls . Meece et al. (1982) concluded that the attitudes of teachers and parents may reflect the stereotype of male math superiority as well as a sense that math skills are more useful for boys than girls; thus undermining girls' confidence, motivation, and ultimate performance in mathematics.

5
Furthermore, the function of ability as a mediator between personal attributes and math performance must also be considered. Fennema and Sherman (1977) pointed out the importance of general ability in the learning of mathematics . When Cooper and Robinson ( 1991) used math ability as a control variable, it accounted for 48% of the variance in math performance. Siegel et al. (1985) also reported that math aptitude accounted for a significant amount of variance in math performance, while math anxiety, sex, and gender schema did not. Conversely, Adams and Holcomb (1986) concluded that math performance was affected by the interaction of math attitude, math anxiety, and basic math skills regardless of overall intellectual level.
The extensive research in this area lends credence to the importance of the issue while suggesting complex and diverse relationships among multiple variables . Differences between men and women regarding math achievement are sometimes identified, and sometimes not. When found, some researchers hold that they are a manifestation of innate sex differences in mathematical ability; whereas others contend that such differences in math performance are a result of the socialization process and the prevalence of stereotypical gender roles . Although gender is not consistently linked to math performance , it has been associated with several variables that are, such as men' s more positive attitudes toward mathematics . This, in turn, has been positively correlated with math self-efficacy which is positively related to math experience which negatively correlates with math anxiety, which men report far less often than women . Add to all this the impact of gender role stereotyping and the confusion over differentiating between math ability, math achievement, and math performance and the need for further investigation becomes apparent.
The task of distinguishing math ability from math achievement and/or math performance is an important and salient issue because the role of ability as a cognitive mediator is a major component of this research project. Math ability has been variously operationalized as the American College Test -Mathematics (ACT-M) score (Cooper & Robinson , 1989, 1991, a test considered analogous to the Scholastic Aptitude Test -Mathematics (SAT-M); as the Wechsler Adult Intelligence Scale (WAIS) Arithmetic subtest score (Selkow , 1985); and as standardized test scores based on the SATs (Singer & Stake , 1986) . References have also been made to "math reasoning ability" (Benbow & Stanley, 1980 and "math aptitude " (Siegel et al., 1985) with the SAT-M being used to measure both these constructs. ''Mathematics performance " has most often been operationalized as actual course or teacher designed test grades (Jacobs , 1991;Norwich , 1987;Rounds & Hendel , 1980a ;Siegel et al., 1985;Watson , 1987), although Lent et al. (1991) used the ACT-M for this purpose . To further complicate things , Benson (1988) and Randall (1990) measured "math achievement" with course grades , while Betz (1978 ) utilized the ACT-M to this end. None of the studies cited examined these nomological and operationalizing issues.
The present study assessed the combination of these variables as a structural equation model (SEM) in an attempt to predict mathematics performance in a college-age sample. Only a few studies in this area have used this technique (Benson, 1988;Marsh , 1987;Meece , Wigfield, & Eccles , 1990;Randhawa, Beamer, & Lundberg , 1993), which provides a comprehensive and appropriate method for thoroughly examining the relationships of several independent constructs with mathematics performance. I used structural equation modeling to examine these types of relationships as they function through a cognitive mediator . In addition, I analyzed the mean differences for sex and gender schema in two sets of multivariate analysis of variance (MANOVA) .
I set out to examine four structural models . Model 1 investigated the relationships among sex, gender schema, math anxiety, math efficacy, math attitude, math experience, math socialization , a cognitive mediator , and math performance. Model 2 eliminated the cognitive mediator, assessing only the direct relationships among the remaining constructs .
Model 3 examined relationships only as they function through the cognitive mediator.
Model 4 treated the cognitive mediator as an independent construct.
I considered the following hypotheses: ( 1) Model 1 will adequately represent the data , (a) direct paths from independent constructs to math performance will not be significant, (b) indirect paths to and from the cognitive mediator will be crucial; (2) Model 2, without the cognitive mediator, will not be as good a representation of the data as Model 1; (3) Model 3 will fit the data reasonably well, and more appropriately than Model 2; (4) In Model 4, mathematics performance can be directly predicted from (a) gender-schema , where those with feminine gender-schema will have poorer performance than those with non-feminine gender-schema ; (b) math anxiety, expected to be negatively related to math performance ; ( c) math self-efficacy, hypothesized to be positively related to math performance ; ( d) math attitude , expected to be positively related to math performance ; (f) math socialization, where perceived favorable math attitudes of significant others will be positively related to math performance ; (g) the cognitive mediator , also expected to be positively related to math performance; ( 5) Sex differences will occur , such that compared to women , men will (a) report less math anxiety, (b) exhibit more math self-efficacy, ( c) display more positive attitudes toward mathematics ; ( d) have better math performance ; 9 (6) Depending on one ' s gender-schema , differences will exit, such that compared to other schemas, individuals with feminine gender-schemas will  (Betz , 1978; split-half reliability estimate= .92) of the Math Anxiety Scale (X6) from Fennema and Sherman ' s (1976) Mathematics Attitude Scales (MAS) , with low scores reflecting high levels of anxiety . For the purposes of this study' s analyses , the revised MAS was reverse scored so that high scores represented high math anxiety .
Although Rounds and Hendel ( 1980b) concluded that these two instruments measured somewhat different aspects of math anxiety, Cooper and Robinson ' s ( 1991)  substantiate the scale ' s validity.
Mathematics Self-Efficacy . The 7-item Math Self-Concept (X7) Scale (internal consistency reliability estimate = . 90; Benson, 1988) and Betz and Hackett ' s ( 1983) 18item Math Self-Efficacy -Tasks (X8) Scale (internal consistency reliability estimate= .90) gauged math self-efficacy . Evidence for validity is provided by Benson ' s finding that higher scores on the Math Self-Concept Scale were associated with higher levels of both math achievement and math self-efficacy . The Math Tasks Scales ' positive correlations with math confidence and low math anxiety (r = .46 and r = .40 respectively ; Betz & Hackett) provide evidence for its validity .
Mathematics Attitude. Aiken ' s (1979)  MAS assessed math attitude . One-item on the Usefulness of Math Scale was slightly modified for use with college students . High scores indicate more favorable attitudes towards mathematics for both of these scales. Validity information for the Aiken scale is provided by Adams and Holcomb ( 1986) who found that it correlated negatively with math anxiety (r = -.50) and positively with skills in arithmetic (I= .30) and algebra (I= .59); and for Usefulness of Math, by its positive correlations (I= .14 tor =.45) with math achievement (Fennema & Sherman, 1977) . · Math Experience . The · number of math courses taken in high school (Xl 1 ); as well as those taken in college (Xl2), were assessed in a checklist questionnaire and served as the basis for establishing participants ' mathematics experience . Validity information is provided by Hackett's (1985) finding that the number of years of high school mathematics preparation predicted math achievement (i.e., ACT-M scores).
Math Socialization . Three 12-item subscales from the Fennema-Sherman (1976) MAS , each with split-half reliability of .89 (Fennema & Sherman, 1977), measured math socialization : Teachers ' Attitude (X13) , Mother ' s Attitude (Xl4), and Father ' s Attitude (Xl 5). One item on both the Mother Scale and the Father Scale was slightly modified for use with college students . Fennema and Sherman ' s (1977) report of positive correlations for each of these scales with math achievement provides validity information .
Cognitive Mediator. Three measures were used to assess cognitive mediation : Scholastic Aptitude Test -Verbal (SAT-V) score (Yl), in that verbal skills are considered to be important for math comprehension (Aiken, 1971) ; Scholastic Aptitude Test -Mathematics (SAT-M) score (Y2) , which measures mathematical thinking calling for algebraic and geometric reasoning without giving an advantage to those who have taken many math courses (Cronbach, 1990) ; and The Wonderlic Personnel Test (Y3) , a timed 12-minute SO-item multiple-choice . test of general ability which has high levels of alternate forms reliability , typically exceeding .90 (Murphy & Davidshofer, 1988) . Evidence for the Wonderlic's validity is provided by correlations in the high . 70 ' s with the original Wechsler Adult Intelligence Scale (WAIS) and the newer revised (W AIS-R) version (Kaufman, 1990) as well as significant correlations with basic arithmetic and algebra skills, r = .56 and r = .44 respectively (Adams & Holcomb , 1986) . Murphy and Davidshofer (1988, p . 202) state that "the Scholastic Aptitude Test (SAT) is one of the most technically outstanding tests of general intellectual level. .. [ and] can be validly regarded as a measure of general intelligence , since it primarily measures comprehension and reasoning ability rather than the knowledge of specific facts ." Kaufman (p . 25) lends support to the use of the SAT as a measure of ability in his claim that "like the SAT, IQ tests assess ... " intellectual skills and knowledge developed through experience ; as does Hanson ( 1993) who contends that SATs are a close kin ofIQ tests . Further , the SATs have internal consistency reliability estimates above . 90 (Murphy & Davidshofer, 1988) and predictive validity estimates for college grades of .37 individually and .41 combined (Kaplan , 1982) .
SAT scores were obtained , with participants ' permission, from student records .

Mathematics Petformance. Two halves of a 25-item Graduate Record
Examination -Quantitative (GRE-Q) practice test (Y4, odd numbered items ; YS, even numbered items) were used to assess mathematics petformance (Gruber & Gruber , 1977 ; beyond copyright) . The GRE-Q relies on deductive quantitative reasoning and requires test takers to actively process , manipulate , and evaluate information . This test has an internal consistency reliability estimate above .90 (Murphy & Davidshofer , 1988).
According to Anastasi (1982), the GRE Aptitude test's quantitative items require both mathematical reasoning and the ability to interpret graphs , diagrams, and descriptive data .

Procedure
Several two-hour testing sessions were arranged . To assure anonymity, SAT-V, SAT-M, Wonderlic, odd numbered GRE-Q items, and even numbered GRE-Q items, as well as the number of math courses taken in high school and also in college.
The results of this PCA were difficult to interpret due to several complex loadings (i.e., variables loading on more than one component ) and various single-item or two-item factors (see Gaudagnoli & Velicer, 1988.for a discussion of the need for a minimum of three variables to reliably and validly identify a latent construct).
Consequently , a second PCA with oblique rotation using the CAX software program (Velicer, 1976) was conducted in order to uncover a statistical solution to the number of components underlying the variables. The minimum average partial solution (see Velicer , 1976) produced the six-component solution shown in representing Math Experience rather than retaining a two-item component (see Gaudagnoli & V elicer, 1988) ; in addition, the inclusion of College Math Experience did not add a significant amount of explained variance to the Math Experience component.
The next step of the analysis attempted a confirmatory factor analysis (CFA) using the EQS statistical package (Bentler, 1995) . Despite the elimination of the six complex or two-item components, model convergence remained unattainable . As a result, the following changes were made to the structure of the independent variables : (a) Component 1 was divided into two separate, but correlated, independent variables; (b) Component 3 was divided into two separate independent variables; ( c) the Math Anxiety Scale (X6) was retained as a single measured variable representing math anxiety; ( d) Math Self-Concept (X7), Math Self-Efficacy -Tasks (X8), Attitudes Toward Mathematics  Table 4) .
A second one-way between-groups MANOV A was performed using gender schema as the grouping independent variable with four levels (feminine, masculine,  Table 5).

Structural Equation Models
I used structural equation modeling (SEM) with the EQS (Bentler , 1995) computer program to assess the combination of the variables under investigation in an attempt to predict mathematics performance. SEM is a statistical technique consisting of a set of procedures designed to analyze hypothesized relationships among a set of latent constructs, each measured by one or more observed variables . SEM is rarely used to evaluate a single model ; ideally, several alternative models are considered in an attempt to identify the model that best fits the data . The goodness of fit between the observed data and proposed models is evaluated by three criteria : (a) theoretical consistency, i.e., theory provides some support for the model ; (b) empirical evidence (based on several indices of fit, as explained below); and (c) parsimony, i.e., when more than one model fits the data equally well, the model with the fewest parameters -i s retained (see Harlow & Rose , 1994).
Empirical evidence refers to the statistical evaluation of the model using several criteria . A frequentl y used overall model fit index is the chi-square (x 2 ) to degrees of freedom ( df) ratio, where it is hoped that the ratio of chi-square to degrees of freedom will be less than 2; retaining the null hypothesis with a probability level greater than .05 indicates that the model adequately fits the data . However, chi-square can not be the sole criteria for model evaluation because of its dependency on sample size. Consequently, the Average Absolute StandardizedResidual (AASR) and Bentler's (1995) Comparative Fit Index (CFI) will be considered to assess the fit between the proposed models and the observed data ; values lower than . 05 for the AASR and closer to 1. 0 for the CFI suggest better model fit.
Structural models are also evaluated in terms of the explained variance in each dependent construct @ 2 , a measure of effect size; e.g., Cohen, 1992). When comparing several models that are nested within a larger Full model, the importance of the eliminated paths is evaluated by subtracting the x 2 and df values of alternative models from the baseline Full Model and testing the significance of the x 2 difference. If there is a significant difference in chi-square values (i.e., probability less than .05) , the Full model should be retained ; the reduced model is not explaining the data as well . In this analysis, several models were evaluated to assess the relationships among personality and socialization variables, gender , gender schema , cognitive mediation , and mathematics performance .
. Model 1 (Full Model), displayed in Figure 1, examined the relationships among sex, gender schema , math anxiety, math efficacy, math attitude , math experience , math socialization , the cognitive mediator , and math performance , hypothesizing that the direct paths from independent constructs to math performance would not be significant and that the direct paths to and from the cogniti ve mediato r would be crucial. This model is well grounded in theory , exhibits good empirical evidence (x2 (80) = 205 .99, Q < .001 ; CFI = . 91; AASR = . 05) , and is relatively parsimonious . Several of the hypothesized parameters (i.e., all direct paths from exogenous variables to math performance) were insignificant , while several other parameters were significant. Correlations among exogenous measured and latent variables are shown in Table 6. The proportion of explained variance in the cognitive mediator (R 2 = .30) and math performance (R 2 = .57) indicated large to very large effect sizes respectively (see Cohen, 1992) . These results suggest that the direct regression paths from the exogenous variables to math performance are not necessary and that, indeed , the relationships function through general ability.
Model 2, shown in Figure 2, eliminating general ability as a cognitive mediator , has rather weak theoretical grounding and poorer empirical fit (X 2 (87) = 293 .58, Q < .001 ; CFI = .85; AASR = .09) ; although it is inherently parsimonious . Correlations among exogenous measured and latent variables are show. n in Table 6. As expected , this model was not as good a representation of the data as Model I . The proportion of explained variance in math performance was moderate (R 2 = .25) . No direct paths from exogenous variables to math performance were significant, leading to the conclusion that general ability can not be eliminated in considering the . predictors of math performance .
Evaluating the importance of the eliminated paths in this model through a chi-square difference test (Q < . 001) revealed that this reduced model does not explain the variance and covariance in the data as well as the Full Model. Figure 3, considering relationships only as they function through general .ability, has impressive theoretical support and relatively good parsimony displaying good empirical evidence (x2 (86) = 230 .66, Q < .001; CFI = .90; AASR == .06) . Direct paths froin exogenous variables (with the exception of sex) to general ability were significant, as was the direct path from general ability to math performance . Correlations among exogenous measured and latent variables are shown in  Figure 4, also has a strong theoretical basis, good empirical fit (x 2 (80) = 205 .94, n < .001; CFI = .91; AASR = .05), and better parsimony than the Full Model 1. However, the only direct path to math performance that proved significant was from general ability, which explained a large proportion of the variance (R 2 = .57) in math performance . The other hypothesized relationships between exogenous variables and math performance were not confirmed. These findings strongly suggest that general ability must be considered in any prediction model of math performance and provide evidence that general ability appears to serve as a mediator between relevant exogenous variables and math performance ( as in the Mediational

Model) . An empirical distinction (chi-square difference test) between the Regression
Model and the Full Model was not possible because the degrees of freedom were the same for both .
An additional SEM combining significant paths from other models, represented by Figure 5, was attempted in·order to identify the "best model" for predicting math performance . This model had adequate empirical fit (X 2 (96) = 244 .63, n < .001; CFI = .90; AASR = .06) and good parsimony, revealing significant paths from gender schema, math anxiety, and high school math experience to general ability as well as a significant relationship between general ability and math performance . Further, the variance explained for general ability was moderate and that explained for math performance was rather large (R 2 = .24 and R 2 = .42 respectively) . A chi-square difference test (n < .005) found that the Full Model was doing a better job explaining the data than this reduced model. Also, the R 2 value for math performance again dropped from .57 in the Full model to .42, indicating that 15% of the variance in math performance can be attributed to the set of exogenous variables even though none of them individually were directly related to the outcome , except through the cognitive mediator.

Content Analysis
A thorough review of the eight follow-up interview transcripts revealed · one dominant theme: higher teacher expectations for boys in regard to mathematics performance . Most of the college-aged men (50%) and women (75%) interviewed clearly reported higher teacher expectations for male students . Half of the respondents ( three women and one man) emphasized that this inequality was most prevalent during junior high and high school. Interestingly, both high ability men indicated that even in grade school math classes, boys were called on more, got more help, were pushed harder, were expected to perform better, and were generally .giv_ en more opportunities in mathematics and sciences than were girls.
Both the high ablity/low performance respondents expressed somewhat negative attitudes toward math, citing their math teachers as having influenced their opinions. The attitudes of the two low ability/low performance students were clearly more negative .
Both expressed the view that high school math had been difficult for them . The high ability/high performance interviewees held strong positive attitudes toward math and attributed their feelings to the logical nature of mathematics and its sense of immediate accomplishment. The low ability/high performance interview participants also expressed positive attitudes toward math, claiming that they had never had problems in math and that it seemed easier than other subjects .
None of the respondents suggested that their parents had manifested or imposed stereotypically gender-typed attitudes concerning math ability. Regardless of their individual abilities and performances as assessed in this study, all the interviewees felt that their parents had been pleased with, and supportive of, their early efforts in mathematics .
Only one person, the low ability/low performance male college student, expressed the opinion that women and men have different math abilities. Specifically, he stated that women were better in math and that his math tutors had all been women . The other interview participants unequivocally asserted that men and women have equal math abilities.
None of the interviewees ascribed to the suggestion that women who excel in math are less feminine. Similarly, they all disavowed the notion that men who do not perform well in math are perceived as less masculine . It may be that college age individuals have more androgynous views of math performance than do younger adolescents . This hypothesis could be examined in future studies using both qualitative and quantitative methods within several age ranges .

Discussion
The present study was designed to assess the relationship among sex, gender schema, math anxiety, math efficacy, math attitude , math experience, math socialization , general ability, and math performance. Specifically, the hypothesis that general ability acts as a mediator between personality and socialization attributes on one hand and mathematics performance on the other was tested . The results from five reasonable alternative models provided support for this hypothesis .
Without exception , none of the personality and socialization characteristics were directly associated with math performance . Contrary to previous findings (Cooper & Robinson , 1989;Eccles & Jacobs , 1986;Hackett, 1985;Lent et al, 1991;Siegel et al, 1985;Signorella & Jamison, 1986), none of these variables showed a direct relationship with mathematics performance in any of the models examined in this study . In fact , the Full Model (Model 1 ), which best explained the data , provided evidence that although gender schema, math anxiety, and math experience were not directly related to mathematics performance ( as evidenced by non-significant pathways to mathematics performance) , they were significantly related to general ability and thereby indirectly 25 · linked to math performance through the mediation of general ability. The Mediational Model , which adequately explained the data, though not as well as the Full Model , found only math anxiety and high school math experience to be indirectly related to math performance through the general ability mediator .
Interestingly , although sex was not significantly related to any other variables and/or factors, women were significantly more likely to view math as a male domain than were men. Furthermore , as regards gender schema, individuals who reported feelings that math was predominantly a male domain demonstrated significantly higher general ability and lower (although not significantly) math performance compared with those who did not exhibit this attitude . In their extensive review of the literature , Signorella and Jamison ( 1986) found that individuals who described themselves as more masculine and less feminine had better math performances . Similarly, Selkow ' s masculine gender-oriented participants performed better than her feminine gender-oriented participants on a test of mathematics ability regardless of sex (1985) . The present study did not support these findings, but rather pointed to the importance of the mediating role of general ability.

26
Although Model 1 did not support a significant link between gender schema and math anxiety, it did reveal a weak relationship in the predicted direction ; those who were more likely to view math as a male domain reported higher math anxiety. However, other research has identified a significant relationship between gender schema and math anxiety using B SRI scores as indicators of gender schema. Heilbrun and Han ( 1984) showed that masculine gender-typed women display less math anxiety than other gender-typed women; similarly, Bander and Betz (1981) found that feminine gender schematic men reported higher math anxiety than other gender schematic men. The fact that the present study was unable to use BSRI scores in the structural models may account for the failure to identify a significant relationship between gender schema and math anxiety . Future research should focus on operationalizing gender-schema as BSRI scores, specifically the BSRI masculine score.
In addition, both gender schema and math anxiety were significantly related to the math socialization factor . Participants who were more likely to endorse math as a male domain and those who reported less math anxiety had experienced more positive mathematics socialization. A close examination of the raw data revealed that women recalled more positive attitudes about their math abilities being expressed by parents than did men; while men recollected more positive teachers ' attitudes than did women . The Eccles and Jacobs ( 1986) explanation that parents ' and teachers' attitudes may influence children's math attitudes , impacting on math anxiety and ultimately on math performance, seems a likely interpretation here as well. It should be noted that the path from math socialization to general ability approached significance, indicating that in this sample of college students positive math socialization may be indirectly linked to math performance through the mediation of general ability. The use of a larger, more homogeneous sample in future structural models may clarify this issue as well as some of the other disparities between this study's findings and the previous research noted here .
An inverse relationship between math anxiety and math performance was clearly identified by Adams and Holcomb (1986) in a canonical analysis. The present findings revealed that participants who reported less math anxiety scored higher on the general ability factor, emphasizing this factor ' s mediating role in the relationship between math anxiety and math performance . Betz (1978) uncovered a negative relationship between math anxiety and years of high school math in a large sample of college students. A similar finding was revealed in Model 1; participants with more high school math experience reported significantly less math anxiety and scored significantly higher on the general ability factor than those with less math experience. This finding again calls attention to the significant mediational path between general ability and math performance .
The positive path from the math efficacy and attitude factor to general ability was quite high ( approaching significance) and was also significantly related to both math socialization and math anxiety. The college students in this sample whose parents and teachers had expressed positive attitudes toward their math abilities scored higher on the math efficacy/attitude factor and also reported less math anxiety. This finding supports the results of previous research that showed math self-efficacy to be positively related to math achievement (Rounds & Hendel, 1980a) and negatively associated with math anxiety (Hackett, 1985). As Siegel et al. (1985) concluded, math self-efficacy may explain a significant portion of the variance in math performance . In the Full Model , it may be the near significant path between the math efficacy/attitude factor and math performance that is contributing to the additional 15% explained variance in math performance that this model provided over and above that found in the Mediational Model which did not allow for this direct path . The fact that the path from the math efficacy/attitude factor to math performance did not reach significance may have been due to the need to treat math efficacy and math attitude as a single combined factor in order to fit this study's structural equation models . Future research should strive to measure these two variables in ways that allow them to maintain their distinct identities. By doing so, math self-efficacy may emerge more clearly as an explanation for a significant portion of the variance in math performance .
Math self efficacy and teacher expectations may also be related to classroom assertiveness . If math teachers do have higher expectations for boys, they may acknowledge them more readily, as the interview participants indicated . Consequently , boys may develop strong math self efficacy along with the assertiveness to take an active part in classroom exercises , volunteering answers and asking questions more often than girls. The concept of classroom assertiveness as it relates to math self efficacy, teachers ' expectations , and ultimately performance, clearly warrants further investigation .
Overall, the results of the present study clarify conflicting findings concerning the predictors of mathematics performance . Much of the previous research has debated the role of sex in predicting math ability, some of it claiming that merely being male was an adequate predictor of enhanced math ability. The present study found no support for a direct link between sex and math performance , but does point to the relationship between gender schema and the attitudes toward mathematics expressed by significant others , and the concurrent links between this socialization factor and math anxiety, math attitude, and math self-efficacy. Although causation can not be inferred by a correlational study of this nature, these results suggest that teachers' and parents ' positive attitudes about children's math abilities may contribute to the development of strong math self-efficacy and a lessening of math anxiety. Future research might undertake the examination of multiple samples, investigating separate models for men and women in an attempt to further explain the roles of sex and gender in mathematics performance .
1. Work with a slide rule 2. Determine how much interest you will end up paying on a $675 loan over 2 years at 14.75% interest . 3. Figure out how much lumber you need to buy in order to build a set of bookshelves . 4. Compute your income taxes for the year. 5. Figure out how much material to buy in order to make curtains . 6. Understand a graph accompanying an article on business profits . 7. Understand how much interest you will earn on you savings account in 6 months, and how that interest is compounded.
9. Estimate your grocery bill in your head as you pick items. 10. Determine the amount of sales tax on a clothing purchase . 11. Figure out the tip on your part of a dinner bill split 8 ways. 12. Figure out how long it will take to travel for City a to City B driving at 5 5 mph. 13. Compute your car's gas mileage. 14. Set up a monthly budget for yourself __ 15 . Balance your checkbook without a mistake. __ 16 . Figure out which of two summer jobs is the better offer: one with a higher salary but no benefits, the other with a lower salary plus room, board , and travel expenses. 17. Figure out how

7.
My mother thinks I'm the kind of person who could do well in mathematics . My mother thinks I could be good in math . My mother has always been interested in my progress in mathematics . My mother has strongly encouraged me to do well in mathematics . My mother thinks that mathematics is one of the more important subjects I have studied . My mother thinks I'll need mathematics for what I want to do after I graduate .
My mother thinks advanced math is a waste of time for me. * 41 8.

10.
As long as I have passed , my mother hasn 't cared how I have done in math . * My mother wouldn't encourage me .to plan a career which involves math . * My mother has shown no interest in whether or not I take more 11. 12. math courses . * My mother thinks I need to know just a minimum amount of math . * My mother hates to do math . * Final score= sum of items 1 through 12 after reverse scoring o asterisked(*) items .      .05 -.32*** .34*** --.07 .05 -.32*** .34***      Table 6 for correlations among exogenous measured and latent variables.  Table 6 for correlations among exogenous measured and latent variables.  Table 6 for correlations among exogenous measured and latent variables.