Understanding the processes that allow all students to successfully learn mathematics has been an important objective for most education systems including those in Canada. Educational systems however, have not achieved this goal as many students with low socioeconomic status, females, and minority students fail to achieve an adequate knowledge of mathematics. Much of the discussion regarding this lack of achievement concerns classroom resources and practices, school policies within educational systems, and the specific domain of mathematics achievement considered. This study conceptualizes a successful mathematics classroom in terms of its level of mathematics achievement and how equitably achievement is distributed. The study employs multilevel models and the Canadian data from the Third International Mathematics and Science Study to address three main research issues: 1) the extent to which differences in mathematics achievement is attributable to gender, family background, classrooms, and the province where a student attends school; 2) whether the variation in achievement is specific to a mathematics domain; and 3) whether the variation among six provinces (Newfoundland, New Brunswick, Ontario, Alberta, British Columbia, and Quebec) in the levels of their mathematics achievement is associated with various aspects of school policy and practices. The analyses indicate a slight male advantage in mathematics achievement, and a large, significant gap in achievement associated with the socioeconomic status (SES) of the students' families. Students from low SES backgrounds are disadvantaged as they tend to have relatively low achievement in mathematics within classrooms, especially in Proportionality, Measurement, and Fractions. The most successful classrooms are those in which students from disadvantaged backgrounds excel in mathematics. Disadvantaged students excel in mathematics classrooms in which there are fewer groupings, the mathematics teachers are specialized, and in schools with lower pupil-teacher ratio. Mathematics achievement is equitably distributed in provinces with high mathematics achievement levels. Provincial achievement levels are stable across mathematics domains; that is, provinces with high achievement levels in one domain also tend to have high achievement levels in other domains. On average, Quebec's mathematics achievement is higher than the other provinces in all mathematics domains, and at all levels of SES. This high achievement level in Quebec is partially attributed to higher teacher specialization, lower pupil-teacher ratio, and lower withinschool remedial tracking. The study recommends a comprehensive longitudinal study employing multilevel models with a focus on what other provinces can learn from Quebec's advantage in mathematics. Such a study should conceptualize successful mathematics classrooms as those in which an average student excels in mathematics and where mathematics achievement is equitably distributed.

This thesis reports on a qualitative study in which three fifth grade children were presented with six nonroutine mathematical problems involving six different 3-D pyramids, constructed out of multi-link cubes1. The children were videotaped while they worked without any adult help as a cooperative group to solve the pyramid problems. During these sessions, the students produced various 3-D cube models, 2-D drawings, and written records of arithmetic calculations as their solutions to the six problems. Through the lens of enactivism, this study describes and interprets the coevolutionary processes of the group's path of mathematical understandings as it unfolded during the six videotaped sessions. The results revealed building, drawing, and numbering as modes of representation of this group's problem solving work. An analysis of these three modes of representation explored the co-emergence of the children's individual and collective understandings, as well as the interrelationships which existed between their spatial structuring and their use of numerical operations in solving the pyramid problems.

This thesis begins with the premise that in order to be mathematical students must first discover and develop their creativity. Within the context of classroom-based action research, the following questions are examined: What is mathematical creativity? Under what conditions does mathematical creativity flourish? And, how is creativity manifested in young children? To this end, the definition of creativity is expanded to include those daily moments of discovery, where clarity is reached and we say, "Oh! I get it!" It outlines how an inquiry methodology increases creativity and allows students to view mathematics from a place of wonder and excitement. In addition, different language-learning strategies are used to gain insight into how these strategies helped a group of grade three French Immersion students begin to define themselves as mathematically creative. Furthermore, the thesis explores the importance of relationship, relevance and rigour in planning for creativity in mathematics. It explains why a culture of not knowing is crucial to the development of mathematical understanding and confidence in young children and how ambiguity, frustration and perseverance are necessary elements in creative thinking. Also, it considers the importance of second language development and its implications for mathematics. Finally, it suggests creativity in mathematics is possible if students use dialogue and reflection to explain how their thinking is changing, or what new things they are discovering about mathematics. / xii, 117 leaves ; 29 cm

The teaching and learning of mathematics has presented a great challenge for mathematics educationalists over many decades. Researchers have been searching for new strategies and techniques for improving the understanding of abstract mathematical concepts. With the current changes in the mathematics curriculum in South Africa, it is important to ensure that no learner is left behind in the pursuit to produce mathematically literate learners nationally. Teachers are encouraged to teach a common curriculum so that all learners have equal opportunities of attaining success in a democratic society in any chosen field. Some teachers achieve mathematical success easily while others struggle to achieve similar outcomes. Whilst we acknowledge that teachers ought to emulate the practices of other good teachers, we often do not seek explanations of what makes a teacher effective and how they achieve success in a classroom. As can be conceived, apart from probing teachers’ content knowledge, it is necessary to know how this knowledge can be used for optimal results in the course of teaching within the diverse South African classroom. In other words, it becomes necessary to interrogate the teacher’s pedagogical content knowledge because of the uniqueness of the South African context. It is for this reason that an in-depth study was done to explore Master teachers’ use of visuals as tools within mathematics classrooms. This study focused on six experienced mathematics teachers or Master mathematics teachers. These teachers were selected from six Dinaledi schools located in KwaZulu- Natal. The schools catered for learners from multicultural and multiracial backgrounds. Activity theory was used as a framework to locate the study. Each activity system was interrogated within an interpretivist paradigm. Data was collected using six methods and five research instruments. / Thesis (Ph.D.)-University of KwaZulu-Natal, Edgewood, 2010.

This study was designed to explore the patterns and trends in attitudes towards mathematics and attainment in mathematics among Indian pre-matriculants. It also aimed at investigating the relationships between attitudes and attainment and the effects of differences in sex, grade, levels and certain background variables on mathematics attainment and attitudes. A set of 24 multiple-choice mathematics test items, compiled to test cognitive outcomes in mathematics at three taxonomic levels, served as a measure of attainment in mathematics. An attitude scale of 48 Likert-type items comprising six dimensions was developed to measure pupil's attitudes towards mathematics (affective outcomes). In addition, questionnaires were used to collect data on selected background variables and teachers' ratings of the pupils. The test, attitude scale and questionnaires were administered to 680 pupils selected randomly from 17 secondary schools in Durban. The 53 teachers responsible for the 151 mathematics class units (Std 9 and Std 10) at these schools also participated in the research project. The data was subjected to statistical analyses (item analyses, correlational analyses, z-scores and ANOVAS) by computerization. The reliability and validity of both the mathematics test and the attitude scale were demonstrated. The potential value of these instruments as measures of cognitive and affective outcomes in mathematics has been presented and argued. The significances of the relationships in respect of the background variables (including sex, grade and levels) and mathematics attitudes and attainment have been carefully documented (see summary - section 6.4). The relationship between attitudes towards mathematics and attainment in mathematics was found to be positive and significant, with no difference between males and females. It was also demonstrated that attainment in mathematics might be predicted from attitude and ability (IQ) scores, and a regression equation was derived for this purpose. Finally, consideration was given to implications of the major findings and problems for future research. / Thesis (Ph.D.)-University of Durban-Westville, 1981.

The purpose of this study was to find out whether there was a relationship between playing chess and learners' achievement at Mathematics. To investigate the relationship an ex post facto, quasi-experimental research design was used. Learners from two Senior Primary Schools in Kwazulu-Natal who had active school chess clubs were selected to participate in the study. The learners' average mathematics marks at entry year to their Senior Primary Schools were considered the pre-test data. These marks were compared to their mathematics marks at their current grade that was considered the post-test data. In addition a further analysis was done with a group of chess players and a carefully selected group of matched non-players using mathematics marks at entry year as the matching criteria. In all cases the treatment was considered to be the current active participation in chess. The data and background information about the groups was obtained from teachers' interviews, existing school records and a questionnaire that was completed by the participating learners. It was found that for the chess players (the test group) the improvement in the average mathematics mark at Grade 7 (post-test) compared to their entry year average mathematics mark (pre-test) was significantly higher than that of non-players. While the chess players' marks improved, the non-players marks (control group) declined. This finding was further supported by analysis of the matched pairs where the same trend was found. Statistical analysis using t-test found that the results were significant. Further detailed analysis of sub groups within the data revealed that current chess players who were below grade average at Grade 4 had improved their mathematical achievement by even more compared to their matched non-players, at Grades 5, 6, and 7. This points to a possible positive causal effect between chess and mathematics achievement for below average achievers. When the amount of exposure to chess was investigated, no correlation was found between the amount of chess played (frequency and length of time) and the level of improvement in mathematical achievement. However, playing chess for a period longer than six months, did positively affect the mathematical achievement of Grade 7 active chess players and the mathematical achievement of the weaker learners at all Grades for which data was collected in the study. This study implies that the incorporation of chess into school activity and further encouragement for all learners to play the game should be seriously considered by the education authorities since it is likely to result in the overall improvement of the mathematical achievements especially in the higher grade of the Senior Primary School. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2004.

This is an empirical study of how teachers in the Maths Centre for Primary Teachers project use instructional materials in teaching mathematics in junior primary schools. The key question of the study is whether teachers use instructional materials in ways that promote quality education. Instead of being guided by the "school effectiveness" paradigm, one which is based on a production function model, this study adopts an approach used in "quality education" research which argues that it is not simply the availability of instructional materials, but the effective use of instructional materials that determines quality instruction, and in turn quality education. Huberman's model of a teacher as an independent artisan describes the role of a teacher I envision as one that is likely to bring about improvements in the quality of instruction. The approach adopted in Huberman's model emphasises teacher-centred methods. (Teacher-centred does not mean "not child-centred", but simply focuses on what role the teacher needs to play). In this study it was found that, with regards to certain aspects, teachers used instructional materials in ways that were appropriate and contributing to improvements in the quality of education. Teachers valued MCPT materials for their power to illustrate and teach mathematical concepts. Teachers applied methodologies that were informed by a constructivist theory of learning, within a classroom environment conducive for this. However, teachers hardly prepared and used their own materials, and they presented MCPT materials in ways that deprived them of opportunities for teacher development in curriculum management. It is argued, therefore, that there is need for advanced training of teachers on the use of instructional materials - training that enables teachers to use materials in ways that fit in with their design of classroom curriculum. / Thesis (M.Ed.)-University of Natal, 1995.

The constitution of Republic of South Africa (Act 108 of 1996) provides the basis for curriculum transformation and assessment for development in South Africa. The curriculum aims to develop the full potential of each learner as a citizen of a democratic South Africa. Formative assessment is seen as an assessment that can develop the standard of education in South Africa. Muller (2004) asserts that the C2005 policy document and assessment policy for General Education and Training make much of the need to shift from this "authoritarian" approach, to assessment which is formative, standard-based and continuous. Therefore, formative assessment is important in the process of teaching and learning. This study explores teachers' knowledge of formative assessment and how they translate it into practice within a context of Mathematics. It examines the nature of assessment techniques used by educators at the school and explore its relationship with practice. Furthermore, it aims to determine whether the educators are willing to adapt formative assessment practice to meet the changing demands of South African school education as prescribed by the New Curriculum Statement (NCS) in grade 8. Data collection and observations for the study were conducted at a high school in Hammarsdale, KwaZulu-Natal, South Africa. Four teachers were interviewed to determine their perception of formative assessment. Two of the four teachers were selected on basis of the interviews for further data collection. These two were observed when conducting lessons. At least two lessons for each teacher were observed. The nature of the task that the two teachers designed for formative purpose and the feedback they gave to learners were analyzed. The findings from this study suggest that teachers do not reject or resist change in practicing formative assessment, but they have not been properly assisted to replace the old practices with new ones. The teachers therefore, interpret formative assessment according to their own accumulated understanding, which differ from teacher to teacher. Thus, the study recommends that if the change in assessment practice is to be "efficient", it must be accommodated by "appropriate" professional development of teachers. / Thesis (M.Ed.) - University of KwaZulu-Natal, Durban, 2009.

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

The purpose of this study was to investigate the assessment practices in Grade 4 Mathematics classrooms. The study sought to determine whether teachers understood what is required by the Department of Education (DoE) assessment policy, and whether they practice what is required by the policy. If they were not practicing what is required (as purported by Ramsuran (1999), it also needed to be determined why this was the case. The study also sought to expose the gap between the policy and practice. Three teachers from different schools were sources of data: one teacher from a school in a deeply rural area, another from a semi-rural area and the last from a semi-urban area. Data were collected using semi-structured one-on-one interviews. Teachers were visited in their schools and each interview took one hour. The data collected revealed that teachers are still not clear about assessment. This was also found by Ramsuran (1999), who stated that teachers were still not clear about how to implement continuous assessment. According to the DoE, continuous assessment is the chief method of assessing learners. The study also revealed that teachers were still using traditional forms of assessment - tests and examinations - and not other forms of assessment as stipulated by the policy. Challenges faced by the teachers when doing assessment were also prominent. An interesting challenge was that most learners came from broken families, and there was no one to help them with schoolwork at home; this resulted in learners not doing their assignments and projects, which delayed the completion of assessment. The study recommends that all teachers should be in possession of the policy, and that workshops should be organised by the DoE to help teachers with assessment. Lastly, proper assessment structures should be set up in each and every school. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2011.