Submitted by Caroline Falcao (caroline.rfalcao@ufpe.br) on 2017-05-24T18:55:25Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação de Mestrado - Sivonaldo de Melo Sales.pdf: 2717745 bytes, checksum: 14edb0a72fbeb00d1f8ab2a373319dc5 (MD5) / Made available in DSpace on 2017-05-24T18:55:25Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação de Mestrado - Sivonaldo de Melo Sales.pdf: 2717745 bytes, checksum: 14edb0a72fbeb00d1f8ab2a373319dc5 (MD5) Previous issue date: 2015-08-07 / Apresentamos nossa pesquisa de mestrado que buscou investigar as ações de formação continuada implementadas nas Redes Municipais de Ensino da Microrregião do Vale do Ipojuca no Agreste Pernambucano para os professores que ensinam nos anos finais do Ensino Fundamental e, em particular, aquelas que focam o Ensino de Matemática. Como referencial teórico apoiamo-nos nos estudos de autores da área da Educação e da Educação Matemática. Para a coleta dos dados utilizamos os seguintes instrumentos: conversas iniciais, com o intuito de obter as primeiras informações sobre o campo de investigação; questionário semiestruturado, aplicado a diferentes participantes (diretores de ensino, coordenadores pedagógicos ou de área e secretários executivos de ensino, dentre outros); entrevistas semiestruturadas, com a finalidade de complementar as respostas obtidas com os instrumentos precedentes; análise documental, de documentos fornecidos pelas redes de ensino sobre as ações de formação no município no período de 2010 a 2014. Para a análise dos dados, baseamo-nos nas seguintes categorias: ações primárias, associadas aos programas e projetos ofertados pelo Ministério da Educação, Secretarias de Educação e por Organizações não Governamentais; e, ações secundárias, caracterizadas por palestras, aulas atividades, seminários, encontros pedagógicos, dentre outras ações correlatas. Também tentamos aproximar as ações de formação continuada com as características dos modelos de racionalidade técnica e racionalidade prática. Como ações do tipo primárias, identificamos nas Redes Municipais de Ensino investigadas dois programas de formação que contemplam o Ensino de Matemática o Programa Qualiescola II e o Programa Gestão da Aprendizagem Escolar (GESTAR II). Quanto às ações do tipo secundária, as análises revelam que raramente elas abordam o Ensino de Matemática. Um dos principais resultados da pesquisa aponta para uma certa omissão por parte das redes de ensino investigadas quanto à implementação de uma política de formação continuada para os professores e, em particular, para aqueles que ensinam Matemática nos anos finais do Ensino Fundamental. / We present our master ́s research who sought to investigate the continuing education action research implemented in the micro-region of the Teaching Municipal Networks Ipojuca Valley in Agreste Pernambucano for teachers who teach in the final years of primary education and, in particular, those that focus on Education Mathematics. As a theoretical framework we support the studies of authors in the field of Education and Mathematics Education. To collect the data we used the following instruments: initial conversations, in order to obtain the first information about the research field; semi-structured questionnaire, applied to different participants (school directors, coordinators or area, and teaching executive secretaries, among others); semi-structured interviews, in order to complement the responses obtained with previous instruments; documentary analysis of documents provided by the school systems on training activities in the municipality in the period 2010 to 2014. For the data analysis, we rely on the following categories: primary actions associated with the programs and projects offered by the Ministry of Education, Departments of Education and non-governmental organizations; and secondary actions, characterized by lectures, classes, activities, seminars, educational meetings, among other related actions. We also tried to approximate the continuous training activities with the characteristics of technical rationality models and practical rationality. As the primary type actions identified in the investigated Teaching Municipal Network two training programs that include the Teaching of Mathematics - the Qualiescola II Programme and the School Learning Management Programme (GESTAR II). As for the actions of the secondary type, the analysis reveals that they rarely approach the Teaching of Mathematics. One of the main results of the research points to a certain failure on the part of the investigated educational networks, as the implementation of a continuing education policy for teachers and, in particular, to those who teach Mathematics in the final years of elementary school.

The present research is linked to the studies of the academic master's degree in Teaching of Natural Sciences and Mathematics by the Universidade Federal de Sergipe / UFS in order to know how and what repercussions the new proposal of the test of the National High School Examination - ENEM determines the educational practice of teachers of Mathematics in High School in the public network of the State of Ceará. The central question of the research is: Which teaching practices of the mathematics teacher are worked on in his classes in High School, and how are these practices articulated to the new conception of the ENEM? This question unfolds in other guiding questions, through the relation of the teacher with the knowledge and its pedagogical discourse. Conceptual approach focuses on the following categories: relationship with knowledge (CHARLOT, 2000, 2005, 2013; SOUZA, 2009), public policies (MACEDO, 2012, MACEDO, DIÓGENES, 2014, LIBÈNEO, 2014), , 1998, 1999, 2002, 2007, 2012, 2015), and Mathematics Teaching (FIORENTINI, LORENZATO, 2006; MOREIRA, DAVID, 2010; COUNTRY, 2013) And ENEM (BRASIL, 1998, 1999, 2000, 2002, 2007, 2009, 2012; DIAS, 2009; MACHADO, 2009; RABELO, 2013 and MOREIRA, 2014). The main subjects of the research were sixteen mathematics teachers from three schools of the state of Ceará (schools A, B and C) and the secondary subjects were seven school coordinators of these respective units of education. The research was structured in two stages, starting with the application of a questionnaire to the subjects participating in the study, whose objective was to collect personal and professional data. The second stage refers to the focus group, carried out with the nine mathematics teachers of two schools (B and C), since the teachers of school A did not make themselves available to participate in the focus group. With the meetings of the focus group some issues related to educational practices were deepened under the perspective of the new conception of ENEM. Research mathematics teachers develop educational practices, such as lesson planning and execution, "long classrooms" (ENEM specific classes that usually involve students of 3 years of each shift, with the purpose of discussing and solving items From Mathematics Proof of previous editions of the exam), simulated and other activities, based on the principles and guidelines present in the official documents, therefore, with a new conception of ENEM. In this sense, his discourse presents itself with pedagogical practices that have invisible and visible rules. They are invisible when, for their work, not for instructional discourse; and visible, when they intentionally plan actions. Also, it was noticed that the relation with the knowledge teachers present themselves, the reflection on the fragilities of the teacher formation; The official pedagogical discourse is a practice of its own. / A presente pesquisa está vinculada aos estudos do mestrado acadêmico em Ensino de Ciências Naturais e Matemática pela Universidade Federal de Sergipe/UFS com o propósito de saber como e quais repercussões a nova proposta da prova do Exame Nacional do Ensino Médio – ENEM determina a prática educativa dos professores de Matemática no Ensino Médio na rede pública do Estado do Ceará. A questão central da pesquisa é: Quais práticas de ensino do professor de matemática são trabalhadas nas suas aulas no Ensino Médio, e como essas práticas estão articuladas à nova concepção do ENEM? Essa questão desdobra-se em outras questões norteadoras, por meio da relação do professor com o saber e do seu discurso pedagógico. Abordagem conceitual tem como foco as seguintes categorias: relação com o saber (CHARLOT, 2000, 2005, 2013; SOUZA, 2009), as políticas públicas (MACEDO, 2012, MACEDO; DIÓGENES, 2014; LIBÂNEO, 2014), Ensino Médio (BRASIL, 1998, 1999, 2002, 2007, 2012, 2015; FELIPPE, 2000; KUENZER, 2007; CARNEIRO, 2012), ensino de matemática (FIORENTINI; LORENZATO, 2006; MOREIRA; DAVID, 2010, PAIS, 2013) e o Ensino Médio e ENEM (BRASIL, 1998, 1999, 2000, 2002, 2007, 2009, 2012; DIAS, 2009; MACHADO, 2009; RABELO, 2013; MOREIRA, 2014). Os sujeitos principais da pesquisa foram dezesseis professores de Matemática de três escolas da rede estadual cearense (escolas A, B e C) e os sujeitos secundários foram sete coordenadores escolares dessas respectivas unidades de ensino. A pesquisa foi estruturada em duas etapas, iniciando com aplicação de um questionário aos sujeitos participantes do estudo, cujo objetivo foi levantar dados pessoais e profissionais. A segunda etapa refere-se ao grupo focal, realizado com os nove professores de Matemática de duas escolas (B e C), visto que os professores da escola A não se disponibilizaram a participar do grupo focal. Com os encontros do grupo focal foram aprofundadas algumas questões relacionadas às práticas educativas sob a perspectiva da nova concepção de ENEM. Os professores de Matemática desta pesquisa desenvolvem práticas educativas, como o planejamento e a realização de aulas, “aulões” (aulas específicas para o ENEM que, em geral, envolvem os alunos dos 3º anos de cada turno, com o objetivo de discutir e resolver itens da prova de Matemática de edições anteriores do exame), simulados e outras atividades, com base nos parâmetros e diretrizes presentes nos documentos oficiais, portanto, com ênfase na nova concepção de ENEM. Nesse sentido, o seu discurso apresenta-se com práticas pedagógicas que têm regras invisíveis e visíveis. São invisíveis quando, ao realizarem seu trabalho, não tomam consciência do discurso instrucional; e visíveis, quando planejam ações de forma intencional. Também, percebeu-se que a relação com o saber desses professores se apresenta, ao refletirem sobre as fragilidades da formação docente; o discurso pedagógico oficial e a própria prática.

Made available in DSpace on 2014-07-29T15:00:25Z (GMT). No. of bitstreams: 1 dissertacao lusitonia1.pdf: 1368129 bytes, checksum: 989173bc992d019898f59fa553e6c318 (MD5) Previous issue date: 2009-03-30 / Concrete materials are part in the searching of learning methods that allow a better understanding in the learning of mathematics. In this work, I research how do students with difficulties in learning express Mathematics comprehension when they deal with the Cuisenaire Material in a learning situation, and what do they understand from it? The investigation basis was the Experiencing Mathematics in Elementary School project developed in CEPAE (Center of Teaching and Research Applied in the Education of UFG). The data collection happened in five meetings/classes performing activities on the basic arithmetic operations. The participants are twelve students from 5º e 6º grades who have a low learning performance, according to their mathematics teachers. In terms of procedure, we used the qualitative research on the perspective of the phenomenological approach. Once a contact was established among the students speech, my interpretations on their speeches and the theories used to support my interpretations, I think this material revealed itself significant and the students demonstrated comprehension on the basic arithmetic operations. Seeing, thinking, combining parts to the numbers, comparing them, putting them in order, compounding and decompounding them, replacing values, working over their own acts and thoughts, sharing ideas with classmates, and being attentive lead students to experience discoveries. Based in what was experienced in this research, I present some contributions to teachers who intend to use the Cuisenaire material to teach their students. / Os materiais concretos fazem parte da busca de métodos de ensino que possibilitem um melhor entendimento no aprendizado da Matemática. Com esta pesquisa, investigo como alunos com dificuldades de aprendizagem expressam compreensões matemáticas ao lidarem com o Material Cuisenaire em situação de ensino, e o que compreendem nessa lida? O solo de investigação foi o projeto Vivenciando a Matemática no Ensino Fundamental, desenvolvido no CEPAE (Centro de Ensino e Pesquisa Aplicado à Educação da UFG). A coleta de dados se deu em cinco encontros/aula, realizando atividades sobre as operações fundamentais. Os sujeitos são doze alunos do 5º e 6º anos que apresentavam baixo rendimento escolar segundo seus professores de Matemática. Em termos de procedimentos, inserimo-nos na pesquisa qualitativa sob a perspectiva da abordagem fenomenológica. Com as interlocuções estabelecidas entre as falas dos alunos, minhas interpretações dessas falas e as teorias que dialogam com as interpretações que fiz, posso dizer que o referido material se mostrou significativo para que os alunos expressassem compreensões acerca das operações fundamentais. Vendo, pensando, relacionando as peças aos números, comparando-as, colocando-as em ordem, compondo, decompondo, trocando valores, agindo sobre seus próprios atos e pensamentos, compartilhando idéias com os colegas, pondo-se em atentividade ao que faziam, os alunos experienciaram a arte de descobrir. Diante do experienciado na trajetória da pesquisa, apresento algumas contribuições ao professor que se propuser utilizar o Material Cuisenaire para ensinar Matemática.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-07-20T12:47:41Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação de Mestrado - Sivonaldo de Melo Sales.pdf: 2717745 bytes, checksum: 14edb0a72fbeb00d1f8ab2a373319dc5 (MD5) / Made available in DSpace on 2017-07-20T12:47:41Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação de Mestrado - Sivonaldo de Melo Sales.pdf: 2717745 bytes, checksum: 14edb0a72fbeb00d1f8ab2a373319dc5 (MD5) Previous issue date: 2015-05-25 / Apresentamos nossa pesquisa de mestrado que buscou investigar as ações de formação continuada implementadas nas Redes Municipais de Ensino da Microrregião do Vale do Ipojuca no Agreste Pernambucano para os professores que ensinam nos anos finais do Ensino Fundamental e, em particular, aquelas que focam o Ensino de Matemática. Como referencial teórico apoiamo-nos nos estudos de autores da área da Educação e da Educação Matemática. Para a coleta dos dados utilizamos os seguintes instrumentos: conversas iniciais, com o intuito de obter as primeiras informações sobre o campo de investigação; questionário semiestruturado, aplicado a diferentes participantes (diretores de ensino, coordenadores pedagógicos ou de área e secretários executivos de ensino, dentre outros); entrevistas semiestruturadas, com a finalidade de complementar as respostas obtidas com os instrumentos precedentes; análise documental, de documentos fornecidos pelas redes de ensino sobre as ações de formação no município no período de 2010 a 2014. Para a análise dos dados, baseamo-nos nas seguintes categorias: ações primárias, associadas aos programas e projetos ofertados pelo Ministério da Educação, Secretarias de Educação e por Organizações não Governamentais; e, ações secundárias, caracterizadas por palestras, aulas atividades, seminários, encontros pedagógicos, dentre outras ações correlatas. Também tentamos aproximar as ações de formação continuada com as características dos modelos de racionalidade técnica e racionalidade prática. Como ações do tipo primárias, identificamos nas Redes Municipais de Ensino investigadas dois programas de formação que contemplam o Ensino de Matemática o Programa Qualiescola II e o Programa Gestão da Aprendizagem Escolar (GESTAR II). Quanto às ações do tipo secundária, as análises revelam que raramente elas abordam o Ensino de Matemática. Um dos principais resultados da pesquisa aponta para uma certa omissão por parte das redes de ensino investigadas quanto à implementação de uma política de formação continuada para os professores e, em particular, para aqueles que ensinam Matemática nos anos finais do Ensino Fundamental. / We present our master´s research who sought to investigate the continuing education action research implemented in the micro-region of the Teaching Municipal Networks Ipojuca Valley in Agreste Pernambucano for teachers who teach in the final years of primary education and, in particular, those that focus on Education Mathematics. As a theoretical framework we support the studies of authors in the field of Education and Mathematics Education. To collect the data we used the following instruments: initial conversations, in order to obtain the first information about the research field; semi-structured questionnaire, applied to different participants (school directors, coordinators or area, and teaching executive secretaries, among others); semi-structured interviews, in order to complement the responses obtained with previous instruments; documentary analysis of documents provided by the school systems on training activities in the municipality in the period 2010 to 2014. For the data analysis, we rely on the following categories: primary actions associated with the programs and projects offered by the Ministry of Education, Departments of Education and non-governmental organizations; and secondary actions, characterized by lectures, classes, activities, seminars, educational meetings, among other related actions. We also tried to approximate the continuous training activities with the characteristics of technical rationality models and practical rationality. As the primary type actions identified in the investigated Teaching Municipal Network two training programs that include the Teaching of Mathematics - the Qualiescola II Programme and the School Learning Management Programme (GESTAR II). As for the actions of the secondary type, the analysis reveals that they rarely approach the Teaching of Mathematics. One of the main results of the research points to a certain failure on the part of the investigated educational networks, as the implementation of a continuing education policy for teachers and, in particular, to those who teach Mathematics in the final years of elementary school.

The aim of this study is to learn more about how teachers experience student’s engagement and how they work to engage their students. The study focuses on teachers who teaches the lower grades. The essential method of the study is semi structured interviews with teachers who teach mathematics in grades 1-3. The study showed that teachers characterize student engagement in that students are positive, curious, involved, show interest and that they take initiative. This indicates a behavioural engagement. The teachers work with level adjustment and varying teaching to engage the students which indicates a cognitive engagement. Important prerequisites for a student involvement were smaller groups and to meet the students’ needs and interests. One condition that was considered to have a negative effect on student engagement was a lack of time in teacher’s planning and teaching. The conclusion shows that teachers look at student engagement through behavioural engagement but that they work to increase student engagement through cognitive engagement.

Orientador: Sergio Roberto Nobre / Resumo: Esta pesquisa é um convite à reflexão sobre a Matemática presente nas práticas educativas no âmbito da Escola Doméstica de Natal, instituição de ensino dedicado à formação feminina, modelada segundo o sistema da École Mánagère de Friburgo (Suíça), idealizada pela Liga de Ensino do Rio Grande do Norte e inaugurada em 1914, funcionando até os dias atuais. Assim, entre tantas outras inquirições é que surgiu a nossa pergunta de pesquisa: como a matemática, enquanto ciência, legitima o discurso de reinvindicação de uma escola doméstica, de modelo suíço, no estado do Rio Grande do Norte, nas primeiras décadas do século XX? As respostas foram sendo construídas ao longo da pesquisa, por meio dos documentos analisados nos arquivos inventariados, principalmente, no Arquivo Público Estadual do Rio Grande do Norte, na Hemeroteca da Biblioteca Nacional, no acervo do Museu da Escola Doméstica e no Repositório do Laboratório de Imagens da Universidade Federal do Rio Grande do Norte, entre estes: boletins, Atas, Ofícios, Relatórios dos Diretores da Instrução Pública; em Leis, Decretos, Mensagens do Governo do estado, além de artigos de jornais e revistas. Para tanto, entrelaçamos no nosso texto as histórias dos intelectuais, história das instituições de ensino, imprensa pedagógica, ensino de matemática e as práticas a ele relacionadas, para discutir acerca do papel social da mulher norte-rio-grandense, nomeadamente, a respeito dos valores educativos a ela voltados – tão caracterizantes daque... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This research is an invitation to reflect on the Mathematics present in educational practices within the scope of the Escola Doméstica de Natal (Domestic School of Natal), an educational institution dedicated to female training, modeled after the École Mánagère system in Friborg (Switzerland), idealized by the Rio Teaching League Grande do Norte and opened in 1914, functioning until today. Thus, among many other inquiries, our research question arose: how mathematics, as a science, legitimizes the claim of a domestic school, of Swiss model, at Rio Grande do Norte state, in the first decades of the 20th century? The answers were constructed throughout the research, through the documents analyzed in the inventoried archives, mainly in the State Public Archive of Rio Grande do Norte, in the National Library's Hemeroteca, in the collection of the Museum of the Domestic School and in the Repository of the Images Laboratory from Rio Grande do Norte Federal University, including: bulletins, Records, Officials, Reports from the Directors of Public Education; in Laws, Decrees, Messages from the State Government, in addition to newspaper and magazine articles. To this end, we intertwine in our text the stories of intellectuals, the history of educational institutions, the pedagogical press, the teaching of mathematics and the practices related to it, to discuss the social role of women from the Rio Grande do Norte State, namely, regarding educational values aimed at it - so characteris... (Complete abstract click electronic access below) / Resumen: Esta investigación es una invitación a reflexionar sobre las Matemáticas presentes en las prácticas educativas dentro del alcance de la Escuela Doméstica de Natal, una institución educativa dedicada a la formación femenina, inspirada en el sistema École Mánagère en Friburgo (Suiza), idealizada por la Liga de Enseñanza de Río Grande do Norte e inaugurado en 1914, funcionando aún en la actualidad. Así, entre muchas otras inquietudes, surgió nuestra pregunta de investigación: ¿Cómo las matemáticas, como ciencia, legitiman el reclamo de una escuela doméstica, de modelo suizo, en el estado de Rio Grande do Norte, en las primeras décadas del siglo XX? Las respuestas se construyeron a lo largo de la investigación, a través de los documentos analizados en los archivos inventariados, principalmente en el Archivo Público del Estado de Rio Grande do Norte, en la Hemeroteca de la Biblioteca Nacional, en la colección del Museo de la Escuela Doméstica como también en el Repositorio del Laboratorio de Imágenes de la Universidad Federal de Río Grande del Norte, incluidos: boletines, actas de funcionarios, informes de directores de educación pública; en Leyes, Decretos, Mensajes del Gobierno del Estado, así como artículos de periódicos y revistas. Con este fin, entrelazamos en nuestro texto las historias de los intelectuales, la historia de las instituciones educativas, la prensa pedagógica, la enseñanza de las matemáticas y con ella sus prácticas relacionadas, para discutir el papel social d... (Resumen completo clicar acceso eletrônico abajo) / Doutor

This thesis deals with an introduction to variables. The aim of the thesis was to compare different approaches to teaching the introduction to variables in teachers who teach a method based on building schemes (known as Hejny method). The theoretical part of the thesis is a search of literature on the topic of introduction to variables and the theoretical background of teaching methods based on building schemes. Further, the thesis analyses textbooks designed for this method with a focus on tasks important for the propaedeutics of the variables. The research itself consisted of interviews with four teachers and observations of the lessons they taught in the 7th and 8th grades of secondary school, the topic of which was an introduction to the "language of letters". In total, there were fifteen lessons taught by these teachers in six classes (2-3 lessons in each class). Data were analyzed by qualitative methods. Although the observed teachers taught using the same method, I identified differences in the approach to the introduction of the variables and in the style of their teaching. There were differences in the organization of the lesson, in the selection of tasks and their style of assignments to pupils, teaching methods and ways in which teachers communicate with pupils. At the moment of entering the...

In traditional schooling, one-way monologue from teacher to student is the established way of communica­tion in the classroom. Modern pedagogues are presently breaking free of this status quo.  This master thesis explores whether there is a change in the student’s attitudes towards their school­ing and whether there is an academic benefit for the student when applying a flipped class­room model. This study was performed in Swedish upper secondary school during the students’ last course in mathematics. The study was carried out using focus group interviews and direct participat­ing observation. During the six-week period of interviews and participating in the class­room written tasks were collected and analysed, and the classroom was filmed to help analysing behav­iour of the students, both with flipped classroom and without. The outcome shows positive reac­tions from the students concerning this change in pedagogics, but also some inertia in some individuals. The result shows a positive attitude change concerning communication and collabora­tion in the classroom, although no difference in academic achievement were visible. More studies are needed, but a theoretical base needs to be built before future studies can be con­ducted. Today flipped classroom is undertheorized in ways of an academic model. Future research could be theorizing flipped classroom and exploring whether implementing this pedagogic model also brings forth a change in academic achievement apart from changing the attitudes of the stu­dents.

Dem Erwerb geometrischer Kompetenzen wird in der Primarstufe im Allgemeinen eine wichtige Bedeutung zugemessen. Geometrische Inhalte finden sich in Deutschland sowohl in den nationalen Bildungsstandards als auch in den Lehrplänen der Bundesländer wieder. An einer strukturierten empirischen Aufarbeitung der Kompetenzentwicklung, der Fähigkeiten sowie der Schwierigkeiten der Schülerinnen und Schüler in der Auseinandersetzung mit diesen Inhalten mangelt es dennoch in einigen dieser Bereiche. Damit einhergehend fehlen auch erforderliche Grundlagen, die es Lehrkräften ermöglichen, Unterricht planen zu können und somit ein anschlussfähiges Verständnis bei den Schülerinnen und Schülern aufzubauen. Aus der Lehrerprofessionsforschung liegen Modelle vor, welche zentrale Wissensfacetten, die eine Rolle bei der unterrichtlichen Vermittlung fachlicher Inhalte spielen, beschreiben (u.a. Weinert, Schrader & Helmke 1990; Shulman 1986; Bromme 1992, 1997; Baumert & Kunter 2006, 2011; Ball, Thames & Phelps 2008). Insbesondere dem fachlichen sowie dem fachdidaktischen Wissen der Lehrperson wird eine entscheidende Rolle bezüglich des Lernerfolgs der Schülerinnen und Schüler zugeschrieben (u.a. Kunter et al. 2013). Ein geometrischer Inhaltsbereich, in dem bereits Wissen vorliegt, auf das Lehrerinnen und Lehrer zurückgreifen können, ist die Achsenspiegelung und -symmetrie. Dieses Wissen bezieht sich jedoch überwiegend auf die Sekundarstufe und ist wenig systematisch angelegt bzw. lückenhaft. Diese Arbeit verfolgt daher das Ziel, systematisch Wissen herauszuarbeiten, auf das Lehrkräfte zurückgreifen können, um im Geometrieunterricht der Grundschule fachlich fundierte Entscheidungen treffen zu können und im Bereich der Achsenspiegelung und Achsensymmetrie mit Bezug auf die individuellen Fähigkeiten der Schülerinnen und Schüler ein anschlussfähiges und tragfähiges Verständnis aufzubauen. Basierend auf einer integrativen Betrachtung der Facetten professionellen Wissens werden inhaltsspezifisch relevante Facetten des Wissens von Lehrkräften herausgearbeitet. Diese Perspektiven der Lehr-Lern-Forschung werden aufgegriffen und bieten eine Rahmung zur fachlichen und fachdidaktischen Einordnung der einzelnen Forschungsarbeiten dieser Dissertation. Die Forschungsschwerpunkte dieser Arbeit werden daraufhin ebenfalls in der Rahmung verankert, anschließend vorgestellt und ihre Ergebnisse zusammengefasst. • Der erste Forschungsschwerpunkt setzt sich mit wichtigen Grundlagen zu spezifischen Anforderungen von Aufgabenstellungen sowie typischen schwierigkeitsgenerierenden Merkmalen bei der Achsenspiegelung und Achsensymmetrie auseinander (vgl. Götz & Gasteiger 2019; Götz et al. 2020; Götz 2018). Dabei führt der Abgleich psychometrisch erfasster Aufgabenschwierigkeiten mit inhaltlich fachdidaktischen Analysen der Fehler und theoretischen Erkenntnissen zur Achsenspiegelung zu einem Kategorienschema mit unterschiedlichen schwierigkeitsgenerierenden Merkmalen bei Aufgaben zur Achsenspiegelung und deren Ausprägungen. • Der zweite Forschungsschwerpunkt nimmt das Wissen über das mathematische Denken von Schülerinnen und Schülern bei der Achsenspiegelung in den Fokus. Um dieser Frage nachzugehen, wurden in dieser Studie Äußerungen der Schülerinnen und Schüler während ihrer Lösungsprozesse bei Aufgaben zur Achsenspiegelung beobachtet und analysiert (vgl. Götz & Gasteiger 2022). Der Mehrwert dieser Arbeit liegt insbesondere in den Erkenntnissen zu fachdidaktischem Wissen bezüglich des Unterrichtens der Achsensymmetrie und Achsenspiegelung in der Grundschule. Ein Kategorienschema zu den schwierigkeitsgenerierenden Merkmalen bei der Achsenspiegelung, ein Überblick über Fehlerarten bei Aufgaben zur Achsensymmetrie sowie Zusammenstellungen, die Rückschlüsse auf das Verständnis von Schülerinnen und Schülern bei der Achsenspiegelung ermöglichen, bieten eine wertvolle Wissensbasis für Lehrkräfte in der Grundschule. Für die Unterrichtspraxis sind die Ergebnisse dieser Arbeit an unterschiedlichen Stellen relevant. Zum einen stellen die Ergebnisse dieser Arbeit ein Handlungsgerüst zur Erstellung adäquater Aufgaben, zum anderen liefern sie eine wertvolle Unterstützung bei der Kompetenzdiagnostik. Gleichzeitig geht aus den Ergebnissen dieser Arbeit die hohe Bedeutung adäquater Unterrichtsmaterialien hervor – wobei diesbezüglich wertvolle Hinweise zur Auswahl geeigneter Arbeitsmittel gegeben werden.

The author shares some of the findings of the research he conducted in 2007 on grade 11 mathematics learners in two schools, one experimental and the other one control. In his study, the author claims that an open-ended approach towards teaching and learning of mathematics enhances understanding of mathematics by the learners. The outcomes of the study can be summarised as follows: 1. In the experimental school, where the author intervened by introducing an open-ended approach to teaching mathematics (by means of giving the learners an open-ended approach compliant worksheet to work on throughout the intervention period), the performance of the learners in the post-test was better than that of the learners from the control school. Both schools were of similar performance in the pre-test. The two schools wrote the same pre-test and same post-test. Both schools were following common work schedule. 2. Within the experimental school, post-test performance of the learners in the class where the intervention was monitored throughout the intervention period (thus ensuring compliance of the teacher to the open-ended approach) out-performed those in which monitoring was less frequent. 3. There was no significant difference in performance between learners from the unmonitored experimental class and those from the control class.