This thesis concerns teaching in mathematics teacher education and is based on the implementation of a learning study at teacher training. The overall purpose was to investigate in what way teacher training could facilitate and improve student teachers’ Mathematical Knowledge for Teaching (MKT). In the learning study design, MKT was conceptualized as an object of learning with a meta-character, which meant that it was applicable to and transferable between different content areas of mathematics. This made it possible to vary the mathematical content between lessons but to keep the object of learning constant. Four critical features of the object of learning were found, giving insight in some of the problems related to teacher education. Student teachers had to be able to formulate proper aims for a lesson and to give detailed descriptions of elements of MKT for coherence in their MKT to occur. A focus on student teachers’ role as mathematics teachers had to be established and finally, sufficient mathematical knowledge was found to be a prerequisite for their MKT to develop. The study shows that enactment of these critical features improved the teaching by the teacher educators, which in its turn improved the student teachers’ learning with regard to MKT. The study also indicates that the prescribed design is worth considering for future collaborative efforts of improving teaching where other objects of learning with a similar meta-character are involved.

It is no unknown fact that South African learners underachieve in mathematics. Due to the fact that the quality of mathematics teaching is one possible factor that has an influence on learners' mathematics achievement, there are valid reasons questioning the conceptual mathematical knowledge of mathematics teachers. In order to facilitate conceptual understanding teachers themselves must possess profound mathematical knowledge. Apart from the influence of a teacher's knowledge for teaching, teachers' attitudes and beliefs play a meaningful role in the way they teach mathematics. The deficient nature of prospective and practising teachers' knowledge of school mathematics, as well as their attitudes and beliefs towards mathematics has serious implications for the training of prospective mathematics teachers. Literature reveals that a technologically enhanced environment can improve the conceptual learning of prospective mathematics teachers. The purpose of this study was to determine the influence of a dynamic technologically enhanced environment on the attitudes and beliefs, as well as the conceptualisation of prospective mathematics teachers regarding the function concept. In this study, prospective teachers were exposed to Geometer's Sketchpad®, a dynamic software programme providing a powerful learning context that promotes the investigation of algebraic relationships. In order to answer the research question, an explanatory mixed method design was used. In the quantitative part of the study, the Study Orientation Questionnaire in Mathematics and a function test were administered to prospective teachers. In the latter, conceptualisation of the function concept was measured in terms of four competence components, namely interpretation, modelling, translation and reification. In the qualitative part of the investigation semi-structured and task-based interviews were held with a group of prospective teachers. Analysis of the results revealed that the dynamic technologically enhanced environment did not contribute to an improvement of the prospective teachers' attitudes and beliefs. In fact, these decreased visibly. Regarding their conceptualisation, only the reification component showed a practically significant improvement. It therefore appears as if prospective teachers are not being prepared to benefit from the dynamic technologically enhanced environment. A model is proposed for the effective use of such a learning environment. The model involves that diagnostic assessment be made of prospective teachers' basic knowledge of the function concept, their study habits, their attitudes and beliefs with respect to mathematics, as well as their mathematics anxiety. The second component comprises recommendations made to prospective teachers as a result of the diagnostic assessment, as well as continuous support being offered as an integrated part of the mathematics module. Support is offered with respect to cognitive and meta-cognitive skills, affective factors and the creation of an advantageous technologically enhanced learning environment. Despite the restricted value of generalisation of the findings from this study, I still recommend the expansion, refining and implementation of the model so that prospective mathematics teachers can effectively benefit from a technologically enhanced environment. Key words for indexing: mathematics education, mathematics teacher education, teacher knowledge, prospective mathematics teachers, function concept, conceptual learning, tertiary education. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2009.

It is no unknown fact that South African learners underachieve in mathematics. Due to the fact that the quality of mathematics teaching is one possible factor that has an influence on learners' mathematics achievement, there are valid reasons questioning the conceptual mathematical knowledge of mathematics teachers. In order to facilitate conceptual understanding teachers themselves must possess profound mathematical knowledge. Apart from the influence of a teacher's knowledge for teaching, teachers' attitudes and beliefs play a meaningful role in the way they teach mathematics. The deficient nature of prospective and practising teachers' knowledge of school mathematics, as well as their attitudes and beliefs towards mathematics has serious implications for the training of prospective mathematics teachers. Literature reveals that a technologically enhanced environment can improve the conceptual learning of prospective mathematics teachers. The purpose of this study was to determine the influence of a dynamic technologically enhanced environment on the attitudes and beliefs, as well as the conceptualisation of prospective mathematics teachers regarding the function concept. In this study, prospective teachers were exposed to Geometer's Sketchpad®, a dynamic software programme providing a powerful learning context that promotes the investigation of algebraic relationships. In order to answer the research question, an explanatory mixed method design was used. In the quantitative part of the study, the Study Orientation Questionnaire in Mathematics and a function test were administered to prospective teachers. In the latter, conceptualisation of the function concept was measured in terms of four competence components, namely interpretation, modelling, translation and reification. In the qualitative part of the investigation semi-structured and task-based interviews were held with a group of prospective teachers. Analysis of the results revealed that the dynamic technologically enhanced environment did not contribute to an improvement of the prospective teachers' attitudes and beliefs. In fact, these decreased visibly. Regarding their conceptualisation, only the reification component showed a practically significant improvement. It therefore appears as if prospective teachers are not being prepared to benefit from the dynamic technologically enhanced environment. A model is proposed for the effective use of such a learning environment. The model involves that diagnostic assessment be made of prospective teachers' basic knowledge of the function concept, their study habits, their attitudes and beliefs with respect to mathematics, as well as their mathematics anxiety. The second component comprises recommendations made to prospective teachers as a result of the diagnostic assessment, as well as continuous support being offered as an integrated part of the mathematics module. Support is offered with respect to cognitive and meta-cognitive skills, affective factors and the creation of an advantageous technologically enhanced learning environment. Despite the restricted value of generalisation of the findings from this study, I still recommend the expansion, refining and implementation of the model so that prospective mathematics teachers can effectively benefit from a technologically enhanced environment. Key words for indexing: mathematics education, mathematics teacher education, teacher knowledge, prospective mathematics teachers, function concept, conceptual learning, tertiary education. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2009.

Made available in DSpace on 2014-06-11T19:24:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-11-19Bitstream added on 2014-06-13T19:11:46Z : No. of bitstreams: 1 oliveira_ce_me_rcla.pdf: 1160470 bytes, checksum: 9583ae0a4372d1d34daee38b260d0afa (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta pesquisa teve como objetivo analisar e discutir de questões relacionadas às expectativas e dificuldades de licenciandos em Matemática associadas ao uso da Tecnologia Informática (TI) na escola. Os participantes desta investigação eram alunos do último ano do curso de Licenciatura em Matemática, da Universidade Federal de Campina Grande (campus de Campina Grande), no Estado da Paraíba. Os dados apresentados nesta dissertação foram coletados basicamente em três momentos: (1) durante a realização de entrevistas com 16 licenciandos sobre suas expectativas para o uso da TI; (2) em um mini-curso organizado para que os participantes planejassem aulas em que a informática estivesse presente, com o objetivo de implementá-los durante o estágio supervisionado, e; (3) na realização de 05 entrevistas, após o término do estágio supervisionado dos participantes do minicurso. Outras informações importantes vieram de conversas síncronas (chats) e trocas de e-mails com os licenciandos ao longo da disciplina de estágio. Após os procedimentos de análise dos dados coletados, foi possível identificar temáticas associadas às expectativas, que versam sobre a própria formação docente dos entrevistados e sobre ao uso pedagógico da TI, e outras associadas às dificuldades destes professores em formação. Além destas, dificuldades surgidas ao planejar o uso da TI, e possíveis causas geradoras de dificuldades, também foram apresentadas e discutidas. No final deste trabalho, considerações necessárias, principalmente aos curso de Licenciatura em Matemática concernente ao uso educacional dessa tecnologia, foram feitas. / This study has aimed to analyse and discuss questions related to expectations and difficulties of pre-service mathematics teacher education students with the use of Computing Technologies (CT) at school. The research was developed with last-year students of Mathematics teacher education at Universidade Federal de Campina Grande (major campus), state of Paraíba, in the Northest of Brazil. The data presented in this research were collected in three stages: (1) through interviews with 16 students about their expectations of the use of CT; (2) in a workshop, where the participants prepared classes plans using that technology with the objective of executing them later during a supervised practice, and; (3) through 05 interviews after the end of the supervised practice carried out by the workshop participants. Other important pieces of information came out from chats and e-mails exchanged among the students along their supervised practice discipline. After the analyses procedures of the collected data, it was possible to identify different thematics associated with the expectations and dificulties. Some thematics deal with the interviewees’ own Teacher Education and about the pedagogical use of CT. Other thematics are linked to difficulties of those teachers in formation, arised during the planning and reflection on the use of CT, as well as possible reasons that had created them. At the end of this work, necessary considerations have been pointed out, especially to graduation courses on Mathematics teacher education concerning the use of educational technology.

Made available in DSpace on 2014-06-11T19:24:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-09-28Bitstream added on 2014-06-13T19:11:41Z : No. of bitstreams: 1 cattai_mds_me_rcla.pdf: 1823472 bytes, checksum: 29fc576e2938cea8acef40d1d4dd008e (MD5) / Fundesp / O objetivo desta pesquisa é discutir a formação dos professores de Matemática que trabalham com projetos e documentar a maneira da implementação desta proposta em sua prática. Sua relevância está no fato de que são muitas as recomendações e poucas as orientações para o desenvolvimento de projetos nas escolas. A inserção dos projetos nas aulas de Matemática visa a tratar problemas sociais e conteúdos curriculares de forma mais investigativa. Seus dados são provenientes de entrevistas com dez professores de Matemática os quais atuam no Ensino Fundamental ou Médio e de duas fichas preenchidas por eles. Seus relatos possibilitam identificar três formas diferentes de trabalhos com projetos: i) individualmente e por iniciativa própria; ii) por sugestão da escola, de forma fragmentada; iii) coletivamente. Não há indícios de que a formação inicial destes professores os tenha influenciado a trabalhar com projetos. Este preparo foi construído ao longo de suas carreiras, através da participação em cursos de formação continuada, da experiência com a prática e das interferências de suas características pessoais. Esta pesquisa poderá contribuir com sugestões aos professores que queiram desenvolver projetos e aos organizadores de cursos de formação de professores, além de alertar para a necessidade de reorganização da estrutura escolar. / The objective of this study is to discuss the education of mathematics teachers who work with projects and document the way this proposal is implemented in their teaching practice. Its relevance lies in the fact that the recommendations are many and guidance minimal regarding the development of projects in the schools. The aim of including projects in mathematics classes is to approach social problems and curriculum contents in a more investigative manner. The data are taken from interviews with ten elementary and high school mathematics teachers as well as two questionnaires filled out by each of them. It was possible to identify three different forms of working with projects: i) individually, by the teachers own initiative; ii) by the school s suggestion, in a fragmented manner; iii) collectively. There are no indications that the initial education of these teachers influenced them to work with projects. This preparation was built during their careers through participation in continuing education courses, practical experience, and interferences in their personal characteristics. This study can contribute suggestions to teachers who want to develop projects and to organizers of courses for teachers, in addition to calling attention to the need to reorganize the school structure.

Orientador: Miriam Godoy Penteado / Banca: Rosana Giaretta Sguerra Miskulin / Banca: Maria Elizabeth Bianconcini Trindade Morato Pinto de Almeida / Resumo: O objetivo desta pesquisa é discutir a formação dos professores de Matemática que trabalham com projetos e documentar a maneira da implementação desta proposta em sua prática. Sua relevância está no fato de que são muitas as recomendações e poucas as orientações para o desenvolvimento de projetos nas escolas. A inserção dos projetos nas aulas de Matemática visa a tratar problemas sociais e conteúdos curriculares de forma mais investigativa. Seus dados são provenientes de entrevistas com dez professores de Matemática os quais atuam no Ensino Fundamental ou Médio e de duas fichas preenchidas por eles. Seus relatos possibilitam identificar três formas diferentes de trabalhos com projetos: i) individualmente e por iniciativa própria; ii) por sugestão da escola, de forma fragmentada; iii) coletivamente. Não há indícios de que a formação inicial destes professores os tenha influenciado a trabalhar com projetos. Este preparo foi construído ao longo de suas carreiras, através da participação em cursos de formação continuada, da experiência com a prática e das interferências de suas características pessoais. Esta pesquisa poderá contribuir com sugestões aos professores que queiram desenvolver projetos e aos organizadores de cursos de formação de professores, além de alertar para a necessidade de reorganização da estrutura escolar. / Abstract: The objective of this study is to discuss the education of mathematics teachers who work with projects and document the way this proposal is implemented in their teaching practice. Its relevance lies in the fact that the recommendations are many and guidance minimal regarding the development of projects in the schools. The aim of including projects in mathematics classes is to approach social problems and curriculum contents in a more investigative manner. The data are taken from interviews with ten elementary and high school mathematics teachers as well as two questionnaires filled out by each of them. It was possible to identify three different forms of working with projects: i) individually, by the teachers’ own initiative; ii) by the school’s suggestion, in a fragmented manner; iii) collectively. There are no indications that the initial education of these teachers influenced them to work with projects. This preparation was built during their careers through participation in continuing education courses, practical experience, and interferences in their personal characteristics. This study can contribute suggestions to teachers who want to develop projects and to organizers of courses for teachers, in addition to calling attention to the need to reorganize the school structure. / Mestre

Orientador: Miriam Godoy Penteado / Banca: Rosana Giaretta Sguerra Miskulin / Banca: Telma Aparecida de Souza Gracias / Resumo: O objetivo dessa pesquisa é identificar aspectos importantes da inserção da tecnologia informática nos programas de formação inicial de professores de Matemática. Utilizando uma abordagem de pesquisa qualitativa, de caráter interpretativo, foi realizada uma investigação sobre o uso da Internet no contexto de um trabalho com projetos, dentro do estágio supervisionado do Curso de Ciências - Habilitação em Matemática da Faculdade Estadual de Educação, Ciências e Letras de Paranavaí - Paraná. Os resultados do trabalho destacam duas situações: a primeira mostrando o que ocorre quando os futuros professores atuam como usuários de alguns recursos da Internet, compreendendo-a como um espaço a ser explorado; a segunda apresenta os sentimentos e impressões dos futuros professores quando atuam como autores, produzindo e divulgando informações na Internet, vista então, como um espaço a ser habitado. A análise dos dados apresenta algumas possibilidades e desafios que as tecnologias digitais trazem para a formação inicial de professores de Matemática, especialmente quando se articulam ao trabalho com projetos. / Abstract: The objective of this research is to identify important aspects of introducing information technology into mathematics teacher education programs. Using a qualitative research approach, of an interpretive nature, an investigation was conducted regarding the use of the Internet in the context of a project work, in a supervised traineeship in the Sciences Program - Qualification in Mathematics, of the State College of Education, Sciences, and Letters of Paranavaí, in the state of Paraná. The results of the study highlight two situations: the first demonstrates what occurs when future teachers act as users of some Internet resources, understanding it as a space to be explored; the second presents the feelings and impressions of future teachers when they act as authors, producing and disclosing information on the Internet, seen then as a space to be inhabited. The data analysis presents some possibilities and challenges offered by digital technologies for the education of future mathematics teachers, especially when they are linked with project work. / Mestre

A presente dissertação é relativa a uma investigação sobre as potencialidades e limitações do trabalho de um grupo colaborativo durante a formação inicial de professores que ensinam frações. Participaram da pesquisa alunos de um curso de Pedagogia. O objetivo principal da pesquisa foi identificar as concepções de frações que os estudantes apresentam e analisar de que modo a participação nas atividades de um grupo colaborativo podem contribuir para o processo de ressignificação de tais concepções. Para tanto, constituiu-se um grupo de oito alunas de um curso de Pedagogia, que interagiram durante um total de oito encontros, nos quais foram produzidos os dados para a análise. Como referencial teórico nos aproximamos da teoria sócio-histórica de Vygostky, da educação matemática crítica de Skovsmose e dos estudos sobre grupos colaborativos e das comunidades de prática, dentre outros que tomam por objeto a formação de professores que ensinam matemática, em especial nos cursos de Pedagogia. A abordagem metodológica adotada foi a qualitativa com a utilização de diferentes tipos de registros, permitindo a triangulação dos dados. Identificamos alguns limitadores durante o percurso: o período curto de realização do trabalho, a postura dos participantes internalizada e apropriada através do ambiente acadêmico que reproduz crenças e discursos sem uma adequada construção conceitual e, principalmente, significativas dificuldades com relação ao conteúdo matemático de frações. Em contrapartida, algumas características ou dimensões de um grupo colaborativo foram evidenciadas. Os participantes demonstraram diferentes identidades de participação, compartilharam um objetivo comum, um empreendimento mútuo e as tarefas foram compartilhadas. A pesquisadora, como sendo também uma integrante do grupo, foi provocada a desenvolver as diferentes dimensões de sua participação. Nesse sentido, a pesquisa mostrou ser viável o trabalho com grupos colaborativos na formação inicial considerando o contexto, particularidades dos participantes da pesquisa e as atividades desenvolvidas. / This thesis reports a research about the potentialities and restrictions of collaborative group work during initial training of teachers who teach fractions. Teaching academics took part in this research. The main objective was to identify the notion of fractions held by the students and to analyze the way in which participation in the activities of a collaborative group may contribute to the process of re-establishing the meaning in those conceptions. In order to do so, a total of eight students of the teaching course interacted in eight meetings through which data was produced for the analysis. As a theoretical basis we used Vykotsky’s Socio-historical Approach, Critical Mathematics Education by Skovsmose and studies about collaborative work, communities of practice, among others whose object is vocational training of Math teachers, especially in teaching courses. The methodological approach chosen was qualitative and interpretative with the use of different types of register, allowing triangulation of data. Some limitations were identified in the process: the short duration of the project, participants’ attitudes internalized and borrowed from the academic environment, which reproduces beliefs and discourses without an appropriate conceptual construction, and, mainly, important difficulties related to the mathematical subject: fractions. On the other hand, some characteristics or dimensions of a collaborative group were evidenced. The participants demonstrated different identities of participation, shared a common objective, a mutual undertaking and the tasks were shared. The researcher, as part of the group, was provoked to develop different dimensions of participation. The group knew how to determine priorities, drawing its paths and building its history of participation. This way, the research showed that working with collaborative groups in teachers’ education is practicable, taking into account the context and particularities of the participants and the activities developed.

A presente dissertação é relativa a uma investigação sobre as potencialidades e limitações do trabalho de um grupo colaborativo durante a formação inicial de professores que ensinam frações. Participaram da pesquisa alunos de um curso de Pedagogia. O objetivo principal da pesquisa foi identificar as concepções de frações que os estudantes apresentam e analisar de que modo a participação nas atividades de um grupo colaborativo podem contribuir para o processo de ressignificação de tais concepções. Para tanto, constituiu-se um grupo de oito alunas de um curso de Pedagogia, que interagiram durante um total de oito encontros, nos quais foram produzidos os dados para a análise. Como referencial teórico nos aproximamos da teoria sócio-histórica de Vygostky, da educação matemática crítica de Skovsmose e dos estudos sobre grupos colaborativos e das comunidades de prática, dentre outros que tomam por objeto a formação de professores que ensinam matemática, em especial nos cursos de Pedagogia. A abordagem metodológica adotada foi a qualitativa com a utilização de diferentes tipos de registros, permitindo a triangulação dos dados. Identificamos alguns limitadores durante o percurso: o período curto de realização do trabalho, a postura dos participantes internalizada e apropriada através do ambiente acadêmico que reproduz crenças e discursos sem uma adequada construção conceitual e, principalmente, significativas dificuldades com relação ao conteúdo matemático de frações. Em contrapartida, algumas características ou dimensões de um grupo colaborativo foram evidenciadas. Os participantes demonstraram diferentes identidades de participação, compartilharam um objetivo comum, um empreendimento mútuo e as tarefas foram compartilhadas. A pesquisadora, como sendo também uma integrante do grupo, foi provocada a desenvolver as diferentes dimensões de sua participação. Nesse sentido, a pesquisa mostrou ser viável o trabalho com grupos colaborativos na formação inicial considerando o contexto, particularidades dos participantes da pesquisa e as atividades desenvolvidas. / This thesis reports a research about the potentialities and restrictions of collaborative group work during initial training of teachers who teach fractions. Teaching academics took part in this research. The main objective was to identify the notion of fractions held by the students and to analyze the way in which participation in the activities of a collaborative group may contribute to the process of re-establishing the meaning in those conceptions. In order to do so, a total of eight students of the teaching course interacted in eight meetings through which data was produced for the analysis. As a theoretical basis we used Vykotsky’s Socio-historical Approach, Critical Mathematics Education by Skovsmose and studies about collaborative work, communities of practice, among others whose object is vocational training of Math teachers, especially in teaching courses. The methodological approach chosen was qualitative and interpretative with the use of different types of register, allowing triangulation of data. Some limitations were identified in the process: the short duration of the project, participants’ attitudes internalized and borrowed from the academic environment, which reproduces beliefs and discourses without an appropriate conceptual construction, and, mainly, important difficulties related to the mathematical subject: fractions. On the other hand, some characteristics or dimensions of a collaborative group were evidenced. The participants demonstrated different identities of participation, shared a common objective, a mutual undertaking and the tasks were shared. The researcher, as part of the group, was provoked to develop different dimensions of participation. The group knew how to determine priorities, drawing its paths and building its history of participation. This way, the research showed that working with collaborative groups in teachers’ education is practicable, taking into account the context and particularities of the participants and the activities developed.

No description available.