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Advanced mathematics course-taking: A focus on gender equifinality
Learning and Individual Differences 22 (2012) 484–489
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Advanced mathematics course-taking: A focus on gender equifinality Sukkyung You a,⁎, Jill D. Sharkey b a b
College of Education, Hankuk University of Foreign Studies, 270 Imun-dong, Dongdaemun-Gu, Seoul 130-791, Republic of Korea Department of Counseling, Clinical, and School Psychology, Gevirtz Graduate School of Education, University of California, Santa Barbara, CA 93106-9490, United States
a r t i c l e
i n f o
Article history: Received 23 June 2011 Received in revised form 7 February 2012 Accepted 3 March 2012 Keywords: Mathematics Gender differences Social cognitive theory Peer factors Family factors
a b s t r a c t High school mathematics achievement predicts future success. Potentially different factors that lead to success for boys versus girls, termed equifinality, are not well understood. Such factors are needed to inform interventions to increase numbers of students taking advanced mathematics courses and going on into science and mathematics careers. With 16,373 diverse tenth grade participants of the 2002 Education Longitudinal Study, we used multi-group logistic regression modeling to investigate advanced mathematics course selection from a social cognitive perspective, testing relations separately by gender. Girls took advanced mathematics courses at significantly higher rates than males. Family background and cognitive factors were related to advanced mathematics coursetaking for both groups. Supporting the equifinality hypothesis, father's expectation, parent communication, and peer academic value were significant for girls yet mother's expectation and parent participation were significant for boys. Implications and future directions are discussed. © 2012 Elsevier Inc. All rights reserved.
1. Introduction
2. Gender equifinality in mathematics coursetaking
Taking advanced mathematics courses in high school is a powerful predictor of college success; research from the U.S. Department of Education (1999) shows that high school students who completed mathematics courses at levels higher than Algebra 2 (e.g., trigonometry or pre-calculus) earn a college degree at twice the rate of those whose high school mathematics curriculum was less rigorous. Other researchers, using nationally-representative data, reported that high school students who take more mathematics courses are at a clear advantage in achieving high school graduation, academic success, and college opportunity (Rock, Ekstorm, Goertz, & Pollack, 1995; Wilkins & Ma, 2002). In 2007, 69% of eighth grade boys and 76% of eighth grade girls reported they intend to pursue postsecondary education (National Center for Education Statistics [NCES], 2008); yet, a much smaller percentage achieves this goal (30%; NCES, 2011a). We examined correlates to advanced coursetaking in order to inform policy and practice designed to encourage mathematics coursetaking for greater numbers of students, recognizing that gender may be a key variable that represents different pathways to success (i.e., equifinality).
Empirical research suggests that factors leading to mathematics success may be different based on gender (Crosnoe, Riegle-Crumb, Field, Frank, & Muller, 2008). The term “equifinality” from General Systems Theory, defined as the same outcome despite different pathways or groups of factors leading to success, has previously been applied to the study of gender and mathematics coursetaking (Crosnoe et al., 2008). Specifically, Crosnoe et al. (2008) argued that different interventions may be needed to promote mathematics coursetaking outcomes for boys and girls, and studied the impact of peer group context on mathematics coursetaking. They found that pathways to mathematics success were similar for boys and girls in that friends' achievement was related to personal mathematics coursetaking and classmates' achievement added additional benefit. However, small deviations in the common trajectory, such as a less consistent influence of friends over time for boys, provided some support for the equifinality hypothesis. Further research is needed to extend this work with a broader framework to explain mathematics coursetaking. Social cognitive theory (Bussey & Bandura, 1999) recognizes the influences of biological, cognitive, and sociological influences on human development. Bandura (1986) describes gender role differences as a psychosocial phenomenon that occurs for boys and girls through their observations of and differential treatment by others — especially the different reactions for the same behaviors as dealt out by parents, peers, and teachers. These observations and reactions are eventually internalized as gender role values that shape goals and expectations in all aspects of life. The expectancy-value model
⁎ Corresponding author. Tel.: + 82 2 2173 3213. E-mail addresses: [email protected] (S. You), [email protected] (J.D. Sharkey). 1041-6080/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.lindif.2012.03.005
S. You, J.D. Sharkey / Learning and Individual Differences 22 (2012) 484–489
indicates that perceived efficacy and understanding of the value related to an academic subject predict the decision to take advanced courses in that academic subject (Eccles, 1994). In social cognitive theory, such internal cognitions interact with biological and environmental influences to produce human behavior (Bussey & Bandura, 1999). Investigating social cognitive factors in the study of mathematics coursetaking will provide insight into key socialization agents of contemporary adolescence that shapes the motivations, attitudes, and values that are so important to understanding gender differences in factors that promote mathematics coursetaking. 3. Purpose and research questions The current study tests equifinality, or potential diverse pathways to similar mathematics coursetaking behaviors, by gender, through social cognitive factors. This study is unique because it examines a contemporary sample needed to examine gender equifinality in mathematics coursetaking and includes a breadth of social and cognitive variables while controlling for important potential confounds. The following research question addressed our purpose: What is the impact of social and cognitive variables on math course-taking for girls and boys? 4. Method 4.1. Data and samples We analyzed data from the Education Longitudinal Study of 2002 (ELS:2002), a national longitudinal study of high school tenth graders enrolled in a national sample of U.S. high schools in 2002 (NCES, 2011b). Data were from the longitudinal sample of 16,373 10th grade students who attended 751 public and private high schools in 2002, who were resurveyed in 2004, and whose transcripts were collected. Therefore, the approximate sample weight (F1PNLWT) was applied so the results generalize to the 2002 tenth-grade sample. 4.2. Measures With these public-use ELS data we were able to construct a comprehensive set of variables to test the research questions. Item descriptions, factor loadings and the internal consistency reliability coefficients of items created based on factor scores are reported in Appendix A. All predictor variables were measured in Wave 1 and the outcome variable was measured two years later in Wave 2. All individual factor composites, including those constructed by NCES, were normalized to a mean of zero and a standard deviation of one. 4.2.1. Family background controls Student and family background characteristics include ethnicity, familial SES, and non-traditional family status. SES is a composite measure developed by NCES based on father's education level, mother's education level, father's occupation, mother's occupation, and family income. Non-traditional family background was coded if the student did not live with both parents. 4.2.2. Academic controls Academic controls were college aspiration and tenth grade mathematics performance. College aspiration, a measure of external motivation to take advanced mathematics courses, was measured by student response on, “Which of the following do you plan to attend?” and coded a “yes” if the participant replied “Four-year college or university” and “no” if the participant replied “Two-year community college,” “Vocational, technical, or trade school,” or if the response was skipped because the participant previously responded negative to continuing education in the future. Tenth grade mathematics performance was measured by the students' standardized test score.
485
4.2.3. Cognitive variables Cognitive variables were measured with constructs of mathematics affection and self-concept. The measure of mathematics affection included three items from the student report (e.g., “Mathematics is important to me personally”) with Likert responses of 1 = strongly agree, 2 = agree, 3 = disagree, and 4 = strongly disagree. The measure of mathematics self-concept included five items from the student report (e.g., “I'm confident that I can do an excellent job on my math tests”) with Likert responses of 1 = almost never, 2 = sometimes, 3 = often, and 4 = almost always.
4.2.4. Parent involvement Four dimensions of parent involvement were created: communication, participation, supervision, and expectation. The measure of parent communication included eight items from the student report (e.g., “How often have you discussed the following with either or both of your parents or guardians…your grades?”) with Likert responses of 1 = never, 2 = sometimes, and 3 = often. Parent participation was measured with seven items from the parent report (e.g., “How often in this school year, do you or your spouse/partner do any of the following…act as a volunteer at the school?”) with a yes or no option. Parent supervision was measured with four items from the parent report (e.g., “How often do you do the following… Check on whether your children have done their homework?”) with Likert responses of 1 = never, 2 = rarely, 3 = sometimes, and 4 = often. Parent expectation variables were developed from single items that asked students, “How far in school do you think your mother and father want you to go?” Separate responses for each parent range from “Less than high school graduation” to “Obtain a Ph.D., M.D., or other advanced degree.”
4.2.5. Peer influences Peer value for education was selected as the peer variable and was measured with three items from the student report (e.g., “Among your close friends, how important is it to them that they…attend classes regularly?”) with Likert responses of 1 = not important, 2 = somewhat important, and 3 = very important. 4.2.6. Coursetaking outcome The primary outcome variable in this study was a measure of whether or not the student had completed any advanced mathematics courses (i.e., Trigonometry, Algebra III, Pre-calculus, or Calculus). Mathematics coursetaking was measured using an ordinal composite variable (F1RMAPIP). This measure indicates the highest level of mathematics for which the student received non-zero credit while in high school. For this study, the outcome variable was a dummy-coded variable indicating whether the student had completed any advanced mathematics courses. 4.3. Overview of the statistical analysis A series of recursive models were developed and tested using Mplus (Muthen & Muthen, 2006). The first model contained only the student background variables, the second model introduced academic control and cognitive variables, and the third model included socializing factors. The models estimated the size and statistical significance of a number of predictors simultaneously; we determined the unique contribution of each variable in the model controlling for the effects of the other variables in the model. The standard errors for the estimated means, percentages reported, and tables of the analysis can be provided upon request. Multi-group testing was conducted to investigate the significance of differences in coefficients across the girl and boy models using Wald test of parameter constraints available in Mplus.
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The models predicted the change in the odds of completing advanced mathematics courses versus not completing any advanced mathematics courses. A value of one signifies no change in the odds or likelihood of taking each level of advanced mathematics courses, while a value greater than one indicates an increased likelihood, and a value less than one indicates a decreased likelihood. The estimated effects for continuous variables were first multiplied by their standard deviation before converting to odds ratios so that the values in the tables represent the estimated effects of a one standard deviation change in the predictor variable on the odds of taking each level of advanced mathematics courses. The effect was considered small when OR = 1.50 (positive) or .67 (negative), medium when OR = 2.00 (positive) or .50 (negative), and large when OR = 4.00 (positive) or .25 (negative; Sanchez-Meca, MarinMartinze, & Chacon-Moscoso, 2003). 5. Results 5.1. Descriptive characteristics of advanced mathematics coursetaking Descriptive results summarized in Table 1 demonstrated that among high school sophomores, 15.7% took Trigonometry, 15.8% took Pre-calculus, and 11.8% took Calculus as their highest mathematics course in high school. Students who were Asian, whose native language is English, who were from the highest SES group, or who lived with both parents were the most likely to take advanced mathematics courses.
Table 2 Descriptive statistics for the variables (weighted) used in the analysis. Source: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 (ELS:2002/04), Waves 1 and 2. Girls (N = 7781) Mean or proportion Family background Asian American .04 African American .13 Latino/a American .16 European American .62 SESα −.01 Non-traditional family .42 Mathematics course taking α Advanced I (Trigonometry) .17 Advanced II (Pre-calculus)α .17 Advanced III (Calculus) .12 Academic control variables 10th Mathematics test scoreα 49.86 College aspirationα .85 Cognitive factors α Mathematics self-concept −.16 Mathematics affectionα −.09 Socializers Mother's expectationα 5.29 Father's expectationα 5.25 α Parental communication .11 Parental participation −.05 Parental supervision −.02 Peer academic valueα .12 Note.
α
Boys (N = 7737) SD
Mean or proportion
SD
.73 .49
.04 .14 .17 .62 .02 .42
.71 .49
.38 .38 .32
.14 .15 .12
.35 .35 .32
9.50 50.81 .36 .79
10.29 .41
1.00 1.00
.14 .04
.98 1.00
1.42 1.49 .97 .96 1.00 .95
5.05 5.01 −.16 −.09 .02 −.20
1.48 1.53 1.00 .96 .99 1.03
Gender difference is significant at p b .05.
5.2. Descriptive comparisons of girls and boys Girls were significantly more likely to take any advanced mathematics courses (46.4%) than boys (40.6%). Table 2 highlights significant differences between girls and boys for the variables selected in this study. Higher percentages of girls (17.2%; 17.4%) than boys (14.2%; 14.6%) took trigonometry and pre-calculus, respectively, but the rate of taking the most advanced mathematics course, calculus, was the same for girls and boys (11.8%). Boys had significantly higher mean scores on standardized mathematics
Table 1 Percentage distribution of 2002 high school sophomores demonstrating advanced mathematics coursetaking patterns by selected student characteristics (weighted sample). Source: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 (ELS:2002/04), Waves 1 and 2. Characteristics
Total Gender Female Male Race-ethnicity Asian American African American Latino/a American European American (Ref) Socioeconomic status Lowest quartile Second quartile Third quartile Highest quartile (Ref) Family composition Two biological parents Other
Advanced mathematics coursetaking patterns⁎ None
Trigonometry
Pre-calculus
Calculus
56.9
15.7
15.8
11.8
53.6 59.4 37.4 65.4 73.1 51.1 74.9 67.3 52.5 33.0 49.6 66.4
a b
a a a b
a a a b
a b
17.2 14.2
b
17.4 14.6
11.6 a 20.4 a 9.9 a 16.6 b
20.5 10.6 11.5 18.1
b
30.4 3.6 5.5 14.1
12.2 14.8 17.4 18.1
8.2 a 11.6 a 19.1 a 24.4 b
4.7 6.2 11.1 24.4
18.6 12.3
15.4 6.6
16.4 14.7
a
a a a b
a b
a b
a a a
a b
11.8 11.8 a a a b
a a a b
a b
Note. Means with different subscripts (in the same mathematics course and the same characteristic) differ significantly (p b .05). ⁎ Indicates the highest course taken by students.
test scores as well as on mathematics-related self-concept and affection yet girls had a higher mean score on college aspiration. Girls reported stronger communication with their parents and higher educational expectations from both parents than boys reported. Girls perceived higher peer academic value than boys reported.
5.3. The impact of social and cognitive variables on math course-taking After controlling for academic background variables (i.e., 10th grade mathematics test scores and college aspirations), all cognitive variables were significant predictors (see Model 2, Table 3). Mathematics self-concept and mathematics affection had small but significant effects for both boys and girls, with odds ratios remarkably similar across the two groups. Odds Ratios ranged from 1.18 to 1.23, which are small effects. Model 3 (Table 3) examined the impact of socializers on mathematics coursetaking without considering cognitive factors. Results demonstrated differential relations of parent and peer influences across gender groups. Peer values for grades and education were significantly related to taking the advanced mathematics coursetaking for girls only (OR = 1.20; small effect) whereas parental participation and mother's expectation were significant for boys only (OR = 1.16 and 1.05, respectively; small effect). Supervision was not associated with adolescents' advanced mathematics coursetaking for either group. Model 4 (Table 3) examined the impact of all control variables, cognitive factors, and socializers simultaneously. Significant associations between mathematics self-concept and mathematics coursetaking held steady, whereas associations between mathematics affection and mathematics coursetaking shifted to nonsignificance, for both boys and girls. The association of socializers to mathematics coursetaking largely remained the same in this final model although father's expectation became related to the outcome for girls (OR = 1.12; small effect) and parental participation shifted to non-significance.
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Table 3 Relative odds of advanced mathematics coursetaking with student-level predictors: academic year 2003–04. Source: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 (ELS:2002/04), Waves 1 and 2. Girls (N = 7781)
Family background Asian American African American Latino/a American SES Non-traditional family Academic control variables 10th Mathematics test score College aspiration Cognitive factors Mathematics self-concept Mathematics affection Socializers Mother's expectation Father's expectation Parental communication Parental participation Parental supervision Peer academic value Note.
α
Boys (N = 7737)
Model 1
Model 2
Model3
Model 4
Model 1
Model 2
Model 3
Model 4
1.92* 1.99* 1.05 1.30* 0.75*
1.86* 1.42* 1.00 1.31* 0.75*
2.08* 1.61* 1.07 1.20* 0.77*
1.88* 1.43α 1.00 1.20* 0.74*
1.76* 1.95* 0.89 1.42* 0.75*
1.95* 1.79* 0.80 1.53* 0.70*
1.81* 2.39* 1.01 1.49* 0.79α
1.79* 2.19* 0.98 1.54* 0.76*
3.95* 2.54*
3.59* 1.40*
4.03* 2.14*
3.74* 1.31*
3.65* 2.92*
3.22* 1.48*
3.72* 2.46*
3.25* 1.40*
α
1.22* 1.18*
1.21* 1.07 0.99α 1.02 1.20* 1.09α 1.00 1.19* α
0.97α 1.12* α 1.19* α 1.07α 1.00 1.16* α
1.23* 1.19*
α
1.25* 1.10 1.05* α 1.01 1.17* 1.16* α 0.99 1.11α
1.09* α 1.01α 1.13α 1.18* α 0.99 1.05α
Gender difference is significant at p b .05, * p b .05.
5.4. Effects of control variables As expected, the control variables were significantly related to mathematics coursetaking (see Table 3). The odds of taking the advanced mathematics were more than two times higher for Asian Americans than for European Americans; the odds of taking advanced mathematics were much lower for Latino/a Americans. Students from a high SES family were much more likely to take advanced mathematics than students from low SES families, with a stronger association for boys. Students not living with both parents were less likely to take advanced mathematics than students living with both parents (see Model 1, Table 3). As predicted, adding the cognitive and social variables generally reduced the relation between family background and outcome (see Models 2 and 3, Table 3). A surprising result was that for boys, the relation between African American status and mathematics-course taking shifted from equal to the reference group, to 1.79 times (see Model 2, Table 3) and then 2.39 times (see Model 3, Table 3) the reference group as additional variables were included. Regarding academic control variables, mathematics test scores yielded the strongest relation with mathematics coursetaking of any variable for both groups. College aspiration had small but significant associations with mathematics coursetaking with remarkably similar odds ratios for boys and girls (see Models 1–3, Table 3). 6. Discussion This study employed multi-group logistic regression with ELS:2002 data to test the premise that pathways to a similar outcome (mathematics coursetaking, i.e., equifinality) might be distinct given the likelihood of different socialization processes based on gender. We found that females not just equaled boys in their advanced mathematics coursetaking behaviors, but surpassed them in all but the highest level of mathematics. Bandura's theory of the role of self-efficacy in future behavior predicts that persons who have high self-efficacy for a certain task will be more likely to engage in that task and persist until they have achieved success (Bandura, 1986). Our results support this hypothesis, indicating that mathematics self-concept is related to mathematics course selection. Taking into account academic control variables, there
appear to be key differences in advanced mathematics persistence for students with high achievement in past mathematics courses, a strong math self-concept, and stronger academic orientations compared to students without these advantages. These findings point to the potential of early, engaging, and rewarding curriculum designed to foster strong mathematics coursetaking and self-concept. Results indicated there were differences in parents' involvement with their daughters and sons, consistent with extant literature. For daughters, there was a positive relation between communication and mathematics coursetaking. For sons, there was a positive relation between parent engagement in school activities outside the home and mathematics coursetaking. Both boys and girls experienced no relation between parental supervision and mathematics coursetaking. Mother's expectation had a significant association with boys' mathematics coursetaking, whereas father's expectation had a significant association with girls' mathematics coursetaking but only when cognitive factors were accounted for. This finding that the opposite sex expectations are related to advanced coursetaking, though a small effect, is unexpected and may warrant further exploration. Changes in odds of mathematics coursetaking when adding and subtracting cognitive factors and socializers provide additional insights into the associations between variables. Affection was significantly related to mathematics coursetaking only before socializers were added. For girls, the socializer impacted by cognitive factors was father's expectation, which became significant when all factors were included. Thus, father's expectation may explain the association between their daughters' feelings about mathematics and mathematics coursetaking. For boys, the socializer impacted by cognitive factors was parental communication. Both mathematics affection and parental communication were not significantly related to mathematics coursetaking in the final model. Perhaps the significant mathematics self-concept explained the association between parental communication and mathematics coursetaking. Peer context was also found to have differential associations across gender related to high school students' advanced mathematics coursetaking. Peer academic values were significantly associated with girls' but not boys' advanced mathematics coursetaking. This finding is consistent with past studies of peer relations that suggest girls have closer and more intimate friendships whose social support is important to academic success, whereas boys' self-confidence in
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mathematics in particular is not reliant on friendships or peers (Crosnoe et al., 2008). As a whole, it appears that the primary social influence for mathematics coursetaking is the expectation of significant others. This result is consistent with resilience literature that conveying high expectations to students relates to strong academic achievement and appropriate behavior (Brooks, 2006). Parent and peer high expectations may promote academic achievement as well as the activities required to take advanced mathematics courses such as studying together. We note that family background and academic control variables were significantly associated with mathematics coursetaking. Once cognitive variables and socializers were considered, the relation between African American status and mathematics course selection became positive and significant with an odds ratio of 2.19. This surprising result suggests that when cognitive variables and socializers are taking into consideration, there is something about African American male status that is associated with a higher likelihood of advanced mathematics course selection than any other ethnic/ gender group. In addition, although cognitive factors and socializers lowered the odds of advanced mathematics course selection for the Asian American group, they remained almost twice more likely to take the advanced mathematics courses. This suggests that an important component of Asian culture also was not accounted for in the current study. Future research should further explore these complex interactions. There are several limitations to this study. Data examined in this study were collected primarily from student self-report and the available measures regarding peer influences were more limited than the measures of parent influences. It would have been optimal to include corroborative information from students' perceptions, parental perceptions, and other sources of information such as diary data or observation. Another limitation in this study is that available social variables measured academics generally and did not allow us to measure socializers specifically for mathematics. Finally, gender differences in relations between parent influences and mathematics coursetaking emerge during middle school; nationally representative longitudinal data is needed to measure students from middle school on (Catsambis, 1994). 7. Conclusions Overall, the results supported the gender equifinality hypothesis. Although pathways to advanced math coursetaking are fundamentally similar and include impacts of family background, academic controls, and math expectations from close social influences, girls and boys differ on who provides the social influence and in what way it is conveyed. Girls are influenced by father and friend expectations and appear to benefit from communication with their parents. Boys are influenced by mother expectations and appear to benefit from active participation by their parents in their school life. This study highlighted some interesting new areas for future research. In particular, the cross-sex influence of parent expectations on mathematics course selection needs further exploration. Qualitative studies may be needed to uncover these interactions in detail. If supported, the model of gender equifinality might help guide efforts to support advanced math coursetaking for more students. Students need early and consistent exposure to mathematics, experiencing success and developing a strong math self-concept. Parents should be made aware of their potential influence on their children's mathematics course selection in terms of their expectations and behaviors. For girls, interventions might focus on group learning experiences that allow them to develop their math self-concept with other girls who also value advanced mathematics coursetaking. As advanced mathematics coursetaking is critical to future success in college and career, gender-specific interventions to develop academic
controls, college aspiration, parent and peer high expectations, and parent involvement may be important. Acknowledgments This work was supported by Hankuk University of Foreign Studies Research Fund granted to Sukkyung You. Appendix A. Descriptions, factor loadings, and reliability of factor composite measures
Variable
Item descriptions
Parental involvement Parental communication (Cronbach's alpha = .86) BYS86C How often discuss things studied in class with parents BYS86A How often discussed school courses with parents BYS86G How often discussed going to college with parents BYS86B How often discussed school activities with parents BYS86D How often discussed grades with parents BYS86I How often discussed troubling things with parents BYS86H How often discussed current events with parents BYS86F How often discussed prep for ACT/SAT with parents Parental participation (Cronbach's alpha = .72) BYP54C Take part in parent-teach organization activities BYP54D Act as a volunteer at the school BYP53H Parent contacted school about fundraising/volunteer work BYP54A Belong to parent–teacher organization BYP54E Belong to other organization with parents from school BYP57A Attended school activities with 10th grader BYP54B Attend parent–teacher organization meetings Parental supervision (Cronbach's alpha = .73) BYP69A Family rules for 10th grader about maintaining grade average BYP69B Family rules for 10th grader about doing homework BYP69C Family rules for 10th grader about doing household chores BYP69D Family rules for 10th grader about watching TV Peer influence Peer value for education (Cronbach's alpha = .82) BYS90A Important to friends to attend classes regularly BYS90B Important to friends to study BYS90H Important to friends to continue education past high school Mathematics attitudes Mathematics self-concept (Cronbach's alpha = .93) BYS89A Can do excellent job on mathematics tests BYS89B Can understand difficult mathematics texts BYS89L Can understand difficult mathematics class BYS89U Can master mathematics class skills BYS89R Can do excellent job on mathematics assignments Mathematics affection (Cronbach's alpha = .78) BYS87A Gets totally absorbed in mathematics BYS87C Thinks mathematics is fun BYS87F Mathematics is important
Factor loading
.776 .756 .736 .747 .704 .629 .658 .658 .752 .725 .660 .664 .587 .577 .567 .504 .507 .511 .521
.760 .756 .753
.874 .879 .899 .892 .896 .760 .882 .862
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S. You, J.D. Sharkey / Learning and Individual Differences 22 (2012) 484–489 Crosnoe, R., Riegle-Crumb, C., Field, S., Frank, K., & Muller, C. (2008). Peer group contexts of girls' and boys' academic experiences. Child Development, 79(1), 139–155. doi:10.1111/j.1467-8624.2007.01116.x. Eccles, J. S. (1994). Understanding women's educational and occupational choices: Applying the Eccles et al. model of achievement-related choices. Psychology of Women Quarterly, 18, 585–609. Muthen, L. K., & Muthen, B. O. (2006). Mplus user's guide. Los Angeles: Author. National Center for Education Statistics (2008). Eighth grade: First findings from the final round of the early childhood longitudinal study, kindergarten class of 1998–99 (ECLS-K). First Look. Washington DC: US Department of Education Retrieved from. http://nces. ed.gov/pubs2008/2008088.pdf National Center for Education Statistics (2011a). The Condition of Education 2011 (NCES 2011–033). Retrieved from. http://nces.ed.gov/programs/digest/d10/tables/ dt10_008.asp
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Learning and Individual Differences journal homepage: www.elsevier.com/locate/lindif
Advanced mathematics course-taking: A focus on gender equifinality Sukkyung You a,⁎, Jill D. Sharkey b a b
College of Education, Hankuk University of Foreign Studies, 270 Imun-dong, Dongdaemun-Gu, Seoul 130-791, Republic of Korea Department of Counseling, Clinical, and School Psychology, Gevirtz Graduate School of Education, University of California, Santa Barbara, CA 93106-9490, United States
a r t i c l e
i n f o
Article history: Received 23 June 2011 Received in revised form 7 February 2012 Accepted 3 March 2012 Keywords: Mathematics Gender differences Social cognitive theory Peer factors Family factors
a b s t r a c t High school mathematics achievement predicts future success. Potentially different factors that lead to success for boys versus girls, termed equifinality, are not well understood. Such factors are needed to inform interventions to increase numbers of students taking advanced mathematics courses and going on into science and mathematics careers. With 16,373 diverse tenth grade participants of the 2002 Education Longitudinal Study, we used multi-group logistic regression modeling to investigate advanced mathematics course selection from a social cognitive perspective, testing relations separately by gender. Girls took advanced mathematics courses at significantly higher rates than males. Family background and cognitive factors were related to advanced mathematics coursetaking for both groups. Supporting the equifinality hypothesis, father's expectation, parent communication, and peer academic value were significant for girls yet mother's expectation and parent participation were significant for boys. Implications and future directions are discussed. © 2012 Elsevier Inc. All rights reserved.
1. Introduction
2. Gender equifinality in mathematics coursetaking
Taking advanced mathematics courses in high school is a powerful predictor of college success; research from the U.S. Department of Education (1999) shows that high school students who completed mathematics courses at levels higher than Algebra 2 (e.g., trigonometry or pre-calculus) earn a college degree at twice the rate of those whose high school mathematics curriculum was less rigorous. Other researchers, using nationally-representative data, reported that high school students who take more mathematics courses are at a clear advantage in achieving high school graduation, academic success, and college opportunity (Rock, Ekstorm, Goertz, & Pollack, 1995; Wilkins & Ma, 2002). In 2007, 69% of eighth grade boys and 76% of eighth grade girls reported they intend to pursue postsecondary education (National Center for Education Statistics [NCES], 2008); yet, a much smaller percentage achieves this goal (30%; NCES, 2011a). We examined correlates to advanced coursetaking in order to inform policy and practice designed to encourage mathematics coursetaking for greater numbers of students, recognizing that gender may be a key variable that represents different pathways to success (i.e., equifinality).
Empirical research suggests that factors leading to mathematics success may be different based on gender (Crosnoe, Riegle-Crumb, Field, Frank, & Muller, 2008). The term “equifinality” from General Systems Theory, defined as the same outcome despite different pathways or groups of factors leading to success, has previously been applied to the study of gender and mathematics coursetaking (Crosnoe et al., 2008). Specifically, Crosnoe et al. (2008) argued that different interventions may be needed to promote mathematics coursetaking outcomes for boys and girls, and studied the impact of peer group context on mathematics coursetaking. They found that pathways to mathematics success were similar for boys and girls in that friends' achievement was related to personal mathematics coursetaking and classmates' achievement added additional benefit. However, small deviations in the common trajectory, such as a less consistent influence of friends over time for boys, provided some support for the equifinality hypothesis. Further research is needed to extend this work with a broader framework to explain mathematics coursetaking. Social cognitive theory (Bussey & Bandura, 1999) recognizes the influences of biological, cognitive, and sociological influences on human development. Bandura (1986) describes gender role differences as a psychosocial phenomenon that occurs for boys and girls through their observations of and differential treatment by others — especially the different reactions for the same behaviors as dealt out by parents, peers, and teachers. These observations and reactions are eventually internalized as gender role values that shape goals and expectations in all aspects of life. The expectancy-value model
⁎ Corresponding author. Tel.: + 82 2 2173 3213. E-mail addresses: [email protected] (S. You), [email protected] (J.D. Sharkey). 1041-6080/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.lindif.2012.03.005
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indicates that perceived efficacy and understanding of the value related to an academic subject predict the decision to take advanced courses in that academic subject (Eccles, 1994). In social cognitive theory, such internal cognitions interact with biological and environmental influences to produce human behavior (Bussey & Bandura, 1999). Investigating social cognitive factors in the study of mathematics coursetaking will provide insight into key socialization agents of contemporary adolescence that shapes the motivations, attitudes, and values that are so important to understanding gender differences in factors that promote mathematics coursetaking. 3. Purpose and research questions The current study tests equifinality, or potential diverse pathways to similar mathematics coursetaking behaviors, by gender, through social cognitive factors. This study is unique because it examines a contemporary sample needed to examine gender equifinality in mathematics coursetaking and includes a breadth of social and cognitive variables while controlling for important potential confounds. The following research question addressed our purpose: What is the impact of social and cognitive variables on math course-taking for girls and boys? 4. Method 4.1. Data and samples We analyzed data from the Education Longitudinal Study of 2002 (ELS:2002), a national longitudinal study of high school tenth graders enrolled in a national sample of U.S. high schools in 2002 (NCES, 2011b). Data were from the longitudinal sample of 16,373 10th grade students who attended 751 public and private high schools in 2002, who were resurveyed in 2004, and whose transcripts were collected. Therefore, the approximate sample weight (F1PNLWT) was applied so the results generalize to the 2002 tenth-grade sample. 4.2. Measures With these public-use ELS data we were able to construct a comprehensive set of variables to test the research questions. Item descriptions, factor loadings and the internal consistency reliability coefficients of items created based on factor scores are reported in Appendix A. All predictor variables were measured in Wave 1 and the outcome variable was measured two years later in Wave 2. All individual factor composites, including those constructed by NCES, were normalized to a mean of zero and a standard deviation of one. 4.2.1. Family background controls Student and family background characteristics include ethnicity, familial SES, and non-traditional family status. SES is a composite measure developed by NCES based on father's education level, mother's education level, father's occupation, mother's occupation, and family income. Non-traditional family background was coded if the student did not live with both parents. 4.2.2. Academic controls Academic controls were college aspiration and tenth grade mathematics performance. College aspiration, a measure of external motivation to take advanced mathematics courses, was measured by student response on, “Which of the following do you plan to attend?” and coded a “yes” if the participant replied “Four-year college or university” and “no” if the participant replied “Two-year community college,” “Vocational, technical, or trade school,” or if the response was skipped because the participant previously responded negative to continuing education in the future. Tenth grade mathematics performance was measured by the students' standardized test score.
485
4.2.3. Cognitive variables Cognitive variables were measured with constructs of mathematics affection and self-concept. The measure of mathematics affection included three items from the student report (e.g., “Mathematics is important to me personally”) with Likert responses of 1 = strongly agree, 2 = agree, 3 = disagree, and 4 = strongly disagree. The measure of mathematics self-concept included five items from the student report (e.g., “I'm confident that I can do an excellent job on my math tests”) with Likert responses of 1 = almost never, 2 = sometimes, 3 = often, and 4 = almost always.
4.2.4. Parent involvement Four dimensions of parent involvement were created: communication, participation, supervision, and expectation. The measure of parent communication included eight items from the student report (e.g., “How often have you discussed the following with either or both of your parents or guardians…your grades?”) with Likert responses of 1 = never, 2 = sometimes, and 3 = often. Parent participation was measured with seven items from the parent report (e.g., “How often in this school year, do you or your spouse/partner do any of the following…act as a volunteer at the school?”) with a yes or no option. Parent supervision was measured with four items from the parent report (e.g., “How often do you do the following… Check on whether your children have done their homework?”) with Likert responses of 1 = never, 2 = rarely, 3 = sometimes, and 4 = often. Parent expectation variables were developed from single items that asked students, “How far in school do you think your mother and father want you to go?” Separate responses for each parent range from “Less than high school graduation” to “Obtain a Ph.D., M.D., or other advanced degree.”
4.2.5. Peer influences Peer value for education was selected as the peer variable and was measured with three items from the student report (e.g., “Among your close friends, how important is it to them that they…attend classes regularly?”) with Likert responses of 1 = not important, 2 = somewhat important, and 3 = very important. 4.2.6. Coursetaking outcome The primary outcome variable in this study was a measure of whether or not the student had completed any advanced mathematics courses (i.e., Trigonometry, Algebra III, Pre-calculus, or Calculus). Mathematics coursetaking was measured using an ordinal composite variable (F1RMAPIP). This measure indicates the highest level of mathematics for which the student received non-zero credit while in high school. For this study, the outcome variable was a dummy-coded variable indicating whether the student had completed any advanced mathematics courses. 4.3. Overview of the statistical analysis A series of recursive models were developed and tested using Mplus (Muthen & Muthen, 2006). The first model contained only the student background variables, the second model introduced academic control and cognitive variables, and the third model included socializing factors. The models estimated the size and statistical significance of a number of predictors simultaneously; we determined the unique contribution of each variable in the model controlling for the effects of the other variables in the model. The standard errors for the estimated means, percentages reported, and tables of the analysis can be provided upon request. Multi-group testing was conducted to investigate the significance of differences in coefficients across the girl and boy models using Wald test of parameter constraints available in Mplus.
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The models predicted the change in the odds of completing advanced mathematics courses versus not completing any advanced mathematics courses. A value of one signifies no change in the odds or likelihood of taking each level of advanced mathematics courses, while a value greater than one indicates an increased likelihood, and a value less than one indicates a decreased likelihood. The estimated effects for continuous variables were first multiplied by their standard deviation before converting to odds ratios so that the values in the tables represent the estimated effects of a one standard deviation change in the predictor variable on the odds of taking each level of advanced mathematics courses. The effect was considered small when OR = 1.50 (positive) or .67 (negative), medium when OR = 2.00 (positive) or .50 (negative), and large when OR = 4.00 (positive) or .25 (negative; Sanchez-Meca, MarinMartinze, & Chacon-Moscoso, 2003). 5. Results 5.1. Descriptive characteristics of advanced mathematics coursetaking Descriptive results summarized in Table 1 demonstrated that among high school sophomores, 15.7% took Trigonometry, 15.8% took Pre-calculus, and 11.8% took Calculus as their highest mathematics course in high school. Students who were Asian, whose native language is English, who were from the highest SES group, or who lived with both parents were the most likely to take advanced mathematics courses.
Table 2 Descriptive statistics for the variables (weighted) used in the analysis. Source: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 (ELS:2002/04), Waves 1 and 2. Girls (N = 7781) Mean or proportion Family background Asian American .04 African American .13 Latino/a American .16 European American .62 SESα −.01 Non-traditional family .42 Mathematics course taking α Advanced I (Trigonometry) .17 Advanced II (Pre-calculus)α .17 Advanced III (Calculus) .12 Academic control variables 10th Mathematics test scoreα 49.86 College aspirationα .85 Cognitive factors α Mathematics self-concept −.16 Mathematics affectionα −.09 Socializers Mother's expectationα 5.29 Father's expectationα 5.25 α Parental communication .11 Parental participation −.05 Parental supervision −.02 Peer academic valueα .12 Note.
α
Boys (N = 7737) SD
Mean or proportion
SD
.73 .49
.04 .14 .17 .62 .02 .42
.71 .49
.38 .38 .32
.14 .15 .12
.35 .35 .32
9.50 50.81 .36 .79
10.29 .41
1.00 1.00
.14 .04
.98 1.00
1.42 1.49 .97 .96 1.00 .95
5.05 5.01 −.16 −.09 .02 −.20
1.48 1.53 1.00 .96 .99 1.03
Gender difference is significant at p b .05.
5.2. Descriptive comparisons of girls and boys Girls were significantly more likely to take any advanced mathematics courses (46.4%) than boys (40.6%). Table 2 highlights significant differences between girls and boys for the variables selected in this study. Higher percentages of girls (17.2%; 17.4%) than boys (14.2%; 14.6%) took trigonometry and pre-calculus, respectively, but the rate of taking the most advanced mathematics course, calculus, was the same for girls and boys (11.8%). Boys had significantly higher mean scores on standardized mathematics
Table 1 Percentage distribution of 2002 high school sophomores demonstrating advanced mathematics coursetaking patterns by selected student characteristics (weighted sample). Source: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 (ELS:2002/04), Waves 1 and 2. Characteristics
Total Gender Female Male Race-ethnicity Asian American African American Latino/a American European American (Ref) Socioeconomic status Lowest quartile Second quartile Third quartile Highest quartile (Ref) Family composition Two biological parents Other
Advanced mathematics coursetaking patterns⁎ None
Trigonometry
Pre-calculus
Calculus
56.9
15.7
15.8
11.8
53.6 59.4 37.4 65.4 73.1 51.1 74.9 67.3 52.5 33.0 49.6 66.4
a b
a a a b
a a a b
a b
17.2 14.2
b
17.4 14.6
11.6 a 20.4 a 9.9 a 16.6 b
20.5 10.6 11.5 18.1
b
30.4 3.6 5.5 14.1
12.2 14.8 17.4 18.1
8.2 a 11.6 a 19.1 a 24.4 b
4.7 6.2 11.1 24.4
18.6 12.3
15.4 6.6
16.4 14.7
a
a a a b
a b
a b
a a a
a b
11.8 11.8 a a a b
a a a b
a b
Note. Means with different subscripts (in the same mathematics course and the same characteristic) differ significantly (p b .05). ⁎ Indicates the highest course taken by students.
test scores as well as on mathematics-related self-concept and affection yet girls had a higher mean score on college aspiration. Girls reported stronger communication with their parents and higher educational expectations from both parents than boys reported. Girls perceived higher peer academic value than boys reported.
5.3. The impact of social and cognitive variables on math course-taking After controlling for academic background variables (i.e., 10th grade mathematics test scores and college aspirations), all cognitive variables were significant predictors (see Model 2, Table 3). Mathematics self-concept and mathematics affection had small but significant effects for both boys and girls, with odds ratios remarkably similar across the two groups. Odds Ratios ranged from 1.18 to 1.23, which are small effects. Model 3 (Table 3) examined the impact of socializers on mathematics coursetaking without considering cognitive factors. Results demonstrated differential relations of parent and peer influences across gender groups. Peer values for grades and education were significantly related to taking the advanced mathematics coursetaking for girls only (OR = 1.20; small effect) whereas parental participation and mother's expectation were significant for boys only (OR = 1.16 and 1.05, respectively; small effect). Supervision was not associated with adolescents' advanced mathematics coursetaking for either group. Model 4 (Table 3) examined the impact of all control variables, cognitive factors, and socializers simultaneously. Significant associations between mathematics self-concept and mathematics coursetaking held steady, whereas associations between mathematics affection and mathematics coursetaking shifted to nonsignificance, for both boys and girls. The association of socializers to mathematics coursetaking largely remained the same in this final model although father's expectation became related to the outcome for girls (OR = 1.12; small effect) and parental participation shifted to non-significance.
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Table 3 Relative odds of advanced mathematics coursetaking with student-level predictors: academic year 2003–04. Source: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 (ELS:2002/04), Waves 1 and 2. Girls (N = 7781)
Family background Asian American African American Latino/a American SES Non-traditional family Academic control variables 10th Mathematics test score College aspiration Cognitive factors Mathematics self-concept Mathematics affection Socializers Mother's expectation Father's expectation Parental communication Parental participation Parental supervision Peer academic value Note.
α
Boys (N = 7737)
Model 1
Model 2
Model3
Model 4
Model 1
Model 2
Model 3
Model 4
1.92* 1.99* 1.05 1.30* 0.75*
1.86* 1.42* 1.00 1.31* 0.75*
2.08* 1.61* 1.07 1.20* 0.77*
1.88* 1.43α 1.00 1.20* 0.74*
1.76* 1.95* 0.89 1.42* 0.75*
1.95* 1.79* 0.80 1.53* 0.70*
1.81* 2.39* 1.01 1.49* 0.79α
1.79* 2.19* 0.98 1.54* 0.76*
3.95* 2.54*
3.59* 1.40*
4.03* 2.14*
3.74* 1.31*
3.65* 2.92*
3.22* 1.48*
3.72* 2.46*
3.25* 1.40*
α
1.22* 1.18*
1.21* 1.07 0.99α 1.02 1.20* 1.09α 1.00 1.19* α
0.97α 1.12* α 1.19* α 1.07α 1.00 1.16* α
1.23* 1.19*
α
1.25* 1.10 1.05* α 1.01 1.17* 1.16* α 0.99 1.11α
1.09* α 1.01α 1.13α 1.18* α 0.99 1.05α
Gender difference is significant at p b .05, * p b .05.
5.4. Effects of control variables As expected, the control variables were significantly related to mathematics coursetaking (see Table 3). The odds of taking the advanced mathematics were more than two times higher for Asian Americans than for European Americans; the odds of taking advanced mathematics were much lower for Latino/a Americans. Students from a high SES family were much more likely to take advanced mathematics than students from low SES families, with a stronger association for boys. Students not living with both parents were less likely to take advanced mathematics than students living with both parents (see Model 1, Table 3). As predicted, adding the cognitive and social variables generally reduced the relation between family background and outcome (see Models 2 and 3, Table 3). A surprising result was that for boys, the relation between African American status and mathematics-course taking shifted from equal to the reference group, to 1.79 times (see Model 2, Table 3) and then 2.39 times (see Model 3, Table 3) the reference group as additional variables were included. Regarding academic control variables, mathematics test scores yielded the strongest relation with mathematics coursetaking of any variable for both groups. College aspiration had small but significant associations with mathematics coursetaking with remarkably similar odds ratios for boys and girls (see Models 1–3, Table 3). 6. Discussion This study employed multi-group logistic regression with ELS:2002 data to test the premise that pathways to a similar outcome (mathematics coursetaking, i.e., equifinality) might be distinct given the likelihood of different socialization processes based on gender. We found that females not just equaled boys in their advanced mathematics coursetaking behaviors, but surpassed them in all but the highest level of mathematics. Bandura's theory of the role of self-efficacy in future behavior predicts that persons who have high self-efficacy for a certain task will be more likely to engage in that task and persist until they have achieved success (Bandura, 1986). Our results support this hypothesis, indicating that mathematics self-concept is related to mathematics course selection. Taking into account academic control variables, there
appear to be key differences in advanced mathematics persistence for students with high achievement in past mathematics courses, a strong math self-concept, and stronger academic orientations compared to students without these advantages. These findings point to the potential of early, engaging, and rewarding curriculum designed to foster strong mathematics coursetaking and self-concept. Results indicated there were differences in parents' involvement with their daughters and sons, consistent with extant literature. For daughters, there was a positive relation between communication and mathematics coursetaking. For sons, there was a positive relation between parent engagement in school activities outside the home and mathematics coursetaking. Both boys and girls experienced no relation between parental supervision and mathematics coursetaking. Mother's expectation had a significant association with boys' mathematics coursetaking, whereas father's expectation had a significant association with girls' mathematics coursetaking but only when cognitive factors were accounted for. This finding that the opposite sex expectations are related to advanced coursetaking, though a small effect, is unexpected and may warrant further exploration. Changes in odds of mathematics coursetaking when adding and subtracting cognitive factors and socializers provide additional insights into the associations between variables. Affection was significantly related to mathematics coursetaking only before socializers were added. For girls, the socializer impacted by cognitive factors was father's expectation, which became significant when all factors were included. Thus, father's expectation may explain the association between their daughters' feelings about mathematics and mathematics coursetaking. For boys, the socializer impacted by cognitive factors was parental communication. Both mathematics affection and parental communication were not significantly related to mathematics coursetaking in the final model. Perhaps the significant mathematics self-concept explained the association between parental communication and mathematics coursetaking. Peer context was also found to have differential associations across gender related to high school students' advanced mathematics coursetaking. Peer academic values were significantly associated with girls' but not boys' advanced mathematics coursetaking. This finding is consistent with past studies of peer relations that suggest girls have closer and more intimate friendships whose social support is important to academic success, whereas boys' self-confidence in
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mathematics in particular is not reliant on friendships or peers (Crosnoe et al., 2008). As a whole, it appears that the primary social influence for mathematics coursetaking is the expectation of significant others. This result is consistent with resilience literature that conveying high expectations to students relates to strong academic achievement and appropriate behavior (Brooks, 2006). Parent and peer high expectations may promote academic achievement as well as the activities required to take advanced mathematics courses such as studying together. We note that family background and academic control variables were significantly associated with mathematics coursetaking. Once cognitive variables and socializers were considered, the relation between African American status and mathematics course selection became positive and significant with an odds ratio of 2.19. This surprising result suggests that when cognitive variables and socializers are taking into consideration, there is something about African American male status that is associated with a higher likelihood of advanced mathematics course selection than any other ethnic/ gender group. In addition, although cognitive factors and socializers lowered the odds of advanced mathematics course selection for the Asian American group, they remained almost twice more likely to take the advanced mathematics courses. This suggests that an important component of Asian culture also was not accounted for in the current study. Future research should further explore these complex interactions. There are several limitations to this study. Data examined in this study were collected primarily from student self-report and the available measures regarding peer influences were more limited than the measures of parent influences. It would have been optimal to include corroborative information from students' perceptions, parental perceptions, and other sources of information such as diary data or observation. Another limitation in this study is that available social variables measured academics generally and did not allow us to measure socializers specifically for mathematics. Finally, gender differences in relations between parent influences and mathematics coursetaking emerge during middle school; nationally representative longitudinal data is needed to measure students from middle school on (Catsambis, 1994). 7. Conclusions Overall, the results supported the gender equifinality hypothesis. Although pathways to advanced math coursetaking are fundamentally similar and include impacts of family background, academic controls, and math expectations from close social influences, girls and boys differ on who provides the social influence and in what way it is conveyed. Girls are influenced by father and friend expectations and appear to benefit from communication with their parents. Boys are influenced by mother expectations and appear to benefit from active participation by their parents in their school life. This study highlighted some interesting new areas for future research. In particular, the cross-sex influence of parent expectations on mathematics course selection needs further exploration. Qualitative studies may be needed to uncover these interactions in detail. If supported, the model of gender equifinality might help guide efforts to support advanced math coursetaking for more students. Students need early and consistent exposure to mathematics, experiencing success and developing a strong math self-concept. Parents should be made aware of their potential influence on their children's mathematics course selection in terms of their expectations and behaviors. For girls, interventions might focus on group learning experiences that allow them to develop their math self-concept with other girls who also value advanced mathematics coursetaking. As advanced mathematics coursetaking is critical to future success in college and career, gender-specific interventions to develop academic
controls, college aspiration, parent and peer high expectations, and parent involvement may be important. Acknowledgments This work was supported by Hankuk University of Foreign Studies Research Fund granted to Sukkyung You. Appendix A. Descriptions, factor loadings, and reliability of factor composite measures
Variable
Item descriptions
Parental involvement Parental communication (Cronbach's alpha = .86) BYS86C How often discuss things studied in class with parents BYS86A How often discussed school courses with parents BYS86G How often discussed going to college with parents BYS86B How often discussed school activities with parents BYS86D How often discussed grades with parents BYS86I How often discussed troubling things with parents BYS86H How often discussed current events with parents BYS86F How often discussed prep for ACT/SAT with parents Parental participation (Cronbach's alpha = .72) BYP54C Take part in parent-teach organization activities BYP54D Act as a volunteer at the school BYP53H Parent contacted school about fundraising/volunteer work BYP54A Belong to parent–teacher organization BYP54E Belong to other organization with parents from school BYP57A Attended school activities with 10th grader BYP54B Attend parent–teacher organization meetings Parental supervision (Cronbach's alpha = .73) BYP69A Family rules for 10th grader about maintaining grade average BYP69B Family rules for 10th grader about doing homework BYP69C Family rules for 10th grader about doing household chores BYP69D Family rules for 10th grader about watching TV Peer influence Peer value for education (Cronbach's alpha = .82) BYS90A Important to friends to attend classes regularly BYS90B Important to friends to study BYS90H Important to friends to continue education past high school Mathematics attitudes Mathematics self-concept (Cronbach's alpha = .93) BYS89A Can do excellent job on mathematics tests BYS89B Can understand difficult mathematics texts BYS89L Can understand difficult mathematics class BYS89U Can master mathematics class skills BYS89R Can do excellent job on mathematics assignments Mathematics affection (Cronbach's alpha = .78) BYS87A Gets totally absorbed in mathematics BYS87C Thinks mathematics is fun BYS87F Mathematics is important
Factor loading
.776 .756 .736 .747 .704 .629 .658 .658 .752 .725 .660 .664 .587 .577 .567 .504 .507 .511 .521
.760 .756 .753
.874 .879 .899 .892 .896 .760 .882 .862
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