Educators are increasingly being asked to interact with data to facilitate students’ learning in the classroom. However, as an educational measurement community, we have little understanding of the factors and/or contexts that facilitate educators’ successful use of data. Educators’ use of score reports and the relationship to the intended use is integral to the concept of validity. A conceptual model, “Data Habit of Mind,” is proposed to study educators’ understanding, interpretation and potential applications of results from large-scale assessments. The metaphor, “Habit of Mind,” was originally coined by Robert Sternberg and Dan Keating, and has been applied in the education sector to describe educators’ habits of inquiry when interacting with assessments. Based on an extensive review of the literature, Data Habit of Mind is defined as a combination of statistical literacy and score report interpretation. Statistical literacy is the extent to which an individual is able to describe, organize and reduce, represent, and analyze and interpret data. Score report interpretation is the extent to which an individual is able to describe, summarize, question, and propose an application for a given set of elements on a score report. The combination of these two makes up an individual’s Data Habit of Mind. Twenty educators were interviewed to assess their level of statistical literacy and their score report interpretation skills. A cognitive interview approach was used to capture the educators’ cognitive processes as they solved performance-based tasks, and protocol analysis procedures were used to encode the responses into the conceptual model. Descriptions of educators’ Data Habit of Mind were then generated through qualitative matrix analysis. Four groups of educators were identified based on the patterns of relationship between their statistical literacy and score report interpretation scores. Demographic factors, including teaching experience, gender and educational background were not meaningful predictors of educators’ Data Habit of Mind. These results add to our understanding of how educators interpret and use test results and have implications for test validation processes.

Educators are increasingly being asked to interact with data to facilitate students’ learning in the classroom. However, as an educational measurement community, we have little understanding of the factors and/or contexts that facilitate educators’ successful use of data. Educators’ use of score reports and the relationship to the intended use is integral to the concept of validity. A conceptual model, “Data Habit of Mind,” is proposed to study educators’ understanding, interpretation and potential applications of results from large-scale assessments. The metaphor, “Habit of Mind,” was originally coined by Robert Sternberg and Dan Keating, and has been applied in the education sector to describe educators’ habits of inquiry when interacting with assessments. Based on an extensive review of the literature, Data Habit of Mind is defined as a combination of statistical literacy and score report interpretation. Statistical literacy is the extent to which an individual is able to describe, organize and reduce, represent, and analyze and interpret data. Score report interpretation is the extent to which an individual is able to describe, summarize, question, and propose an application for a given set of elements on a score report. The combination of these two makes up an individual’s Data Habit of Mind. Twenty educators were interviewed to assess their level of statistical literacy and their score report interpretation skills. A cognitive interview approach was used to capture the educators’ cognitive processes as they solved performance-based tasks, and protocol analysis procedures were used to encode the responses into the conceptual model. Descriptions of educators’ Data Habit of Mind were then generated through qualitative matrix analysis. Four groups of educators were identified based on the patterns of relationship between their statistical literacy and score report interpretation scores. Demographic factors, including teaching experience, gender and educational background were not meaningful predictors of educators’ Data Habit of Mind. These results add to our understanding of how educators interpret and use test results and have implications for test validation processes.

Submitted by William Paiva (williampaiva17@hotmail.com) on 2015-05-22T19:32:45Z No. of bitstreams: 1 DAIANE LEMOS DE SÁ.pdf: 1198546 bytes, checksum: 955a6b142a89c036a8893dfec945a6b7 (MD5) / Approved for entry into archive by Vitor de Carvalho (vitor_carvalho_im@hotmail.com) on 2015-06-08T17:08:48Z (GMT) No. of bitstreams: 1 DAIANE LEMOS DE SÁ.pdf: 1198546 bytes, checksum: 955a6b142a89c036a8893dfec945a6b7 (MD5) / Made available in DSpace on 2015-06-08T17:08:48Z (GMT). No. of bitstreams: 1 DAIANE LEMOS DE SÁ.pdf: 1198546 bytes, checksum: 955a6b142a89c036a8893dfec945a6b7 (MD5) Previous issue date: 2015 / Esta pesquisa visa investigar quais informações o instrumento desenvolvido neste estudo pode fornecer a respeito do Letramento Estatístico de um determinado grupo de estudantes concluintes do Ensino Médio. Para elaborar o instrumento, selecionamos questões da prova do ENEM dos anos de 2009 a 2013, relativas à Estatística e Probabilidade. Estas foram classificadas quanto às Habilidades, estabelecidas pela Matriz de Referência para o ENEM 2009, e às Capacidades, formuladas por Iddo Gal (2002). Neste processo, percebemos que existia uma aproximação entre as referidas Habilidades e Capacidades, a qual consiste na identificação de conceitos afins em ambas. Tal percepção resultou em três Aproximações, cada uma composta por uma Habilidade e uma Capacidade. Foram selecionadas duas questões de cada Aproximação para compor o instrumento, bem como foi adaptada uma questão do ENEM para verificar duas das cinco Capacidades que não apresentavam correspondências conceituais. Isto originou um instrumento com sete questões, aplicado para dezoito estudantes concluintes do Ensino Médio, o que gerou dados a respeito do Letramento Estatístico do corpus, os quais foram analisados em quatro etapas. Na primeira, foi analisado o perfil dos estudantes, enquanto que, na sequência, os dados foram sistematizados coletivamente e individualmente. Por fim, foi estabelecida uma relação entre o perfil e o número de acertos nas questões. A presente pesquisa se justifica na medida em que são necessários estudos para investigar se os concluintes do Ensino Médio estão se apropriando dos conceitos atinentes à área da Educação Estatística, previstos na Legislação Brasileira. As informações coletadas a respeito do Letramento Estatístico do corpus (Habilidades, Capacidades e Nível de Letramento Estatístico) nos permitiram concluir que a maioria dos participantes da pesquisa, de modo geral, não apresenta domínio dos referidos conceitos. Cabe salientar que o Letramento Estatístico é fundamental no cotidiano dos cidadãos, tendo em vista que contribuem para a tomada de decisões pessoais com base em informações estatísticas. / This research aims to investigate what information the instrument developed in this study can provide about the Statistical Literacy in a particular group of students finishing the high. To prepare the instrument, we selected questions of a test called ENEM from the year 2009 to 2013, such questions related to Statistics and Probability. These questions were classified according to the Skills established by the Matrix of Reference for the ENEM 2009 and also according to the Keyparts, formulated by Iddo Gal (2002). In this process, we noticed that there was a connection between these Skills and Keyparts; this connection is the identification of related concepts in both. This perception resulted in three approaches, each one consisting of a Skill and a Keypart. We selected two questions of each approach to compose the instrument; we adapted a question of ENEM to verify two of the five Keyparts that have not presented conceptual matches. It originated an instrument with seven questions, applied to a convenience sample composed by eighteen graduating high school students, which generated data on the Statistical Literacy corpus, and it was analyzed in four stages. In the first stage, the profile of the students was analyzed, while following, the data were organized collectively and individually. Finally, a relationship between the profile and the number of correct answers on questions has been established. This research is justified in so far as studies are needed to investigate whether high school graduates are grabbing the concepts relating to the area of Statistics Education, under the Brazilian legislation. The information collected about the corpus of Statistical Literacy (Skills, Keyparts and Statistical Literacy Level) allowed us to conclude that most of the participants, in general, does not present domain of those concepts. It should be emphasized that the Statistical Literacy is fundamental in the daily lives of citizens, considering that it contributes to making personal decisions based on statistical information.

The research concerns presented in this dissertation addresses aspects of students’ interaction with commonly occurring graphical artefacts in teaching and learning environments. In particular, focus is on how the students make sense of these artefacts in relation to subject specific tools and forms of expression. The dissertation comprises of four studies guided by a semiotics cultural- historical perspective to cognition. The first study which is largely quantitative, analyses the percentage scores from students’ responses to selected items from OECD PISA surveys for items containing graphical elements. The second and the third studies in keeping with a more sociocultural perspective to learning as point of departure, examine the students’ collaborative interaction around tasks containing graphical elements. The fourth study explores the nature of students’ solutions from the Swedish national test in mathematics based on a tools and forms of expression sensitive empirically derived construct of Identification contra Critical-analytical approach to graphicacy. The main outcomes of these studies can be summarised as follows: first there is justification for re-examining the predominant characterisation of students’ interaction with graphical artefacts. Secondly, while it is not uncommon for students to take a more visual-perceptive and intuitive approach to graphicacy, results from task items interactions indicate that a Critical-analytical approach seems to be more reliable and capable of yielding desirable outcomes. The outcomes of these studies call for vigilance on the type of tasks used in relation to graphicacy and how these can be used to foster students’ Critical-analytical disposition.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2016-10-04T17:04:18Z No. of bitstreams: 1 Cassio Cristiano Giordano.pdf: 4551902 bytes, checksum: 697d60cac97ad320f4c82afae50f1c6b (MD5) / Made available in DSpace on 2016-10-04T17:04:18Z (GMT). No. of bitstreams: 1 Cassio Cristiano Giordano.pdf: 4551902 bytes, checksum: 697d60cac97ad320f4c82afae50f1c6b (MD5) Previous issue date: 2016-06-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Statistical literacy is critical for academic education, for professional life, and, above all, for the exercise of empowerment in our society, given the ease of access to data streaming from diverse media. Reading and interpreting these data, as well as expressing ideas informed by them, have become essential for every individual. However, despite the principles conveyed in Brazilian national and state curriculum guidelines, the teaching and learning of statistics have not received their deserved space in São Paulo schools, either in the Caderno do Aluno (a printed material provided by the São Paulo State Department of Education) or in the majority of textbooks marketed for use in high schools. Project-based teaching and learning of statistics constitute opportunities to promote statistical literacy. Moreover, this approach has the potential to change, in a notable manner, the relationship among teacher, student, and knowledge, promoting greater autonomy for students to develop their own research. To analyze the development of literacy and changes in the didactic contract under a project-based approach, a case study was conducted. The subjects were 43 students aged 17-20 years from two classes of the third (i.e., final) year of high school, who were distributed into nine groups of four or five members. During two months they participated in the entire process of developing a statistical investigation, from selecting themes and formulating research questions to the dissemination of results. The results revealed that this approach encourages the development of statistical literacy, creating conditions for a breach of the didactic contract – an important step in the development of students’ autonomy, preparing them for future challenges in their lives, the university, the labor market, and any other situation / O letramento estatístico é fundamental para a formação acadêmica, para a vida profissional e, sobretudo, para o exercício da cidadania em nossa sociedade, dada a facilidade de acesso a dados estatísticos por meio de diversos veículos de informação. Ler e interpretar tais dados, bem como expressar ideias neles embasadas, tornaram-se essenciais para cada um de nós. No entanto, apesar das orientações curriculares nacionais e estaduais, o ensino e a aprendizagem da Estatística não têm recebido nas escolas da rede estadual de São Paulo o merecido espaço, tanto no Caderno do Aluno (material institucional oferecido pela Secretaria de Educação), quanto pela maioria dos livros didáticos disponíveis para o Ensino Médio. Vemos no ensino e na aprendizagem da Estatística por meio de projetos uma oportunidade para o desenvolvimento do letramento estatístico. Além disso, a abordagem da Estatística por meio de projetos muda, de forma notável, as relações entre professor, aluno e saber, promovendo maior autonomia por parte dos alunos no desenvolvimento de suas pesquisas. Para analisar esses dois fenômenos – o desenvolvimento do letramento e as mudanças no contrato didático – em uma abordagem por meio de projetos, realizamos um estudo de caso. Nossos sujeitos de pesquisa foram 43 alunos com idades de 17 a 20 anos oriundos de duas turmas de terceiro ano do Ensino Médio, divididos em nove grupos de quatro ou cinco integrantes. Eles participaram, durante um bimestre letivo, de todo o processo de desenvolvimento de uma pesquisa estatística, desde a escolha do tema e elaboração da questão de pesquisa até a análise e divulgação dos resultados. Os resultados revelaram que essa abordagem favorece o desenvolvimento do letramento estatístico, bem como gera condições para uma quebra de contrato didático, importante para o desenvolvimento da autonomia dos alunos, preparando-os para os desafios futuros de suas vidas, na universidade, no mercado de trabalho ou em qualquer outra situação

The thesis Didactics of statistics is devoted to the problem of understanding of the basic concepts of probability theory and statistics. I have conducted a research in which I studied the understanding of the basic statistical concepts such as average, randomness, chance, variability, and sample by college students. I also studied whether the students are able to work with statistical data, whether they can read values from a chart, identify, and interpret their arithmetic mean. I interpreted the data obtained from the research using the model of the French psychologist Jean Piaget, according to which it is possible to distinguish three stages in the development of a theory, which Piaget named INTRA, INTER and TRANS. My research indicates that students' ideas about the basic statistical concepts are often very different from the ideas of the teacher. There is also interference between the scientific concepts and the similarly sounding terms of the everyday language. It is important that the teacher is aware of these differences and explains them using appropriate examples.

No description available.

Made available in DSpace on 2016-04-27T16:57:30Z (GMT). No. of bitstreams: 1 Carlos Ricardo Bifi.pdf: 753483 bytes, checksum: 81b61fcbaae31876717f2475e9e74724 (MD5) Previous issue date: 2014-04-25 / Secretaria da Educação do Estado de São Paulo / The purpose of this study was to diagnose the modes of functioning of pedagogical and mathematical knowledge held by a group of primary school teachers (1st to 5th grades) in Brazil. The investigation sought to identify elements that signaled these teachers perceptions of their knowledge of Statistics, Probability, and Combinatorics for the primary school curriculum. The question that guided the investigation was: Which aspects of pedagogical and specific statistical knowledge are mobilized in situations of class design and management by a group of teachers during their teaching practices? Nine teachers participated in the study, one of whom, who had received specific training (Teaching Degree in Mathematics) and held a Master s Degree in Science and Mathematics Teaching, spontaneously stood out as the group leader. This case study was developed in three stages, using the following instruments: observation of discussions in periods officially allotted to collective pedagogical work, observation of the teachers practice during lessons addressing the block of contents termed Treatment of information , and interviews. The first two stages guided the construction of a set of activities that formed the basis for the interviews. The data thus collected revealed the pedagogical and specific knowledge related to the Treatment of information block to be insufficient for the teachers to meet the needs of students findings that converge with those from investigations in Statistics Education. The behavior of the group leader ensured some sort of continuing education to the other members, raising their awareness of the effectiveness of collaborative work and socialization of their knowledge. In some sessions, the group admitted their own lack of knowledge on topics proposed for discussion e.g., Probability and fractions. The results indicated the importance of working collectively and investing in training or mentoring, beyond the hours officially allotted to collective pedagogical work, so as to foster the construction of pedagogical and specific knowledge related to Statistics, Probability, and Combinatorics by these teachers. Also identified was the need for providing teachers with training capable of empowering them (by constructing knowledge) to the use and complementation of teaching materials, textbooks, and other materials available in the school. Additional specific investigation should elucidate the functioning mode of the knowledge held by the participants, given the noteworthy specific features of the modes detected in the group features not fully described by the theoretical framework adopted. Further research is required to map more thoroughly these novel features detected in knowledge functioning modes / Esta pesquisa teve como principal objetivo diagnosticar o tipo de funcionamento dos conhecimentos didáticos e matemáticos por meio da observação de atividades relacionadas à prática de um grupo de professores do Ciclo I do Ensino Fundamental. Buscamos identificar elementos que sinalizassem a percepção desses professores sobre seus conhecimentos em Estatística, Probabilidade e Combinatória, relativos ao nível de escolaridade no qual esses docentes estavam em exercício. Com isso, buscamos responder à seguinte questão: Que conhecimentos estatísticos didáticos e específicos são mobilizados em situação de concepção e gestão de aula por um grupo de professores em suas práticas docentes? Participaram do estudo nove professoras, dentre as quais destacou-se espontaneamente uma líder que dispunha de formação específica (licenciatura em Matemática) e mestrado em Ciências e Ensino de Matemática. Este estudo de caso foi desenvolvido em três etapas, com os seguintes procedimentos metodológicos: observação das reuniões em Horário de Trabalho Pedagógico Coletivo (HTPC), observação da prática das professoras durante as aulas que tratavam de conteúdos do bloco Tratamento da informação e, por fim, entrevistas. As duas primeiras etapas nortearam a construção de um conjunto de atividades que serviu de base para as entrevistas. As análises do material coletado diagnosticaram no grupo estudado um conhecimento pedagógico e especifico do bloco Tratamento da informação insuficiente para atender às necessidades dos alunos, convergindo com resultados de pesquisas em Educação Estatística. Pudemos observar que o fato de a professora-líder promover uma espécie de formação continuada nos encontros suscitou nas demais professoras a consciência de um trabalho colaborativo, com socialização de conhecimentos. Em alguns momentos, o grupo verbalizou a ausência de conhecimento sobre temas propostos para debate por exemplo, Probabilidade e frações. Os resultados obtidos apontam a importância do trabalho coletivo de professores e do investimento em formações ou assessorias não limitadas ao HTPC, visando a construção de conhecimentos didáticos e específicos relacionados aos conteúdos de Estatística, Probabilidade e Combinatória. Também se identificou a necessidade de formações que permitam ao professor a construção da autonomia (pela construção de conhecimento) na utilização e complementação de materiais didáticos, livros-textos e outros materiais disponíveis na escola. Os resultados também apontam a necessidade de pesquisas específicas sobre a compreensão do tipo de funcionamento dos conhecimentos identificados, visto que apresentaram características importantes e específicas não inteiramente descritas pelos referenciais utilizados. Análises mais aprofundadas poderão permitir que tais características inéditas dos níveis de funcionamento dos conhecimentos sejam adequadamente mapeadas

Made available in DSpace on 2016-04-27T16:57:37Z (GMT). No. of bitstreams: 1 Amari Goulart.pdf: 1675483 bytes, checksum: 6d2b9f9d31168e34e68b20b1bc9462ce (MD5) Previous issue date: 2015-04-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The purpose of this study was to identify the relationships operating between the teaching of Statistics to Basic Education students (up to the 12th grade) and the teaching of Statistics at Teaching Degree programs in Mathematics relationships that might enhance the professional education of Brazilian teachers towards the development of Statistical Literacy among their future students. The Anthropological Theory of the Didactic, in its ecological perspective, was the theoretical framework adopted, from which two ecosystems were hypothesized: those of Mathematics teaching in Basic Education and in Teaching Degree programs in Mathematics. To examine whether these ecosystems are currently promoting the development of Statistical Literacy, the following documents were analyzed: the National Curriculum Parameters (PCN) for 6th-9th Grades (Mathematics), the PCN for 10th-12th Grades (Natural Sciences, Mathematics, and their Technologies), the PCN+ (Natural Sciences, Mathematics, and their Technologies), the Curriculum Guidelines for 10th-12th Grades (Natural Sciences, Mathematics, and their Technologies), the National Curriculum Guidelines for Mathematics Programs Teaching and Non-Teaching Degrees (DCN-BL), and the National Curriculum Guidelines for Higher-Education Training of Teachers for 1st-12th Grades Full Teaching Degree (DCN-FP). The following national exams were also evaluated: SAEB, Prova Brasil, ENEM, and ENADE. The analysis also included two textbook series (one for 6th-9th grades and the other for 10th-12th grades) approved by the National Textbook Program for Basic School (PNLD). The analyses of these documents and materials revealed that neither ecosystem currently promotes the development of Statistical Literacy. Between the teaching of Statistics to Basic Education students and the teaching of Statistics at Teaching Degree programs in Mathematics, no relationships were found to operate which might enhance the professional education of teachers towards the development of Statistical Literacy among their future students / Esta pesquisa teve por objetivo determinar as relações que podemos estabelecer entre o ensino de Estatística na Educação Básica e o Ensino de Estatística nos cursos de Licenciatura em Matemática, visando potencializar a formação de professores para o Letramento Estatístico. Utilizando como base teórica a Teoria Antropológica do Didático (TAD) e sua perspectiva Ecológica, formulamos, por hipótese, dois ecossistemas: o ecossistema do Ensino de Matemática na Educação Básica e o ecossistema do curso de Licenciatura em Matemática. Para verificar se esses ecossistemas potencializam o desenvolvimento do Letramento Estatístico, foram analisados os seguintes documentos: os PCN de terceiro e quarto ciclos do Ensino Fundamental (Matemática), os PCN do Ensino Médio (Ciências da Natureza, Matemática e suas Tecnologias), os PCN+ (Ciências da Natureza, Matemática e suas Tecnologias), as Orientações Curriculares para o Ensino Médio (Ciências da Natureza, Matemática e suas Tecnologias), as Diretrizes Curriculares Nacionais para os Cursos de Matemática, Bacharelado e Licenciatura (DCN-BL) e as Diretrizes Curriculares Nacionais para a Formação de Professores da Educação Básica, em Nível Superior, Curso de Licenciatura, de graduação plena (DCN-FP), bem como os seguintes exames de larga escala: SAEB, Prova Brasil, ENEM e ENADE e também duas coleções de livros didáticos aprovadas pelo PNLD e destinadas à Educação Básica. A partir das análises dos documentos, concluímos que nenhum desses ecossistemas potencializa o desenvolvimento do Letramento Estatístico. Não foram encontradas relações que possam ser estabelecidas entre o ensino de Estatística na Educação Básica e o Ensino de Estatística nos cursos de Licenciatura em Matemática visando aprimorar a formação de professores para o Letramento Estatístico

Globally, a wealth of educational data has been collected on learner performance in a bid to improve and monitor the quality of education. Unfortunately, the data seem to have had only limited influence on learning and teaching in classrooms. This thesis aimed to bridge this gap between the availability of learner performance data and their use in informing planning and action in schools. A design research approach was used to optimise the feedback system for the South African Monitoring system for Primary schools (SAMP). Design research aims to produce both an intervention to address a complex real-world challenge and to develop design guidelines to support other designers faced with similar challenges in their own context. In this research, the process of developing and improving the feedback system was also used to examine ways of facilitating the use of the feedback. Multiple cycles of design, implementation and evaluation of four different prototypes of the feedback system were conducted, employing evaluations from both experts (e.g. Dutch and South African academics, research and educational psychologists, instrument designers and teacher trainers) as well as school users (teachers, principals and HoDs). Mixed methods were employed throughout the study, with different sub-samples of school users sampled from the population of 22 schools (English, Afrikaans and Sepedi) in the Tshwane region participating in SAMP. The various research cycles incorporated interviews, observations, journals, questionnaires, the Delphi technique and expert evaluations to examine not only data-use, but also aspects such as problem-solving, planning, data-literacy and attitudes towards evidence-based practice in the schools. Data was analysed using Rasch Modelling, descriptive statistics and computer-aided qualitative data analysis. The study showed that an effective feedback system facilitates appropriate use through a gradual process of enlightenment, is flexible and responsive to user inputs, values collaboration and includes instrument, reporting and support components in its design. An optimum feedback system also positively influences school feedback and monitoring culture by providing opportunities for positive experiences with feedback and increasing data-literacy. This improves the chances of feedback being used for planning, decision-making and action in the schools. An effective feedback system must also offer a comprehensive package to accommodate different users, with various levels of data sophistication, functioning in diverse contexts. The research also showed that an effective feedback system mediates thinking about educational instruction and curriculum and can therefore be a potent change agent. Use of clear, simple, intuitive data presentation in the feedback system allows for experiential learning to increase user data-literacy. The design research approach employed in this study offers an appropriate and powerful approach to adapting, developing and optimising a feedback system. User involvement in design research ensures greater contextualisation and familiarity with the system, while engendering trust and a greater sense of ownership, all of which increase the receptiveness and responsiveness of users to feedback. Finally, the research also contributed design guidelines for other developers of feedback systems, an integrated conceptual framework for use of monitoring feedback and a functioning feedback system employed by 22 schools in the Tshwane region. / Thesis (PhD)--University of Pretoria, 2010. / Science, Mathematics and Technology Education / unrestricted