Licentiatavhandlingen riktar blicken mot planeringsarbete i förskolan. Syftet är att beskriva och analysera förskollärares autentiska planering av barns möten med matematik. Studiens teoretiska inramning utgörs av den reflektiva skoldidaktiska teorin som betonar, oavsett skolform, lärares ansvarstagande för undervisning. Med den reflektiva skoldidaktiska teorin beskrivs planeringsprocessen som betydelsefull för undervisning. Planeringsprocessen utgörs av tre pedagogiska aktiviteter: intention – handling – reflektion. I denna studie fokuseras det pedagogiska arbete som sker distanserat från handling vilket gör intention och reflektion till studiens centrala begrepp. Studiens empiriska material har producerats med hjälp av deltagande observation. Fältarbetet har genomförts i en förskola på deltid under två terminer läsåret 2012/13 i ett arbetslags återkommande och autentiska planeringssamtal. Resultatet visar att arbetslaget planerar barns möten med matematik genom att de tar sin utgångspunkt i reflektion över planerade och dokumenterade pedagogiska skeenden. Det finns därmed en koppling mellan intention och reflektion. Resultatet visar att arbetslaget har konstruerat en egen planeringsmodell. Förskollärarna utgår inte från explicit uttryckta målformuleringar som anger vad som ska läras utan resonemang om möjligt lärande kommer in som en del i deras samtal om aktiviteter. Resultatet visar även att arbetslagets planering skapar förutsättningar för möten med en mångfald av matematik. Dock visar resultatdiskussionen att det finns utrymme för att utveckla resonemang kring vilka sätt barn kan få göra övergångar från vardagliga matematiska representationsformer till mer abstrakta. Resultatet visar även att det finns ett behov av att utveckla ett matematikdidaktiskt yrkesspråk i förskolan. / Nyckelord: förskola, planering, didaktik, matematikundervisning  This Licentiate thesis focuses on planning in Swedish preschool. The aim is to describe and analyze pre-school teacher's authentic planning of children's meetings with mathematics. The theoretical framing of the study consists of the reflective school didactic theory emphasizing, regardless of school form, teachers' responsibility for teaching. With the reflective school didactic theory, the planning process is described as important for teaching. The planning process consists of three pedagogical activities: intention – action – reflection. This study focuses on the pedagogical work that takes place away from action, which makes intention and reflection to the central concept of the study. The empirical material of the study has been produced using participatory observation. Field work has been carried out in a preschool on part time for two semesters in the academic year 2012/13 in a regular and authentic planning conversation. The results show that the pre-school teachers do plan children's meetings with mathematics by taking their starting point in reflection on planned and documented pedagogical events. There is thus a link between intention and reflection. The result shows that the team has construct a planning model of their own. The planning is not based on explicit expressed goal formulations about what to learn. The reasoning of possible learning comes in as part of their conversations about activities. The result also shows that planning creates conditions for meetings with a multitude of mathematics. However, the results discussion shows that there is room to develop reasoning about the ways in which children can make transitions from everyday mathematical representations to more abstract. The result also shows that there is a need to develop a mathematics didactic language in preschool. Nyckelord: förskola, planering, didaktik, matematikundervisning  This Licentiate thesis focuses on planning in Swedish preschool. The aim is to describe and analyze pre-school teacher's authentic planning of children's meetings with mathematics. The theoretical framing of the study consists of the reflective school didactic theory emphasizing, regardless of school form, teachers' responsibility for teaching. With the reflective school didactic theory, the planning process is described as important for teaching. The planning process consists of three pedagogical activities: intention – action – reflection. This study focuses on the pedagogical work that takes place away from action, which makes intention and reflection to the central concept of the study. The empirical material of the study has been produced using participatory observation. Field work has been carried out in a preschool on part time for two semesters in the academic year 2012/13 in a regular and authentic planning conversation. The results show that the pre-school teachers do plan children's meetings with mathematics by taking their starting point in reflection on planned and documented pedagogical events. There is thus a link between intention and reflection. The result shows that the team has construct a planning model of their own. The planning is not based on explicit expressed goal formulations about what to learn. The reasoning of possible learning comes in as part of their conversations about activities. The result also shows that planning creates conditions for meetings with a multitude of mathematics. However, the results discussion shows that there is room to develop reasoning about the ways in which children can make transitions from everyday mathematical representations to more abstract. The result also shows that there is a need to develop a mathematics didactic language in preschool.

Ambitionen med detta arbete är att undersöka problemlösning som undervisningsmetod och dess eventuella påverkan på elevernas attityd kring matematik. Problemlösning kan, när den används och anpassas efter elevernas behov, vara ett fruktbart verktyg i matematikundervisning som gynnar lärandet och förståelse. Enligt forskningen som presenteras i texten kan elever dra fördel av problemlösning. Vissa länder som exempelvis Japan, har problemlösning som norm i sin matematikundervisning. Sveriges undervisningsnorm när det gäller matematik tenderar mer att vara kateder/konventionell undervisning i vilken matematikläroböcker spelar en central roll. Matematikläroböckerna i sin tur underbygger imitation som uppgiftslösningsmetod och är vanliga i det svenska klassrummet, och problemlösningsmetoder är mindre användbara (Sidenvall, 2019). Problemlösning är centralt i området matematik och är en viktig del av läroplanen i det svenska gymnasiet (Skolverket, 2022), och visar sig förstärka matematisk förståelse hos elever. Å andra sidan utgör problemlösning inte alltid kärnan av matematikundervisning. Vissa av anledningarna till det beskrivs bland annat av Rodley & Bailey (2021).    Matematisk problemlösning innebär att elever bygger upp sin förståelse genom att utveckla sin egen repertoar av strategier för att lösa problem. I processen kommer de sannolikt att uppleva perioder av osäkerhet och behöver stöd för att fortsätta. Problemlösning kan vara tidskrävande eftersom ett verkligt problem kräver tid för elever att utforska och diskutera möjliga strategier (Rodley & Bailey, 2021). Implementeringssvårigheter och strategier utvecklas närmare i resultatet där det framgår att problemlösning är fördelaktigt och att elever uppvisar positiva attityder till problemlösning. Å andra sidan kan implementeringen av exempelvis undervisningsmetoder som används i andra länder medföra kulturella skillnader som kan vara svårt att bortse ifrån. Dessutom krävs för en problemlösande undervisningsmetod lämpligt material och resurser som för lärarna, enligt forskningen, kan vara utmanande att komma åt.

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The purpose of the study was to highlight how and why teachers choose to plan and implement theirmathematics teaching using manipulatives for grades Pre-school class to grade 3. To obtain datacontaining thoughts and descriptions of a phenomenon, we used the semi-structured interview method.Ten teachers from grades F-3 distributed across seven schools in central Sweden answered our interviewguide which contained seventeen questions. The answers were analyzed using a phenomenographicanalysis to bring out data with similarities and differences. The results showed that there weredifferences in how teachers described the use of manipulatives and this affected the degree to which theychose to plan and carry out their teaching using informal learning. The respondents clearly expressedthat manipulatives were important to use, but that there were several reasons why they were not used.The result also showed that manipulatives methods were associated with the manipulatives just as wehave seen in previous research that has focused on manipulatives and not the working method. Thismeans that our study can contribute new knowledge about possibilities and challenges when it comes tothe use of laborative methods by teachers when they plan and carry out mathematics teaching. / Syftet med vår studie var att belysa hur och varför lärare väljer att planera och genomföra sinmatematikundervisning med hjälp av laborativa arbetssätt för årskurs F-3. För att få fram den data somvisade lärarens perspektiv kring användandet av laborativa arbetssätt i matematikundervisningenanvände vi oss av metoden semistrukturerad intervju. Tio lärare från årskurserna F-3 fördelat på sjuskolor i mellersta Sverige besvarade vår intervjuguide som innehöll 17 frågor. Svaren analyserades medhjälp av en fenomenografisk analys för att få fram data med likheter och skillnader. Resultatet visade attdet fanns skillnader i hur lärare beskrev användandet av laborativa arbetssätt. Detta påverkade i vilkengrad de valde att planera och genomföra sin undervisning med hjälp av laborativa arbetssätt. Trots attrespondenterna tydligt uttryckte att laborativa arbetssätt var något viktigt att använda sig av fanns detflera orsaker till att de inte användes. Resultatet visade också att laborativa arbetssätt förknippades meddet konkreta materialet precis som vi sett i tidigare forskning som riktat in sig på laborativt material ochinte arbetssättet. Detta gör att vår studie kan bidra med nya kunskaper kring möjligheter och utmaningarmed laborativa arbetssätt hos lärare när de planerar och genomför matematikundervisningen.

Thesis advisor: Lillie Richardson Albert / The purpose of this research is to identify the categories of South Korean elementary teachers' knowledge for teaching mathematics. Operating under the assumption that elementary teachers' knowledge for teaching affects students' learning, eleven South Korean elementary teachers volunteered to participate in this study. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers' knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. A notable conclusion of this study is that Pedagogical Content Knowledge might not be the sum of the other categories of knowledge for teaching mathematics. These findings may be connected to results from relevant studies in terms of the significant role of teachers' knowledge in their mathematics instruction. This study contributes to the existing literature in that it provides empirical bases for understanding teachers' knowledge for teaching mathematics and reveals the relationship among categories of knowledge for teaching mathematics. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Lynch School of Education. / Discipline: Teacher Education, Special Education, Curriculum and Instruction.

Made available in DSpace on 2016-04-04T18:32:58Z (GMT). No. of bitstreams: 1 Regis Forner.pdf: 1235167 bytes, checksum: bda94113e98a785d43b2adac7fa90ac9 (MD5) Previous issue date: 2005-06-07 / This work is part of the line of research University, Teaching and Teacher Formation . It investigates the influences of Paulo Freire s theory upon the formation of mathematics teachers from the point of view of eight renowned researchers of the Mathematical Education area. Its objective is to present possible relationships between Mathematical Education and the theory of Paulo Freire to teachers of basic and higher education and to obtain useful material for the discussion of their formation, both initial and continued. A brief bibliography of Paulo Freire, ideas about his theory and teaching Mathematics were presented with the intention of raising points they have in common. The methodological approach of Oral History was used in order to find new elements for the intended analysis. Theme type interviews made it possible to survey some categories that show how much Paulo Freire s theory can contribute to the formation of Mathematics teachers. The study points out convergences between the referred theory related to Paulo Freire s theory and teaching Mathematics and Oral History since in general both focus on the oppressed. The study instigates the exploration of other paths in Paulo Freire s work that could contribute to teaching Mathematics and helping the formation of the Mathematics teacher. / O presente trabalho, inserido na linha de pesquisa Universidade, Doc?ncia e Forma??o de Professores , busca investigar as influ?ncias da teoria de Paulo Freire, sob a ?tica de oito renomados pesquisadores da ?rea da Educa??o Matem?tica, na forma??o do professor de Matem?tica. Tem por objetivo apresentar aos docentes da educa??o b?sica e ensino superior as poss?veis rela??es entre a Educa??o Matem?tica e a teoria de Paulo Freire, e obter subs?dios para discutir sua forma??o, seja inicial ou continuada. Apresentou-se um breve relato bibliogr?fico de Paulo Freire, e id?ias sobre sua teoria e sobre a Educa??o Matem?tica, buscando levantar pontos comuns entre elas. Utilizou-se a Hist?ria Oral como abordagem metodol?gica por considerar prop?cia ? busca de novos elementos para a an?lise pretendida. A entrevista tem?tica possibilitou o levantamento de algumas categorias que mostram o quanto a teoria de Paulo Freire pode contribuir para a forma??o do professor de Matem?tica. A pesquisa aponta converg?ncias entre o referencial te?rico, relacionado ? teoria de Paulo Freire e ? Educa??o Matem?tica, e a Hist?ria Oral, visto que, de forma geral, ambos t?m como foco o oprimido, e instiga outros caminhos a serem explorados na obra de Paulo Freire que podem contribuir para a Educa??o Matem?tica e para a forma??o do professor de Matem?tica.

Submitted by Eunice Novais (enovais@uepg.br) on 2018-03-01T13:43:37Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) -Alessandra-Assad.pdf: 8992837 bytes, checksum: 39109f11342ebe17bfb50e8dcd0365a8 (MD5) / Made available in DSpace on 2018-03-01T13:43:37Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) -Alessandra-Assad.pdf: 8992837 bytes, checksum: 39109f11342ebe17bfb50e8dcd0365a8 (MD5) Previous issue date: 2017-12-14 / O presente trabalho teve como finalidade a investigação dos níveis do pensamento geométrico de estudantes de um colégio público da cidade de Paranaguá/PR, tendo como fundamentação teórica a Teoria de Van Hiele. Dessa forma para atingir o objetivo proposto utilizou-se das Tecnologias Educacionais, por meio de atividades desenvolvidas com o software Geogebra. Os participantes da pesquisa eram estudantes de três turmas do primeiro ano do Ensino Médio de um colégio público da cidade de Paranaguá. Estes realizaram 13 (treze) atividades correspondentes as 15 (quinze) habilidades indicadas no referencial teórico utilizado, divididas em três níveis: nível 0 (visualização), nível 1 (análise), nível 2 (dedução informal). A metodologia utilizada para esta pesquisa tratou-se da forma exploratória e aplicada. Pela análise dos dados coletados na resolução das atividades, pode-se concluir que o nível 0 foi atingido pela maior parte dos estudantes, uma menor porcentagem dos estudantes conseguiu atingir o nível 1. Em relação ao nível 2 pode-se verificar que foi o nível com maior dificuldade nas três turmas. Estes resultados apontam que os estudantes do colégio, onde se realizou a pesquisa, não detêm as habilidades visual, verbal, lógica, desenho e aplicação condizentes com o nível de ensino, segundo a Teoria de Van Hiele. Diante da evidente defasagem no conteúdo de Geometria apresentada pelos estudantes, pode-se dizer que além do objetivo proposto, esta pesquisa corrobora com os trabalhos de Pavanelo(1993), Lorenzato (1995), Passos (2000) e Barbosa (2003) entre outros que dissertam a respeito do abandono da geometria nas escolas do Brasil. Os resultados obtidos são preocupantes, pois esta defasagem acarreta a não compreensão dos conteúdos que serão trabalhado posteriormente. Assim, algumas ações no planejamento do processo de ensino-aprendizagem da geometria precisam ser repensadas. No âmbito local, pretende-se apresentar os resultados desta pesquisa à equipe pedagógica da escola, assim como aos professores da área de Matemática para que planejamentos e estratégias sejam organizados a fim de melhorar as habilidades do pensamento geométrico dos estudantes para que possam se aproximar do nível que é condizente a eles, segundo a teoria utilizada. / The present dissertation had the purpose to investigate the levels of geometric thinking of students of public school in the city of Paranagua/PR, having as theoretical foundation the Theory of Van Hiele. Thus, in order to achieve the proposed objective, it was used the Educational Technologies, through activities developed with Geogebra software. The research participants were students of three classes of the first year of the High School of a public school of the city of Paranaguá. They performed 13 (thirteen) activities corresponding to 15 (fifteen) skills indicated in the theoretical framework used, divided into three levels: level 0 (visualization), level 1 (analysis), level 2 (informal deduction). The methodology used for this research was exploratory and applied. By analyzing the data collected in the resolution of activities, it can be concluded that the majority of the students reached level 0 and a lower percentage of the students managed to reach level 1. In relation to level 2, it can be verified that it was the most difficult level to achieve in the three classes. These results point out the students of the school where the research was carried out do not hold the visual, verbal, logical, design and application skills that correspond to the level of education, according to Van Hiele Theory. In addition to the proposed objective, this research corroborates the works of Pavanelo (1993), Lorenzato (1995), Passos (2000) and Barbosa (2003) among others who talk about the abandonment of geometry in Brazilian schools. The results obtained are worrisome, as this lag causes the lack of understanding of the contents that will be worked on later. Therefore, some actions in the planning of the teaching-learning process of geometry need to be rethought. At the local level, it is intended to present the results of this research to the pedagogical team of the school, as well as teachers in the Mathematics area, so that the planning and strategies are organized in order to improve students' geometric thinking abilities so that they can approach the level that is appropriate to them, according to the theory used.

Made available in DSpace on 2016-04-27T16:57:25Z (GMT). No. of bitstreams: 1 Adriana Santos Morgado.pdf: 4861076 bytes, checksum: b28e138a41b70c4b96624bac5ed378be (MD5) Previous issue date: 2013-06-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research is a product of the Project Challenges to Inclusive Education: teacher training in thinking about the processes of the field of mathematics in the early grades of Basic Education approved the program of the Centre of Education CAPES / INEP, 2010 announcement. This study investigates through pedagogical practices used in teaching mathematics to students with disabilities the early years of basic education in the public schools of the State of São Paulo. For this, participants were four teachers who teach at the elementary school and the regular school that had students with disabilities placed in their classrooms. Meetings were held for reflection and discussion, in which activities are designed to teach mathematics to students with disabilities. These activities were conducted in the form of workshops for all interested teachers from schools where teachers taught. The works by Nóvoa (2009) were used as theoretical benchmark to discuss teacher training focused on school. Participatory observations and interviews conducted after the development of workshops were used as instruments of data collection. As analysis of the results were presented two activities developed by the training group, explaining the necessary adaptations for students with disabilities. Moreover, narratives were prepared for two teachers, in order to highlight the needs for teacher training. This research shows that the teachers realized enrich their pedagogical practices in the teaching of mathematics and also that it is possible to make the disabled student participant of Mathematics classes, developing activities with adaptations to suit their inclusion / Esta pesquisa é um dos produtos do Projeto Desafios para a Educação Inclusiva: pensando na formação de professores sobre os processos de domínio da Matemática nas séries iniciais da Educação Básica, aprovado no Programa Observatório da Educação da CAPES/INEP, edital 2010. Este trabalho buscou investigar práticas pedagógicas utilizadas no ensino da Matemática aos alunos com deficiência dos anos iniciais da educação básica, em escolas públicas do Estado de São Paulo. Participaram da pesquisa quatro professoras que lecionam no Ensino Fundamental I da rede regular de ensino e que possuíam alunos com deficiência inseridos em suas salas de aula. Foram realizados encontros para reflexão e discussão, em que foram criadas atividades para ensinar Matemática para alunos com deficiência. Estas atividades foram desenvolvidas em forma de oficinas para todos os professores interessados das escolas em que as docentes lecionavam. Utilizamos como referencial teórico os trabalhos de Nóvoa (2009), para discutir a formação de professores centrada na escola. Foram adotados como instrumentos de coleta de dados observações participativas e entrevistas realizadas após o desenvolvimento das oficinas. Como análise dos resultados, foram apresentadas duas atividades elaboradas pelo grupo de formação, explicitando as adaptações necessárias aos alunos com deficiência. Além disso, foram elaboradas narrativas para duas professoras, a fim de evidenciar as necessidades para a formação de professores. Como resultado, este trabalho aponta que as professoras perceberam o enriquecimento de suas práticas pedagógicas no ensino da Matemática e também que é possível tornar o aluno com deficiência participante das aulas de Matemática, desenvolvendo atividades com adaptações para atender sua inclusão

Made available in DSpace on 2016-04-27T16:57:26Z (GMT). No. of bitstreams: 1 Regiane Silva dos Santos.pdf: 3757338 bytes, checksum: 0f2d14ba72fbc1b4fea92bd60eec9a60 (MD5) Previous issue date: 2013-06-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present research is one of the products from the Research Project: Challenges for the inclusive education: thinking the teachers training through the processes of mastering Mathematics in the early grades of primary and secondary education. It has been approved by INEP/CAPES public notice n.38/10 Observatory of Education and is coordinated by Doctor Ana Lúcia Manrique, from the Program of Studies of postgraduate degrees in Mathematical Education of PUC-SP. Its main goal is to answer the following question: Which grants are offered to primary school teachers to develop pedagogical practices when teaching Mathematics to disabled students in public schools? To answer to such a question, a survey was carried out in three levels, national, state and municipal. The method used was the textual and documental analysis, which helped on the search, carrying out data and cataloguing them, thus, making a corpus. After the corpus constitution we categorized and established theme units in each level: National Programs and actions, Publications and the training and resource centers, State- Programs and Projects which reach not only the teacher but also the student; Municipal Programs, Projects and Publications. After doing the theme units we ve chosen one item from each level, naming the units of analysis, this means the checked and interpreted object of study upon the historical and critical conception of Dermeval Saviani, turning the constitution of the text possible. When the text was ready it was possible to analise and check if the programs, projects, publications, actions and centers, which were ruled by laws and decrees, offered grants for teachers to work with students with difficulties at Mathematics. We consider that there are a few proposals about specific subjects / Esta pesquisa é um dos produtos do Projeto de Pesquisa: Desafios para a Educação Inclusiva: pensando a Formação de Professores sobre os Processos de Domínio da Matemática nas Séries Iniciais da Educação Básica , aprovado pelo INEP/CAPES no Edital n. 38/10 Observatório da Educação e sob a coordenação geral da Profa. Dra. Ana Lúcia Manrique, do Programa de Estudos de Pós-Graduados em Educação Matemática da PUC-SP. Esta pesquisa tem o objetivo de responder a questão: Que subsídios são oferecidos aos professores do ciclo I para desenvolverem práticas pedagógicas no ensino da matemática com alunos com deficiência nas escolas públicas? Para responder tal questionamento foi realizado um levantamento de documentos oficiais em três níveis: Nacional, Estadual e Municipal. Utilizamos como método a análise textual e documental que nos auxiliou na busca, no levantamento e na catalogação de dados, assim, constituindo um corpus. Após a constituição deste corpus realizamos um processo de categorização e o estabelecimento de unidades temáticas em cada nível: Nacional Programas e ações, Publicações e os Centros de formação e recursos; Estadual Programas e projetos que atinge tanto o docente quanto o aluno; e Municipal Programas, Projetos e Publicações. Após a constituição das unidades temáticas, selecionamos um item de cada nível, denominando as unidades de análise, isto é, o objeto de estudo analisado e interpretado sob a concepção histórica crítica de Dermeval Saviani, tornando assim possível a constituição do metatexto. Com o metatexto elaborado foi possível analisar e verificar se os programas, projetos, publicações, ações e centros instituídos por leis e decretos oferecem subsídios para os docentes atuarem com alunos com deficiência no ensino da matemática. Consideramos que existem poucas propostas voltadas para as disciplinas específicas