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South African learners underachieve in mathematics. The many different factors that influence this underachievement include mathematics teachers' role in teaching mathematics with understanding. The question arises as to how teachers' mathematical content knowledge states can be transformed to positively impact learners' achievement in mathematics. In this study, different kinds of teachers' knowledge needed for teaching mathematics were discussed against the background of research in this area, which included the work of Shulman, Ma and Ball. From this study an important kind of knowledge, namely mathematical content knowledge for teaching (MCKfT), was identified and a teacher's ability to unpack mathematical knowledge and understanding was highlighted as a vital characteristic of MCKfT. To determine further characteristics of MCKfT, the study focussed on the nature of mathematics, different kinds of mathematical content knowledge (procedural and conceptual), cognitive processes (problem solving, reasoning, communication, connections and representations) involved in doing mathematics and the development of mathematical understanding (instrumental vs. relational understanding). The influence of understanding different problem contexts and teachers' ability to develop reflective practices in teaching and learning mathematics were discussed and connected to a teacher's ability to unpack mathematical knowledge and understanding. In this regard, the role of teachers' prior knowledge or current mathematical content knowledge states was discussed extensively. These theoretical investigations led to identifying the characteristics of MCKfT, which in turn resulted in theoretical criteria for the development of MCKfT. The theoretical study provided criteria with which teachers' current mathematical content knowledge states could be analysed. This prompted the development of a diagnostic instrument consisting of questions on proportional reasoning and functions. A qualitative study was undertaken in the form of a diagnostic content analysis on teachers' current mathematical content knowledge states. A group of secondary school mathematics teachers (N=128) involved in the Sediba Project formed the study population. The Sediba Project is an in-service teacher training program for mathematics teachers over a period of two years. These teachers were divided into three sub-groups according to the number of years they had been involved in the Sediba Project at that stage. The teachers' current mathematical content knowledge states were analysed with respect to the theoretically determined characteristics of and criteria for the development of MCKfT. These criteria led to a theoretical framework for assessing teachers' current mathematical content knowledge states. The first four attributes consisted of the steps involved in mathematical problem solving skills, namely conceptual knowledge (which implies a deep understanding of the problem), procedural knowledge (which is reflected in the correct choice of a procedure), the ability to correctly execute the procedure and the insight to give a valid interpretation of the answer. Attribute five constituted the completion of these four attributes. The final six attributes were an understanding of different representations, communication of understanding in writing, reasoning skills, recognition of connections among different mathematical ideas, the ability to unpack mathematical understanding and understanding the context a problem is set in. Quantitative analyses were done on the obtained results for the diagnostic content analysis to determine the reliability of the constructed diagnostic instrument and to search for statistically significant differences among the responses of the different sub-groups. Results seemed to indicate that those teachers involved in the Sediba Project for one or two years had benefited from the in-service teacher training program. However, the impact of this teachers' training program was clearly influenced by the teachers' prior knowledge of mathematics. It became clear that conceptual understanding of foundation, intermediate and senior phase school mathematics that should form a sound mathematical knowledge base for more advanced topics in the school curriculum, is for the most part procedurally based with little or no conceptual understanding. The conclusion was that these teachers' current mathematical content knowledge states did not correspond to the characteristics of MCKfT and therefore displayed a need for the development of teachers' current mathematical content knowledge states according to the proposed criteria and model for the development of MCKfT. The recommendations were based on the fact that the training that these teachers had been receiving with respect to the development of MCKfT is inadequate to prepare them to teach mathematics with understanding. Teachers' prior knowledge should be exposed so that training can focus on the transformation of current mathematical content knowledge states according to the characteristics of MCKfT. A model for the development of MCKfT was proposed. The innermost idea behind this model is that a habit of reflective practices should be developed with respect to the characteristics of MCKfT to enable a mathematics teacher to communicate and unpack mathematical knowledge and understanding and consequently solve mathematical problems and teach mathematics with understanding. Key words for indexing: school mathematics, teacher knowledge, mathematical content knowledge, mathematical content knowledge for teaching, mathematical knowledge acquisition, mathematics teacher education / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2007.

Orientador: Raquel Gomes de Oliveira / Resumo: A presente pesquisa de Mestrado pertence à linha de pesquisa "Processos formativos, ensino e aprendizagem" do Programa de Pós-Graduação em Educação da FCT/Unesp. O ensino híbrido é uma abordagem pedagógica que combina atividades presenciais e atividades realizadas online por meio das Tecnologias Digitais de Informação e Comunicação (TDIC). Compreender quais são os saberes (conhecimentos, competências e habilidades) que os docentes utilizam quando há a integração entre o ensino presencial e online é fundamental para identificar as demandas em relação ao processo formativo docente. O ensino híbrido em uma perspectiva de metodologias ativas de aprendizagem altera o papel do professor de um transmissor de informações para um mediador/orientador do processo de ensino e aprendizagem, e os estudantes tornam-se ativos durante sua aprendizagem. Nessa perspectiva, esta pesquisa buscará responder à seguinte questão: Como o ensino híbrido pode ser desenvolvido em uma perspectiva de metodologias ativas de aprendizagem e a partir da base TPACK? A partir do referencial teórico TPACK, que articula os três tipos de conhecimentos: o conhecimento pedagógico, o conhecimento de conteúdo e o conhecimento tecnológico, este estudo investigou em uma Instituição de Ensino Superior privada, localizada em Presidente Prudente - SP, as disciplinas a distância ofertadas nos cursos de graduação presencial, que desenvolveram o ensino híbrido em um contexto em que se estimula o uso de metodologias ativas de a... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This study bound to the research line of "Practices and Formative Processes in Education" of the postgraduate program in Education of FCT/UNESP. Blended learning is an approach to education that combines online educational materials and opportunities for interaction online with traditional face-to-face methods. Understanding what the knowledge are (knowledge, skills and abilities) that teachers use when there is the integration between face-to-face and online teaching is essential to identify teacher training demands. Blended Learning for active learning context changes the role of the teacher from an information transmitter to a teaching mediator/mentor, and students have more flexible and personalized pathways becoming active during their learning. This research which aims answer the question: How can Blended Learning be developed in the context of active learning and based on TPACK? Given this theoretical framework that articulates the three types of knowledge: pedagogical knowledge, content knowledge and technological knowledge. This study investigated in a non-public higher education institution, located in Presidente Prudente - SP, the Distance Education subjects offered in the presential undergraduate courses, which developed blended learning and active learning methodologies. Therefore, this research has a qualitative approach, with data obtained from the researcher's contact with the research question. Specifically, the research uses assumptions of an exploratory res... (Complete abstract click electronic access below) / Mestre

The process of ‘learning to teach’ is still not well understood. In particular, existing research does not fully reflect the complexities of the process; how student teachers’ level of subject matter knowledge influences their teaching, or how their placement affects the process. This study provides an alternative nonlinear, relational model for understanding the process of ‘learning to teach’. I study the ways in which 66 BEd students teach during eight school-based Teaching Experience sessions, conducted over the four year duration of their preservice teaching degree. I primarily draw on evidence obtained from lesson observation reports written by university tutors as they respond to lessons taught by this cohort of student teachers. I cluster their comments into five facets necessary for enabling learning, namely, student teachers’ knowledge and understanding of content; their preparation; their teaching strategies; their classroom management; and the ways in which they monitor learning. These five facets have links to the process of teaching described by Shulman’s (1987b) Model of Pedagogical Reasoning and Action. Within each of these five facets, varying levels of competence were demonstrated by the student teachers in this study. I develop an analytical tool that describes four developmental levels of student teaching over each of the five facets of the teaching process. An in-depth study of the developmental teaching portraits of five student teachers illustrates that they are often more advanced in some facets of their teaching, and less so in others. The portraits highlight the ways in which certain facets affect teaching in other facets. The interactions between these differing levels and facets give rise to particular challenges that student teachers experience as they ‘learn to teach’. Some of these challenges are more significant than others, as certain inter-facet relationships are essential to the development of pedagogically reasoned action, and other relationships are less crucial. My findings suggest that although ‘learning to teach’ is a non-linear process, there nevertheless exists a logical hierarchy within the facets, whereby some facets create conditions of possibility for others. In particular, I find that the way in which student teachers use their knowledge and understanding of the content to inform other facets, establishes the 2 logical conditions necessary for the development of teaching as pedagogically reasoned action.

A Educação Física (EF) escolar no Brasil passa por um momento bastante delicado. Situações como a diminuição de carga horária dessa disciplina nas escolas e a sua baixa presença no planejamento curricular nacional para o Ensino Médio, são indícios que a sociedade atribui pouca importância a esse componente curricular no ambiente escolar. Colabora para isso o fato de que mesmo com o aumento do número de professores atuando com práticas inovadoras nos últimos anos, o modo tradicional – centrado em poucas modalidades esportivas – e os casos de abandono docente ainda são maioria nas aulas da EF brasileira. Frente a isso, pesquisadores que assumem um posicionamento propositivo, para além de criticar as atuações dos professores nas escolas, têm apontado a formação continuada como uma possibilidade de mudança. No entanto, o formato da maioria das formações para os docentes de EF apresenta características de carga horária reduzida, poucos encontros e desconsideração pelos saberes e interesses dos professores. A partir desse diagnóstico, chega-se ao entendimento que passa a ser fundamental o investimento público em formação continuada de longo prazo baseada em estudos colaborativos com os professores. Tendo esse contexto como referência, esta pesquisa se centra na seguinte questão: de que modo um processo de formação continuada de longa duração, pautado nos pressupostos de uma EF renovada, pode contribuir para uma mudança na concepção de ensino de professores na qual o direito a aprender a pluralidade dos temas da cultura corporal de movimento seja central? Especificamente, buscou-se: compreender os conceitos e sentidos que orientam os docentes no processo de ensino na EF escolar; verificar a ocorrência – ou não – de uma mudança nas concepções dos professores em relação aos processos de ensino em decorrência de uma formação continuada oferecida; identificar os fatores que possibilitam a mudança na concepção de ensino dos professores; analisar como o formato e a condução da formação continuada, na lógica de uma experiência colaborativa, potencializa o processo de mudança de concepção. Para tanto, operou-se metodologicamente com a realização de uma investigação de abordagem qualitativa, caracterizada como uma pesquisa documental com a utilização de dados secundários como técnica de levantamento/aquisição de informações. Mais precisamente, foram analisados os seguintes documentos: materiais didático-pedagógicos produzidos por professores, anotações realizadas por docentes, imagens, transcrições das falas dos professores, um questionário com questões abertas, entrevistas com os participantes, anotações de um acadêmico-bolsista que acompanhou os encontros. Todos estes materiais são de propriedade da 36ª Coordenadoria Regional de Educação do Estado do Rio Grande do Sul, responsável por uma formação continuada que contou com a participação regular de 15 professores de EF, em 26 encontros de estudos realizados de novembro de 2015 a agosto de 2018. A análise dos documentos permite afirmar que: a) os professores possuem concepções prévias, enraizadas ao longo de sua vida profissional, que freiam o processo de mudança de concepção; b) à medida que o sentido da EF na escola não é claro para os docentes, eles não têm certeza sobre o que ensinar. Consequentemente, optam por abordar alguns esportes com os quais sentem-se mais à vontade; c) os professores se mostram incomodados com essa forma de atuação uma vez que não conseguem oportunizar aos alunos a aprendizagem acerca da pluralidade de temas da cultura corporal de movimento; d) ao tomarem contato com temas que desconheciam, os docentes passaram a suspeitar de suas concepções e de suas atuações nas aulas. Em consequência, emergiu um estado de angústia que diminuía ou aumentava de acordo com o que fazia sentido para eles; e) todos os participantes da formação continuada alteraram suas concepções de ensino sobre a EF escolar, contudo em níveis distintos. A partir da ideia de gradualidade, constatou-se que não houve um momento único gerador de mudança, ao contrário, vários fatores influenciaram a constituição de novos saberes, sendo os principais: o direito dos alunos aprender a pluralidade de temas da cultura corporal de movimento, a experimentação corporal dos temas estudados e a construção coletiva de uma proposta curricular para a EF em âmbito regional; f) o formato e a condução da formação continuada pelo viés dos estudos colaborativos, considerando as opiniões dos professores e incentivando sua participação ativa, foram fundamentais para as transformações nas formas de compreender a EF escolar. / The Physical Education (PE) at school in Brazil is going through a very delicate moment. Situations such as the decrease in the number of hours for that subject in schools and its low presence in the national curricular planning for high school are indications that society attaches little importance to it in the school environment. Such reality contributes to the fact that even with the increase in the number of teachers working with innovative practices in recent years, the traditional mode – centered on only a few sports modalities – and cases of teacher abandonment are still a majority in Brazilian PE classes. Against that, researchers who assume a propositional position, instead of just criticizing the teachers’ actions in schools, have pointed to continuing education as a possibility of change. However, the format of most formations for PE teachers presents characteristics of reduced workload, few meetings and disregard for the knowledge and teachers’ interests. Based on this diagnosis, it is concluded that public investment in long-term continuing education based on collaborative studies with teachers is essential. Taking this context as a reference, this research focuses on the following question: how can a long-term continuing education process, based on the assumptions of a renewed PE, contribute to change the conception of teacher education in which the right to learn a plurality of body culture of movement themes is central? Specifically, we searched: understanding the concepts and meanings that orient the teachers in the teaching process in the school PE; verifying the occurrence – or not – of change in the teachers’ conceptions in relation to the teaching processes as a result of a continuous formation offered; identifying the factors that make it possible to change the teacher’s education conception; analyzing how the format and the conduction of the continuous formation, in the logic of a collaborative experience, potentiates the process of change of conception. In order to do so, we performed methodologically with the accomplishment of a qualitative approach research, characterized as a documentary research with the use of secondary data as information gathering/acquisition technique. More precisely, the following documents were analyzed: educational materials produced by teachers, notes made by teachers, images, transcripts of teachers' speeches, a questionnaire with open questions, interviews with the participants and notes from an university student who’s accompanied the meetings. All these materials are the 36th Regional Education Coordination of Rio Grande do Sul State property, responsible for a continuous training that had the regular participation of 15 PE teachers in 26 meetings held from November 2015 to August 2018. The analysis of the documents shows that: a) the teachers have previous conceptions, rooted throughout their professional life, that restrain the process of conception change; b) as the sense of EF in school is not clear to teachers, they are not sure about what teaching. Consequently, they choose to approach some sports with which they feel more comfortable; c) teachers are uncomfortable with this form of action since they fail to give students the opportunity to learn about the plurality of themes of movement body culture; d) when they came into contact with unknown subjects, the teachers began to suspect their conceptions and their performances in the classes. As a consequence, a state of anguish emerged that diminished or increased according to what made sense to them; e) all participants in continuing education changed their conceptions of teaching on school PE, however in different levels. From the idea of graduality, it was verified that there was not a unique moment generating change, on the contrary, several factors influenced the constitution of new knowledge, being the main ones: the right of students to learn the plurality of themes of movement body culture, the corporal experimentation of the subjects studied and the collective construction of a curricular proposal for PE at the regional level; f) the format and conduct of continuing education through the collaborative studies bias, considering the teachers' opinions and encouraging their active participation, were fundamental for the transformations in the ways of understanding the school PE.

O presente trabalho apresenta uma análise dos saberes docentes desenvolvidos por futuros professores de física e algumas razões das dificuldades encontradas para a inserção de tópicos de Física Moderna e Contemporânea no Ensino Médio. A partir das definições dos saberes de Tardif (2002) procuramos identificar quais destes saberes estão sendo desenvolvidos pelos futuros professores e de que maneira a experiência de ensino vivenciada por eles contribuiu para sua formação profissional. A pesquisa é de natureza qualitativa e foi desenvolvida com alunos do último ano do curso de Licenciatura em Ciências Exatas (habilitação: Física), do Instituto de Física da USP de São Carlos - Universidade de São Paulo. Com os resultados encontrados, buscamos estabelecer algumas das dificuldades dos futuros professores para trabalhar tópicos de Física Moderna e Contemporânea em sala de aula e quais rumos podem ser tomados à procura de soluções que possam servir de base para o desenvolvimento de propostas de ensino desta natureza. / This research presents an analysis of teacher knowledge developed by prospective teachers of physical reasons and some of the difficulties in the inclusion of topics of Modern and Contemporary Physics in high school. From the definitions of knowledge by Tardif (2002) sought to identify which of these knowledge are being developed by prospective teachers and how the experience of teaching experienced by them contributed to their professional training. The research is qualitative in nature and is designed with students in their last year of the BSc in Exact Sciences (qualification: Physics), Institute of Physics of USP in São Carlos - University of Sao Paulo. With these results, we tried to establish some of the difficulties of future teachers to work topics Modern and Contemporary Physics classroom and what paths can be looking for solutions that can serve as a basis for the development of the education proposals of this nature.

O presente trabalho apresenta uma análise dos saberes docentes desenvolvidos por futuros professores de física e algumas razões das dificuldades encontradas para a inserção de tópicos de Física Moderna e Contemporânea no Ensino Médio. A partir das definições dos saberes de Tardif (2002) procuramos identificar quais destes saberes estão sendo desenvolvidos pelos futuros professores e de que maneira a experiência de ensino vivenciada por eles contribuiu para sua formação profissional. A pesquisa é de natureza qualitativa e foi desenvolvida com alunos do último ano do curso de Licenciatura em Ciências Exatas (habilitação: Física), do Instituto de Física da USP de São Carlos - Universidade de São Paulo. Com os resultados encontrados, buscamos estabelecer algumas das dificuldades dos futuros professores para trabalhar tópicos de Física Moderna e Contemporânea em sala de aula e quais rumos podem ser tomados à procura de soluções que possam servir de base para o desenvolvimento de propostas de ensino desta natureza. / This research presents an analysis of teacher knowledge developed by prospective teachers of physical reasons and some of the difficulties in the inclusion of topics of Modern and Contemporary Physics in high school. From the definitions of knowledge by Tardif (2002) sought to identify which of these knowledge are being developed by prospective teachers and how the experience of teaching experienced by them contributed to their professional training. The research is qualitative in nature and is designed with students in their last year of the BSc in Exact Sciences (qualification: Physics), Institute of Physics of USP in São Carlos - University of Sao Paulo. With these results, we tried to establish some of the difficulties of future teachers to work topics Modern and Contemporary Physics classroom and what paths can be looking for solutions that can serve as a basis for the development of the education proposals of this nature.