A thesis submitted in fulfilment of the requirements for the degree of DOCTOR OF PIIILOSOPHY in the SCHOOL OF SCiENCE EDUCATION (MATHEMATICS) UNIVERSITY OF THE WITWATERSRAND / Cognitive gender differences in mathematics, which were noted in past research have latterly been found to be declining. but are still observed at secondary school level in the field of spatial skills and geometry. However, due to divergent geometry curricula and the multidimensional nature of spatial skills, results from gender studies have led to broad conclusions being drawn from investigations which were affected by random elements. Research results have been influenced by imbalanced representation of the two gender groups in samples and also by differential gender exposure to previous mathematical experience. Both these limitations in research have produced outcomes reflecting negatively On females. Internationally divergent geometry curricula are a result of the traditional synthetic approach to the teaching of Euclidean geometry falling Into disfavour in western countries. Thus, Euclidean geometry has been largely overlooked in current educational research and the cognitive processes such as deductive reasoning, proof writing and hypothesis testing, have received scant attention within geometry teaching over the past decade. The standardized system in most South African secondary schools coupled with a uniform core curriculum for mathematics lends itself to an advantageous environment for empirical studies in mathematics performance. The present gender investigation involved almost an equal number of males and females from 5' selected secondary schools near Johannesburg in South Africa. Performance in Euclidean geometry was evaluated for possible gender differences by means of multiple choice and open ended questions. In keeping with most existing research, mean differences were compared. No statistically significant gender difference in mean performance on Euclidean geometry was found. Further analysis at item level was undertaken for the multiple choice component of the test instrument by means of the one dimensional three parameter logistic model in Item Response Theory, This model, is considered to be very sensitive in identifying differences at different ability levels -a shortcoming in existing research. Four out of a total of twenty Euclidean geometry items, were identified as producing differential gender performance. Similar gender tendencies were observed for all four items. The performance was in favour of most males for each of these items. Females of lower ability (as measured by the item) did not perform as well as males of similar ability level. In all four Cases females of higher ability surpassed males of a corresponding ability level. Perceptual difficulties in females were more pronounced than in males for some of the items. / AC 2018

Female students continue to lag behind their male counterparts in STEM degree attainment despite performing as well as boys in mathematics and science in high school. Female students who expressed interest in mathematics and science may opt out of majoring in STEM once in college. Given that women may not be perceived as mathematics doers, this perception may affect their decision to pursue STEM careers. In many instances, it is the parents’ encouragement that helps their children to be persistent in mathematics and science. It is important to understand how parents’ involvement in the lives of high-achieving female college students contribute to them persisting and belonging in the STEM domain. In this narrative study, I explored parental influence on mathematics performance, self-efficacy and the factors that may contribute to high-achieving female college students’ interest and persistence in the STEM domain. The participants are eight high-achieving female students from an urban community college who are matriculated STEM majors. This study used Eccles et al.’s (1994) Expectancy-Value Theoretical Model of Achievement Choices and Phelan, Davidson & Yu’s (1998) Multiple Worlds Model to explore parent involvement and the factors that contribute to high-achieving college female’ persistence in STEM. Narratives of the female students’ mathematics experiences were constructed from data collected through multiple sources: student interviews, a parent interview, mathematics autobiographies, and questionnaires. Findings indicate that parents and other family members played an integral role in the students’ mathematics performance, mathematics self-efficacy and persistence in STEM. Furthermore, the depth of parental involvement of several of the participants was consistent throughout their college years.

Applying mathematics to real world problems, mathematical modeling, has risen in priority with the adoption of the Common Core State Standards for Mathematics (National Governors Association and the Council of Chief State School Officers, 2010). Teachers are at the core of the implementation of the standards, but resources to help them teach modeling are relatively undeveloped. This multicase study explored the perspectives of teachers regarding mathematical modeling pedagogy (the modeling cycle), instructional materials, and professional collaboration, with the assumption that understanding teachers’ views will assist authors, publishers, teacher educators, and administrators to develop better support for modeling instruction. A purposeful sample of six high school mathematics teachers from a variety of school settings across the country was interviewed using a semi-structured protocol. A conceptual framework developed by applying the theories of Guy Brousseau (1997) to the modeling literature guided the analysis. Qualitative methods including elements of grounded theory were used to analyze the data and synthesize the study’s results. The research showed that teachers structure their instruction consistently with the modeling cycle framework, but it also uncovered the need for additional detail and structure, particularly in the initial steps when students make sense of the problem and formulate an approach. Presenting a modeling problem is particularly important and challenging, but there is inadequate guidance and support for this teaching responsibility. The study recommends the development of additional materials and training to help teachers with these steps of the modeling cycle. Furthermore, teachers find that modeling problems are engaging, and they help students make sense of mathematical concepts. Teachers would employ modeling problems more often if they were more available and convenient to use. The study recommends that features for an online depository of modeling materials be researched and developed, including a course-based, chronological organization, a diverse variety of materials and formats, and tapping teachers to contribute their lessons.

Turning to online educational technology is a growing trend in our society. In particular, many community college Mathematics Departments have adopted online preparation and rigorous enhancement platform (OPREP) such as WebAssign. Nationally educators are attempting to address the low passing rates in developmental mathematics. Developmental mathematics courses are the gatekeepers to higher education. Slow progression through these courses can adversely affect a student’s ability to persist to graduation, which in turn impacts an individual’s employment opportunities and quality of life. The literature shows that OPREPs are typically employed to replace the tedious and time-consuming task of grading paper-based homework. Ignoring the testing management features of an OPREP and limiting it to a web-based homework tool is a reflection on implementation strategy. The purpose of this research is to develop a grounded theory about effectively implementing OPREP, which is informed by the perspectives and beliefs of the developmental mathematics students who use them. This mixed method study critically analyzed the student comment sheets, student evaluations, and the responses from 129 Elementary Algebra students who completed a questionnaire about their experiences using WebAssign. Analysis through an adult learning theory lens revealed the central phenomenon of the students’ needs for immediate feedback and the role that feedback plays in facilitating self-regulated learning. The findings reveal that the nature of the feedback extended beyond correctness. Students preferred to use interactive step-by-step tutorials, practicing different versions of the problem and watching lectures more than any other learning tool. The instructor’s implementation was a point of emphasis for key students. Multiple repeaters of elementary algebra stressed the importance of the OPREP implementation strategy on their achievement. Comments range from differences in the availability and strategic deployment of the learning tools to proper instruction on how a student should use the OPREP. Although this study confirms a significant and relative large correlation between homework and an exit examination, it also shows that OPREP assessments such as quizzes and practice examinations have stronger positive correlations. Results showed that OPREP quiz average was the best sole predictor of student achievement. OPREP quiz average was also the only OPREP assignment category included as a predictor of student achievement in the best multiple linear regression model.

丁銳. / 論文(哲學博士)--香港中文大學, 2007. / 參考文獻(p. 161-168). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in Chinese and English. / Lun wen (zhe xue bo shi)--Xianggang Zhong wen da xue, 2007. / Can kao wen xian (p. 161-168). / Ding Rui.

published_or_final_version / Education / Doctoral / Doctor of Philosophy

M. Tech. Education / Given the challenges of shortage of skills as informed by low performance in Grade 12 Mathematics, it seemed appropriate that a study on factors behind poor performance in Mathematics amongst grade 12 learners be undertaken. The study explored various factors that contribute to poor performance of learners in Mathematics in grade 12.

published_or_final_version / Education / Master / Master of Education

published_or_final_version / abstract / toc / Education / Master / Master of Education

The aim of the study was to investigate whether self-regulated learners are developed in Grade 8 mathematics classrooms. The research was conducted at Khula High School, which is situated at Magabheni, near Umkomaas in Kwa-Zulu Natal. Qualitative research approach was adopted for the study. Data was collected through the observation of one Grade 8 mathematics class. A total of eight mathematics lessons were observed and a semi-structured interview was conducted with the mathematics teacher. The findings of the study reveal that the educator did try to develop self-regulated learners through the use of teaching strategies that match the requirements of Outcomes Based Education. / Thesis (M.Ed.)-University of KwaZulu-Natal, 2004.