Este trabalho revisa e problematiza a usual associação entre a matemática escolar e o desenvolvimento do raciocínio lógico, introduzindo a argumentação e a prova em matemática como um elo de tal associação. Assim, desenvolve-se uma investigação tanto teórica quanto de campo, visando compreender por que, embora central na matemática acadêmica, a prova é tão pouco explorada na matemática escolar. A investigação teórica reviu diversas referências, em geral oriundas da Educação Matemática, mas também da História da Matemática, com vistas a: (1) compreender o papel de destaque da prova no contexto atual da Matemática, a partir do entrelaçamento entre a noção de demonstração e o próprio desenvolvimento dessa ciência; (2) discutir aspectos conceituais e epistemológicos da prova matemática que podem contribuir para um trabalho significativo com o tema na educação básica; e (3) compreender as razões da ausência de um trabalho significativo com a prova matemática na educação básica do Brasil nas últimas décadas. A investigação de campo complementa a investigação teórica apresentando um estudo de caso sobre conhecimentos, crenças e concepções de um pequeno grupo de professoras de matemática da educação básica a respeito do raciocínio lógico e da prova matemática. Essas investigações permitiram concluir que são diversas as causas do suposto abandono do trabalho com a prova matemática na educação básica, entre as quais destacamos a falta de uma discussão aprofundada sobre o tema na formação inicial de professores e a presença de práticas de ensino de matemática pautadas numa concepção tecnicista / In this dissertation, we review and problematize the usual association between school mathematics and the development of logical reasoning, introducing the proof in mathematics as a link of this association. Therefore we conducted both theoretical research and field research, in order to understand why the mathematical proof, although central to academic mathematics, is so little emphasized in school mathematics. In theoretical research, we reviewed several references, usually arising from the Mathematics Education, but also from the History of Mathematics, in order to: (1) understand the important role of proof in the current context of mathematics, from the entanglement between the notion of demonstration and even the development of this science; (2) discuss conceptual and epistemological aspects of the mathematical proof that can contribute to meaningful work with this theme in basic education; and (3) understand the reasons for the absence of meaningful work with mathematical proof in basic education in Brazil in recent decades. The field research complements the theoretical research presenting a case study on knowledge, beliefs and conceptions of a small group of mathematics teachers of basic education about logical reasoning and mathematical proof. These investigations allowed us to conclude that there are various causes for the alleged abandonment of work in mathematical proof in basic education, among which we highlight: the absence of thorough discussion of this topic school teacher education and the presence of current practice of a technical approach to math teaching

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-07-21T18:26:47Z No. of bitstreams: 1 thaissenadelannaalbino.pdf: 1810352 bytes, checksum: 807e107a597babc72bf6c6eedb687ea6 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-09T13:24:27Z (GMT) No. of bitstreams: 1 thaissenadelannaalbino.pdf: 1810352 bytes, checksum: 807e107a597babc72bf6c6eedb687ea6 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-09T13:25:49Z (GMT) No. of bitstreams: 1 thaissenadelannaalbino.pdf: 1810352 bytes, checksum: 807e107a597babc72bf6c6eedb687ea6 (MD5) / Made available in DSpace on 2017-08-09T13:25:49Z (GMT). No. of bitstreams: 1 thaissenadelannaalbino.pdf: 1810352 bytes, checksum: 807e107a597babc72bf6c6eedb687ea6 (MD5) Previous issue date: 2017-04-26 / Este trabalho teve como objetivo investigar como acontece o ensino de Matemática, em especial a Educação Financeira, em uma escola Waldorf através de um estudo aprofundado da Pedagogia Waldorf e seus fundamentos e, também, da imersão da pesquisadora no contexto educacional. Sendo assim, ele trata de uma pesquisa qualitativa do tipo Estudo de Caso. Como referencial teórico, pautamo-nos, fundamentalmente, em Rudolf Steiner para compreender a Pedagogia Waldorf. A pesquisa contou com a realização de um trabalho de campo, em uma escola Waldorf do estado de Minas Gerais, que consistiu em observações participantes das aulas de Matemática de uma turma do 6º ano do Ensino Fundamental composta por 20 alunos. Além disso, os dados produzidos e registrados no caderno de campo foram complementados com análise documental, entrevista semiestruturada realizada com a professora e diálogos informais na escola. A análise dos dados revelou e confirmou que o ensino de Matemática, de acordo com a Pedagogia Waldorf, acontece levando em consideração alguns elementos, que são: a estruturação do ensino em épocas, a consideração da etapa evolutiva em que a criança se encontra, o ensino através das artes, vivência, ritmo e repetição, uso do cálculo mental e oral, a metodologia do “ensino em três fases”, flexibilidade para o professor adequar o ensino, inter, multi e transdisciplinaridade sempre que possível, o trabalho com os temperamentos, dentre outros. O ensino levando em consideração esses elementos faz com que as crianças desenvolvam o querer, o sentir e o pensar de forma equilibrada, que é um dos princípios da Pedagogia Waldorf. A Educação Financeira foi trabalhada dentro de uma das épocas de Matemática do 6º ano escolar, intitulada “Vida Econômica e Financeira”. O estudo é muito amplo em sua proposta e alcance, e não se reduz apenas à prática de cálculos e ao estudo das finanças pessoais e atitudes financeiras. Como fruto desta pesquisa e com a intenção de direcionar os professores, foi produzida uma sugestão pedagógica para a Educação Financeira no 6º ano do Ensino Fundamental. / This research is about a study of Waldorf Schools’ Financial Education method through an in-depth investigation and the author’s immersion. The paper presents a qualitative case study. We used Rudolf Steiner literature as a reference for Waldorf Education method. The research includes a fieldwork in a Waldorf School, located in Minas Gerais (Brazil), based on participative observation in Mathematics classes of a 6th grade Elementary School, composed by 20 students. Besides, collected and registered workbook data were assembled by bibliography study, teachers interview and informal chats in school. The data analysis revealed and confirmed that Math instruction, as state Waldorf Pedagogy, happens taking into consideration some elements, as such: Teaching structured in seasons, considering child evolutionary stage, education through arts, experience, rhythmic movements and repetition, mental and oral calculation, methodology “teaching in three steps”, inter, multi and transdisciplinarity as many as possible, dealing with different tempers, etc. A teaching considering those elements allows students to develop the thinking, feeling and willing in a balanced way. Financial Education subject was taught during a season in 6th grade, named “Financial and Economic Life”. It is very broad in its proposal and scope, not restraint only to calculation practices and to personal financial studies and attitudes. As a result of this research, a pedagogical suggestion grounded on Waldorf Education is presented for Financial Education within 6th grade Elementary School.

Made available in DSpace on 2014-08-20T13:57:34Z (GMT). No. of bitstreams: 1 Lisiane Jaques Rodrigues Scherwenske_Dissertacao.pdf: 914972 bytes, checksum: f18b5fbff77858c0f8793195d7cf7194 (MD5) Previous issue date: 2013-08-23 / This paper is the description of the research project Knowledge mobilized by the Mathematics teacher in adults and youths education: searching for what weaves this relationship together which has investigated: How does the teaching knowledge permeate the teaching performance of the Mathematics lecturer in adults and youths education? To answer this question strategic methods have been utilized, such as the semi-structured interview, as well as the focus groups and lookalike replacement techniques. The project is about a qualitative study of character developed in a local school in Pelotas, in which Mathematics teachers working in the adults and youths education field have been the studied group. Theoretical references about teaching knowledge which weaves the teachers performance have been searched in the concepts of Tardif (2012) and Gauthier et al. (1998). To answer the research issue, the results of the semi-structured interview and the lookalike replacement technique have been analyzed by using the technique of content analysis. The information that has come from the focus group subsidized the formation of the final product: a website, which intends to contribute to the teaching performance of Mathematics teachers who work with adults and youths. / O presente trabalho é a descrição da pesquisa Saberes mobilizados pelo professor de Matemática na Educação de Jovens e Adultos: buscando fios que tecem esta relação - que investigou: Como os saberes docentes permeiam a prática do professor de Matemática na Educação de Jovens e Adultos? Para responder a esta interrogação utilizou-se como estratégias metodológicas a entrevista semi-estruturada e as técnicas de grupo focal e de sósia substituto. Trata-se de um estudo de caráter qualitativo desenvolvido em uma escola da rede municipal de Pelotas, cujas professoras de Matemática da modalidade de Educação de Jovens e Adultos foram o grupo estudado. Buscou-se nos conceitos de Tardif (2012) e Gauthier et al. (1998) referências sobre os saberes docentes que permeiam as práticas do educador. Os resultados da entrevista semi-estruturada e da técnica sósia substituto foram analisados usando a técnica de análise de conteúdo para responder o problema da pesquisa. As informações advindas do grupo focal subsidiaram a formulação do produto final: site, que pretende contribuir para a prática das e dos professores de Matemática que atendem jovens e adultos.

Det här är en studie om sambandet mellan matematiklärares syn på begreppet formativ bedömning och deras undervisning i gymnasieskolan. Det har genomförts intervjuer med fem matematiklärare på gymnasiet och observationer av deras matematiklektioner. Empirisk data presenteras tillsammans med teori och tidigare forskning kring formativ bedömning. Insamlad data pekar på att medverkande matematiklärare har en positiv syn på formativ bedömning även om det beskrivs som tidskrävande. Det verkar samtidigt vara mycket som ryms inom begreppet vilket förtydligas genom medverkande matematiklärares stundtals skilda sätt att applicera det i sin undervisning. En av lärarna menar att formativ bedömning ska stärka elevernas självkänsla genom uppmuntran i form av positiva kommentarer som exempelvis ”jättebra”. Samtidigt finns det medverkande lärare som istället vill framhålla formativ bedömning som detaljerad information till eleven om deras kunskapsläge och utvecklingsmöjligheter. / This is a study about mathematics teachers‟ views on the relation between formative assessment and their teaching in upper secondary school. In the study there have been five interviews with five mathematics teachers on upper secondary school and observations of their teachings. Empirical data is presented together with theory and previous research on formative assessment. Collected data indicates that participating mathematics teachers have a positive view on formative assessment even if it also is described as time consuming. It also seems as it is a wide term which clarified by the participating mathematics teachers sometimes different ways to apply it in their teaching. One of the teachers believes that formative assessment should strengthen students‟ self-esteem with positive comments like for example “well done”. At the same time there is participating teachers who emphasize formative assessment as detailed information to students about their knowledge and development.

Orientador: Ivete Maria Baraldi / Resumo: Este trabalho tem como objetivo elaborar uma compreensão da inclusão escolar em escolas públicas Inovadoras e Criativas do Estado de São Paulo por meio de narrativas de sujeitos escolares. Para atingir tal objetivo, foram produzidas 14 narrativas utilizando como metodologia a História Oral, por meio de entrevistas. Para analisar utilizamos a convergência/divergência em que foram elaborada duas temáticas de discussões. A primeira delas é Escolas Inovadoras e Criativas: Um olhar para a inclusão escolar e o ensino de Matemática, subdividida em seis tópicos: Gestão Escolar, Envolvimento com outras instituições, Metodologia de Ensino, Ensino de Matemática. A segunda temática é Deficiência e inclusão escolar: discussões, na qual são discutidos os conceitos e as compreensão dos professores entrevistados ao respeito do estudante com deficiência nessas escolas. Diante disso, compreendeu-se que houve um avanço em termos de gestão, organização curricular e envolvimento com a comunidade, mas que ele pouco reflete na metodologia de ensino, em particular quando se considera o estudante com deficiência. Dessa forma, ainda são necessários mais esforços, bem como políticas públicas voltadas para a formação do professor de Matemática para que, efetivamente, a educação seja inclusiva para todos / Abstract: This work intends to comprehend the educational inclusion inside the “Innovative and Creative” public school in the State of São Paulo through some narratives constructed by students and teachers. To achieve this goal, 14 narratives have been produced and appropriated as Oral History Methodology. Through the convergence/divergence analysis, two discussion strategies were constructed. The first one is on “Innovative and Creative Schools”: school management, involvement with other institutions, teaching methodology, and teaching mathematics. The second strategy is on “Deficiency and Educational Inclusion”: theme that brings up discussions about the concepts and comprehension from the interviewed teachers regarding their respect for the deficient student of these educational institutions. Thus, there is an advance in terms of organization, curricular organization and involvement with the community that is somewhat specific in its form of education, particularly when considering a student with disability. These are a few necessary practices and efforts to effectively prepare the mathematics teacher in formation to provide an education that is inclusive for every student. / Doutor

The essay is a study concerning mathematics teaching in preschool; which type of mathematics preschool teachers visualise in practice in preschool teaching, and preschool teachers’ view on the subject of teaching math. The study marks the importance of the existence of mathematics teaching in preschool, as well as its positive effect on childrens’ future attitude towards mathematics. Therefore this subject can be considered as highly relevant to further contribute with information to both people who work in preschool and those who don't.  To collect data for the study, telephone interviews were conducted with preschool teachers, and digital questionnaires were sent out to the same target group. The data is analyzed with the conventional content analysis as a tool and an examination of the results is also made in relation to the developmental pedagogical perspective.  The results that have emerged show that in spontaneous teaching, mathematics is integrated by taking advantage of the surrounding environment. Furthermore, in the planned teaching situations it was made clear that the mathematics teaching occured by using prepared mathematical materials, forming thematic projects or during a predetermined teaching time. Similarities can be seen in the type of mathematics that was emphasized; the preschool teachers mentioned numbers, symbols, shapes, quantities and placement words as central. All preschool teachers express a favorable view of mathematics, regardless of previous experiences. In addition, they also believe that their attitude affects the children's view on the subject and what enjoyment the children see in it. This goes hand in hand with all of the participants’ valuing of forming a positive foundation in mathematics for the children to further work on during the school years.

Denna studie undersöker hur laborativt material används i matematikundervisningen i åk. F-3. Studien tittar även på bakomliggande förklaringar till varför lärare använder materialet eller ej, samt vad som krävs för en ökad användning. Metodvalen i föreliggande studie är av både kvantitativ- och kvalitativ karaktär och består utav en online-enkät som besvarats av 199 lärare. Resultatet visar att laborativt material är ett relativt vanligt inslag i matematikundervisningen. Det påvisar även att lärares teoretiska kunskaper om, och erfarenheter av laborativt material påverkar i vilken utsträckning det nyttjas i undervisningen. Slutligen framgår det att lärare upplever att fortbildning skulle öka deras användande av laborativt material i undervisningen. / This study examines how laboratory material is used in mathematics teaching in class. F-3. The study also looks at the underlying explanations for why teachers use the material or not, as well as what is required for an increased use of the laboratory methods in mathematics teaching. The method choices in the present study are of both a quantitative and qualitative nature and consist of an online questionnaire answered by 199 teachers. The results show that laboratory materials are relatively common in mathematics teaching. It also shows that teachers' theoretical knowledge of, and experiences of laboratory materials affects the extent to which it is used in teaching. Finally, it appears that teachers feel that continuing education would increase their use of laboratory material in teaching.

Skolan ska vara en lugn och trygg miljö, där eleverna ska kunna fokusera på sitt lärande utan att bli störda. Denna fallstudie syftar därför till att undersöka hur en matematiklärare kan skapa och bibehålla studiero. Genom observationer och en intervju har jag undersökt en lärares arbete med studiero. Resultatet visade att en lärare kan informera eleverna på ett tydligt sätt om vilka regler som gäller i matematikklassrummet, för att skapa studiero. Resultatet visade även att det sociala samspelet mellan elever, och lärarens tillgänglighet, har betydelse för arbetet med studiero. / The school should be a calm and safe environment, where students should be able tofocus on their learning without being disturbed. This case study therefore aims to investigate how a mathematics teacher can create and maintain a calm environment conducive to learning. Through observations and interviews, I have investigated a teacher's work with a calm environment conducive to learning. The results showed that a teacher can inform students in a clear way about the rules that apply in the mathematics classroom to create a calm environment conducive to learning. The results also showed that the social interaction between students and the teacher's availability is important for the work with a calm environment conducive to learning.

This study explores the leadership role of the Head of Department (HoD) in the teaching of Mathematics.It focuses on the perspectives that the educators hold about the leadership role of HoDs in the teaching of Mathematics in two Gauteng primary schools.The study was framed by the following research question: What perspectives do educators hold about the leadership role of the HoD in the teaching of Mathematics in primary schools? A qualitative case study was employed whereby data were collected in two primary schools in Gauteng Province. To examine the relevance and clarityinterview questions used, a pilot study wasat first conducted in which one HoD and one teacher were interviewed.For the actual study, ten individual semi-structured interviews were conducted with four HoDs, two principals and four teachers in two township schools in a Gauteng district. Documents such as monitoring instruments of HoDs were also collected and analysed for purposes of triangulation. Key findings were that HoDsnever received any formal preparation to lead the teaching of Mathematics. They learned about the role by participating in professional development activities offered by outside actors, upgrading themselves, assisting the Education district department in facilitating workshops for teachers as well as serving as acting HoDs.They provided leadership by monitoring teaching and teachers’ work,checking lesson plans, doing class visits, checking learners’ books and assessment tasks and doing follow ups.Challenges that were identified in relation to the leadership role of the HoD leadership in the teaching of Mathematics includedHoDs’ lack of Mathematics knowledge (SMK) and pedagogical content knowledge (PCK), lack of teaching resources, teachers’ lack of knowledge of the new curriculum, a heavy workload, overcrowded classrooms, demotivated teachers, teacher absenteeism and too much paperwork.The perceived strategies that were used by HoDsto address challenges includedthe following:engaging in discussions with teachers in an attempt to collectively find solutions, substituting absent teachers, taking work home, using the expertise of other teachers through delegation, leading by example by presenting lessons for teachers, making learners their first priority followed by paperwork as well as engaging with some stakeholders for support. The following were the recommendations: there should be more clarity about what is expected of HoDs.Sufficient time should be allocated in order for HoDs to be able to balance their leadership duties and teaching effectively;current as well as prospective HoDs should be trained in both the subject in which they are expected to provide leadership as well as the generic leadership part of their job.HoDs should involve Mathematics teachers in the development of the monitoring tools since Mathematics teachers are familiar with a sensible blend of tools, methodologies and approaches that can meet the needs of their learners.HoDs should also be developed on what they should look for as they monitor teachers’ work.In that way they may be able to effectively use the results of their monitoring to support teachers.A final recommendation is that the workload of HoDs be reduced through the allocation of administrative tasks to school administrators and appointing paid HoD assistants such as subject heads. / Dissertation (MEd)--University of Pretoria, 2013. / gm2014 / Education Management and Policy Studies / unrestricted

The progress of the pandemic has affected many people in the outside world and digitalization has therefore reached new levels. Previous research and reports have shown that teachers in mathematics rarely use digital learning resources when teaching in the classroom. With the help of a questionnaire study, the use and knowledge of digital learning resources for primary and middle school teachers and whether the pandemic has had any impact on this is investigated. The analysis of the results will take place in the TPACK in situ framework. This shows that teachers´ use of digital learning resources have increased in connection with the Covid- 19 pandemic. The teachers´ digital competence has to a large extent been developed when the pandemic set new demands and challenges. The study suggests that the effects of the pandemic have led to higher collegial collaboration in the search for and use of digital learning resources. / Pandemins framfart har påverkat många i omvärlden och digitaliseringen har nått nya nivåer. Tidigare forskning och rapporter har visat på att lärare i matematikundervisningen sällan använder digitala lärresurser. Med hjälp av en enkätstudie undersöks låg- och mellanstadielärares användning och kunskap kring digitala lärresurser samt om pandemin har haft någon påverkan på detta. Analysen av resultatet kommer ske med hjälp av ramverket TPACK in situ. Detta visar att lärares användning av digitala lärresurser har ökat i samband med Covid-19 pandemin. Lärarnas digitala kompetens har i hög utsträckning utvecklats när pandemin ställt nya krav och utmaningar. Studien antyder att pandemins effekter har givit ett högre kollegialt samarbete vid sökande och användande av digitala lärresurser.