A autorregulação é um dos vários elementos considerados essenciais no processo de aprendizagem, pode-se afirmar que um aluno autorregulado em sua aprendizagem é aquele que aprendeu a planejar, controlar e avaliar seus processos cognitivos, motivacionais, afetivos, comportamentais e contextuais; possui autoconhecimento sobre o próprio modo de aprender, suas potencialidades e limitações. Com esse conhecimento o estudante controla e regula o próprio processo de aprendizagem em direção a seus objetivos e metas. Por sua vez o professor autorregulado é capaz de auxiliar no desenvolvimento dos processos autorregulatórios de seus estudantes e oferecer oportunidades para que também autorregulem sua própria atuação. É nesta perspectiva que este estudo pré-experimental se fundamenta, na instrução direta dos processos de autorregulação da aprendizagem. Com esse intuito foi proposta uma Oficina Online de Estratégias de Estudo, com um grupo de 76 estudantes universitários do Curso de Licenciatura em Matemática a Distância, da Universidade Federal de Pelotas, universidade participante do Consórcio Universidade Aberta do Brasil. Os participantes mostraram semelhanças ao perfil do aluno virtual brasileiro, sendo a maioria do sexo feminino, com idade média de 33 anos e que exercem atividade remunerada com dedicação média de 39 horas semanais. Buscou-se avaliar o impacto no processo autorregulatório da aprendizagem e no conhecimento pedagógico do conteúdo do futuro professor de matemática. Para avaliar o impacto da experiência de ensino com adaptação do Programa de Gervásio ao contexto online, foram analisadas quantitativamente as variáveis autorregulação da aprendizagem (IPAA), o conhecimento de estratégias de aprendizagem (CEA) e o conhecimento pedagógico do conteúdo equação do segundo grau (CPC), antes e após a experiência de ensino. Também foi realizada a análise dessas variáveis em função das variáveis categóricas pessoais e acadêmicas dos participantes. Para aferir a relação entre a autorregulação da aprendizagem e o conhecimento do conteúdo pedagógico foi realizada a análise de correlação entre o IPAA (pós), CEA (pós), CPC (pós) e as variáveis categóricas - idade e rendimento acadêmico médio. Além deste conjunto de análises, foi avaliada a variável entrega da atividade. Para uma interlocução com a análise quantitativa, foi realizada a análise dos dados qualitativos obtidos através do Chat e dos Fóruns de Discussão e, por fim, foram determinadas as frequências relativas das respostas à Ficha de Avaliação da Oficina, bem como realizada a análise qualitativa das questões abertas desta avaliação. Através desta investigação foi possível verificar que o ensino dos processos autorregulatórios, na educação a distância é um constructo fundamental e viável para formação de um educador matemático, pois permitiu uma mudança significativa no conhecimento declarativo das estratégias de aprendizagem e do conhecimento pedagógico do conteúdo matemático do futuro professor. Além das mudanças cognitivas decorrentes da experiência de ensino foi possível observar outros fatores que possibilitam a gerência dos comportamentos, pensamentos e sentimentos, voltados e adaptados para obtenção de metas pessoais e guiados por padrões gerais de conduta, tais como: a identificação de fatores que influenciam a aprendizagem, a antecipação dos resultados das ações, experimentação de satisfação com o próprio esforço, crenças de autoeficácia positivas, autorreflexão, gerenciamento do tempo disponível, o monitoramento do próprio desempenho, percepção do valor do aprendizado. Pelos resultados obtidos, parece pertinente, que a competência de autorregulação da aprendizagem componha a arquitetura pedagógica de cursos de formação inicial de professores de matemática, na modalidade a distância. / The self-regulation is one of several elements considered essential in the learning process, it can be said that a self-regulated learner in their learning is one who has learned to plan, monitor and evaluate their cognitive, motivational, affective, behavioral and contextual processes; it has self knowledge about the proper way to learn, its potential and limitations. With this knowledge the student controls and regulates the learning process itself toward its goals and objectives. On the other hand self-regulated teacher is able to assist in the development of self-regulatory processes of their students and provide opportunities for them to also self regulate their own performance. It is in this perspective that this pre-experimental study is based on the direct instruction of self-regulation processes of learning. In this sense, we propose an Online Workshop Study Strategy for a group of 76 college students of the Degree in Mathematics distance, from Federal University of Pelotas, which is participant of the university consortium “Universidade Aberta do Brasil”. The participants of Workshop showed similarities to the profile of Brazilian virtual student. The most of them are female with mean age of 33 years and performing paid work with dedication average of 39 hours per week. We sought to assess the impact on auto-regulatory process of learning and pedagogical content knowledge of future teachers of mathematics. To assess the impact of teaching experience with adaptation of Gervasio´s program to the online environment, were quantitatively analyzed the learning of self-regulation variables (IPAA), knowledge of learning strategies (CEA) and the pedagogical content knowledge of the quadratic equation (CPC) before and after the teaching experience. Also carried out analysis of these variables on the basis of personal and academic categorical variables of the participants. To assess the relationship between self-regulation of learning and knowledge in the educational content was performed the correlation analysis between the IPAA (post), CEA (post), CPC (post) and categorical variables - age, average academic performance. In addition to this set of analyzes, the variable delivery activity was evaluated. For a dialogue with the quantitative analysis, the analysis of qualitative data obtained through the Chat and Forums was held and, finally, were determined relative frequencies of responses to the Workshop Evaluation Form and carried out a qualitative analysis of open questions of this evaluation. Through this research we found that the teaching of self-regulatory processes in distance education is a fundamental construct and feasible to form a mathematics educator, it allowed a significant change in declarative knowledge of learning strategies and pedagogical knowledge of the mathematical content of future teacher. In addition to the cognitive changes resulting from the teaching experience we observed other factors that enable the management of behaviors, thoughts and feelings, directed and adapted for achieving personal goals and guided by general standards of conduct, such as the identification of factors that influence learning, the anticipation of the results of actions, trial of satisfaction with their own efforts, positive self-efficacy beliefs, self-reflection, available time management, monitoring one's own performance, perception of the value of learning. The results obtained, it seems pertinent that the competence of learning self-regulation compose the pedagogical architecture of initial training courses for mathematics teachers, in the distance.

A autorregulação é um dos vários elementos considerados essenciais no processo de aprendizagem, pode-se afirmar que um aluno autorregulado em sua aprendizagem é aquele que aprendeu a planejar, controlar e avaliar seus processos cognitivos, motivacionais, afetivos, comportamentais e contextuais; possui autoconhecimento sobre o próprio modo de aprender, suas potencialidades e limitações. Com esse conhecimento o estudante controla e regula o próprio processo de aprendizagem em direção a seus objetivos e metas. Por sua vez o professor autorregulado é capaz de auxiliar no desenvolvimento dos processos autorregulatórios de seus estudantes e oferecer oportunidades para que também autorregulem sua própria atuação. É nesta perspectiva que este estudo pré-experimental se fundamenta, na instrução direta dos processos de autorregulação da aprendizagem. Com esse intuito foi proposta uma Oficina Online de Estratégias de Estudo, com um grupo de 76 estudantes universitários do Curso de Licenciatura em Matemática a Distância, da Universidade Federal de Pelotas, universidade participante do Consórcio Universidade Aberta do Brasil. Os participantes mostraram semelhanças ao perfil do aluno virtual brasileiro, sendo a maioria do sexo feminino, com idade média de 33 anos e que exercem atividade remunerada com dedicação média de 39 horas semanais. Buscou-se avaliar o impacto no processo autorregulatório da aprendizagem e no conhecimento pedagógico do conteúdo do futuro professor de matemática. Para avaliar o impacto da experiência de ensino com adaptação do Programa de Gervásio ao contexto online, foram analisadas quantitativamente as variáveis autorregulação da aprendizagem (IPAA), o conhecimento de estratégias de aprendizagem (CEA) e o conhecimento pedagógico do conteúdo equação do segundo grau (CPC), antes e após a experiência de ensino. Também foi realizada a análise dessas variáveis em função das variáveis categóricas pessoais e acadêmicas dos participantes. Para aferir a relação entre a autorregulação da aprendizagem e o conhecimento do conteúdo pedagógico foi realizada a análise de correlação entre o IPAA (pós), CEA (pós), CPC (pós) e as variáveis categóricas - idade e rendimento acadêmico médio. Além deste conjunto de análises, foi avaliada a variável entrega da atividade. Para uma interlocução com a análise quantitativa, foi realizada a análise dos dados qualitativos obtidos através do Chat e dos Fóruns de Discussão e, por fim, foram determinadas as frequências relativas das respostas à Ficha de Avaliação da Oficina, bem como realizada a análise qualitativa das questões abertas desta avaliação. Através desta investigação foi possível verificar que o ensino dos processos autorregulatórios, na educação a distância é um constructo fundamental e viável para formação de um educador matemático, pois permitiu uma mudança significativa no conhecimento declarativo das estratégias de aprendizagem e do conhecimento pedagógico do conteúdo matemático do futuro professor. Além das mudanças cognitivas decorrentes da experiência de ensino foi possível observar outros fatores que possibilitam a gerência dos comportamentos, pensamentos e sentimentos, voltados e adaptados para obtenção de metas pessoais e guiados por padrões gerais de conduta, tais como: a identificação de fatores que influenciam a aprendizagem, a antecipação dos resultados das ações, experimentação de satisfação com o próprio esforço, crenças de autoeficácia positivas, autorreflexão, gerenciamento do tempo disponível, o monitoramento do próprio desempenho, percepção do valor do aprendizado. Pelos resultados obtidos, parece pertinente, que a competência de autorregulação da aprendizagem componha a arquitetura pedagógica de cursos de formação inicial de professores de matemática, na modalidade a distância. / The self-regulation is one of several elements considered essential in the learning process, it can be said that a self-regulated learner in their learning is one who has learned to plan, monitor and evaluate their cognitive, motivational, affective, behavioral and contextual processes; it has self knowledge about the proper way to learn, its potential and limitations. With this knowledge the student controls and regulates the learning process itself toward its goals and objectives. On the other hand self-regulated teacher is able to assist in the development of self-regulatory processes of their students and provide opportunities for them to also self regulate their own performance. It is in this perspective that this pre-experimental study is based on the direct instruction of self-regulation processes of learning. In this sense, we propose an Online Workshop Study Strategy for a group of 76 college students of the Degree in Mathematics distance, from Federal University of Pelotas, which is participant of the university consortium “Universidade Aberta do Brasil”. The participants of Workshop showed similarities to the profile of Brazilian virtual student. The most of them are female with mean age of 33 years and performing paid work with dedication average of 39 hours per week. We sought to assess the impact on auto-regulatory process of learning and pedagogical content knowledge of future teachers of mathematics. To assess the impact of teaching experience with adaptation of Gervasio´s program to the online environment, were quantitatively analyzed the learning of self-regulation variables (IPAA), knowledge of learning strategies (CEA) and the pedagogical content knowledge of the quadratic equation (CPC) before and after the teaching experience. Also carried out analysis of these variables on the basis of personal and academic categorical variables of the participants. To assess the relationship between self-regulation of learning and knowledge in the educational content was performed the correlation analysis between the IPAA (post), CEA (post), CPC (post) and categorical variables - age, average academic performance. In addition to this set of analyzes, the variable delivery activity was evaluated. For a dialogue with the quantitative analysis, the analysis of qualitative data obtained through the Chat and Forums was held and, finally, were determined relative frequencies of responses to the Workshop Evaluation Form and carried out a qualitative analysis of open questions of this evaluation. Through this research we found that the teaching of self-regulatory processes in distance education is a fundamental construct and feasible to form a mathematics educator, it allowed a significant change in declarative knowledge of learning strategies and pedagogical knowledge of the mathematical content of future teacher. In addition to the cognitive changes resulting from the teaching experience we observed other factors that enable the management of behaviors, thoughts and feelings, directed and adapted for achieving personal goals and guided by general standards of conduct, such as the identification of factors that influence learning, the anticipation of the results of actions, trial of satisfaction with their own efforts, positive self-efficacy beliefs, self-reflection, available time management, monitoring one's own performance, perception of the value of learning. The results obtained, it seems pertinent that the competence of learning self-regulation compose the pedagogical architecture of initial training courses for mathematics teachers, in the distance.

Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-20T14:00:11Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_MiriamFerrazzaHeck.pdf: 2176140 bytes, checksum: d350ec6bb3b796fe029f23b3ef533029 (MD5) / Made available in DSpace on 2018-08-20T14:00:11Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_MiriamFerrazzaHeck.pdf: 2176140 bytes, checksum: d350ec6bb3b796fe029f23b3ef533029 (MD5) Previous issue date: 2017-01-09 / This qualitative research had as general objective to analyze mathematics students´ difficulties when solving a question about numerical sequences, aiming at the elaboration, application and analysis of a set of activities on this content, for use on mathematics teachers training courses. A test was applied to four classes of students, two composed of academics of the mathematics teacher education courses of the two higher education courses, one by academics of an information system course of one of the institutions and, finally, a class composed by graduated in mathematics, attending a master degree in mathematics teaching at one of the institutions. The answers analysis was supported by Duval's Theory of Registers of Semiotic Representation. In addition, an interview was conducted with two professors of the mathematics teacher education course of one of the institutions, to know their opinions about the errors detected in the answers. Subsequently, a set of activities on numerical sequences was analyzed by academics of the master course, who knew the proposal of the activities on the sequence content and were invited to express their opinion on its use for the teaching of this content. After analyzing the data, it was concluded that the research reached its objectives and, in terms of registers of representation, it was noticed that the conversion of the natural language to the algebraic, in any of the items, was performed by most of the students. Conversion from natural language to figural was used as an initial resource to understand the problem. The set of proposed activities can be explored as an introduction to the study of sequences if presented in a mathematics teachers training courses, but can also be worked within the study of teaching methodologies, in initial or continuing training courses. / Esta pesquisa, de caráter qualitativo, teve como objetivo geral analisar as dificuldades demonstradas por alunos de disciplinas matemáticas ao resolver uma questão sobre sequências numéricas, visando à elaboração, aplicação e análise de um conjunto de atividades sobre esse conteúdo, para uso em cursos de formação de professores. Foi aplicado um teste a quatro turmas de alunos, duas compostas por acadêmicos dos cursos de Licenciatura em Matemática das duas Instituições de Ensino Superior, uma por acadêmicos de um curso de Sistema de Informação de uma das instituições e, por fim, uma turma composta por Licenciados em Matemática, cursando mestrado na área de Ensino de Matemática em uma das instituições. A análise das respostas foi apoiada na Teoria dos Registros de Representação Semiótica, de Duval. Além disso, foi realizada uma entrevista com duas professoras do curso de Licenciatura em Matemática de uma das instituições, para saber suas opiniões sobre os erros detectados nas respostas. Posteriormente foi elaborado um conjunto de atividades sobre sequências numéricas, analisado por acadêmicos do curso de Mestrado em Ensino de Matemática de uma das instituições, que conheceram a proposta das atividades sobre o conteúdo de sequência e foram convidados a opinar sobre seu uso para o ensino desse conteúdo. Após a análise dos dados, conclui-se que a pesquisa atingiu seus objetivos e, em termos de registros de representação, notou-se que a conversão da linguagem natural para a algébrica, em qualquer dos itens, foi realizada pela maior parte dos alunos que não deixaram em branco qualquer dos itens. Já a conversão da linguagem natural para a figural foi usada como recurso inicial para compreender o problema. O conjunto de atividades propostas pode ser explorado como uma introdução ao estudo de sequências, se for apresentado em um curso de Licenciatura em Matemática, mas também pode ser trabalhado dentro do estudo de metodologias de ensino, em cursos de formação inicial ou continuada.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2015-03-25T19:10:49Z No. of bitstreams: 2 Dissertação - Jackelyne de Souza Medrado - 2014.pdf: 2766058 bytes, checksum: 1960823720b93105944a3e53908591bd (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2015-03-26T17:05:03Z (GMT) No. of bitstreams: 2 Dissertação - Jackelyne de Souza Medrado - 2014.pdf: 2766058 bytes, checksum: 1960823720b93105944a3e53908591bd (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-03-26T17:05:03Z (GMT). No. of bitstreams: 2 Dissertação - Jackelyne de Souza Medrado - 2014.pdf: 2766058 bytes, checksum: 1960823720b93105944a3e53908591bd (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-11-27 / The Education of Young and Adults (EJA) presents itself as a mode of basic education in current braziliancontext, but, for that, there was a long journey of political and ideological struggle for the same subjects. Considering this context and the needfor progress in discussions and proposals forthe formation of teachers for EJA, this research aims to elucidate the following issues: What are the knowledge of mathematics teachers, constituted in their teaching practice in adult education, based on the Freire’s conceptions to the formation of a progressive teacher?Therefore, the research was subject, a recent graduate math teacher, active in EJAin a State public school in the city of Goiania -GO.From Freire's ideas, the categories were developed for the analysis of teaching knowledge, namely: Knowledge of Formal Teacher Formation, Knowledge of Educational Action, KnowledgeExperientialand Knowledge forthe Liberation. However,also support ourselves in other authors who studying teacher’s education,particularly, math teachers, as well asthe specifics of the Youth and Adult Education. The research question referred us to a case study, for which we used observation, questionnaires, semistructured interviews and narrative, in addition to document analysis concerning the course of the project the Educational Institution in which the subject of this held your formation, lesson plans produced by this subject, the reference curriculum adopted by the school field, as well as the Political Pedagogical Project this school. The analysis was done through oftriangulation of the data collected. This analysis allowed us to identify several articulated knowledge by subject teacher in their teaching practice in EJA, which demonstrates the act of thinking right necessary to progressive education to promote a liberating education,according to freireanas perspectives. / A Educação de Jovens e Adultos(EJA) apresenta-se como uma modalidade da educação básica no contexto brasileiro atual, mas, para isso, houve um longo percurso de lutas políticas e ideológicas pelos sujeitos da mesma. Considerando este contexto e a necessidade de avanços nas discussões e proposições para a formação do professor para a EJA,esta pesquisa pretende elucidar a seguinte problemática: Quais são os saberes do professor de matemática,constituídos em sua prática docente na EJA,tomando por base as concepções de Freire para a formação de um professor progressista?Para tanto, a pesquisa teve como sujeito, um professor de matemática recém-formado, atuante na EJA em uma escola pública Estadual, da cidade de Goiânia -GO. A partir das ideias de Freire,foram elaboradas as categorias para a análise dos saberes docentes,quais sejam: Saberes da Formação Formal do Professor, Saberes da Ação Educativa, Saberes Vivencias eSaberes Para a Libertação.Contudo,nos apoiamos também em outros autores que estudam a formação de professores, em especial, professores de matemática, bem comoas especificidades da Educação de Jovens e Adultos.A questão de investigação nos remeteu a um Estudo de Caso, para qual utilizamos observação, questionário,entrevistassemiestruturadae narrativa, além da análise documental referente ao projeto do cursoda Instituiçãode Ensinoem que o sujeito desta pesquisa realizou sua formação, os planos de aula elaborados porestesujeito, o currículo referência adotado pela escola campo, assim como o Projeto Político Pedagógico desta escola. A análise se deu por meio da triangulação dos dados coletados. Esta análise nos possibilitou identificar vários saberes articulados pelo professor sujeito em sua prática docente na EJA, os quais evidenciam o ato de pensar certo necessário ao educador progressista para a promoção de uma educação libertadora,segundo perspectivas freireanas.

Justification and argumentation have been identified as important mathematical practices; however, little work has been done to understand the knowledge and pedagogy teachers need to support students in these ambitious practices. Data for this research was drawn from the Justification and Argumentation: Growing Understanding in Algebraic Reasoning (JAGUAR) project. JAGUAR was a multi-year research and professional development project in which 12 middle school math teachers and a group of researchers explored the knowledge and pedagogy needed to support student justifications. This dissertation consists of three case study analyses. The first paper describes the development of teacher conceptions of justification, including their proficiency with justification and purpose of justification in the middle school classroom. The second paper examines the relationship between teacher understanding of empirical reasoning and their use of examples in their classrooms. The final paper describes the relationship between task scaffolding and student forms of reasoning in the context of a justification task. Collectively, this body of work identifies important relationships between teacher knowledge, practice, and student justification activity.

Although there has been a substantial amount of research on the topic of teacher professional development, few studies adequately captured the types and frequency of formal and informal professional learning teachers undertake to improve as educators. The purpose of this study was to examine the types of activities middle and high school mathematics teachers engaged in to improve their abilities as educators, analyzed by the participants’ school setting, years of teaching experience, level of education, degree major, certificate type, and their school’s Title I status. Teachers from two large school districts in Florida participated. The Teachers’ Opportunity to Learn (TOTL) survey was used to collect the data. The TOTL measured the professional learning activities of teachers based on seven learning categories: (a) workshops, (b) teacher collaboration, (c) university courses, (d) conferences, (e) mentoring/coaching, (f) informal communication, and (g) individual learning activities. Teachers were solicited to participate two times; which generated 245 responses for analysis. The results of this study indicated that teachers devoted an extensive amount of time on professional development, with the majority of time spent on informal learning activities. Every participant in the study engaged in at least one professional development activity; most engaged in four or more activities. The activity with the highest amount of participation (99.2%) and greatest amount of time spent (36.62 hours per month) was individual learning activities. Other notable areas of participation were professional development programming, teacher collaboration, and informal communication. When the activities were analyzed by demographic variable, 16 comparisons were found to be statistically significant. Mentoring/coaching activities produced more significant results than any other activity in the study. Analyses also confirmed that the professional learning practices of new teachers were significantly different from their more experienced peers. The findings from this study could serve as the impetus for programmatic changes and policy reform within the education community. School districts could benefit by creating professional development programs that support teacher collaboration, informal communication, and self-directed learning. State education departments could encourage these endeavors by redirecting funding and redesigning certification systems to recognize these non-traditional individualized activities.

The shift towards collegiality is a new setting for many teachers. Most teachers work alone, in isolation from their colleagues and collegial collaboration requires organisational structures. The aim of the study is to describe and analyse upper secondary mathematics teachers’ collective practice,developed in a professional development initiative. This study is a case study and the empirical data is generated through observations and an interview of a group of four teachers at a school who met on a weekly basis throughout a term. Their discussions focused on the mathematical concept of slope in a setting of learning study. This thesis is the case of when mathematics teachers focus discussions on slope and draws on Wenger’s Communities of Practice Perspective, as a unitof analysis, and addresses the question: What are the characteristics of practice when upper secondary mathematics teachers focus discussions on slope in the setting of a learning study? The analysis accounts for characteristics of the aspects of practice, through the coherence of mutual engagement, joint enterprise and shared repertoire in the community of practice. The teachers are engaged around finding small changes in their teaching that could give major effect in students learning. They negotiate what the students need to know in order to understand the relation between Δy and Δx. The characteristic of practice is a conceptual mapping of the concept of slope. It reveals students’ partial understanding of related concepts due to how they were given meaning through previous teaching. The conceptual mapping of slope goes back as far as to the student’s partial understanding of the meaning of subtraction. However, what emerges is in relation to the teachers’ experience of avoiding students’ difficulties with negative difference when teaching slope. It turns out to be a negotiation and a renegotiation of teaching slope for instrumental understanding or conceptual understanding. An overall characteristic of practice is that it develops in a present teaching culture.

M.Ed. (Subject Didactics) / Research shows that "the aims of secondary school's teaching of mathematics are often not realized with many pupils leaving the school with passive knowledge of mathematics" (H.S.R.C. 1981:8). This means that knowledge of mathematical facts are reproduced on demand, instead of active mathematical knowledge " which is congruent with the aims of teaching secondary mathematics" (Crooks, 1988 : 6/7). Active knowledge of mathematics implies and characterised by the understanding of concepts, principles that underlie facts and ideas and principles and concepts that are connected to each other" (Entwistle & Entwistle, 1992 : 2). Active knowledge also enables pupils to act intellectually independently. One reason for the previously mentioned predicament is that "teaching often encourage passive knowledge because the teaching practice of mathematics teachers are often not in accordance with their educational aims" (Gravett, 1994 :6). Thus, a discrepancy exists between teacher's intentions of teaching mathematics and their conduct during teaching. It can be argued also that teachers teach mathematics in the classroom but that the pupils not always effectively learn. It is from the perception above that a constructivistic view of learning as a conceptual change underlies the idea that teaching "as the creation of a classroom context conducive to learning" (Strike & Posner, 1985:117). Biggs (1993 : 74) thus argues that "if knowledge is constructed, rather than recorded as received, it does not make sense to think of teaching as imparting knowledge, but rather as creating learning environments that enhance the process of mathematical knowledge construction". Russell (1969: 14) mentions that "mathematics is a subject in which we never know what we are talking about, nor whether what we are saying is true". The views, amongst others Oosthuizen, Swart and Gildenhuys (1992:2) see mathematics as "an essential language of a creative but deductive process which has its origins in the problems of the physical world", In the light of this, the origin of mathematics in the real world, it can be argued that from a "constructivistic perspective, mathematical learning is an active process by which pupils construct their own mathematical knowledge in the light of their existing knowledge and through interaction with the world around them" (Gravett, 1994 : 6/7). "Construction, not absorption or unfocused discovery, enables learning" (Leder, 1993 : 13). Mathematics is not something discovered by mankind, mathematics is a creation of mankind and is transmitted and changed from one generation to the next.

Philosophiae Doctor - PhD / "This study is guided by theories about educational policy implementation and their implications for teaching. These theories underline the notion that educational reform is a progress and it iv comes in cycles. According to Tyack and Cuban (1995), the first cycle (policy talk) is for diagnosing problems and for advocacy of solutions. It is followed by policy action; then actual implementation of the plan. The implications for these theories therefore imply that teachers play an important role in any educational reform and as such should be involved in any decision making and policy implementation in order to make any change in education a worthwhile process (Fullan, 2001; Helsby, 1999; Tyack and Cuban, 1995). This study focused on the implementation of the policy document Towards education for All: A development brief for education, culture, and training and its implications on mathematics teachers at secondary schools. The policy document highlights the main features of Learner-Centered approaches. Therefore, the aim of the study is to investigate how mathematics teachers implement Learner-Centered Education in Mathematics classrooms in Namibia..."

This mixed-methods study examined the extent to which teacher performance and student performance measures correlated, and to understand which specific practices of mathematics teachers in Grades 3-5 related to student performance. Research was conducted at five elementary schools in a large, urban north Texas school district. Data sources included component scores and recorded evidence from observation rubrics, interviews with campus administrators, and value-added modeling (VAM) student growth scores. Findings indicated a modest relationship between teacher performance levels and student performance levels. Lack of access to individual teacher VAM data, per district policy, might have impacted the strength of the relationship. Interviews with administrators and an examination of the evidence cited in the observation rubrics identified specific practices associated with highly rated mathematics teaching. Differences in administrators’ experience levels with both mathematics instruction and the observation instrument might have influenced rubric scores and the level of specificity shown in evidence statements.