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In this study, senior certificate (standard 10) pupils' attainment of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum was investigated. With regard to the attainment of the cognitive objectives and aims, senior certificate pupils' performance in their mathematics examination, in terms of three broad categories of cognitive abilities (lower level, middle level and higher level mathematical abilities) was analysed and examined. As no norms (criteria) for mathematical attainment in respect of these three categories of cognitive abilities could be identified, these norms had to be firstly developed by the researcher. However, suitable standardised scales were identified and administered to determine senior certificate pupils' attainment of the affective aims and objectives (attitude towards and interest in mathematics). Besides the quantitative analysis, qualitative assessments of senior certificate pupils' attainment of the cognitive and affective aims and objectives were also made using information obtained, by way of a questionnaire, from teachers of senior certificate mathematics classes. The main findings that emerged from this investigation were: * The senior certificate pupils are attaining the desired proficiency levels in the cognitive objectives and aims of the senior certificate mathematics curriculum. However, these pupils are not adequately attaining the affective aims and objectives of the mathematics curriculum. * Qualitative information elicited from senior certificate teachers of mathematics tends to support the above findings which were obtained from the quantitative analysis. * There is a need for curriculum development in certain areas of the senior certificate mathematics curriculum, particularly in Euclidean geometry, for standard grade pupils. In terms of the general findings, certain recommendations were also formulated. In several ways, the present research is a pioneering effort in evaluating the efficacy of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum. It is hoped that this study will serve as a catalyst for future research. / Curriculum and Instructional Studies / D. Ed. (Didactics)

Mathematics anxiety is a personal characteristic which is widespread and continuing. It has a debilitating effect on mathematics performance and contributes to perceptions and attitudes that perpetuate a dislike for mathematics and a lack of confidence when dealing with mathematical problems. An investigation of relevant literature on mathematics anxiety identifies sources and symptoms and emphasises a need for a comprehensive approach to remediation. The historical development of an appropriate measuring instrument is documented and statistical evidence is used to create a mathematics anxiety rating scale suitable for measuring anxiety levels of secondary school pupils and student teachers. The extensive literature interest, research publications and remedial programmes emphasise the problem of mathematics anxiety and thus the need for a comprehensive approach to remediation. Mathematics teaching and curriculum design is expounded to provide the necessary direction to the alleviation of mathematics anxiety. General perspectives on curriculum design are discussed and a cyclical systems approach is recommended. Elements of this approach are detailed and are linked to important personal characteristics to add a humanistic and socio-cultural view of curriculum design in mathematics. The didactic viability of constructivism as an approach to mathematics curriculum design is investigated. Constructivism embodies a philosophy and a methodology which addresses the critical aspects influencing mathematics anxiety. Classroom topics and activities are reviewed in terms of a constructivist approach and the sources of mathematics anxiety are discussed from a constructivist perspective. A longitudinal case study of pupils during their five years at secondary school as well as a study involving student teachers was undertaken. Mathematics performance, perceptions, attitudes and levels of anxiety were investigated by means of tests, questionnaires, and mathematics anxiety rating scales. The statistical results of this research provide evidence to support a comprehensive approach to the remediation of mathematics anxiety. Constructivism is seen as the synthesis of critical aspects of teaching and curriculum development which will stem the perpetuation of mathematics anxiety. Constructivism provides the didactic approach to develop each individual's intellectual autonomy and mathematics power, by instilling a problem solving attitude and a self-confidence when doing mathematics. / Curriculum and Instructional Studies / D. Ed. (Didactics)

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)

Made available in DSpace on 2016-04-27T16:57:18Z (GMT). No. of bitstreams: 1 ALEX SANDRO MARQUES.pdf: 7139616 bytes, checksum: f96912783b8a80ca4b7918ade2f51542 (MD5) Previous issue date: 2005-11-04 / The purpose of our search, to verify how mathematics was organized at junior high school in 1950 s, it s located between two fundamental moments in brazilian mathematics education history: the born of mathematics as a subject, in 1929, and the advent of Modern Mathematics Movement (MMM), in the beginning of 1960 s decade. Inicially, to analyse this question, we worked out on a synthesis about the educational reforms Francisco Campos and Gustavo Capanema, that are responsable for the criation of mathematics as a subject and junior high school, respectivily. After that, based on the new educational legislation, the Ministry Edict of 1951 we verified the estabilishment of Minimum Programs to be carried out obrigatorily, motivating a worry about the possibility of that among the teachers. On this context, we analysed the Annals of the 1st National Congress of Mathematics Teaching in High School, that happened in Salvador in 1955, witch counted on the participation of the teacher and author of the school books Osvaldo Sangiorgi, one of the protagonists of MMM in Brazil, and we verified that the discussion epicenter wasn t around the programs but had been dislocated to the quastion of weekly number of this subject classes. With the purpouse to get traces of the school daily we analysed the collection of the most representative brazilian school books of pre-modern times, that authorized us to certificate the subject estability on this decade. That way, we conclued that the pre-modern times didn t represent an ideal setting for a revolution on this subject; on the contrary, were years of agreement among the teachers about the methods and contents to be taught, were years of estability / O objeto de nosso trabalho, a verificação de como estava organizada a matemática escolar do ginásio nos anos 1950, está situada entre dois momentos fundamentais da história da educação matemática brasileira: o nascimento da disciplina matemática, em 1929, e o advento do Movimento da Matemática Moderna (MMM), no início do decênio de 1960. Inicialmente, para análise desta questão, elaboramos uma síntese sobre as reformas educacionais Francisco Campos e Gustavo Capanema, responsáveis pela criação da disciplina matemática e do ginásio, respectivamente. Em seguida, partindo da nova legislação educacional, a Portaria Ministerial de 1951, verificamos o estabelecimento de Programas Mínimos a serem cumpridos obrigatoriamente, motivando uma preocupação entre os professores em relação à viabilidade de tal medida. Nesse contexto, analisamos os Anais do I Congresso Nacional de Ensino da Matemática no Curso Secundário realizado em Salvador no ano de 1955, que contou com a participação do professor e autor de livros didáticos Osvaldo Sangiorgi, um dos protagonistas do MMM no Brasil, e verificamos que o epicentro das discussões não estava em torno dos programas e havia se deslocado para a questão do número de aulas semanais para a disciplina matemática. Com a finalidade de obter indícios do cotidiano escolar analisamos as coleções de livros didáticos brasileiros mais representativas dos tempos pré-modernos, o que nos autorizou atestar sobre a estabilidade da disciplina nessa década. Assim, concluímos que os tempos pré-modernos não representavam um cenário ideal para uma revolução na disciplina; pelo contrário, foram anos de consenso entre os professores sobre métodos e conteúdos a serem ministrados, foram anos de estabilidade

The aim of the study is to examine factors influencing students’ feelings of pleasure or pain associated with school mathematics. Own experience of students’ frustration about mathematics and concern about students not reaching desired goals is the driving force in this study. It contributes with knowledge from the students' perspective. Hopefully the result can help others, teachers and parents, to strengthen pupils’ desire and ability to learn. Students’ emotions about mathematics are important for learning and mathematics can cause joy as well as anxiety. The students who are positive often need stimulation and challenge, but are usually not a problem for the adults. The negative emotions, especially fear, is something that adults should take into account and try to develop for the better. Anxiety can be described as "a lack of well-being". It can cause panic, paralysis and mental disorganization when students are required to solve math tasks. Math anxiety can also be defined as a combination of stress before the test, low self-esteem, fear of failure and negative attitudes towards learning mathematics. Symptoms can include avoidance of formal mathematics instruction, poor test results and that instructions will not have the expected effect. There is a phenomenological approach of the study. Phenomenology studies how the consciousness creates meaning. The focal point is trying to learn about the students’ experience of their 'Being-in-the-World'. How do students view school mathematics, and why? What can create desire for learning mathematics? What can create uneasiness in learning mathematics? In order to get a better view of this complex area four different data sources are used. Eight pupils are interviewed individually. 19 students participated in focus group interviews. 134 students, ages 11-13, answered questions in a web survey. One class observation was also made. The result was formed into three important factors, Student’s own view of capacity and attitude to mathematics, Importance of relations to others (teachers, class mates, parents) and Content and working forms. Three different themes came into focus – Understanding, Working atmosphere and Safety. The four main areas of importance, as seen in this study, are Interaction student-teacher, Understanding and feeling of success, Good atmosphere in the classroom and Awareness about the use of mathematics. The results show areas of importance for pupils who are feeling math anxiety. They are less aware of how mathematics can be of use for them also outside school and the importance of mathematics in their future lives. They need a much stronger support from adults, teachers and parents, in their math studies, than pupils without anxiety. The classroom environment can also cause problems, if students do not feel safe or feel stressed or disturbed by other pupils or teachers. There are also a few differences between the girls’ and the boys’ experiences, where girls seem to reflect more about their uneasiness when it comes to mathematics, sometimes caused by the boys. What can teachers learn from this study? In short: motivate, teach and let the pupils talk.

In this study, senior certificate (standard 10) pupils' attainment of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum was investigated. With regard to the attainment of the cognitive objectives and aims, senior certificate pupils' performance in their mathematics examination, in terms of three broad categories of cognitive abilities (lower level, middle level and higher level mathematical abilities) was analysed and examined. As no norms (criteria) for mathematical attainment in respect of these three categories of cognitive abilities could be identified, these norms had to be firstly developed by the researcher. However, suitable standardised scales were identified and administered to determine senior certificate pupils' attainment of the affective aims and objectives (attitude towards and interest in mathematics). Besides the quantitative analysis, qualitative assessments of senior certificate pupils' attainment of the cognitive and affective aims and objectives were also made using information obtained, by way of a questionnaire, from teachers of senior certificate mathematics classes. The main findings that emerged from this investigation were: * The senior certificate pupils are attaining the desired proficiency levels in the cognitive objectives and aims of the senior certificate mathematics curriculum. However, these pupils are not adequately attaining the affective aims and objectives of the mathematics curriculum. * Qualitative information elicited from senior certificate teachers of mathematics tends to support the above findings which were obtained from the quantitative analysis. * There is a need for curriculum development in certain areas of the senior certificate mathematics curriculum, particularly in Euclidean geometry, for standard grade pupils. In terms of the general findings, certain recommendations were also formulated. In several ways, the present research is a pioneering effort in evaluating the efficacy of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum. It is hoped that this study will serve as a catalyst for future research. / Curriculum and Instructional Studies / D. Ed. (Didactics)

Mathematics anxiety is a personal characteristic which is widespread and continuing. It has a debilitating effect on mathematics performance and contributes to perceptions and attitudes that perpetuate a dislike for mathematics and a lack of confidence when dealing with mathematical problems. An investigation of relevant literature on mathematics anxiety identifies sources and symptoms and emphasises a need for a comprehensive approach to remediation. The historical development of an appropriate measuring instrument is documented and statistical evidence is used to create a mathematics anxiety rating scale suitable for measuring anxiety levels of secondary school pupils and student teachers. The extensive literature interest, research publications and remedial programmes emphasise the problem of mathematics anxiety and thus the need for a comprehensive approach to remediation. Mathematics teaching and curriculum design is expounded to provide the necessary direction to the alleviation of mathematics anxiety. General perspectives on curriculum design are discussed and a cyclical systems approach is recommended. Elements of this approach are detailed and are linked to important personal characteristics to add a humanistic and socio-cultural view of curriculum design in mathematics. The didactic viability of constructivism as an approach to mathematics curriculum design is investigated. Constructivism embodies a philosophy and a methodology which addresses the critical aspects influencing mathematics anxiety. Classroom topics and activities are reviewed in terms of a constructivist approach and the sources of mathematics anxiety are discussed from a constructivist perspective. A longitudinal case study of pupils during their five years at secondary school as well as a study involving student teachers was undertaken. Mathematics performance, perceptions, attitudes and levels of anxiety were investigated by means of tests, questionnaires, and mathematics anxiety rating scales. The statistical results of this research provide evidence to support a comprehensive approach to the remediation of mathematics anxiety. Constructivism is seen as the synthesis of critical aspects of teaching and curriculum development which will stem the perpetuation of mathematics anxiety. Constructivism provides the didactic approach to develop each individual's intellectual autonomy and mathematics power, by instilling a problem solving attitude and a self-confidence when doing mathematics. / Curriculum and Instructional Studies / D. Ed. (Didactics)

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)