This study attempted to determine the specific mathematics necessary to a student in a beginning course in behavioral science research statistics. To determine the most desirable form for a review of mathematics prior to a research statistics course,, it was first necessary to determine the following: (1) the specific overall content of such a course, (2) the specific mathematics topics of such a course, and (3) the specific mathematics operations utilized in such a course. The study consisted of three parts. The first phase was a determination of the content of a typical beginning course in research statistics for the behavioral sciences. To make this determination, a survey was conducted among forty universities chosen by random sampling from those in the United States offering the Doctor of Education degree. Course outlines and textbooks used by these universities were analyzed, and topics were tabulated. In addition, a selection of recent statistics texts was analyzed, and these topics were also tabulated. These tables were used as a means of content determination.

A research report submitted to the Faculty of Humanities, School of Education, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Education, September 2018 / Access to mathematical concepts has for long been a major talking point, not only in South Africa, but throughout the world. Sadly, debate on ways of assisting learners to improve their understanding of mathematical concepts appear not to be yielding desirable results. One of the major barriers to effective and meaningful mathematics learning is errors which usually arise from misconceptions. To my knowledge and experience, learners hold a lot of misconceptions in the area of variability of data. In spite of this, little ground has been covered in misconception research around the study of statistics. In this regard, the study aimed at establishing the nature of errors which arise from misconceptions which learners hold particularly in representing and interpreting variability of data on ogives, frequency polygons and box plots. In addition, the study sought to establish the extent to which teaching intervention could assist towards error minimisation. Using ideas of constructivism and sociocultural theory, the study involved a group of eighteen Grade 11 learners and the researcher. It was conducted at a township high school in Gauteng, South Africa. The researcher was involved in the delivery of ten lessons on statistics. Upon completion of the topic, two tasks were assigned to learners prior to as well as after conducting a constructivist-based intervention lesson. The rationale for conducting the lesson was to determine the extent to which remediation could assist in minimising incidences of these errors. In order to capture as much data as possible, particularly on the thinking behind the errors, an interview was conducted on a sample of four learners. The study found that most errors made by learners emanated from application of irrelevant prior knowledge (conceptual errors) which led to the use of unsuitable methods (procedural errors). Through interviews, it emerged that misconceptions in the study of statistics arise from poor language proficiency. Learners struggled to express themselves in giving verbal responses to questions posed to them by the interviewer. The study recommends that teachers should always use the language of teaching and learning all the time so as to enable learners to improve their communication skills as well as enhance understanding of statistical concepts. Moreover, this study recommends that future studies be carried out on the statistical content knowledge of teachers as this could be yet another source of misconceptions held by learners in statistics. / XL2019

published_or_final_version / Education / Master / Master of Science in Information Technology in Education

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-07-27T13:30:57Z No. of bitstreams: 1 Danilo Saes Corrêa da Silva.pdf: 1860021 bytes, checksum: d63b0b3a3c442de33a36d490a793b1e4 (MD5) / Made available in DSpace on 2018-07-27T13:30:57Z (GMT). No. of bitstreams: 1 Danilo Saes Corrêa da Silva.pdf: 1860021 bytes, checksum: d63b0b3a3c442de33a36d490a793b1e4 (MD5) Previous issue date: 2018-04-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The growing dissemination of news, driven by social networks, makes society need to be increasingly critical. And it is within this context that Statistical Education can play an important role in the formation of this society, since it is possible for this Education to facilitate the formation of a more critical society, since the Statistical and Probabilistic Literacy help in this framing. Our general objective is to analyze which elements of Statistical Letting and Probabilistic Literacy are worked with students of the sixth year of elementary school and study the possible articulation among them through activities that involve critical posture for data analysis. During our studies we indicate how points in agrément can promote a new Literacy, the Stochastic Letters. In order to analyze how these two Literacies interact and articulate with the students, we performed an activity, based on assumptions of Didactic Engineering, which consisted in the launching addicted dice and construction of graphs to verify the relative frequency associated with each of the faces, so as to aid in the learning of Frequency Probability. To verify the critical posture of the students were inserted in the activity some addicted dice, resulting in non-equiprobable launches. The results of the activity pointed to some points in common in the Statistical and Probabilistic Literacy, such as the importance of working on Statistics and Probability concomitantly, and the relevance of working with dice, which are elements of the students' familiarity, which are the context of the students, we also indicate some difficulties encountered, such as the absence of verification of non-equipotentiality / A crescente divulgação de notícias, impulsionada pelas redes sociais, faz com que a sociedade necessite ser cada vez mais crítica. E é dentro desse contexto que A Educação Estatística pode ter papel importante na formação dessa sociedade, visto que há a possibilidade dessa Educação facilitar na formação de uma sociedade mais crítica, já que os Letramentos Estatístico e Probabilístico auxiliam nessa construção. Nosso objetivo geral é analisar quais elementos do Letramento Estatístico e do Letramento Probabilístico são trabalhados com alunos do sexto ano do ensino fundamental e estudar a possível articulação entre eles por meio de atividades que envolvam postura crítica para análise de dados. Durante nossos estudos indicamos de que forma pontos consonantes podem promover um novo Letramento, o Letramento Estocástico. Para analisar a forma como esses dois Letramentos interagem e se articulam com os alunos, realizamos uma atividade, baseada em pressupostos da Engenharia Didática, que consistiu no lançamento de dados cúbicos e construção de gráficos para a verificação da frequência relativa associada à cada uma das faces, para assim auxiliar na aprendizagem da Probabilidade Frequentista. Para a verificação da postura crítica dos alunos foram inseridos na atividade alguns dados viciados, resultando em lançamentos não equiprováveis. Os resultados da atividade apontaram para alguns pontos em comum nos Letramentos Estatístico e Probabilístico, como a importância de se trabalhar a Estatística e a Probabilidade de forma concomitante, e a relevância de se trabalhar com dados, que são elementos do convívio dos alunos, aprimorando levantamentos que são do contexto dos estudantes, indicamos também algumas dificuldades encontradas, como a ausência da verificação da não-equiprobabilidade

published_or_final_version / abstract / toc / Education / Master / Master of Education

Made available in DSpace on 2014-11-10T11:09:47Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-04-24Bitstream added on 2014-11-10T11:58:04Z : No. of bitstreams: 1 000789865.pdf: 3467712 bytes, checksum: 5f07845f7f30b2ab6dfbfbce88f5e0b5 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Quando se fala em Estatística na Escola Superior de Agricultura Luiz de Queiroz (ESALQ/USP), o primeiro nome lembrado é o do professor Frederico Pimentel Gomes. Ele assumiu a Cadeira de Matemática em 1959, e a partir de então passou a atuar fortemente no campo da Estatística, publicando livros que foram amplamente referenciados, tornando-se destaque neste campo. O objetivo inicial desta pesquisa foi o de investigar e analisar o Ensino de Estatística na ESALQ no período anterior à atuação do professor Frederico Pimentel Gomes. Para constituir esta história, tivemos acesso a alguns depoimentos e a diversos documentos, como por exemplo, Diários de Classe, Programas de Cadeiras, Caderno de Aluno, Livros e Apostilas de Estatística. Diante da análise das informações advindas destas fontes identificamos a importância de outros personagens: Edgard do Amaral Graner (Cadeira de Genética e, posteriormente, Cadeira de Agricultura), Friedrich Gustav Brieger (Cadeira de Genética) e Carlos Teixeira Mendes (Cadeira de Agricultura). Partindo da atuação destes personagens, escrevemos uma história sobre o Ensino de Estatística na ESALQ, discutindo também sobre as abordagens no Ensino de Estatística deste período e algumas problemáticas enfrentadas / When someone mentions Statistics in the Agriculture College Luiz de Queiroz, called ESALQ, in Sao Paulo University (USP), Brazil, the first name that is remembered is Frederico Pimentel Gomes. He assumed the Mathematics‟ Cathedra in 1959 and, since then, worked in Statistic. Frederico has published Statistics books that were widely referenced making him essential for this field. In this study we investigated and analyzed the Statistics Teaching in ESALQ, prior to the arrival of professor Frederico Pimentel Gomes. In order to construct this history, we had access to some testimonials and documents, such as Class Diaries, Course Programs, Handouts, books and a Student‟s Notebook. After analyzing these sources, we identified the importance of others people, such as: Edgard do Amaral Graner (Genetics Cathedra and subsequently Agriculture Cathedra), Friedrich Gustav Brieger (Genetics Cathedra) and Carlos Teixeira Mendes (Agriculture Cathedra). Starting from the participation of these people we wrote a history on the Statistics Teaching at ESALQ. We also discussed approaches and problematics encountered in Statistics Teaching at that period

Acompanha: Material manipulável e manipulável virtual para o ensino de estimativa de proporção populacional na formação inicial de professores / O presente trabalho teve como objetivo principal avaliar como os acadêmicos do 3º ano de um curso de Licenciatura em Matemática veem a utilização de material manipulável e manipulável virtual para o Ensino de Estimativa de Proporção Populacional. Na intenção de alcançar tal objetivo, foi desenvolvida uma pesquisa aplicada de natureza qualitativa organizada em quatro etapas: 1-Levantamento do referencial teórico, na perspectiva de verificar situações do Ensino de conteúdos da Estatística na Educação Básica; 2-Busca por materiais para o Ensino de Estimativa de Proporção Populacional, na qual se encontrou o material manipulável elaborado pela professora Lisbeth Kaiserlian Cordani e pela falta de recursos tecnológicos existentes, a pesquisadora desenvolveu um manipulável virtual, em parceria com um acadêmico do curso de Ciência da Computação da Universidade Estadual do Norte do Paraná; 3 -Intervenção ou aplicação da pesquisa, em se referindo ao momento da aplicação dos materiais ditos na etapa 2, em uma turma do 3º ano de um curso de Licenciatura em Matemática em que foi realizada a coleta dos dados; 4 -Análise dos dados coletados, em que se utilizou a Análise Textual Discursiva embasada em Moraes e Galiazzi (2016). Após a análise dos dados, pôde-se observar que os acadêmicos aprovam a utilização de material manipulável e manipulável virtual para o Ensino de Estimativa de Proporção Populacional, constatado que: os materiais são vistos como estímulos para a Aprendizagem, é considerado uma inovação para o Ensino, proporcionam uma ligação entre o conhecimento teórico e o prático e somam positivamente na formação dos professores de Matemática, quando estes passam a conhecer esses materiais, ainda durante o curso de formação, estimulando-os a desenvolver o conteúdo futuramente na Educação Básica. / This work aimed to evaluate how the 3rdgrade students in a Mathematics Degree course judge, conceptualize or qualify the use of manipulable material and virtual manipulable for the Population Proportion Estimate Teaching. In order to meet this target, an applied qualitative research was developed and then organized in 4 steps: 1-Theoretical framework production to verify situations of Statistics contents Teaching in the Basic Education; 2-Search for materials for the Population Proportion Estimate Teaching, in which the manipulable material elaborated by the professor Lisbeth Kaiserlian Cordani was found and for the lack of existent technological resources the researcher developed a virtual manipulable in partnership with a student of the Computer Science course of Universidade Estadual do Norte do Paraná; 3-Intervention or application of the research, it refers to the application moment ofthe materials mentioned on the step 2 in a 3rdgrade class of a Mathematics Degree course where data were collected, 4-Data collection analysis, in which the Discursive Textual Analysis based upon Moraes and Galiazzi (2016) was used. Through data analysis, it was possible to observe that the students approve the use of manipulable material and virtual manipulable for the Population Proportion Estimate Teaching, beacuse: they help the teacher in the teaching process, they facilitate a contextualized teaching applied to the students’ reality, they provide a connection between the theoretical and practical knowledge and they contribute positively to the graduation of mathematics teachers when these ones get to know these materials still during the graduation course, stimulating them to develop the content futurely in the Basic Education.

Acompanha: Sequência de ensino: uma proposta de ensino contextualizado de correlação e regressão linear para um curso de Engenharia de Computação / O presente trabalho teve como objetivo analisar as contribuições que um material de ensino de Correlação e Regressão Linear, pautado nos pressupostos da contextualização podem trazer para alunos de um curso de Engenharia de Computação de uma universidade pública no interior do Paraná. Para a realização desta pesquisa, dezesseis alunos do curso de Engenharia de Computação sugeriram temas que pudessem abordar conteúdos de Correlação e Regressão Linear em uma situação que fosse específica de sua área de atuação. Foram então selecionados dois Algoritmos de Ordenação: Bubble Sort e Merge Sort, comparando o tamanho do vetor e o tempo de ordenação de cada método. Os alunos foram divididos em duplas e quatro destas utilizaram o primeiro método e quatro duplas, o segundo método. A sequência de ensino foi sendo aplicada a partir da coleta de dados no algoritmo pelas duplas e cada novo item a ser estudado foi sendo inserido no decorrer da pesquisa. No final, os alunos fizeram as definições de cada categoria estudada dentro do conteúdo e cada descrição foi apreciada a partir da Análise de Conteúdo. Ao final foi possível visualizar os itens de maior aprendizado e os conceitos que não haviam ficado muito claros. Como produto final deste trabalho foi confeccionado um material didático de apoio ao professor, que abrange uma sugestão de ensino de Correlação e Regressão Linear para alunos de um curso de Engenharia de Computação, que se encontra anexo a esta dissertação. / The present article aimed to verify the contributions that a certain teaching material of Correlation and Linear Regression, based on the assumptions of the contextualization, can bring to Computer Engineering students of a public University on Paraná’s countryside. To fulfill this research, sixteen Computer Engineering students suggested themes that could approach Correlation and Linear Regression contents in a specific situation of their area. Then two Ordination Algorithms were selected: Bubble Sort and Merge Sort, comparing the vector size and the ordination time of each method. The students were divided in pairs and four of this pairs used the first method and the other four pairs, the second method. The teaching sequence was applied on the data gathering on the algorithm by the pairs and each new item to be studied was inserted along the research. In the end, the students made the definitions of each studied category inside the content and each description was appreciated from the Analysis Content. In the ending it was possible to visualize the most learned items as well as the concepts that had remained unclear. As work’s final product a Professor’s didactic support material has been confectioned, such material includes a suggestion for teaching Correlation and Linear Regression to students taking Computer Engineering, which is annexed to this essay.

Orientador: Dione Lucchesi de Carvalho / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-06T10:15:47Z (GMT). No. of bitstreams: 1 Biajone_Jefferson_M.pdf: 1483830 bytes, checksum: d11c0b484d69e5f7bd89596968a03c54 (MD5) Previous issue date: 2006 / Resumo: Esta pesquisa consiste em um estudo de intervenção que analisa as potencialidades e possibilidades didático-pedagógicas da abordagem do trabalho de projetos na formação estatística do Pedagogo administrador escolar. Os sujeitos da pesquisa são trinta e um alunos matriculados na disciplina de Estatística Aplicada à Educação do segundo ano do curso de Pedagogia de uma Instituição de Ensino Superior particular no interior do Estado de São Paulo. Desejoso em melhorar a sua própria prática pedagógica e ajudar a transformar as práticas educativas no ensino da Estatística em cursos de Pedagogia, o professor desta disciplina e também pesquisador direciona a intencionalidade de sua ação no sentido de (re)significar a aprendizagem estatística dos sujeitos, bem como instigá-los para uma reflexão do papel que irão exercer enquanto profissionais da educação e consumidores de informações. O material de análise originou-se de várias fontes: o diário de campo do professor pesquisador, os trinta e um diários dos alunos, as tarefas realizadas pelos grupos, questionários e entrevistas semi-estruturadas, além de registros em áudio e vídeo de alguns dos encontros e atividades realizados em sala de aula. A análise das informações produzidas configurou-se a partir de dois eixos: (1) O trabalho de projetos e o aluno da Pedagogia (2) O trabalho de projetos e o professor Jefferson. No primeiro eixo foram contemplados aspectos relativos à contribuição didático-pedagógica do trabalho de projetos e os saberes estatísticos adquiridos pelo aluno da Pedagogia. Já o segundo eixo se dedicou aos aspectos relativos à mudança da prática, concepções e saberes docentes do professor Jefferson e os percalços, decepções e quebras de expectativas que ele teve com relação ao trabalho de projetos vivenciado. Os resultados do estudo indicam que o trabalho de projetos não só permite propiciar ao aluno da Pedagogia um ensino e aprendizagem da Estatística em consonância com as suas necessidades formativas, como também (re)significar posturas negativas que este aluno possa ter em relação àquele saber, ao desestimular ansiedades e estatifobias fomentadas por uma escolaridade pregressa muitas vezes influenciada pela ação da ideologia da certeza da Matemática. Resultou também desta pesquisa o fato de que a opção pela abordagem de projetos pôde efetivamente (re)significar a prática docente do professor-pesquisador, seus saberes, posturas e abordar questões envolvendo as implicações do trabalho em grupo de alunos universitários, a integração entre diferentes abordagens de ensino da Estatística e a necessidade da formação deste saber nos cursos de Pedagogia / Abstract: This research consists of an intervention study that verifies the pedagogical-didactics potentialities and possibilities of the work project approach in the statistical professional development of the Pedagogy student as a future school administrator. The subjects of this study are thirty-one sophomore students of a Pedagogy course enrolled in a basic-level Statistics discipline of a private college in the countryside of São Paulo State. Eager to improve his own teaching practice and improve educational practices related to the teaching of Statistics in Pedagogy courses, the instructor and also researcher of this study directs the intentions of his actions to (re)define the statistics learning of the subjects, as well as to motivate them to reflect upon the role they will perform as education professionals and consumers of information. The material for the analysis came from several sources: the diary of the instructor-researcher, the thirty-one student diaries, the activities done by the groups, questionnaires and semi-structured interviews. Data from audio and video recording of classes was also provided. The data analysis was accomplished through two main axes: (1) the project work and the Pedagogy student (2) the project work and the instructor of the discipline. In the first axis, aspects related to the pedagogical-didactic contribution of the project work and the statistical knowledge acquired by the Pedagogy student were put into discussion. As to the second axis, considerations were made about those aspects related to the improvement of professional practice, conceptions and deceptions concerning his experience under the project work approach. The results of this study indicate that the project work not only allows Pedagogy students to have a meaningful Statistics teaching and learning process in conformity to their professional development needs, but also a (re)definition of negative postures that these students may possess in relation to that knowledge, as it removes anxieties and statiphobias produced, in many cases, by previous school experiences plagued with the misdeeds of the Mathematics certainty ideology. Other relevant results are related to the fact that teaching statistics through project work helped to (re)define the instructor¿s teaching practice, professional knowledge and postures. This teaching approach also pointed out questions involving the implications of group work among college students, the integration between opposite statistics teaching methods and the need of this knowledge education in Pedagogy courses / Mestrado / Educação Matematica / Mestre em Educação

The crucial role of representation in mathematical and statistical modeling and problem solving as evident in learners' arrangement and representation of statistical data were investigated with focus points data arrangement, data representation and statistical thinking levels. The representation tasks required learners to arrange and represent data through modeling, focusing on spontaneous representations. Successful transnumeration determine the ultimate success of a representation and the ability to organise data is regarded as critical. Arrangement types increased in sophistication with increased grade level and the hierarchical nature of arrangement types became apparent when regarded in the context of an adapted SOLO Taxonomy framework. A higher level arrangement strategy pointed to a higher SOLO level of statistical thinking. Learners in the two tasks produced a rich variety of representations which included idiosyncratic, unsophisticated responses as well as standard statistical representations. The context of the two tasks, the quantitative versus qualitative nature of the data in the tasks, and the statistical tools or representational skills learners have at their disposal, played an important role in their representations. Well-planned data handling activities develop representational and higher order thinking skills. The variety of responses and different response levels elicited in the two tasks indicate that the nature of the tasks rather than the size of the data set play a conclusive role in data tasks. Multiple representations by an individual were an indication of successful modeling, are effective in problem solving and are associated with good performance. The SOLO model which incorporates a structural approach as well as a multimodal component proved valuable in the analysis of responses. Using this model with accompanying acknowledgement of different problem solving paths and the contribution of ikonic support in the concrete symbolic mode, promote the in-depth analysis of responses. This study contributes to the research in the field of data representation and statistical thinking. The analysis and results led to an integrated picture of Grade 4-7 learners' representation of statistical data and of the statistical thinking levels evident in their representations. / Educational Studies / D. Ed. (Didactics)