Thesis advisor: Marina Vasilyeva / This research explored the nature of gender differences in math performance across development. It examined potential mechanisms underlying gender differences by testing a mediation model in which females' higher anxiety taxes their working memory resources leading to underperformance on a mathematics test. Further, this research examined stereotype threat effects on math performance by testing whether female students presented with a scenario activating the stereotype would perform worse than females not exposed to the stereotype. Participants in Study 1 were 71 fourth, 107 eighth, and 147 twelfth grade students from high performing school districts. Students completed anxiety measures and a challenging mathematics test either in the stereotype threat condition or the no-threat condition. Results showed that there were consistent gender differences in math performance across all three grade levels; however, stereotype threat did not impact girls' math performance. Importantly, the relation between gender and math performance at the eighth and twelfth grade levels was mediated by the worry component of anxiety. This finding suggests that girls' heightened worry can explain their underperformance on a math test. In Study 2, the mediating relation observed in Study 1 was further explored by testing whether working memory mediated the relation between worry and math performance. Participants were 90 college students who were assigned to either the stereotype threat or no-threat condition. Students completed anxiety measures, two working memory tasks (verbal and visual), and a challenging math test. Again, findings showed a significant gender difference in math performance but no stereotype threat effects. Further, there was a mediating chain from gender to the worry component of anxiety to visual working memory to math performance. The results suggest that females' heightened worry taxes their working memory leading to gender differences in math performance. Both studies contribute to our understanding of affective and cognitive factors underlying gender differences in math performance. The findings of this research are discussed in terms of their implications for interventions and the future of women's participation in STEM careers. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Lynch School of Education. / Discipline: Counseling, Developmental, and Educational Psychology.

Self-efficacy is individuals' judgments regarding their capabilities to carry out future tasks or challenges. These judgments of capability are related to important learning behaviours such as effort and persistence, performance, and choice of career path. In order to support students' continued engagement with and learning of mathematics, it is important to consider how students make sense of their mathematical experiences as well as the relationship between students' mastery experiences and mathematics self-efficacy. In this thesis I address important gaps in the literature in regard to the conceptualisation of the self-efficacy construct, the relationship between self-efficacy and mathematics performance, the stability and change of self-efficacy when learning new topics in mathematics, and self-efficacy development over a series of lessons in mathematics across cycles of self-efficacy and mastery experiences. The thesis included two phases of data collection and analysis. The first phase involved students in grades 5, 8, and 9 (N = 756) and included measures of students' self-efficacy and national test performance. The second phase involved students in grades 6 and 10 (N = 181) and included repeated measures of students' self-efficacy and mastery experiences from a series of lessons in mathematics, when students were introduced to new topics. I analysed the data using different methods, including confirmatory factor analyses to investigate the structural validity of my measures, and structural equation models to investigate stability and change over time, and relationships between constructs. Major findings from the analysis include the following: students considered levels of difficulty when appraising their experiences in mathematics and when forming their self-efficacy; students' test performance predicted their self-efficacy one year later, but not the other way around; the mean-level of students' self-efficacy grew significantly across lessons when students were introduced to new topics, even as the rank-order of their self-efficacy remained highly stable; and there was a reciprocal relationship between students' self-efficacy and their mastery experiences, where substantial effects from both constructs on gains in the other construct remained stable across a sequence of lessons in mathematics. The findings have important implications for how we conceptualise self-efficacy, mastery experiences, and their relationship over time. Furthermore, the findings from my thesis have implications for teacher practice. In order to support adaptive self-efficacy, teachers need to consider the experiences students have with mathematics, not just the skills they learn. If teachers themselves gain knowledge about how individual students make sense of their mathematical experiences, they can support students' appraisals of these experiences, and prevent maladaptive cycles from occurring. In short, students need support not just to develop their mathematical skills, but also to develop adaptive appraisals of their mathematical experiences, in order to form self-efficacy beliefs that are reflective of each student's potential to learn mathematics.

Growth mindset interventions have been shown to give small but significant boosts to mathematics performance. These interventions are both brief and cheap, making them attractive for boosting mathematics performance. Is it possible that South African students can benefit from a growth mindset intervention? Mindset assessments and interventions have predominantly been developed in the United States. There have been applications of the assessments and interventions to other cultural contexts, often with minimal adaptions. Adaptions are not reported in detail (or thoroughly evaluated) in existing research literature. In a series of four studies, I establish that South African high school students do have mathematics mindsets akin to the fixed and growth mindsets reported elsewhere. Using an iterative design process and item analysis, I modified a mathematics mindset assessment for use with disadvantaged students in South Africa. In two correlational studies I established validity and reliability for a mindset assessment I call “Thinking About Maths”. I examined the contribution of mathematics mindsets to mathematics performance, in comparison with mathematics anxiety, study attitude and study milieu (or environment). I found that whilst mindsets do contribute to performance, the contribution is minimal compared to other variables measured. Additionally, I found that in an impoverished study environment males have high mathematics anxiety which inhibits mathematics performance whereas females have high study attitude, boosting mathematics performance. With assistance from students and teachers, I developed a mindset intervention that is culturally appropriate and relevant. 305 Grade 9 students participated in a field-based quasi-experiment, which had a passive control group. The intervention was delivered on WhatsApp over four weeks. Each week contained a growth mindset message, a YouTube clip, advice on a learning strategy, and an integration activity. The groups were facilitated by young adult mentors. It was clear that WhatsApp groups were an effective mode of delivery and there was good evidence of participation from students. Mathematics performance at the intervention school improved significantly beyond that of the control school. The strength of the intervention seems to lie in the combination of mindset messaging and the teaching of effective strategies.

This study is limited to the mathematics performance of two intact groups of culturally deprived kindergarten students, mostly blacks, with a few whites and Mexican-Americans, who were enrolled at Robert E. Lee Elementary School (Denton, Texas) for the entire school year of 1970-1971. The purposes of the study are to compare the effectiveness of two methods of teaching mathematics to culturally disadvantaged children and to check for interaction of treatments when these children are classified by sex.

This thesis systematically examined the link between developmental dyscalculia, a specific learning difficulty of mathematics, and mathematics anxiety, a negative emotional reaction to mathematics tasks. The link between these maths learning issues was examined by measuring their prevalence in large samples of English primary (N = 1004; N= 830) and secondary school (N = 927) students. Gender differences were also explored. Systematically varying diagnostic criteria for dyscalculia revealed that its prevalence ranged between 0.89-17.23 percent. When absolute performance thresholds were used, there was no gender difference in dyscalculia prevalence. The association of mathematics performance with other cognitive skills and mathematics anxiety was investigated longitudinally in subsamples of children with dyscalculia (n =10), typical mathematics performance (n=10) and high maths ability (n = 11). 80 percent of the children in the dyscalculia group still met the criteria for diagnosis at the final time point. Mathematics performance was positively associated with working memory performance and negatively associated with mathematics anxiety. Furthermore, children with dyscalculia had higher maths anxiety than the other two groups. The relationship between dyscalculia and high maths anxiety was estimated in a larger sample (N = 1757). Relatively few children with dyscalculia had high maths anxiety and the majority of students with high maths anxiety in fact had mathematics performance within or above the average range. Girls had higher maths anxiety than boys, and more girls had both dyscalculia and maths anxiety than boys. There was an expected negative correlation between maths anxiety and maths performance in the total sample, but this correlation was negligible in the children with dyscalculia. Collectively, these results suggest that cognitive and emotional mathematics problems are dissociable, and indicate that children with dyscalculia and maths anxiety likely require different types of intervention. Furthermore there appears to be no gender difference in maths performance or in the prevalence of dyscalculia. However, girls have higher maths anxiety than boys, and are more likely to be affected by maths anxiety alongside developmental dyscalculia. Maths anxiety may be a potential explanation for the underrepresentation of females in careers involving mathematics.

The problem of this study was to determine if the mathematics achievement of selected second and third grade students is significantly improved by having had instruction in the Chisanbop technique. The purposes of this study were as follows: 1. To determine if the Chisanbop technique, when used in conjunction with a regular program of instruction, can significantly improve the mathematics performance of selected second and third grade students. 2. To determine if instruction by the Chisanbop technique is more effective with above average academic, average academic, or below average academic second and third grade students in improving mathematics performance. 3. To extend the body of knowledge with regard to the teaching of mathematics at the elementary school level.

Studiens syfte är att undersöka sambandet mellan elevers förståelse av formellt matematiskt språk och deras prestationer inom ämnet matematik. Syftet är också att förklara skillnaden mellan matematikens formella språk och det informella språket för att tydliggöra det matematiska språkets betydelse och reflektera över prestationer i matematik. Studien fokuserar på matematiklärare i årskurs f-3 och deras integration av matematiskt språk, samt hur de explicit förklarar detta formella språk för eleverna.

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The aim of the study was to investigate what influence the use of computers using MS Excel and RJS Graph software has on grade 11 Eritrean students' understanding of functions in the learning of mathematics. An empirical investigation using quantitative and qualitative research methods was carried out. A pre-test (task 1) and a post-test (task 2), a questionnaire and an interview schedule were used to collect data. Two randomly selected sample groups (i.e. experimental and control groups) of students were involved in the study. The experimental group learned the concepts of functions, particularly quadratic functions using computers. The control group learned the same concepts through the traditional paper-pencil method. The results indicated that the use of computers has a positive impact on students' understanding of functions as reflected in their achievement, problem-solving skills, motivation, attitude and the classroom environment. / Educational Studies / M. Ed. (Math Education)

Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2008