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)

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-01-11T14:24:18Z No. of bitstreams: 1 sandrogrossinascimento.pdf: 2231755 bytes, checksum: f4dcf0be78a151521c555619230ce31e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T13:37:19Z (GMT) No. of bitstreams: 1 sandrogrossinascimento.pdf: 2231755 bytes, checksum: f4dcf0be78a151521c555619230ce31e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T14:08:51Z (GMT) No. of bitstreams: 1 sandrogrossinascimento.pdf: 2231755 bytes, checksum: f4dcf0be78a151521c555619230ce31e (MD5) / Made available in DSpace on 2017-02-07T14:08:51Z (GMT). No. of bitstreams: 1 sandrogrossinascimento.pdf: 2231755 bytes, checksum: f4dcf0be78a151521c555619230ce31e (MD5) Previous issue date: 2015-12-18 / O presente trabalho é uma pesquisa, cujo objetivo é investigar atividades didáticas de estatística para alunos do Ensino Médio. Essas atividades propiciaram a construção e/ou a reconstrução das medidas de centralidade e, assim, obter um olhar mais detalhado para o estudo dessas medidas, com o intuito de preparar os alunos de forma mais eficiente no uso de situações problemas do cotidiano. Concomitantemente, analisar, a partir da Educação Estatística, com o viés da Literacia Estatística, a compreensão dos resultados obtidos na análise dessas medidas. A teoria da Engenharia Didática subsidiou a metodologia desta investigação enquanto as situações didáticas e as situações a-didáticas foram os aportes teóricos na análise das atividades propostas aos estudantes, culminando assim, em uma proposta de sequência didática para o Produto Educacional. Vale salientar que os sujeitos desta pesquisa são os estudantes de uma escola estadual, turma do terceiro ano do Ensino Médio da cidade de Paraíba do Sul, do Estado do Rio de Janeiro. / This work is a research whose aim is to investigate teaching of statistical activities for high school students. These activities led to the construction and / or reconstruction of the centrality measures and thus a more detailed look at the study of these measures, in order to prepare students more effectively in the use of everyday problems situations. Concomitantly, analyze, from the statistics, with the bias of Literacy Education Statistics, the understanding of the results obtained in the analysis of these measures. The theory of Didactic Engineering supported the methodology of this research while teaching situations and situations-teaching were the theoretical contributions in the analysis of the proposed activities to students, so culminating in a proposal of didactic sequence for the Educational Product. It is worth noting that the subjects of this research are students of a state school, class of third year of high school in the city of Paraiba do Sul, State of Rio de Janeiro.

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Math anxiety, defined as feelings of apprehension and fear of courses involving mathematics, often interferes with student learning in a variety of college-level courses. A related phenomenon, statistics anxiety, affects the performance of many students in statistics courses. Researchers have found evidence that including collaborative problem solving as an instructional methodology is effective at reducing the negative effects of statistics anxiety. The purpose of this qualitative case study was to explore adult perceptions of collaborative problem solving as an instructional methodology focused on improving the learning environment in a business statistics course. Behaviorist, constructivist, and adult learning theories provided the foundation for this study that gathered narrative interview data from 14 adult students. The narratives were analyzed by first coding responses to questions into 7 frames of reference. Further refining of the data was accomplished by grouping responses in each frame of reference into common realms of response. Findings indicated that the adult participants perceived collaboration to be effective at reducing stress levels and improving course performance. Additionally, the participants identified weekly learning tasks, collaborative partner selection methods, and student resource materials that could benefit from redesigning. The project that stemmed from this research involved restructuring the instructional methodologies, learning tasks, and student resources to better align with adult learning preferences identified by the participants. The benefits to positive social change resulting from this project study included improving the course learning environment for adults and identifying adult preferences for implementing collaboration as a learning methodology.

Made available in DSpace on 2016-04-27T16:58:55Z (GMT). No. of bitstreams: 1 Osmar Antonio de Lima.pdf: 2129827 bytes, checksum: e41fc4037496877bf659e92892dcbe21 (MD5) Previous issue date: 2009-08-04 / Secretaria da Educação do Estado de São Paulo / The purpose of this study was introducing the content of Normal Distribution to high school students, being an approach proposed, aiming at the interaction of two environments, classroom and computer lab. The study was held with 11 high school students, bearing in mind the presentation of Normal Distribution by data simulation, using an electronic worksheet (Excel). The theoretical referential was based on the Anthropological Theory of the Didactics ATD to accomplish the intended purpose by the researcher: ease the comprehension of the stochastic concepts involving Normal Distribution by the students, by means of experiment simulations, using the electronic worksheet (Excel) and, also, interactive exercises. With this proposal, it was realized that the High School students began to recognize the characteristics and the graphical representation of a Normal Distribution, and from the analyses held in the classroom, it was verified that it was possible to relate the descriptive statistical contents with the probability ones and, this way, the students began to bear a sense of the relation between statistics and probability. Summarizing everything, the use of the electronic worksheet (Excel) with the interactive exercises enabled to guide the students towards the identification of concepts involving Normal Distribution, easing its interaction with the study object. Therefore, the students realized the idea of the existing relation between statistics and probability, which in this essay, was named as stochastic / O objetivo deste estudo foi introduzir o conteúdo da Distribuição Normal para alunos do Ensino Médio, sendo proposta uma abordagem, buscando a interação de dois ambientes, sala de aula e laboratório de informática. O estudo foi realizado com 11 alunos egressos do ensino médio, tendo em vista apresentar a Distribuição Normal pela simulação de dados, utilizando uma planilha eletrônica (Excel). O referencial teórico apoiou-se na Teoria Antropológica do Didático TAD para alcançar o objetivo pretendido pelo pesquisador: facilitar a compreensão dos conceitos estocásticos envolvendo a Distribuição Normal pelos alunos, por meio de simulação de experimentos, utilizando a planilha eletrônica (Excel) e, também, exercícios interativos. Com essa proposta, percebeu-se que os alunos do Ensino Médio passaram a reconhecer as características e a representação gráfica de uma Distribuição Normal, e a partir das análises realizadas em sala de aula, verificou-se que foi possível relacionar os conteúdos da estatística descritiva com os de probabilidade e, dessa forma, os alunos passaram a ter uma noção da relação entre estatística e probabilidade. Em síntese, o uso da planilha eletrônica (Excel), com os exercícios interativos possibilitaram encaminhar os alunos a identificação dos conceitos envolvendo a Distribuição Normal, facilitando sua interação com o objeto de estudo. Assim, os alunos perceberam a idéia da relação existente entre a estatística e a probabilidade, que neste trabalho, foi denominado como estocástica

Syftet med denna studie är att bidra med ökad kunskap om lärande och undervisning i informell statistisk inferens. I studien användes en kvalitativ forskningsstrategi inriktad mot prövning och generering av teorier med inspiration av grounded theory. Studiens kunskapsfokus är riktad mot karakterisering av statistiska processer och begrepp där system av begreppsramverk om informell statistisk inferens och modellering utgör en central del av forskningen. För att erhålla adekvat empiri utformades en undervisningssituation där elever engagerades med att planera och genomföra en undersökning. Studien genomfördes i en normal klassrumssituation där undervisningen inriktades mot ett område inom sannolikhet och statistisk där bland annat lådagram och normalfördelning med tillhörande begrepp introduceras. Det empiriska materialet samlades in genom videoinspelning och skriftliga redovisningar. Materialet analyserades genom ett sammansatt ramverk om informell statistisk inferens och modellering. Resultatet av analysen visar exempel på hur elever kan förväntas uttrycka aspekter av informella statistisk inferens då de genomför statistiska undersökningar. Vidare utvecklades ett ramverk som teoretiskt beskriver informell statistisk inferens i modelleringssituationer. Studien pekar på att ISI-modellering har potential att användas för att analysera hur informell statistisk inferens kan komma till uttryck och att identifiera potentiella inlärningsmöjligheter för studenter att utveckla sin förmåga att uttrycka informella statistisk slutledning och att identifiera potentiella inlärningsmöjligheter för elever att utveckla sin förmåga att uttrycka informella inferenser. / The purpose of this study is to improve our knowledge about teaching and learning of informal statistical inference. A qualitative research strategy is used in the study that focuses on the testing and generation of theories inspired by grounded theory. The knowledge focus of the study is aimed at the characterisation of statistical processes and concepts where systems of concept frameworks about informal statistical inference and modelling represent an essential part of the research. In order to obtain adequate empirical data, a teaching situation was devised whereby students were involved in planning and implementing an investigation. The study was conducted in a normal classroom situation where the teaching was focused on an area in probability and statistics that included the introduction of box plots and normal distribution with related concepts. The empirical material was collected through video recordings and written reports. The material was analysed using a combined framework of informal statistical inference and modelling. The results of the analysis highlight examples of how students can be expected to express aspects of informal statistical inference within the context of statistical inquiry. A framework was also developed aimed to theoretically depict informal statistical inference in modelling situations. The study suggests that this framework has the potential to be used to analyse how informal statistical inference of students are expressed and to identify potential learning opportunities for students to develop their ability to express inferences.

Despite agreement among researchers about the powerful influence of attitudes and beliefs on the development of students’ mathematical knowledge base (Leder, Pehkonen, & Törner, 2002), relatively little is known about these constructs in statistics education. This study investigated the relationship between mathematics-and statistics-related attitudes and beliefs of 11 high school students in an introductory statistics course designed around a 13-week long service-learning project. Service-learning is a pedagogical approach that situates academic learning in the context of community service. The study utilized qualitative, teacher-researcher (Cochran-Smith & Lytle, 1993) methodology from an interpretivist perspective. The three primary modes of data collection were journals, narratives, and an open-ended survey (Survey of Mathematical and Statistical Affect). Observations and reflections were also recorded regularly in a researcher journal. Inquiry adhered to guidelines for trustworthiness and rigor as outlined by Lincoln and Guba (1985). Item, pattern, and structural levels of analysis were employed (LeCompte and Schensul, 1999b). Investigation into attitudes and beliefs was framed in accordance with Op t’ Eynde, De Corte, and Verschaffel’s (2002) conceptualization of the mathematics-related belief system and McLeod’s (1992) framework of the affective domain in mathematics education. Results indicate that participants’ attitudes toward mathematics and statistics tended to converge while participants’ beliefs regarding mathematics and statistics tended to diverge. Participants like mathematics and statistics that involve real-life scenarios. Participants also like mathematics and statistics that do not require complex mathematical tasks. Participants’ beliefs regarding statistics were generally more positive than beliefs regarding mathematics. Participants reported greater confidence doing statistics than mathematics and contribute this confidence, in part, to service-learning. Participants also experienced a heightened sense of social awareness and social responsibility through the service-learning project. These results provide evidence that service-learning can be utilized to solidify positive attitudes and beliefs regarding statistics among high school students, in spite of potentially less positive ones toward mathematics.