This thesis examines students’ experiences of learning to teach mathematics as they complete a primary Postgraduate Certificate in Education to gain qualified teacher status. The research data are drawn from students’ accounts of learning to teach mathematics, which include email communications during their studies and interviews with eight students at the end of the course. Analysis is informed by post-structuralist feminist understandings of discourse, power and knowledge. These tools are used to explore the complexities of learning to teach, the ways in which beginning teachers are ‘produced’, what counts as mathematics and the effects of power relations within pedagogical encounters. I use a reflexive approach to methodology, acknowledging the ways in which my own subjectivity permeates the enquiry, and the ways in which power permeates the research process. The study found performances of gender in students’ accounts of their experiences of the course, both on campus and in schools. Dominant discourses of teaching and mathematics create tensions for students and act as a form of control and categorisation as they strive to be recognised as legitimate mathematics teachers. It is argued that students’ subjectivities are shaped by discursive practices and peer and pedagogical relationships in the context of the course and that students are constituted as mathematical subjects often in inequitable ways. They are both powerful and powerless in different instances as they take up competing discourses, positioning themselves and their peers in shifting locations. Some students are silenced, categorised and marginalised within discourses of mathematics. Most report complying with the established practices of the school and class teacher and focused on the struggle to achieve legitimacy as successful student teachers. They 2 demonstrate both compliance with and resistance to dominant discourses as they are caught between the tensions and inconsistencies of competing and conflicting discourses. A key implication of this study is that teachers, teacher educators and student teachers need opportunities to explore their own gendered subjectivities as learners and teachers and to acknowledge that learning to teach mathematics is not solely a cognitive endeavour but one deeply located in social relations and contexts. Within teacher education more spaces need to be opened up to enable student teachers to embody themselves as mathematics subjects and primary teachers differently.

This thesis reports empirical and theoretical research into learning of mathematics and statistics at university level, with particular regard to students views of their self-confidence and experiences, and the effects of these on achievement. This study was conducted at a time of widespread national concern about difficulties in mathematics education in England, particularly at the transition from school to university Science, Technology, Engineering and Mathematics (STEM) courses. Factors which affected non-specialist students learning of mathematics and statistics were investigated using student surveys in 2004/5, 2005/6 and 2006/7 (701 questionnaires) in the a-typical setting of a University College specialising in rural and land-based higher education. 52 student interviews were also carried out, primarily in 2008 and 2009, and are referred to but are not the main focus of this thesis. Both deductive and inductive approaches were used. Self-confidence was defined using three Mathematics Self-confidence Domains: Overall Confidence in Mathematics, Topic confidences for specific tasks, and Applications Confidence. Self-confidence was considered a belief, whilst liking of the subjects was an attitude, both forming part of affect , where affect comprised beliefs, attitudes and emotions. Student motivation was also investigated. The survey data, and examination and assignment marks, of engineering students learning mathematics and other non-specialist students learning statistics, were analysed both quantitatively (by descriptive statistics, ANOVA, Kruskal Wallis, Correlation, Multiple Regression, Factor and Cluster analyses) and qualitatively. Previous success in mathematics, primarily GCSE Mathematics grade, was found to be the greatest determinant of university students success in mathematics and statistics, but self-confidence and other affective variables also had significantly measurable effects. Significant effects on student confidence were also found for gender and dyslexia despite good achievement. Findings indicate that students self-confidence in mathematics does matter, as evidenced by significant relationships between confidence and achievement, but it was also concluded that these inter-relations were complex. Educators are encouraged to adopt student-focussed teaching styles which improve students self-confidence as a means to improving attainment.

Mathematical reasoning can be considered to be the pursuit of a line of enquiry to produce assertions and develop an argument to reach and justify conclusions. This involves processes such as conjecturing, generalising and forming arguments. The pursuit of a line of mathematical reasoning is not a routine process and perseverance is required to overcome difficulties. There is a lack of research on pedagogy to foster children’s perseverance in mathematical reasoning, hence this study sought to answer the research question: how can primary teachers improve children’s perseverance in mathematical reasoning? The study took place in two year 6 classes in different English schools. The study group comprised eight children, purposively selected for their limited capacity to persevere in mathematical reasoning. An action research approach was used to develop and evaluate two interventions. Data relating to the children’s cognitive and affective responses and the focus of their attention, a conative component, were collected by observation and interview. Data analysis synthesised the children’s reasoning processes with their affective responses and their conative focus. The use of this tripartite psychological classification to analyse children’s mathematical reasoning offered a new approach to analysing the interplay between cognition and affect in mathematics learning and revealed the role that engagement and focus play in both restricting and enabling children’s perseverance in mathematical reasoning. The interventions comprised providing children with representations that could be used in a provisional way and embedding a focus on generalising and convincing in mathematics lessons. These enabled children to improve their perseverance in mathematical reasoning; they were able to strive to pursue a line of enquiry and progress from making trials and spotting patterns to generalising and forming convincing arguments. This study found that children were not necessarily aware of when they encountered a difficulty. This lack of cognisance impacted on their capacity to apply the self-regulatory actions needed to monitor and adapt their use of reasoning processes. One outcome of this was that they tended towards repetitious actions, in particular, creating multiple trials even when they had spotted and formed conjectures about patterns. Their perseverance in mathematical reasoning was further compromised by their enjoyment of repetitious actions. When the children engaged in activities involving reasoning, their common affective response was pleasure, even in instances when they demonstrated limited perseverance. However, when they were able to persevere in reasoning so that they generalised and formed convincing arguments, they expressed pride and satisfaction. They attributed these emotions to their improved mathematical understanding. The bi-directional interplay between children’s cognition and affect in mathematics is discussed in literature; however, the impact of children’s focus on their cognitive understanding and affective experience augments existing literature.

The purpose of this study was to investigate the effects of teaching linear equations with Dynamic Mathematics Software (GeoGebra) on seventh grade students&rsquo / achievement compared to the regular instruction. Randomized posttest-only control group design was utilized in the study. 60 seventh grade students (32 girls and 28 boys) of a public school in Yenimahalle district in Ankara participated in the study. The study was conducted in 2011-2012 fall semester, lasting 9 class hours in three weeks. The data was collected by three Mathematics Achievement Tests: Cartesian coordinate system achievement test (MAT1), linear relation achievement test (MAT2) and graph of linear equation achievement test (MAT3). The quantitative analysis was conducted by using analysis of covariance (ANCOVA). The results revealed that teaching Cartesian coordinate system and linear relation by using Dynamic Mathematics Software had no significant effect on seventh grade students&rsquo / achievement compared to the regular instruction. On the other hand, the results also indicated that teaching graph of linear equations by using Dynamic Mathematics Software had a significant effect on seventh grade students&rsquo / achievement positively.

Investigating the teacher education phenomenon of mathematics teacher education through the perspectives of teacher educators was aimed in this study. It was designed to understand the problems and the needs of teacher education in Turkey, to conceive the imperatives of the reforms mathematics teacher education reforms, namely 1982 reform, 1998 reform, and 2006 reform, and to determine whether these reforms satisfy the existing needs in Turkey. Based on the principles of qualitative research methods, documents of mathematics teacher education programs were investigated after the date when teacher education has been replaced under universities. As a second data collection tool, interviews with past and present deans of the education faculties, department chairs of mathematics education departments, and the academic staff were conducted. The data collected were analyzed through qualitative data analysis methods and the meanings and importance of the imperatives, processes, and consequences of the reforms were explored as well as the problems and the needs of teacher education in Turkey and solutions for them were investigated. The findings of this study showed that mathematics teacher education took a great step after establishing education faculties under universities in 1982. However, it has to be improved in order to eliminate the problems and the needs of teacher education in Turkey. It was expected to develop a source for the future teacher education reforms while paying attention to the imperatives and the consequences of educational changes in 1982, 1998 and 2006, and to be beneficial to generate a Turkish teacher education framework.

This thesis contains ten chapters: three of them are background literature and five have resulted from practical work during the whole period of the research. Chapter 9 is an attempt to extend the idea of the demand of a task, while the last chapter contains conclusions and suggestions for further research. In Chapter 1, the theories of Piaget, Gagne and Ausubel are described and compared with each other. Piaget's stages of intellectual development and how learning processes take place are described and explained. The contribution of the theory in the domains of curriculum, teaching Piagetian tasks as subject matter and matching instruction to development stages is stressed. However, the serious challenges to the theory are (i) horizontal decalage phenomenon, (ii) relating stages with age, (iii) assessing competence and readiness. Gagne's model of an hierarchy of learning comes from theories of transfer. It is built from the top down. The conditions of learning are internal and external and ranged from signal learning to problem solving. The learning process is based on associational chains. The difficulty of the model comes from the nature of a learning hierarchy and its validation. Ausubel's theory of meaningful learning is based on what the learner already knows. It is built up from seven elements which range from meaningful learning to the advance organizer. Meaningful learning occurs as a result of interaction between new and existing knowledge and its variation is due to the growth of differentiation and integration of relevant items in cognitive structure. Failure in learning may occur in situations such as those of conflicting ideas and forgetting. In Chapter 2, Information Processing Theories of Learning are described and the justification of these theories as a fourth paradigm to guide thinking about research is stressed. A model of human memory is given and the components of memory and their features are listed. Stress is placed upon the memory processes and their levels, organization of knowledge, working memory and chunking as a remedy for overload. Two examples of these theories are given namely Neo-Piagetian Theory and the Predictive Model of Holding-Thinking Space. The main goal of the former is to make Piaget's theory functional not just structural. The latter relates performance to the amount of information to be processed in learning and problem solving. This model is applied in both University and Algerian samples. This can be found in Chapter 3. In Chapter 4, the field dependent-independent cognitive style is considered as an important factor affecting performance. The differences between field dependent-independent people may be related to the perceptual field, selected information and the level of guidance. The reason for these differences may be due to the way in which information is both analysed and represented in memory. The practical work has been done with both University and Algerian samples. In Chapter 5, some other factors are described. Most of them are concerned directly with the subject matter. The activities involved in learning mathematics are classified and attention is given to Polya's version of heuristic strategies. The concept of understanding is considered as a basic goal of education and its meaning is given in three different aspects. Most attention is given to the third one, which is known as alternative framework or misconception. The levels of understanding of Skemp are defined and their goals are stressed. The causes of learning difficulties in mathematics are listed, while the different forms of mathematical language are described and their effect on learning is noted. In Chapter 6, the analysis of Paper I (multiple-choice questions) has been done for preliminary Examination of four Scottish schools (a fifth school used only traditional questions). The experimental work is concerned with language, formulation and type of question.

Thesis (M.A.)--University of Toronto, 2006. / Source: Masters Abstracts International, Volume: 44-06, page: 2527. Includes abstracts in English and Hungarian.

Thesis (M.A.)--University of Toronto, 2004. / Adviser: Ruth Childs.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M. Ed.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 70-77).