Introduction

Beliefs about and attitudes concerning mathematics show significant impact on one’s decisions about the amount and nature of mathematics one will study in the future. To state differently, students’ mathematics-related career trajectories are likely to be influenced by their emotions, feelings and self-beliefs toward mathematics. Hence, attitudinal constructs either guide students to study mathematics or mathematics-related fields or they push students away from careers that require even moderate mathematics competencies (^{Hafner, 2008}). As a result, educating learners with strong self-beliefs in mathematics and positive attitudes towards mathematics should be the overarching aim of all educators. Thus, there has been a major shift to study contributions of affective variables, such as self-efficacy, attitudes and dispositions, on cognitive skills (^{Aiken, 1970}; ^{Pajares, 2006}; ^{Schunk & Mullen, 2012}).

Motivational and emotional variables involving belief, anxiety and attitudes are also important in understanding mathematics achievement (^{Soleymani & Rekabdar, 2016}). Thus, despite the fact that mathematics is viewed as a cognitive discipline, the affective dimension should not be ignored; so, understanding the nature of attitudinal constructs and their relationships with demographic characteristics and mathematics achievement should be a major research concern. In other words, in this research we aimed to investigate how seventh grade students’ academic self-efficacy, mathematics anxiety, attitudes toward mathematics, and mathematics achievement differ according to gender and school type. We also explored how well academic self-efficacy, mathematics anxiety and attitudes toward mathematics together with gender and school type predict mathematics achievement.

Methods

Results

The first aim of this study is to investigate differences in seventh grade students’ mathematics self-efficacy scores, mathematics anxiety, mathematics attitude, and achievement scores in terms of gender and school type. Mean and standard deviation regarding self-efficacy scores, mathematics anxiety, mathematics attitude, and achievement scores of the participants by gender and school types are given in Table 1.

Table 1: Self-Efficacy, Math Anxiety, Attitude, Achievement Mean Scores by Gender and School Type. 

In order to test the significance of the results, two-way ANOVAs were performed. Before conducting the analysis, main assumptions, including level of measurement, independence of observations, normality and homogeneity of variance were checked. More specifically, mathematics self-efficacy, mathematics anxiety, attitudes toward mathematics, and mathematics achievement scores were measured by the scores of the participants which are continuous; hence, the level of measurement assumption was assured. In the present study, there was no interaction between participants during the data collection. Hence, it was assumed that independence of observations assumption was also assured. The skewness and kurtosis values with respect to gender and school type ranged between -.89 and .36 for self-efficacy, between - .15 and 1.02 for anxiety, between -.62 and -.26 for attitude, and between .37 and -.75 for achievement scores respectively which indicates that there was no violation of the normality assumption. In order to determine whether homogeneity of variance was ensured, Levene’s Test of Equality was examined. Results revealed that the variance within each population was equally distributed for self- efficacy ENT#091;F (3,930) = 2.469, p = .061ENT#093;, anxiety ENT#091;F (3,930) = 2.210, p = .085ENT#093;, attitude ENT#091;F (3,930) = 1.899, p = .128ENT#093;, and achievement ENT#091;F (3,930) =1.277, p =.281ENT#093;, an indication that homogeneity of variance assumption was met.

Results revealed that there was a significant main effect of gender on mean self-efficacy scores. In other words, gender had significant main effect on mean self-efficacy scores ENT#091;F(1,930) = 4.139, p = .042ENT#093; where mean self-efficacy scores of males (M = 48.01, SD = 11.53) were significantly higher than that of females (M = 46.42, SD = 12.59). Moreover, the effect size for gender (Partial eta square) was calculated as .004. According to Cohen’s criterion, the effect size of gender for the present study was relatively small. Results also revealed that school type did not have significant main effect on mean self-efficacy scores ENT#091;F(1,930) = 1.334, p = .248ENT#093; with relatively higher mean self-efficacy scores of public school students (M = 47.66, SD = 12.12) than that of private school students (M = 46.77, SD = 12.03)

The analysis for mathematics anxiety was conducted with total scores of the items to obtain a mathematics anxiety mean score for each student. As can be seen in Table 1, the mean anxiety score of students in public school students (M = 111.12, SD = 37.08) was slightly less than that of private school students (M = 112.96, SD = 36.69). In other words, results revealed that school type did not have significant main effect on anxiety scores ENT#091;F(1,930) = .588, p = .443ENT#093;. On the other hand, results revealed that gender had significant main effect on anxiety scores ENT#091;F(1,930) = 5.197, p = .023ENT#093;. This indicated that the difference between females’ mean anxiety scores (M = 114.86, SD = 38.028) and males’ mean anxiety scores (M = 109.29, SD = 35.577) was statistically significant, favoring female students. Moreover, the effect size for gender (Partial eta square) was calculated as .006, a relatively small value.

According to the mean and standard deviation of mathematics attitude, private school students (M = 62.98, SD = 17.66) were relatively higher than that of public school students (M = 58.50, SD = 16.89). Two-way ANOVA results revealed that this difference is statistically significant ENT#091;F(1, 930) = 15.830, p = .000ENT#093;. That means the attitude scores of private school students were significantly higher than the mean attitude scores of public school students. The effect size for school type was calculated as .017, a small effect size. When gender was investigated, females’ mean score was 61.69 (SD = 17.08) and that of males was 59.42 (SD = 17.636). That is, males’ average attitude score was significantly less than females’ average attitude scores ENT#091;F(1,930) = 5.260, p = .022ENT#093;. Moreover, the effect size for gender was calculated as .006. That is, the actual differences in the mean values were small which means that the difference between females and males seemed to be of little practical significance.

Students Level Determination Examination (SLDE) was analyzed in order to obtain a mathematics achievement score for each student The mean achievement score for public school student was 10.00 (SD = 2.682) and that of private school students was 10.09 (SD = 2.393). In other words, school type did not have significant effect on achievement scores ENT#091;F(1,930) = 1.301, p = .654ENT#093;, where private school students slightly scored higher than their public school counterparts. Results also revealed that there was a statistically significant main effect for gender on achievement scores ENT#091;F(1,930) = 3.992, p = .046ENT#093;. That is, the difference between achievement scores of males (M = 10.20, SD = 2.548) and females (M = 9.88, SD = 2.533) was statistically significant. Moreover, the effect size for gender was calculated as .004. That is, it was concluded that the effect size of gender for the present study was relatively small and the difference between females and males seemed to be of little practical significance.

The second aim of this study is to investigate the role of mathematics anxiety, attitude towards mathematics, mathematics self-efficacy, gender or school type on predicting mathematics performance of seventh grade students. Multiple regression analysis was performed to accomplish this aim. Before conducting the analysis, the assumptions of multiple regressions, including sample size, multicollinearity and singularity, linearity, outliers, normality, and homoscedasticity, were checked. There were five predictor variables, mathematics self-efficacy, mathematics anxiety, attitude towards mathematics, gender and school type. According to ^{Tabachnik and Fidell (2007}), the required sample size for predictor variables was should be at least 90 participants (N > 50 + 8*5). The sample of this study consisted of 934 seventh grade elementary school students which satisfies the sample size assumption. For multicollinearity and singularity assumptions, analysis revealed that bivariate correlations among predictor variables was not above .7. Hence, multicollinearity and singularity assumptions was not violated (Tabachnik & Fidell, 2007). Displayed distribution of cases’ standardized residuals in scatterplot revealed that there exist five or six extreme cases with standardized residual values above about 3.3 or less than -3.3, reflecting the outliers. However, as Tabachnik and Fidell (2007) stated few outliers in a given study could be ignored with large sample size. Thus, the outliers assumption was assured. As stated before, the distribution of self-efficacy, anxiety, attitude and achievement scores with respect to gender and school type was normal. Hence, it was concluded that the normality assumption was assured for all variables. Analyses revealed that residuals were equally distributed below and above the zero line on the scatterplot which satisfies linearity assumption of regression analysis. Displayed scatterplot of the standardized residuals revealed that the residuals plot will be roughly rectangularly distributed, with most of the scores concentrated in the center. Hence, it was assured that there was no violation of homoscedasticity assumption.

Results revealed that the linear combination of affective variables (self-efficacy, anxiety and attitude) and demographics (gender and school type) was significantly related to achievement scores ENT#091;F(5,928) = 100.295, p = .000ENT#093;. That is, the provided model consisted of affective variables and demographics significantly predicted the achievement scores. The sample multiple correlation coefficient was .592 and R2 was .351 ENT#091;F(5,928) = 100.295, p = .000ENT#093;. That is, approximately 35% of the variance of achievement scores in the sample can be accounted for by the linear combination of affective variables and demographics of interest. Correlation between variables is also given in Table 2.

Table 2: Correlation between Variables. 

As seen from Table 2, apart from the correlation between school type and achievement, self-efficacy, and anxiety, there is a significant correlation between variables. In addition, as observed in Table 3, except school type, all other variables made a statistically significant contribution to the prediction of achievement scores. From standardized beta values, it was found that self-efficacy (β = .314, p = .000), anxiety (β = -.135, p = .000), attitude (β = .224, p = .000) and gender (β = -.063, p = .021) significantly predicted achievement scores. Anxiety had negative beta values. That is, for anxiety, negative beta indicated that high anxiety scores accounted for low achievement scores. On the other hand, for gender, negative beta indicated that males’ achievement scores were higher than that of females. According to these B weights, the regression equation is as follows:

Achievement = .048efficacy ? .009anxiety+ .046attitude? .318gender + 6.604

Table 3: The Results of the Multiple Linear Regression Analysis for the Predictors. 

According to Table 3, self-efficacy was recorded the highest part correlation coefficient, (Part-R = .210, p < .001), indicating that self-efficacy uniquely explains 4.5 percent of the variance in achievement scores. Moreover, anxiety had a moderate part correlation coefficient, (Part-R = -.110, p < .001), indicating a 1.2% contribution of total variance to achievement scores. Similarly, attitude scores reported the lowest part correlation coefficient, (Part-R = .144, p < .01), indicating a 2.1% contribution to total variance. Besides, gender was recorded the lowest significant part correlation coefficient, (Part-R = -.061, p < .01), meaning .4% of variance in achievement scores could be explained uniquely by this variable; yet, the school type did not make a significant contribution to total variance.

Discussion

The results revealed that there was a significant mean difference between males and females regarding their mathematics self-efficacy scores, favoring males. The fact that males outperformed females in mathematics self-efficacy beliefs was consistent with previous studies (^{Ferla et al., 2009}; ^{Louis & Mistele, 2012}; ^{Peters, 2013}). For instance, it was found that males in high school were superior over females in mathematics self-efficacy scores (^{Hyde et al., 1990}). This difference might be a reflection of the stereotype that males are better than females in mathematics. To state differently, ^{Moe and Pazzaglia (2006}) stated that if in a specific task gender difference is mentioned, the task can motivate students and enhance the quality of performance. Therefore, males might have felt themselves more confident in mathematics than females. On the contrary, if the superiority of opposite gender is stressed, the subject matter can demotivate students and reduce their performance. Thus, in the present study, based on the cultural factors some of the female participants might have felt inferior to males in mathematics by their parents, teachers or peers in their school and daily life. This might have influenced females’ motivation negatively for learning mathematics and decreased the amount of time and energy that they spent on mathematics. Additionally, it is possible that males’ higher mathematics performance leads to higher self-efficacy scores. Therefore, in the future, researchers should investigate how gender differences in mathematics achievement is associated with mathematics self-efficacy at different grades.

In the present study, anxiety levels of females were found to be higher than males, which was consistent with other research findings (^{Bonnstetter, 2007}). One possible reason for this gender difference in mathematics anxiety might be biological. That is, the difference might stem from genetic sex hormones. ^{Seeman (1997}) explained, “The estrogens are neuroprotective with respect to neuronal degeneration, growth and susceptibility to toxins. The cyclic fluctuations of estrogens enhance the response to stress, which confers susceptibility to depression and anxiety” (p.1641). Another reason for the gender difference in anxiety might be psychosocial. That is, social roles in the culture and experiences might be an important factor for the gender difference in mathematics anxiety. Historically, boys are given more freedom, authority and responsibility than girls in Turkish culture. Hence, boys may not hesitate to take risks; whereas, females may take less or even none. Therefore, males feel less anxious to try when they meet a challenging task. This might be the reason of males’ lower anxiety scores in this study.

Another concern for gender difference was to investigate mean difference in seventh grade males’ and females’ attitude towards mathematics scores. Results showed that there was a significant mean difference in attitude scores of males and females. In particular, females’ attitude towards mathematics was higher than that of males. The fact that females outperformed males on attitude scores contradicts with earlier studies that reported males’ superiority in attitude scores (^{Asante, 2012}; ^{Michelli, 2013}; ^{Tasdemir, 2009}). However, there exist some recent studies favoring females’ attitude towards mathematics in elementary years (^{Savas & Duru, 2005}). Savas and Duru (2005) reported that females’ attitudes towards mathematics were higher than that of males and females also had a significantly more positive career interests related to mathematics than males. The source of this difference might be attributed to the large number of female mathematics teachers in Turkish classrooms. According to the Turkish Ministry of National Education (MoNE, 2013a), the number of female mathematics teachers in elementary and middle schools has been increased. When the teachers’ influence as a role model on students’ expectations, attitudes and future career plans is considered, this might enhance females’ emotional disposition toward mathematics positively. Hence, this may explain the superiority of female students’ attitudes towards mathematics in this study. In other way, gender difference regarding mathematics achievement also supports the finding concerning self-efficacy and mathematics anxiety. In other words, findings of the present study show that there was significant mean difference in mathematics achievement scores of males and females. Males outperformed females with respect to mathematics scores. The fact that males are superior in mathematics supports the findings of previous studies (^{Alacaci & Erbas, 2010}; ^{Clewell & Campbell, 2002}; ^{Robinson & Lubienski, 2011}; ^{Soleymani and Rekabdar, 2016}; Tasdemir, 2009). This difference might stem from the sociocultural practices and stereotype effect. In particular, the stereotype that boys are better in mathematics is still alive and strong. A possible reason of this difference might be the biologically secondary mathematics abilities. ^{Geary (1996}) stated that males and females have two sets of mathematics abilities: Biologically primary and biologically secondary mathematics abilities. It was noted that biologically primary mathematics abilities were innate set of mathematics characteristics such as numeriosity, ordinality, counting and simple arithmetic which should explain why young males and females perform similarly in school mathematics. On the contrary, biologically secondary characteristics were more complex algebra and calculus skills. These skills are fostered when the learner participate and interact with the relevant sociocultural practices (Geary, 1996). Male students’ significantly higher performance over female students in the present study can be explained by Geary’s view that sociocultural practices might have enhanced the development of male students’ secondary mathematical abilities more than female students’ abilities. Moreover, the difference in mathematics achievement might stem from genetics of males and females (^{Kimura & Hampson, 1994}). That is, in the literature, it was claimed that the left hemisphere of an individual realizes for analytical/logical thinking in both verbal and numerical operations while right hemisphere is specialized in social tasks, artistic efforts and body image (^{Capraro, 2001}). In particular, males are more likely to use their left hemisphere (Kimura & Hampson, 1994) and hence they become more advantageous over females in mathematics (Capraro, 2001).

The findings also indicate that students’ attitude towards mathematics were differentiated in favor of private schools, while there was not a significant influence of school type on mathematics self-efficacy beliefs, mathematics anxiety and mathematics achievement. This result partially contradicts with previous studies reporting significant difference with respect to mathematics achievement between public and private schools favoring public school students (S. ^{Lubienski, C. Lubienski, & Crawford Crane, 2008}). It should be noted that the Lubienski study was conducted in the US; but, the present study was carried on with Turkish students. It is possible that Turkish private and public schools provide similar learning opportunities for students; therefore, school type differences did not exist in the Turkish context. One other possible explanation for the lack of school type effect might be the fact that the differences in affective variables and achievement regarding gender do not appear until late elementary years. To state differently, both male and female students’ emotions, feelings and beliefs about mathematics begin to shape through high school years because it was found out in a study conducted in the US that males in high school were superior over females in mathematics self-efficacy scores (^{Hyde et al., 1990}). Therefore, in line with these views, one can conclude that students in different type of elementary schools might have similar achivement scores, expectations and beliefs towards mathematics during primary and elementary years. Hence, this might lead to similar confidentiality or fears and worry on mathematics performances of seventh grade students in both public and private schools.

The results also showed that seventh grade students’ attitudes towards mathematics were significantly different with respect to school type. In particular, private school students’ attitudes towards mathematics were higher than that of public school students. One possible reason for this difference might be the fact that private schools are commercial business enterprises; that is, to be able to enhance their market price and gain more students, emotional and academic satisfaction may be given more importance in private schools than in public schools. For this purpose, investments in technology and physical facilities have been made by private schools to enhance the quality of education and draw parents’ attention to school as well as students’. Hence, these facilities might enhance the private school students’ emotional dispositions towards mathematics more than public school students’.

The last aspect of the present study was investigating the role of personal factors (self-efficacy, anxiety and attitude) and demographics (gender and school type) on predicting mathematics achievement. The provided model significantly predicted mathematics achievements of students and each variable except school type made significant contribution to mathematics scores of students. This result is consistent with previous research supporting the influence of self-efficacy, mathematics anxiety, attitude and gender in predicting mathematics achievement (^{Schunk & Mullen, 2012}). In addition, self-efficacy produced the highest unique contribution. This supports findings of studies that have reported that self-efficacy is one of the best predictors of achievement (^{Pajares & Miller, 1994}). On the other hand, school type does not have significant contribution in explaining mathematics performance. The reason might be the fact that the gap between public and private schools’ level of achievement is getting smaller with the reform movements in Turkey. In fact, the Turkish Education System promotes equal educational opportunities and excellence which can balance the achievement levels of private and public schools (C. ^{Lubienski & S. Lubienski, 2013}). For instance, the nationwide mathematics curriculum highly promotes use and implementation of reform-based mathematics teaching ideas in all type of elementary schools (^{Koc, Isiksal, & Bulut, 2007}). In addition, all students in different schools are provided with the same mathematics textbooks for free. That is, students in private and public schools have similar educational opportunities. This might be an indication of similar mathematics performances in public and private schools (C. Lubienski & S. Lubienski, 2013).

Conclusion

As discussed above, females and males differ significantly regarding their self-efficacy and mathematics anxiety scores. Females’ relatively lower self-efficacy and higher mathematics anxiety scores indicate that school curricula and other programs should be designed in a way to help improve females’ beliefs about their own competence in mathematics and diminish their level of anxiety in dealing with mathematics-related tasks. For example, adapting the cognitive level of mathematical tasks to students’ needs, interests and skills could be a viable way to help females as well as males find some value in learning mathematics and improve their self-beliefs. In Turkey, school mathematics curricula highly encourage teachers to consider individual, cultural and gender differences as assets of classroom rather than some sort of disadvantages (^{Koc et al., 2007}; MoNE, 2013b). In fact, in the present study, females’ attitude towards mathematics was found to be more positive than males; so, it is believed that it may be relatively easier to help them improve their self- efficacy beliefs and decrease anxiety levels. Having positive attitudes may increase the likelihood of developing self-efficacy beliefs and decreasing anxiety. Lastly, in-service teacher education programs should be designed in a way to help teachers understand the fact that all students can enjoy and do mathematics. The classroom environments should promote the substantial participation of all students regardless of their gender.

In Turkey, only a small fraction of elementary and middle school schools are privately managed (MoNE, 2013a); all others are financed by public sources. Private schools are generally known as providing high quality education and supporting students’ individual and social development better than public schools; on the other hand, results of nationwide standardized assessments show that public and private schools’ performances are not much different from each other. This observation was also supported with the findings of the present study; yet, participants from private schools show a significantly higher level of positive attitude towards mathematics. Although the findings cannot be generalized to the entire country, based on the significant results, public school students’ relatively negative attitudes should be addressed at all opportunities. Knowing the fact that attitude towards mathematics at least partly predicts student involvement in mathematics and mathematics achievement, learning environments should support students’ enjoyment of mathematics.

Although the present study provided interesting findings that contribute to the literature and teaching practices, there is still more to do. Conducting comparative studies investigating both cognitive and non-cognitive constructs is necessary to better understand how various variables interact in different cultures. In the present study, we studied the Turkish context, a relatively more collectivist society; future studies can compare such collectivist social groups with more individualistic cultures. Also, it is suggested that future studies may consider interviewing some of the participants about reasons of low self- efficacy and high mathematics anxiety. Such studies may uncover some of the causes of individuals’ self-beliefs and emotions in learning mathematics. Another future research question could be if the relation among emotional variables and math performance is moderated by gender and school type.