Interplay Among School Climate, Gender, Attitude Toward Mathematics, and Mathematics Performance of Middle School Students

Mathematics is an important area of study that plays a major role in adolescents’ academic development and career planning, serving as a defining subject for adolescents’ present and future lives. In a longitudinal study of Canadian high school students’ career aspirations,

Shapka, Domene, and Keating (2006) reported that ninth graders with low mathematics achievement started their ninth grade school year with lower level career aspirations than those with high mathematics achievement, and that low mathematics achievers’ aspirations had deteriorated even further by the end of their high school education. Their empirical evidence for the significant effect of adolescents’ mathematics achievement on their subsequent career trajectories illustrates the importance of identifying the factors that are related to adolescents’ mathematics achievement.

The literature abounds with studies reporting various student-, family-, and school-related factors that contribute to the mathematics performance of adolescents. In their review of this topic, Lee and Shute (2010) hierarchically organized the various personal and social-contextual factors that have been reported in the fields of educational, cognitive, and social psychology to be directly or indirectly related to reading and mathematics academic achievement at the K-12 level. The extensive list of more specific study variables in numerous studies that they found to be significantly related to mathematics achievement is indicative of the complex interplay between a host of factors and mathematics achievement at the K-12 level.

This study applied multilevel modeling to a U.S. national database, the Trends in International Mathematics and Science Study (TIMSS) 2007, to achieve a set of conclusions with high generalizability that primarily concerned school climate at the class level. At the student level, we examined gender, attitude toward mathematics, student educational aspiration, parent education level, and language spoken at home to see how they related to mathematics achievement. By conducting a statistical analysis that specified the personal and contextual variables hierarchically, the study attempted to achieve its goal of identifying the important factors influencing the mathematics achievement of students in middle school.

School climate as a group-level variable has recently attracted a great deal of attention due to the increasing number of empirical findings that have reported its significant relationship with student achievement. Depending on one’s theoretical perspective, it is possible to view school climate as either a property of the school or a psychological property of an individual (Van Horn, 2003), yielding numerous definitions of the construct (Hoy & Hannum, 1997). Confirming the hierarchical and multidimensional nature of school climate, Lee and Shute (2010) listed a number of subconstructs for components of school climate, including academic emphasis, collective teacher efficacy, teacher affiliation, teacher empowerment, principal influence, resource support, school policies, and class sizes, that are perceived by various constituents of the school.

As a way to explore the significance of school climate while avoiding distractions due to the complexity of its construct, many educational researchers have chosen to focus on a single component of school climate in relation to academic achievement. For example, some have focused on the relationship between the academic emphasis dimension of school climate and academic achievement (Hoy & Hannum, 1997; Hoy, Sweetland, & Smith, 2002), while others have examined the relationship between the collective teacher efficacy dimension of the construct and student achievement (Goddard, LoGerfo, & Hoy, 2004; Ware & Kitsantas, 2007). This study shares the approach of Lee and Shute (2010) by opting to look at the impact of school climate on student academic performance.

In their delineation of a conceptual framework that describes the interplay among personal factors, social-contextual factors, and K-12 achievement variables, Lee and Shute (2010) cited numerous empirical studies that reported significant relationships between different dimensions of school climate and K-12 students’ academic achievement. According to the authors, the academic emphasis dimension is a major dimension that is closely linked to academic achievement, especially in mathematics and reading. They reported that the academic emphasis dimension of school climate explained about 47% of the variability in mathematics achievement in one study (Hoy et al., 2002) and was a significant predictor (β = .28, p < .01) of middle school students’ mathematics achievement scores, controlling for school SES, in another study (Hoy & Hannum, 1997). Lee and Shute also cited many other studies that reported significant relationships between student academic achievement and teacher-related dimensions of school climate (e.g., collective teaching efficacy, teacher empowerment, teacher affiliation), with correlation coefficients ranging from the low .20s to the mid .60s. These findings show unequivocally that teacher-related factors are a crucial element in creating a healthy school climate that is conducive to student learning. The authors also posit that personal, parental and peer-related factors may also influence school climate and thus, in turn, separately and collectively influence academic achievement.

Gender is arguably the student-level personal factor that has generated the most intense scrutiny. Unlike the early reports, which indicated a significant gender difference in academic performance (see Glennon & Callahan, 1968), findings in the last four decades have been mixed. While some have reported higher performance for male students (Fennema & Sherman, 1978), others have shown the opposite findings (Swafford, 1980), and yet others have indicated no significant gender difference until the most advanced courses in high school, where males were overrepresented and outperformed their female counterparts (Fierros, 1999; Meelissen & Luyten, 2008; Tate, 1997; Tsui, 2007).

One context that is likely to contribute to the controversy regarding gender difference in mathematics achievement is the type of test. According to Liu (2009), when measured by classroom tests, female students performed higher than or as well as male students. The gender pattern, however, tended to be reversed on several of the standardized tests. In other words, as Liu pointed out, female students tended to earn higher math grades while male students tended to earn higher math scores. From a gender role socialization perspective, this aspect of gender difference is not surprising; female students tend to be more socially oriented in their learning strategies and behaviors, whereas male students are more independent and autonomous in completing learning tasks. Math grades usually reflect different dimensions in learning which include not only classroom test scores but also in-class learning behaviors and social collaborative skills. Male students, on the other hand, tend to show advantage in impersonal and independent standardized testing conditions. Liu summarized gender difference in performance on the four mathematics subtests from PISA 2003 as not substantial but consistent, with Cohen’s d index ranging from .04 to .14.

In their search for the factors determining mathematics performance, several researchers have looked at affective variables such as mathematics confidence, attitude toward mathematics, or mathematics anxiety in relation to middle grades mathematics achievement, and have found a significant association of those variables with mathematics performance (Eklof, 2007). Hammouri (2004) analyzed eighth-grade Jordanian student data from TIMSS 2003 and reported a significant correlation between mathematics achievement and attitudinal measures. Specifically, Hammouri reported that mathematics achievement was statistically and significantly correlated with mathematics confidence (r = 0.34, p < .05), perceived importance of mathematics (r = 0.24, p < .05), and attitude toward mathematics (r = 0.21, p < .05). These correlations indicate that mathematics achievement shares a significant amount of variance with attitudinal variables yet modest enough without having severe multicollinearity problems, ranging from approximately 4% to 12% for the students in this study. Adopting a similar perspective, House and Telese (2008) examined whether each of 12 items measuring attitude toward mathematics (which they termed mathematics beliefs) on data from TIMSS 2003 was a significant predictor of students’ performance on an algebra subtest. Their findings indicated that ten items significantly predicted algebra performance. Liu (2009) also reported that two affective variables, mathematics selfconfidence and mathematics anxiety, were significant predictors of the mathematics performance of 15-year-old U.S. students. Those who had high levels of mathematics self-confidence performed better, while those who displayed high degrees of mathematics anxiety performed poorly on the PISA 2003 assessment.

While there is a general consensus that taking mathematics courses is an important way to reduce the gender gap in mathematics performance, some studies suggest there is still a gender difference in attitudes toward mathematics. Traditionally, mathematics is viewed as a male domain that is in conflict with feminine roles, and thus male students tend to have high level of mathematics confidence and their mathematics confidence seems unrelated to external feedback (Crosnoe, Riegle-Crumb, Field, Frank, & Muller, 2008). Simpkins, Davis-Kean, and Eccles (2005) reported that mothers encouraged their sons to participate in math and science activities and to acquire skills in math and science significantly more than their daughters. Perceiving parents’ low expectations of their achievement in a male domain and experiencing “academic sexism” (Leaper & Brown, 2008, p. 685) may partly explain girls’ lack of confidence in their mathematics ability (Eccles & Wigfield, 2002), even when talented female students have the potential to perform at a high level in mathematics (Reis & Park, 2001)

Other important student-level factors that are reported to be related to academic performance include parental education levels, educational aspiration, and home language status. As an indicator of socioeconomic status, the level of parent education has been shown to have a significant effect on the reading achievement of Swedish third graders through mediating variables, such as the number of books at home (Myrberg & Rosen, 2009). Parental educational background is also reported to have a long-term effect on children’s educational pathways (Dubow, Boxer, & Huesmann, 2009). According to Ojeda and Flores (2008), parent education levels alone explained about 10% of the variance in the educational aspiration of Mexican-American high school students over and above their other demographic variables.

Educational aspiration is a variable that is significantly and positively correlated with mathematics achievement (Shen, 2002). The findings reported by Hammouri (2004) revealed multiple paths showing how educational aspiration affects mathematics achievement. The author reported that educational aspiration had significant direct positive effects on both attitude toward mathematics (β = 0.24) and on mathematics achievement (β = 0.10), as well as an additional indirect positive effect (β = 0.06) on mathematics achievement.

The language used as the medium in learning appears also to be a significant factor affecting learning for English language learners (ELL), especially in a multicultural society such as the United States. Since ELL learners have to transition between two or more languages, some researchers (e.g., Teranishi, 2004, as cited in Chang, 2008) believe that language minority students’ learning could be detrimentally affected. In a longitudinal study of kindergartners, Chang (2008) reported that language minority students in general did not perform as well as their majority counterparts.

This study used data for eighth-grade U.S. students from the Trends in International Mathematics and Science Study (TIMSS) 2007 assessment, the largest international comparative study of math and science achievement to date. TIMSS is an international database that is collected by the International Association for the Evaluation of Educational Achievement (IEA) with a 4-year cycle, starting in 1995, and is designed to reveal trends in students’ mathematics and science achievement. TIMSS 2007 is the fourth and most recent round in the series. In addition to measuring the mathematics and science achievement of fourth and eighth-grade students, TIMSS 2007 collected extensive information from students, teachers, and school principals about mathematics and science curricula, instruction, home contexts, and school characteristics and policies in more than 60 countries around the world. The mathematics achievement test contains items on numbers, algebra, geometry, and data/chance.

The international sample design for TIMSS is generally referred to as a two stage stratified cluster sample design. The first stage consists of a sample of schools; the second stage consists of a sample of one or more classrooms from the target grade in sampled schools.

Because this research focused primarily on U.S. middle school education, the study used data only from the eighth^-grade students’ questionnaire in the United States. A total of 8,912 eighth-grade students completed the students’ survey and they attended 212 U.S. schools. A major sample characteristics are as follows: 50.4% were girls, 90.3% were those who speak English as the primary language spoken at home, and 42.5% were those who have parents with university or higher education.

The main analytical tool used by the study was two-level multilevel modeling. It was hypothesized that there are teacher effects that contribute toward explaining students’ achievement differences in mathematics.

In this study, the multilevel analysis began with an unconditional model that contained no predictor variables from any level. The unconditional model was used to estimate how much variance could be attributed to the class and the student level. The final model was specified to examine the main effects of student gender, student’s attitude toward mathematics, student educational aspiration, parent educational background, student linguistic status, teacher perceived school climate, teacher gender, and an interaction effect of student gender and teacher perceived school climate. The two levels of the final model were specified as follows:

At Level 1,

MathAch = β₀ + β₁(Sex) + β₂(Mathematics Attitude) + β₃(Educational Aspiration) + B₄(Parent Educational Background) + β₅(Student Linguistic Status) +r,

At Level 2,

β₀= γ₀₀ + γ₀₁(Teacher Perceived School Climate) + γ₀₂(Teacher Sex) + u₀

β₁= γ₁₀

β₂= γ₂₀ + β₀₂ (Teacher Perceived School Climate)

β₃= γ₃₀

β₄= γ₄₀, and

β₅= γ₅₀.

For multilevel analysis of the study, HLM was chosen as the software program as it has the capacity to perform integrated analyses for handling problems such as the aggregation bias in standard error estimates and erroneous probability values. To increase the generalizability of the results, a total student weight (totwgt) at the student level and a weight for mathematics teachers (matwgt) at the class level were applied. One additional benefit of the application of weights was the option to adjust the multistage sampling methods of TIMSS. This study also paid careful attention to the design effect of the stratified sampling utilized by TIMSS and used five plausible values of dependent variables throughout, even for the preliminary analyses. Descriptive statistics and correlations were weighted and generated using AM Statistical Software Beta Version 0.06 (American Institutes for Research & Cohen, 2005).

As dependent variable, the study adopted five plausible values of mathematics achievement scores. TIMSS provides five plausible values to estimate students’ performance level because each individual student does not answer all test items. Plausible values are calculated through an item response modeling system (Eklof, 2007), and estimate a probability distribution for a student’s ability, rather than simply obtaining a point-estimate for the student’s ability. Thus, these five plausible values provide benefits in assessment situations where individuals are administered too few items to allow precise estimates of their ability. TIMSS reported Cronbach’s alpha coefficients of 0.88 for international samples and 0.89 for the United States’ samples for these items (Olsen et al., 2008). Furthermore, the researchers noted that serious measures were taken to ensure content validity by analyzing test items to look for discrepancies or bias toward any country (Olsen et al., 2008).

Among the variables of Level 1, the student gender was coded 0 for male and 1 for female. Approximately 49.6% of the U.S. participants were male and 50.4% were female in the TIMSS 2007 data.

A composite variable measuring student’s attitudes toward mathematics was created using 12 items that measure positive affect toward mathematics, valuing mathematics, and self-confidence in learning mathematics on a 4-point scale (1 = disagree a lot; 4 = agree a lot), with the possible score ranging from 12 to 48 (see Table 1 for detailed information on the 12 items). Although TIMSS 2007 does not provide clear guidance regarding the use of these 12 items, Martin and Preuschoff (2008) presented evidence supporting three underlying dimensions for the 12 items, which were loosely referred to as items measuring student attitudes toward mathematics (Eklof, 2007). The internal consistency reliability of the scores from the 12 items from the current sample was .86, which was acceptable for research purposes (Henson & Roberts, 2006).

The variable of parent education level was specified at Level 1 in the study (1 = less than lower secondary education, 2 = completed lower secondary education, 3 = completed upper secondary education, 4 = completed postsecondary education but not university, and 5 = university degree). The variable indicating student educational aspiration was dichotomized in this study (0 = below bachelor degree and 1 = bachelor or higher degree).

The variable of student linguistic status was also categorized in terms of two groups: a nonEnglish group speaking a language other than English as their primary language and an English-speaking group. TIMSS asked students, “How often do you speak the language of the test (in this case, English) at home?”(1 = always; 2 = almost always; 3 = sometimes; 4 = never). The study merged the “Always English speaking” group and the “Almost Always” group into one English-speaking group and the “Sometimes” group and the “Never” group into one non-English speaking group.

The main predictor variables at Level 2 were teacher perceived school climate and teacher sex (1 = male; 2 = female). The school climate variable in the study was measured by summing eight items guided by the TIMSS database. These eight items measured the participating teachers’ perceptions of various aspects of school-related issues, such as the teacher’s job satisfaction, their degree of success in implementing the school’s curriculum, their expectations for student achievement, and the parental support for student achievement. Each item was measured on a 5-point scale (1 = very low; 5 = very high), with a maximum score for school climate of 40. The internal consistency reliability of the eight item scores in this study was 0.88 (see Table 1 for detailed information on the eight items).

The descriptive statistics and correlation coefficients for all the variables generated by the AM software are presented in Table 2. As expected, when students had positive attitude toward mathematics, higher educational aspiration, and higher parent education, they tended to display higher mathematics achievement scores. Girls and students who speak other languages than English showed lower mathematics achievement scores than their counterparts. These results indicate that eighth graders who possessed a positive attitude toward mathematics, who had high educational aspirations, whose parents had a higher level of education, who were male, and whose home language was English tended to be high mathematics achievers when measured by the TIMSS 2007 assessment.

The unconditional model for mathematics achievement was first examined to see whether there was sufficient variation among teachers in student mathematics achievement. The results indicated that there was indeed a significant (p < 0.01) amount of variation among teachers in students’ mathematics achievement, χ² (371) = 7477.11. The obtained intraclass correlation coefficient (ICC) of .54 suggests that about 54% of the variance in student mathematics scores was due to teacher level variables. This high intraclass correlation also confirms the importance of multilevel modeling for analysis.

The results from the final model (see Table 3) revealed that teacher perceived school climate had a significant effect on the average performance of student math performance (γ₀₁ = 3.42, p < 0.01), indicating that when a teacher had a positive perception of their school climate, the average class performance in math was high. Despite the significant teacher gender difference in perceived school climate, with a higher mean for female teachers, no effect of teacher gender on student mathematics achievement was found in the study.

Each of the five predictors at Level 1 (student variables), on average, was found to be significantly related to mathematics achievement. Student’s gender (β₁ = -4.88,p < 0.01 was statistically significant, indicating that girls, on average, scored 4.88 points lower than boys on mathematics achievement. Its effect size (Cohen’s d) was 0.05, indicating that the average mathematics score of girls was 0.5 standard deviation lower than that of boys. Students’ attitudes toward mathematics also had a significant effect on their mathematics performance (β₂ = 2.43, p < 0.01); when a student had a positive attitude toward mathematics, he or she, on average, scored higher on math performance. Interestingly, the cross-level interaction effect between student’s mathematics attitude and teacher’s perceived school climate was statistically significant (γ₂₁ = 0.07,p < 0.05), suggesting that the relationship between the student’s mathematics attitude and his or her mathematics achievement depended to some extent on the teacher’s perceptions of the school climate. In other words, a student with a teacher who perceived the school climate as positive tended to show a high math performance. However, when students’ attitude scores toward mathematics were low, there was no easily discernable relationship pattern between their teachers’ perceptions of the school climate and their mathematics achievement. As students’ attitude scores toward mathematics increased, a clear pattern emerged between the perceived school climate and student mathematics achievement: higher levels of perceived school climate were associated with higher mathematics achievement and vice versa. To gain a better understanding of this pattern, the school climate variable was separated into three groups and the resulting patterns plotted, as shown in Figure 1.

Not surprisingly, the effect of student’s educational aspiration was significant (β₄ = 14.90, p < 0.01). When a student planned to have a bachelor or higher degree, he or she tended to score 14.90 points higher in mathematics than those whose educational aspirations were below bachelor’s degree. The effect of parent educational level was also significant (β₃ = 4.24, p < 0.01); having parents with high educational backgrounds had a significantly positive effect on the student’s math performance.

Student’s language status (β₅ = -14.14, p < 0.01) also had a significant negative effect, with ELL students exhibiting a math performance score that was 14.14 points lower than non-ELL students. As Figure 2 illustrates, a gender difference in mathematics achievement was noticed in both the non-ELL and ELL subgroups.

The major objective of the study was to examine the effects of student’s gender, attitude toward mathematics, student educational aspiration, parent education, and primary language at home which may have nested influences under teacher gender and teacher attitude toward school climate. In the analysis, we considered the nested structure of factors to predict student mathematics performance in school by employing HLM to TIMSS 2007. The use of the advanced statistical method (HLM) and a nationally representative sample (TIMSS 2007) allowed us to reach research conclusions with high generalizability.

A main finding from this study was the significant effect of school climate on eighth graders’ mathematics achievement. Despite varying operational definitions of the school climate construct across the published empirical studies, similar findings have been reported in the literature (Goddard, LoGerfo, & Hoy, 2004; Goddard, Sweetland, & Hoy, 2000; Ware & Kitsantas, 2007). This finding of the current study adds to the accumulating evidence that classroom teachers who feel satisfied with their job, with the level of parental support, and with the school’s high academic emphasis, are more likely to create a positive and healthy learning environment that enhances middle school students’ mathematics achievement. Furthermore, there was also a significant cross-level interaction between school climate and students’ attitudes toward mathematics. Although mathematics attitude as an individual variable was a significantly positive predictor of mathematics achievement, the significant cross-level interaction indicates that its predictive potency may be most evident where students adopt a more positive attitude toward mathematics in what their teachers perceive to be a highly constructive school climate. These findings suggest that school climate matters, and it matters even more for students whose attitude toward mathematics is positive.

Another major finding was the significant gender difference in mathematics achievement, with female students performing at a lower level. This confirms some previous findings (Fierros, 1999; Meelissen & Luyten, 2008; Tate, 1997; Tsui, 2007). Another important finding of the study was the strikingly similar gender pattern difference observed in mathematics achievement of the ELL middle school students in schools throughout the United States, which highlights the added disadvantage suffered by female ELL students when learning mathematics. With regard to the overall significant gender difference, it is worth noting that mathematics performance in this study was measured by a standardized test, thus lending credence to Liu’s (2009) assertion that male students as a group consistently perform at a higher level than their female counterparts on standardized tests. This gender pattern difference in mathematics achievement has several practical implications. As female students perform at far below their optimal level on mathematics tests, their intrinsic mathematics motivation will inevitably decrease (Gottfried, Marcoulides, Gottfried, Oliver, & Guerin, 2007), and they will be less likely to take mathematics courses over the course of their education. One consequence of this would be the limited subsequent career and occupational choices available for otherwise capable female students. The fact that most career paths require them to take standardized mathematics tests would further limit their career options. Thus, it is important that future studies should examine precisely why female students perform better than their male counterparts on classroom tests, but not on standardized tests.

Closely related to gender difference in mathematics achievement is the gender difference in attitudes toward mathematics. Female middle school students showed a significantly less positive attitude toward mathematics than their male counterparts, after controlling for mathematics achievement. These findings support the gender role socialization perspective in that girls are not encouraged to excel in math as boys are. As the findings from the family cohort longitudinal study by Simpkins et al. (2005) suggest, parents’ beliefs about math/science/computers and their relevant socializing behaviors (such as providing encouragement, arranging children’s activities, and engaging in those activities together) are likely to have a long-lasting influence on their children in a multitude of ways. As gender role expectations are inculcated in both boys and girls from early childhood onwards by various social groups (i.e., parents, siblings, peers, and teachers) girls become less competent in mathematics (Shapka & Keating, 1998, as cited in Shapka et al., 2006) and more likely to choose certain gender-stereotypical career paths (Eccles, 2005). One serious consequence of the socialization of the gendered domain of school subjects in middle school girls is the resulting limited access to various career and occupational opportunities. Due to their less than optimal performance in early mathematics performance, they are less likely to choose high-level high school mathematics courses (Watt, 2006), which in turn leads to less prestigious occupations in adulthood (Shapka et al., 2006).

In summary, at the student-level the findings of this analysis of the data from TIMSS 2007 indicate that a middle school student who had a positive attitude toward mathematics, who was male, who spoke English as a primary language, and whose parents were highly educated tended to perform at a higher level on the mathematics test. These findings are consistent with and further solidify those of previous studies reported by Liu (2009), Chang (2008), and Ojeda and Flores (2008). At the teacher level, teacher perceived school climate was significantly related to middle school students’ mathematics performance, and also interacted positively with attitude toward mathematics to improve middle school students’ mathematics performance.

One final comment relates to a limitation of this study; the nature and structure of the school climate construct. It was mentioned earlier that numerous definitions of school climate coexist due to its hierarchical and multidimensional nature. In fact, a quick scan of the relevant literature presents a number of nebulous definitions, yielding varied measuring instruments with widely different specifications for the dimensions of the construct. The operational measure of school climate adopted in this study reflects the participating eighthgrade teachers’ perceptions of various aspects of school-related issues, such as the teacher’s job satisfaction, their degree of success in implementing the school’s curriculum, their expectations for student achievement, and the parental support for student achievement. One fundamental issue relevant to achieving healthy school climate seems to be a consensus on what school climate really means. Clearly, there is a need for the development of a psychometrically sound measurement tool based on a sound theoretical foundation for the school climate construct.

Another limitation of the study is based on survey questionnaires which limit our inference on causal relationship of variables. Although we evidenced the significant effects of school climate, student gender, student attitude toward mathematics, student educational aspiration, parent education, and primary language at home affect student performance, they are not the only factors. The relational dynamics of variables should be further studied using more controlled research designs rather than correlation studies. While we are making careful conclusions regarding the results of our study, we believe that our research findings will have implications for educational researchers and practitioners.