A qualitative case study was presented in order to explore an inquiry-based learning approach to teaching risk in two different grade 11 mathematics classes in an urban centre in Canada. The first class was in an all-boys independent school (23 boys) and the second class was in a publicly funded religious school (19 girls and 4 boys). The students were given an initial assessment in which they were asked about the safety of nuclear power plants and their knowledge of the Fukushima nuclear power plant accident. Following the initial assessment, the students participated in an activity with the purpose of determining the empirical probability of a nuclear power plant accident based on the authentic data found online. The second activity was then presented in order to determine the impact of a nuclear power plant accident and compare it to a coal power plant accident. The findings provide evidence that the students possess intuitive knowledge that risk of an event should be assessed by both its likelihood and its impact. The study confirms the Levinson et al. (2012) pedagogic model of risk in which individuals’ values and prior experiences together with representations and judgments of probability play a role in the estimation of risk. The study also expands on this model by suggesting that pedagogy of risk should include five components, namely: 1) knowledge, beliefs, and values, 2) judgment of impact, 3) judgment of probability, 4) representations, and 5) estimation of risk. These ii components do not necessarily appear in the instruction or students’ decision making in a chronological order; furthermore, they influence each other. For example, judgments about impact (deciding not to consider accidents with low impact into calculations) may influence the judgments about probability. The implication for mathematics education is that a meaningful instruction about risk should go beyond mathematical representations and reasoning and include other components of the pedagogy of risk. The study also illustrates the importance of reasoning about rational numbers (rates, ratios, and fractions) and their critical interpretation in the pedagogy of risk. Finally, the curricular expectations relevant to the pedagogy of risk from the Ontario secondary curriculum are identified.

A qualitative case study was presented in order to explore an inquiry-based learning approach to teaching risk in two different grade 11 mathematics classes in an urban centre in Canada. The first class was in an all-boys independent school (23 boys) and the second class was in a publicly funded religious school (19 girls and 4 boys). The students were given an initial assessment in which they were asked about the safety of nuclear power plants and their knowledge of the Fukushima nuclear power plant accident. Following the initial assessment, the students participated in an activity with the purpose of determining the empirical probability of a nuclear power plant accident based on the authentic data found online. The second activity was then presented in order to determine the impact of a nuclear power plant accident and compare it to a coal power plant accident. The findings provide evidence that the students possess intuitive knowledge that risk of an event should be assessed by both its likelihood and its impact. The study confirms the Levinson et al. (2012) pedagogic model of risk in which individuals’ values and prior experiences together with representations and judgments of probability play a role in the estimation of risk. The study also expands on this model by suggesting that pedagogy of risk should include five components, namely: 1) knowledge, beliefs, and values, 2) judgment of impact, 3) judgment of probability, 4) representations, and 5) estimation of risk. These ii components do not necessarily appear in the instruction or students’ decision making in a chronological order; furthermore, they influence each other. For example, judgments about impact (deciding not to consider accidents with low impact into calculations) may influence the judgments about probability. The implication for mathematics education is that a meaningful instruction about risk should go beyond mathematical representations and reasoning and include other components of the pedagogy of risk. The study also illustrates the importance of reasoning about rational numbers (rates, ratios, and fractions) and their critical interpretation in the pedagogy of risk. Finally, the curricular expectations relevant to the pedagogy of risk from the Ontario secondary curriculum are identified.

Made available in DSpace on 2016-04-29T14:32:21Z (GMT). No. of bitstreams: 1 dissertacao_mauro_cesar_goncalves.pdf: 542312 bytes, checksum: f2b3303ef8b32aa7f9b9c51e1aa6ec08 (MD5) Previous issue date: 2004-05-03 / The Aim of our research was to identify the current Mathematics teachers conceptions of probability and to verify if there is a relation between these conceptions and the ones used in the 1970s, 1980s and 1990s.To do so, our work was done through studies and analyses of didaction books and institutional organization since the 1970s, having theYves Chevallard (1995) Praxeology Organisation as a source, which provided us with conditions to identify the different tendencies related to the Probability teaching. This analysis contributed directly to our studies of Didactical Transposition along with Probability according to Yves Chevallard s proposals and identifying the Pedagogical Knowledge and the one used at school. As a part of our research we had twenty teachers answer a questionnaire which was divided into two parts. The first one was to acquire information about their profile; and the second one was about their own conception of Probability. The results were related to the conceptions presented by Goded (1996) and the different periods of the Probability teachings by means of the software C.H.I.C. This way, we could obtain simultaneously, information related to the type of conception and period of basic formation. On the whole, the analysis of the obtained information enabled us to say that there is evidence that Teachers actions influence the conception changes, inasmuch as teachers, who had their basic education in the same period and teach different levels have, too, different conceptions / Nossa pesquisa teve como objetivo identificar as concepções atuais dos Professores de Matemática em exercício no Ensino Fundamental sobre Probabilidade, e verificar se há relação entre estas concepções e as diferentes tendências do Ensino de Probabilidade nas décadas de 70, 80 e 90. Para isso, nosso trabalho foi composto de estudos e análises de livros didáticos e de orientações institucionais desde a década de 70, por meio da Organização Praxeológica de Yves Chevallard (1995), o que nos deu condições de identificar as diferentes tendências quanto ao Ensino de Probabilidades. Esta análise contribuiu diretamente com o estudo que fizemos da Transposição Didática em torno de Probabilidades, de acordo com as propostas de Yves Chevallard (1991), atuando diretamente na identificação dos saberes a ensinar e no saber escolar. Num outro momento, recorremos a uma amostra composta por vinte professores que responderam ao nosso instrumento diagnóstico, um questionário, constituído por duas partes, sendo a primeira, responsável por nos fornecer informações sobre o perfil de cada docente, e a segunda, relacionada às suas concepções probabilísticas. Os resultados dos questionários foram relacionados com os tipos de concepções apresentados por Goded (1996) e os diferentes períodos do Ensino de Probabilidades, ambos por meio do software C.H.I.C. Com isso, pudemos obter, simultaneamente, informações referentes ao tipo de concepção e período de formação básica. De modo geral, a análise das informações obtidas permite-nos afirmar que há indícios de que a prática docente influencia na mudança de concepções, pois, em nossa amostra, professores que obtiveram sua formação básica no mesmo período e atuam em séries ou níveis distintos possuem concepções, também, distintas

Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-20T14:10:11Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_DeniseRitter.pdf: 8038871 bytes, checksum: 560e6570b68009c1e275ada781962ed5 (MD5) / Made available in DSpace on 2018-08-20T14:10:11Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_DeniseRitter.pdf: 8038871 bytes, checksum: 560e6570b68009c1e275ada781962ed5 (MD5) Previous issue date: 2017-02-17 / Whereas the content of Geometric Probability is usually not worked in math class, this dissertation presents the results of a survey that sought to investigate what are the contributions of teaching Geometric Probability in learning the concept of Probability. The participants of this research were students of the junior year of high school from a school in the municipality of Santa Maria. The activities were organized in a learning unit, structured according to the methodological approach of the Three Pedagogical Moments (TPM) proposed by Delizoicov and Angotti (1990). The resources used in the development of the learning unit were practical experiments, manual and digital games, computational simulation, videos, problem situations and the GeoGebra software. The theory behind this study regarding the development of learning is the Significant Learning. This research is qualitative, with the following tools for its data collection: questionnaires (pre-test and post-test), the records of students and participant observation. The discovery that the students presented difficulties in concepts of areas of geometric shapes in two dimensions was made. Thus, it can be concluded that the activities developed in this research have contributed with the students as to reinforce the concepts of areas of geometric shapes in two dimensions, and also they have helped understand the concepts of probability, promoting meaningful learning of them. It was also noticed that the developed activities stimulated students' autonomy, their creativity and engagement to work in group, a fundamental characteristic to learn to deal with and overcome the challenges that are presented daily. / Considerando que o conteúdo de Probabilidade Geométrica normalmente não é trabalhado nas aulas de Matemática, esta dissertação apresenta os resultados de uma pesquisa que buscou investigar quais são as contribuições do ensino de Probabilidade Geométrica na aprendizagem do conceito de Probabilidade. Os participantes dessa pesquisa foram estudantes do segundo ano do Ensino Médio de uma escola do município de Santa Maria. As atividades foram organizadas em uma unidade de aprendizagem, estruturada de acordo com a abordagem metodológica dos Três Momentos Pedagógicos (TMP) proposta por Delizoicov e Angotti (1990). Os recursos empregados no desenvolvimento da unidade de aprendizagem foram, experimentos práticos, jogos manuais e digitais, simulações computacionais, vídeos, situações problema e o software GeoGebra. A teoria que embasa esse estudo quanto ao desenvolvimento da aprendizagem é a da Aprendizagem Significativa. Essa pesquisa tem caráter qualitativo, sendo utilizados como instrumentos para a coleta de dados, os questionários (pré-teste e pós-teste), os registros dos estudantes e a observação participante. Verificou-se que os estudantes apresentaram dificuldades nos conceitos de áreas de figuras planas. Com isso, pode-se concluir que as atividades desenvolvidas nessa pesquisa contribuíram para que os estudantes reforçassem os conceitos de áreas de figuras planas, e que estes auxiliaram na compreensão dos conceitos de Probabilidade, promovendo uma aprendizagem significativa dos mesmos. Também se percebeu que as atividades desenvolvidas estimularam a autonomia dos estudantes, sua criatividade e engajamento no trabalho em grupo, características essas fundamentais para aprender a lidar e a superar os desafios que se apresentam cotidianamente.

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-08-29T18:27:21Z No. of bitstreams: 1 DissLAAC.pdf: 944767 bytes, checksum: 6434b7c6041d9144b754372b88c6e43f (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-26T19:57:12Z (GMT) No. of bitstreams: 1 DissLAAC.pdf: 944767 bytes, checksum: 6434b7c6041d9144b754372b88c6e43f (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-26T19:57:19Z (GMT) No. of bitstreams: 1 DissLAAC.pdf: 944767 bytes, checksum: 6434b7c6041d9144b754372b88c6e43f (MD5) / Made available in DSpace on 2017-09-26T20:01:33Z (GMT). No. of bitstreams: 1 DissLAAC.pdf: 944767 bytes, checksum: 6434b7c6041d9144b754372b88c6e43f (MD5) Previous issue date: 2017-03-21 / Não recebi financiamento / The aim of this research was to analyze the concept of probability through the diversity of semiotic representation records arranged in the statement of the tasks (learning situations) contained in the second volume of the Teacher's notebook for the second high school series and their possible contributions to the development of probabilistic literacy. The study was based on Raymond Duval's Theory of Semiotic Representations and on the Probabilistic Letters of Iddo Gal. We sought to answer the following research questions: What and how are the records of semiotic representation in the learning situations proposed in the teacher's book? Do such records contribute to the development of probabilistic literacy? In order to fulfill the purposes of our work, we resorted to bibliographical and documentary research and based on our theoretical contributions, we analyzed the content of four learning situations. Among the several records of semiotic representation, the tree diagram was little explored in the proposed tasks. The mobilization and coordination of records of this nature has the function of contributing to the construction of concepts, but in the case of problems of combinatorial analysis, they did not present contributions to the development of probabilistic literacy, due to the absence of internal connections between the basic notions of With the calculation of probabilities. / Esta pesquisa teve por objetivo avaliar o conceito de probabilidade por meio da diversidade de registros de representação semiótica dispostos no enunciado das tarefas (situações de aprendizagem) contidas no segundo volume do Caderno do Professor para a segunda série do ensino médio e, suas possíveis contribuições para o desenvolvimento do letramento probabilístico. O estudo fundamentou-se na Teoria dos Registros de Representações Semióticas de Raymond Duval e no Letramento Probabilístico de Iddo Gal. Buscou-se responder as seguintes questões de investigação: Quais e como são articulados os registros de representação semiótica nas situações de aprendizagem propostas no Caderno do professor? Tais registros contribuem para o desenvolvimento do letramento probabilístico? Para o cumprimento dos propósitos do nosso trabalho, recorremos à pesquisa bibliográfica e documental e com base em nossos aportes teóricos, analisamos o conteúdo de quatro situações de aprendizagem. Entre os diversos registros de representação semiótica, o diagrama de árvore foi pouco explorado nas tarefas propostas. A mobilização e coordenação de registros dessa natureza tem a função de contribuir na construção de conceitos, porém, no caso dos problemas de análise combinatória, os mesmos não apresentaram contribuições ao desenvolvimento do letramento probabilístico, devido a ausência de conexões internas entre as noções básicas de combinatória com o cálculo das probabilidades.