A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 28 May 2016. / This qualitative study sets out to examine a teacher’s metacognitive preparation for and reflection on the mathematical content and pedagogy of a short series of Grade Six Probability lessons, with their contribution to the development of a general framework for lesson preparation from a metacognitive perspective. An action research methodology is followed in which teaching episodes are collaboratively assessed by a panel of three colleagues. These fora serve to enlighten the author of their observations after the preparation and teaching of a series of Probability lessons, which also capture audio data for deep reflections and dialogue post teaching and fora. The analysis of the data will serve as the foundation for the development of a metacognitive framework that teachers can use in their preparation for and reflection of lessons that will pay particular attention to higher cognitive engagement of teachers with content and facilitating lesson delivery, always striving for them to be of higher quality. The efficacy of this framework for the teacher-researcher’s teaching practice is also examined.

Humans are born with a basic sense of number. This number sense, which is now called the Approximate Number System (ANS), allows us to represent numerosity without the use of symbols. There has been a debate on whether this nonsymbolic ANS contributes to our symbolic mathematics skills, and the recent findings are inclined to support the link between the two. However, what remains unclear is the mechanism underlying the relationship between the ANS and our mathematics skills, and whether children with Mathematics Learning Disabilities (MLD) suffer from a defective ANS. The present thesis aimed at addressing the above issues in two studies. Study 1 aimed at identifying the mechanism of how the ANS contributes to children’s mathematics skills. A group of 210 kindergarteners were tested on their ANS acuity, number-numerosity mapping skills (measured by counting and estimation tasks), and their arithmetic skills. They were then re-tested twice when they were in Grade 1.Using Structural Equation Modeling, it was found that children’s ANS acuity in kindergarten predicted their arithmetic skills one year later, and the relationship was mediated by their number-numerosity mapping skills. This suggested that ANS may contribute to mathematics learning by enabling more precise mapping between number symbols and the corresponding numerosity representation, hence making numbers meaningful. Studies 2A and 2B aimed at verifying whether children with MLD suffered from deficits in their ANS as well as their number-numerosity mapping skills. The same group of participants was followed one more time in Grade 2. Using the standard low-achievement method (Study 2A) and a more data-driven method known as the latent class growth analysis(Study 2B), two groups of children with MLD were identified. Both groups of children had deficits in both the ANS and their number-numerosity mapping skills as compared with their normally-achieving peers. Other groups of low-achieving children were also identified, and their difficulties seemed to be contributed by factors other than their ANS. While one of the low-achieving groups seemed to have deficit lying mainly on the number-numerosity mapping skills, the other low-achieving group did not show any cognitive deficits but had much lower SES compared to other groups. The relationship between the ANS and children’s mathematics achievement was supported and elaborated in the present study. The findings not only articulated a potential mechanism of how children learned about mathematics, but they also allowed educators to have better understanding of the cognitive profiles of children with MLD, thus facilitating early identification and intervention. The different profiles of the low-achieving groups also highlighted the need for differential intervention for different groups of low-achieving children. / published_or_final_version / Psychology / Doctoral / Doctor of Philosophy

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This thesis is the result of some extensive research in England, Canada and the United States of America. Prominent educationalists were interviewed and research institutions were visited. Ideas and projects have been investigated and used to provide a foundation for remedial suggestions in the South African context. The nature of mathematics anxiety is fully discussed and provides a background to the complexities of the problem. The question of why mathematics is unique as a school subject is discussed and the manifestation of mathematics anxiety is described in terms of the interaction of socio-cultural, emotive, cognitive and educational influences. The measurement of mathematics anxiety is an important aspect of remediation and various assessment techniques are reviewed. Mathematics anxiety scales have evolved from scales measuring general and test anxiety. For the assessment of large groups the Mathematics Anxiety Rating Scale (MARS) or an adapted version of this scale is recommended whilst individual assessment is seen as the ideal when small groups of mathematics anxious pupils have been identified. Two adaptations of the MARS test were used in an exploratory study in a Durban primary school and a College of Education and the results of these tests are discussed. Treatment methods are categorised in terms of socio-cultural, emotive, cognitive and educational factors. In each category the idea of creating an awareness of the problem of mathematics anxiety amongst pupils, teachers and parents is seen as an important aspect of the remedial process. For this reason, background research and ideas are discussed before treatment methods are suggested. Intervention procedures involve general strategies as well as attention to individual difficulties. The importance of an early intervention programme is stressed but remedial methods are seen as flexible and adaptable to all education institutions. Proposed procedures are interrelated and overlapping In parts but provide a comprehensive answer to the complex problem of mathematics anxiety. The ultimate aim of a mathematics anxiety remediation programme should be to provide a better understanding of mathematics, a long-lasting improvement in mathematics ability and a greater enjoyment and appreciation of the subject. / Thesis (M.Ed.) - University of Natal, 1986

Bibliography: leaves 355-375. / 375 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / To establish that an increase in the level of anxiety causes a decrease in the level of achievement or whether a lack of achievement causes an increase in anxiety. / Thesis (Ph.D.)--University of Adelaide, Dept. of Education, 1998?

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The purpose of this study was to investigate student attitudes towards mathematics and mathematics anxiety. In the past, mathematics anxiety has been measured by using different instruments and characterized as a unidimensional construct. However, prior studies concerning mathematics anxiety have not established construct validity of the scales used. This study was designed to establish the construct validity of the scales used to measure mathematics anxiety and to investigate the possibility that it may be a multidimensional construct. A series of self-report questions and survey instruments was administered in 17 freshmen college mathematics classes containing 491 students. Eight instruments were selected, namely: (1) Usefulness of Mathematics, (2) Test Anxiety Inventory, (3) Mathematics Anxiety, (4) Adjective Check List, (5) Short-form Dogmatism, (6) Attitude Toward Success in Mathematics, (7) Effectance Motivation in Mathematics, (8) Confidence in Learning Mathematics. Factor analysis techniques were used to treat the data: (1) To analyze the scores from the eight tests and reduce the responses to six principal factors which describe the nature of mathematics anxiety, (2) To determine the strength of the relationships of these attitudes to sex, socioeconomic status, college curriculum, high school mathematics background, college grade point level and achievement in current mathematics courses. The results suggest that mathematics anxiety is a unidimensional construct related to students' attitude towards mathematics more than to their personality characteristics. A finding contrary to the literature was that females did not suffer mathematics anxiety more than males. Recommendations arose from consideration of which attitudes in the mathematics anxiety complex were potentially modifiable by educators. It was recommended that schools actively seek to improve these attitudes. It was also recommended that females be encouraged to success in mathematics and that colleges seek to identify and help entering students who exhibit mathematics anxiety. / Ed. D.

The purpose of this study was to identify factors that are associated with encourage the persistence of undergraduate women majoring in Engineering and Math (EM) at Florida Atlantic University, University of Central Florida, and University of South Florida. The persistence factors were examined through an analysis of university data and the use of a survey for enrolled senior standing students who declared their first major in engineering or math. Both quantitative and qualitative methods were utilized to collect and analyze data from the three sites. Factor analysis and logistic regression were used to analyze the quantitative data. The quantitative data retrieved from the survey instrument revealed that participants who were self motivated, felt they had a safe learning environment, and were engaged by the university were more likely to persist in engineering and math. Additionally, the survey revealed that race and ethnicity does not predict persistence of undergraduate women maj oring in engineering and math. Qualitative analysis of open-ended survey questions revealed that the most important factor that helps female students persist in engineering and math major was self-confidence and determination. They also indicated that discrimination and stereotyping were the most difficult factors for female students to overcome. To enable more women to be successful in the pursuit of a engineering or math degree, participants made an overwhelming reference to intervention as student engagement. / Student engagement consists of the following: outreach programs, support programs, study groups, homework sessions, women clubs, engineering or math clubs, math and sciences activities, math and science tours, engineering and math societies, educational programs focusing on engineering and math, online courses, women organizations in STEM, positive role models, female teachers, women mentors, exposure to engineering and math, and expanding the career outlooks of young women. They suggested that student engagement must start early and must be continuous throughout every level of the educational pathway and professional life. Recommendations are provided for policymakers and university administrators to continue supporting women majoring in EM and to increase awareness and access that encourage persistence of women in the pursuit of EM career goals. / by Jessica Pena-Lopez. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

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