This thesis looks at young children's attempts to express generality within specific learning situations with the aid of carefully designed tools, and at how, given appropriate means of expression, they are able to justify their generalisations. The literature on representation and abstraction leads to a focus on construction of meaning through pupils' concretising of mathematical objects by means of the development of representations and interconnections between representations of those objects. The study involved eight pairs often and eleven year old children. I devised a series of tasks centred on the creation of simple "function machines" expressed in the Logo programming language. The children's work involved the construction and empirical testing of these functions within a game-like situation. Part of the game involved verbally justifying the validity of the Logo procedures to a partner and to the Researcher. These activities provided a window onto children's construction of meaning. Analysis of the data revealed that within the specific learning situation designed for the study: children were able to make formalised generalisations of mathematical relationships, often webbed by "semi-generalisation"; the expressive powers of the symbolism achieved a more functional role by the symbols' association with a history of specific numerical examples; children constructed situated abstractions for the justification of generality using "generic structuring" and "naturalised formalism" as powerful forms of webbing; and the apparent "rift" between empirical and deductive starting points for generalisation, justification and proving activities appeared less clear than the literature suggests.

The purpose of this thesis was to observe people’s abilities to compute probability problems at a fundamental level. The problems in this study were presented in an abstract format to ensure non-ambiguity in its interpretation. The study was administered to university level students. The focus was to determine people’s ability to answer probability questions that combined the probabilities of two single events, using the most basic types of operations: AND and OR. The study found that while most people were able to compute AND type probability questions, most had trouble with OR operations. Of special interest was a switching strategy that was employed in computing OR operations as the probability of a single event varied. The study also revealed that statistically sophisticated people were able to adopt the mindset of people who were statistically naïve. Further research is required in order to develop a better framework in understanding people’s logical process of computing these basic probability questions as well as its application to our everyday lives.

The purpose of this thesis was to observe people’s abilities to compute probability problems at a fundamental level. The problems in this study were presented in an abstract format to ensure non-ambiguity in its interpretation. The study was administered to university level students. The focus was to determine people’s ability to answer probability questions that combined the probabilities of two single events, using the most basic types of operations: AND and OR. The study found that while most people were able to compute AND type probability questions, most had trouble with OR operations. Of special interest was a switching strategy that was employed in computing OR operations as the probability of a single event varied. The study also revealed that statistically sophisticated people were able to adopt the mindset of people who were statistically naïve. Further research is required in order to develop a better framework in understanding people’s logical process of computing these basic probability questions as well as its application to our everyday lives.

Orientador: Arlete de Jesus Brito / Banca: Antonio Vicente Marafioti Garnica / Banca: Maria Ângela Miorim / Resumo: Neste trabalho, buscamos identificar justificativas explicitadas em entrevista, por cinco professores vinculados ao Programa de Pós-Graduação em Educação da UNICAMP, para utilização ou não da obra de Caraça em suas atividades docentes. Para tanto, adotamos alguns dos procedimentos metodológicos da História Oral para nos auxiliar na realização das entrevistas e assumimos como necessárias a pluralidade de perspectivas, a inexistência de uma única verdade, a ampliação do conceito de documento (fontes orais, fotos, filmes, ...) e a crítica ao documento, entre outros. Após termos nos familiarizado com os depoimentos concedidos a esta pesquisa, jornais, livros, sites e outros textos, identificamos algumas justificativas. E, percebemos que estas justificativas baseavam-se na importância da inserção histórica e filosófica no ensino de Matemática, na utilização da dialética na escrita da obra, no pioneirismo de Caraça quanto ao estilo de escrita, e na concepção de Matemática abordada por este autor. Após termos refletido sobre as justificativas encontradas concluímos esta pesquisa alegando que seria necessário elaborar uma proposta para o ensino de Matemática em todos os níveis de ensino que abordem a Matemática em dimensões histórico-filosóficas, epistemológicas e didático-pedagógicas, relacionas ao saber matemático e consideradas fundamentais à formação do professor. / Abstract: In this research, we're looking for reasons explained in interviews, with five professors linked to the Postgraduate Program of Education at UNICAMP, for using or not the work of Caraça in their educational activities. To accomplish this, the study adopted some of the methodological procedures of oral history to assist us in carrying out the interviews and undertakes as necessary the plurality of perspectives, the lack of a single truth, broadening the concept of document (oral sources, photos, movies ...) and the criticism to the document, among others. After we became familiar with the depositions given to this research, newspapers, books, websites and other texts, we identified some justifications. We realized that these justifications were based on the importance of integrating historical and philosophical aspects to teach Mathematics, the use of dialectics in the writing of the work, in the pioneering writing style of Caraça, and in the conception of Mathematics approached by this author. After having reflected about the justifications found, we conclude this research claiming that it would be necessary to develop a proposal for teaching Mathematics at all levels of education, addressing the Mathematics in historic-philosophical, epistemological and didactic-pedagogical dimensions, related to mathematical knowledge and considered to be fundamental to formation of teachers. / Mestre

Orientador: Ubiratan D'Ambrosio / Banca: Sérgio Roberto Nobre / Banca: Antonio Vicente Marafioti Garnica / Banca: José Luiz Goldfard / Banca: Elza Furtado Gomide / Resumo: O intento, neste trabalho, é evidenciar a presença dos judeus na Matemática, bem como procurar compreender possíveis relações entre a condição judaica e o fazer matemático. Nesse encalço, empreenderam-se estudos sobre história e cultura judaicas e uma visita à literatura sobre a Matemática relativamente aos judeus. Também se realizaram entrevistas com judeus que atuam no campo da Matemática, cujo tratamento contemplou gravação, transcrição e análise. Parte deste estudo foi efetivado durante um estágio de pesquisa realizado em Israel. Constatou-se que a presença de judeus na Matemática é vultosa, principalmente nos últimos duzentos anos, e que, decorrente dessa expressividade, estudos foram engendrados sobre a proeminência judaica na Ciência. Verificou-se também que a condição de ser matemático e ter uma origem judaica são questões não claramente interligadas. Há, contudo, algumas convergências possíveis no perfil do judeu que se revelou neste grupo, metaforicamente configurado aqui, na análise, por meio de um mosaico. Das multifaces dessa configuração detectaram-se alguns elementos invariantes sobre "ser judeu", "Matemática" e "Educação Matemática". Dessas três asserções depreenderam-se qualificativos comuns que remetem a um mesmo campo de sentido, o da autodefinição. / Abstract: Mathematics and the Jews and possible relationships between the Jewish condition and the making of Mathematics are provided. Studies on Jewish history, culture and the literature on Mathematics related to the Jews are investigated. Jews who deal with Mathematics are interviewed and interviews are recorded, transcribed and analyzed. Current investigation has been partly undertaken during a research spell in Israel. Since the presence of Jews in the Mathematical camp is highly conspicuous, especially during the last two hundred years, studies have been initiated on Jewish prominence in the science. It has also been verified that there is no clear link between the mathematician's condition and being of Jewish origin. There are, however, certain possible convergences in the Jew's profile revealed in the group which is metaphorically represented by a mosaic in current analysis. Invariable elements on "being a jew", "Mathematics" and "Mathematical Education" have been detected through the many faces of such a configuration. Common qualifications that lead towards the same significance, or rather, auto-definition, have been brought forth from these three statements. / Doutor

The study of mathematical anxiety has seen an increased importance in the past few decades in the field of mathematical education. As this topic is of great interest in education research, this thesis investigates the previous contributions made by other researchers via a literature review of mathematical education papers. Furthermore, a literature review of mathematical models of learning is presented. In the hopes of closing the gap between these two streams of research, this thesis conducts a study of mathematical anxiety at the first year university level through a survey and data analysis, and proposes a theoretical model of learning. Throughout the data analysis, the prevalence, effects, and correlates of mathematical anxiety are examined. Using a version of the Mathematical Anxiety Rating Scale refined by Plake \& Parker in 1982, factors such as gender, high school performance, and program choices are shown to be correlated to mathematical anxiety, as is consistent with previous literature. On the other hand, the model of learning offers a theoretical perspective in understanding the relationship between knowledge, effort, and anxiety, and how these variables interact during a learning experience. This model suggests that given an individual's aptitude, drive, and susceptibility for anxiety, that they may reach various levels of knowledge, effort, and anxiety throughout an academic term. / Thesis / Master of Science (MSc)

Esse trabalho visa comparar o desempenho de diversos países no exame do PISA, em especial Brasil e Japão. Além da comparação de dados estatísticos, será realizada uma análise curricular desses dois países, na tentativa de perceber a influência do currículo em seus desempenhos no exame. Será possível também observar em muitos países políticas públicas desenvolvidas com o objetivo de aumentar o nível de igualdade na educação, oferecendo a todos as mesmas oportunidades. Fatores como condição socioeconômica, estrutura familiar, histórico de imigração, entre outros fatores serão atrelados ao desempenho escolar e será possível verificar o poder de suas influências. Após a análise de todos os dados, percebe-se que o fator que afeta de maneira mais acentuada o nível de igualdade na educação e o desempenho dos alunos em geral é a condição socioeconômica. É possível observar também que os currículos de Brasil e Japão são muito similares, mesmo existindo uma diferença tão grande no desempenho de ambos os países no exame. Sendo assim, os currículos são extremamente importantes na construção da equidade educacional, mas não são determinantes no que diz respeito à qualidade de educação. / This dissertation is meant to compare the performance of many countries in the PISA (Programme for International Student Assessment) exam, but especially Brazil and Japan. Besides the statistical data, it will be done curricula analysis in order to understand the weight of the curricula in the exam results. Moreover, it will be possible to observe public policies developed to raise the levels of equity in many countries, giving to all the students the same opportunities. Variables such as socioeconomic status, family structure, immigration background and others will be related to the students achievement and it will be possible to verify their strength on these relationships. After all the analysis is done, it is possible to realize that one of the factors that mostly affect the students performance is the socioeconomic status. In addition, it is possible to verify that the Brazilian and the Japanese curricula are very similar, regardless both countries achievement on the exam. Therefore, it is possible to infer that the curriculum is extremely important on the educational scenario, but does not determine the quality of education offered.

Nas últimas décadas o aumento do acesso à Internet vem modificando a maneira como interagimos com a informação e, em consequência, com o conhecimento. A educação no mundo digital exige a adoção de novas metodologias de ensino que desenvolvam competências e habilidades necessárias a formação crítica, reflexiva e participativa de nossos educandos. Dessa maneira busca-se desenvolver a autonomia dos alunos em relação às escolhas que farão durante sua vida, fazendo-as de maneira consciente e planejada. Considerando o baixo índice de acertos nas questões de porcentagens de um simulado realizado em uma escola estadual do interior do Estado de São Paulo foi elaborada a WebQuest BMW Vermelho com o objetivo de avaliar: Em que medida a metodologia WebQuest contribui para a aprendizagem de porcentagem? Durante a aplicação da WebQuest, em dois nonos anos do Ensino Fundamental, foi possível perceber como a metodologia, através da motivação, provoca mudanças no comportamento dos alunos no que diz respeito a disciplina, a concentração e o desejo em aprender o conteúdo, indicando uma grande potencialidade de uso em revisões de conteúdo, uma vez que deixa de ser uma repetição podendo ser uma maneira de apresentar novos significados aos temas revistos e promover a interdisciplinaridade. / Since the advent of technological age, the widespread use of Internet has been modifying the way we interact with information and, in consequence, with knowledge. The education in the digital and connected world requires the adoption of new teaching methodologies which seek for being innovative and that develop skills that a critical, reflexive, participative and professional formation of our students requires, reaching to develop their autonomy about the decisions they will take in their lives, by making them in a conscious and planned way. Observe that the importance of the content of percentage and the low index of right answers in questions of a test in a state school on the interior of São Paulo state, based on the questions of SARESP, it was elaborated the WebQuest BMW Vermelho with the objective to evaluate the use of review of content methodology. During the application of WebQuest, it was revealed how the methodology, trough the motivation, is associated with changes in the students behavior, in regards to discipline, concentration and the desire of learning the content, indicating a great potential in using review of contents, since it stops being a repetition and starts being a way of present new meanings to the themes reviewed and advocate interdisciplinarity.

Orientador: Heloisa da Silva / Resumo: Elaborar uma compreensão sobre as mobilizações de narrativas e suas abordagens na (e para a) formação de professores no âmbito dos subprojetos Pibid, da Unesp/Rio Claro, foi o objetivo desta pesquisa. Elegeu-se o Pibid como cenário a ser investigado por se tratar de uma política pública de formação de professores e porque se verificou, por meio de uma análise do projeto institucional da Unesp (Unesp-Pibid, 2013), que muitos de seus subprojetos apresentavam propostas de formação com abordagens narrativas. Para tanto, sob os pressupostos da História Oral na Educação Matemática, lançamos um olhar para as ideias que envolvem o trabalho com narrativas no processo de formação formal de professores, tendo como disparador de perspectivas, entrevistas realizadas com os professores coordenadores de área de seis diferentes subprojetos Pibid da Unesp/Rio Claro, a saber: Educação Física, Física, Geografia, Interdisciplinar/EJA, Matemática e Pedagogia. Por meio do estudo dessas entrevistas, buscamos compreender como as narrativas vêm sendo mobilizadas em processos formativos no âmbito do Pibid da Universidade Estadual Paulista, campus de Rio Claro. A pesquisa tende a contribuir com os trabalhos do Grupo História Oral e Educação Matemática – Ghoem, do qual o pesquisador é integrante, e com uma de suas linhas de pesquisa, intitulada História Oral, Narrativas e Formação de Professores: pesquisa e intervenção, cujo objetivo principal é o de elaborar, aplicar e analisar estratégias alternativas... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Elaborating an understanding of narrative mobilizations and their approaches to (and for) teacher training within the scope of the Unesp/Rio Claro Pibid subprojects was the objective of this research. The Pibid was chosen as the scenario to be investigated for being a public policy of teacher training and because, through an analysis of Unesp's institutional project (Unesp-Pibid, 2013), many of its subprojects presented training proposals with narrative approaches. Therefore, under the assumptions of Oral History in Mathematics Education, we take a look at the ideas that involve the work with narratives in the process of formal teacher training, taking as a perspective trigger, interviews with teachers coordinators of area of six different Pibid subprojects of Unesp/Rio Claro, namely: Physical Education, Physics, Geography, Interdisciplinary/EJA, Mathematics and Pedagogy. Through the study of these interviews, we sought to understand how the narratives have been mobilized in formative processes within the scope of the Pibid of the Universidade Estadual Paulista, campus of Rio Claro. The research tends to contribute to the work of the Group Oral History and Mathematical Education – Ghoem, of which the researcher is a member, and one of his lines of research, entitled Oral History, Narratives and Teacher Training: research and intervention, whose The main objective is to elaborate, apply and analyze alternative strategies for the formation of teachers who teach mathematics cons... (Complete abstract click electronic access below) / Doutor

Orientador: Pedro Paulo Scandiuzzi / Banca: Maria Teresa Eglér Mantoan / Banca: Rosana Giaretta Sguerra Miskulin / Resumo: O trabalho intitulado "A Etnomatemática no contexto do ensino inclusivo: possibilidades e desafios" é uma pesquisa, de caráter etnográfico, que tem como objetivo observar, descrever e analisar como os professores de uma escola inclusiva lidam com os alunos, na disciplina Matemática, de modo a corroborar com o processo de inclusão. A pesquisa foi realizada em uma escola do projeto CIEJA - Centro Integrado de Educação de Jovens e Adultos - da Secretaria de Educação da cidade de São Paulo, que oferece o ensino fundamental na modalidade supletivo para 1308 alunos. Foram observados quatro professores, sendo três formados em matemática e um formado em pedagogia. O trabalho aponta que o processo de inclusão, baseado na perspectiva etnomatemática, está ligado à postura ética em que se preza o respeito, a solidariedade e a cooperação, ambiente onde as diferenças são valorizadas e, portanto, propício à inclusão. Salienta também que, para o processo de inclusão, não há um modelo pronto; o que existe é a transição da integração para a inclusão e, por isso, podem ser detectadas práticas não inclusivas mesmo em um ambiente com proposta inclusiva. / Abstract: The work entitled "Ethnomathematics in the teaching context for inclusion: possibility and challenge" is an investigation of ethnographic type that has the purpose to observe, describe and analyse how the teachers of an inclusive school deal with the students in the mathematics subject so as to corroborate with the process of inclusion. The research was accomplished in a school of the project CIEJA - Integrated Center of Youngs and Adults Education - of Education Secretaryship of São Paulo's city, that offer adult education fundamental teaching for 1308 students. Four teachers were observed, of which three are graduated in mathematics and one is graduated in pedagogy. The work indicates that the process of inclusion, grounded in the ethnomathematics perspective, is linked with the ethical posture that values the respect, solidarity and co-operation, environment where the differences are valorized and, thus, propitious for the inclusion. It emphasizes too that the process of inclusion isn't a ready model, on the contrary what exists is the transition from the integration to the inclusion and, therefore, it can be detect non-inclusive practices even so in this environment with inclusive proposal. / Mestre