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Teaching science using an inquiry approach is encouraged by several organisations responsible for defining teaching and learning guidelines in North America. However, using this approach can be difficult because of the complexity of inquiry. One source of difficulty is an inability to make sense of the data. Error variation, in particular, poses a significant barrier to the correct interpretation of data and therefore successful inquiry learning. A study was conducted to examine middle school students' ability to make sense of the data they collected in three related experiments. These data involved taking measurements of two continuous variables that were affected by error variation. The results indicated that students tended not to use abstract patterns to describe the data but rather used more local patterns that did not make use of the whole data set. However, many students also indicated an intuitive understanding that a greater amount of data could be used to generate results that are more accurate. This suggests a disparity between what the students understand about data and what they are capable of doing with data. Educational implications are that students may benefit from learning ideal patterns that can be compared to non-ideal data they collect.

Research on tutoring has shown that the student's interaction with the tutor determines the learning outcomes. In human tutoring, the responsibility of the interaction is shared between the tutor and the student. In the case of a computer coach such as the McGill Statistics Tutor, the control of the interaction is put entirely in the hands of the learners. Learners' ability to interact with the system productively therefore represents a critical aspect affecting the learning outcomes. This ability of help seeking (Nelson-LeGall, 1981) has not been well researched from a cognitive science point of view in the context of computer-supported learning (Aleven et al., 2003). The aims of the present work were to elaborate and test a cognitive model of help seeking and to examine the prevalence of help seeking in a problem-based computer-supported learning situation, as well as individual differences and the effect of the progression in a sequence of tasks with respect to help seeking. / Participants were 18 graduate students from a faculty of Education of a Canadian university. The seven-hour experiment involved working in pairs to solve a very challenging statistics problem for which students did not have sufficient background. A computer coach based on human tutoring, the McGill Statistics Tutor, was available to provide help with every aspect of the task. / Data consisted of two complementary sources. The main source was the dialogue between the participants as they worked on the statistics problem using the computer coach. The students' use of the computer coach and solutions to the tasks were also integrated into the database. / Data analysis consisted of statistical analyses using log-linear models. Conditional probability graphs were also constructed from the data. / The results were consistent with the help seeking model. Individual differences were found in terms of emphasis on certain help seeking activities. Effects of the progression in the sequence of tasks were also found. The quality of the solutions students elaborated corresponded to specific profiles of help seeking. The structure of help seeking episodes was established and corresponded to the model. These results have implications for the design of computer coaches and instructional situations.

Today, education is arguably one of the most important facets used to prepare and train students for the future. Society expects that students will acquire the requisite knowledge and competence in their respective fields to prepare them to successfully navigate the demands of today's competitive markets. This expectation has consequences on teachers at all levels of education across many domains. Teachers have a significant role: to prepare students for the future. Competent teachers spend a great deal of time reflecting on their own practices and beliefs, reviewing their teaching goals and evaluating if students have met these goals effectively. The process of reflection in teaching is vital in the preparation and training of students. / The purpose of this dissertation therefore was to investigate how statistics professors reflect on their practice. The research questions were designed to access what statistics teachers thought about before giving their courses and before giving two of their classes (hypothesis testing, t-tests). Post class evaluation interviews were conducted to determine where professors thought they were effective and whether they considered a need for change based on student understanding. More specifically, the questions asked: 1) What are the main themes in teacher reflection? 2) How is the content of reflection similar or different between statistics teachers? 3) How is the content of teacher reflection defined in statistics? / The design was based on a grounded theory approach whereby data collection consisted solely of interviews conducted throughout the semester: one pre-course interview and two sets of pre-class and post-class interviews. There were 13 participants in total. Participants were either statistics teachers from Quebec Cegeps or university professors. Participants were from the following departments: anthropology, economics, psychology, sociology, education, math, and biology. The analyses dealt with three data sources: pre class reflection, in class reflection, and post class reflection. / Data analysis focused on defining the main themes of teacher reflection that emerged from the data, identifying the content of reflection between and within participants in terms of similarities or differences. The pre course interview revealed five main themes: the course (logistics), the teacher as 'self, teaching approaches (what do they say they do in the classroom?), teaching and learning influences, and evaluation of teaching. / The pre and post class interviews addressed class planning. What did the professors foresee as any issues students might have in understanding hypothesis testing and t-tests? What changes would they make the next time they taught these concepts? Results showed that the focus of professor reflection centered around three main categories: the class, the student, and the teacher. For the main category, class, some professors reviewed lecture notes, added examples that emphasized authentic statistical problems, and others did no preparation. Student related themes addressed issues students had with understanding statistical content, learning associated difficulties, and student affect. The last category, the teacher, looked at self evaluation, their in-class strategies, methods of promoting and gauging student understanding, and decisions made in class and for future classes. Recommendations for future research include examining the role of experience in professor's level of reflection as well as defining the process of decision making and its role in reflection.

Diagnostic cognitive assessment (DCA) was explored using Bayesian networks and evidence-centred design (ECD) in a statistics learning domain (ANOVA). The assessment environment simulates problem solving activities that occurred in a web-based statistics learning environment. The assessment model is composed of assessment constructs, and evidence models. Assessment constructs correspond to components of knowledge and procedural skill in a cognitive domain model and are represented as explanatory variables in the assessment model. Explanatory variables represent specific aspects of student's performance of assessment problems. Bayesian networks are used to connect the explanatory variables to the evidence variables. These links enable the network to propagate evidential information to explanatory model variables in the assessment model. The purpose of DCA is to infer cognitive components of knowledge and skill that have been mastered by a student. These inferences are realized probabilistically using the Bayesian network to estimate the likelihood that a student has mastered specific components of knowledge or skill based on observations of features of the student's performance of an assessment task. / The objective of this study was to develop a Bayesian assessment model that implements DCA in a specific domain of statistics, and evaluate it in relation to its potential to achieve the objectives of DCA. This study applied a method for model development to the ANOVA score model domain to attain the objectives of the study. The results documented: (a) the process of model development in a specific domain; (b) the properties of the Bayesian assessment model; (c) the performance of the network in tracing students' progress towards mastery by using the model to successfully update the posterior probabilities; (d) the use of estimates of log odds ratios of likelihood of mastery as a measure of "progress toward mastery;" (e) the robustness of diagnostic inferences based on the network; and (f) the use of the Bayesian assessment model for diagnostic assessment with a sample of 20 students who completed the assessment tasks. The results indicated that the Bayesian assessment network provided valid diagnostic information about specific cognitive components, and was able to track development towards achieving mastery of learning goals.

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This study explored the completion rates (the number of years a student takes to complete a degree) of graduates at the University of the Western Cape. Differences between students who finished their studies in the prescribed time of three years and those who took longer than the prescribed time was highlighted.

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Acompanha: Ensino de estatística para os anos finais do ensino fundamental. / O presente trabalho teve como objetivo investigar as contribuições de uma sequência didática, utilizando a realidade dos discentes, na aprendizagem de conceitos estatísticos pelos alunos do nono ano do Ensino Fundamental. A revisão de literatura referente ao ensino de Estatística apoia-se em Rumsey (2002), Lopes (1998, 2003, 2008, 2010), Campos (2007), Silva (2007), Estevam (2010), Walichinski (2012), dentre outros. Com a intenção de alcançar o objetivo proposto, foi desenvolvida no ano de 2014 uma pesquisa aplicada, qualitativa com análise interpretativa e descritiva em uma turma de alunos do 9° ano do Ensino Fundamental de um colégio da rede privada de um município do norte do Paraná. Quanto a característica da pesquisa apoiou-se em Bogdan e Biklen (1994), Roesch (1996), Rosa (2009) e Silva e Menezes (2005). Em um primeiro momento foi aplicado um teste diagnóstico denominado pré-teste, no intuito de analisar o desempenho prévio dos alunos com relação aos conteúdos básicos de Estatística. Após a aplicação foi desenvolvida uma sequência didática que contemplou conteúdos básicos de Estatística. Durante a aplicação da sequência, observou-se uma participação mais efetiva dos alunos, isto é, apresentaram maior envolvimento e interesse pelos conteúdos abordados, uma vez que puderam coletar, organizar e tabular dados. Com base nos resultados do desempenho dos alunos após a aplicação é possível inferir que a sequência didática mostrou-se eficaz quanto a aquisição ao conhecimento de conceitos estatísticos, contribuindo assim, para o desenvolvimento das competências de raciocínio, pensamento e letramento estatístico. Como produto final desta pesquisa, apresenta-se um caderno pedagógico de apoio ao professor contendo uma sequência didática com conteúdos básicos de Estatística voltada para os anos finais do Ensino Fundamental, que se encontra anexado a esta dissertação. / The present study aimed to examine the contributions that a didactic sequence, using the reality of the students learning of statistical concepts by students in the ninth year of basic school. The literature review concerning the teaching of statistics relies on Rumsey (2002), Lopes (1998, 2003, 2008, 2010), Campos (2007), Silva (2007), Estevam (2010), Walichinski (2012), among others. With the intention of achieving the proposed goal, was developed in the year 2014 a applied research, interpretive analysis and qualitative, descriptive in a batch of students of 9° year of basic school to a College’s private network of the city the north of Paraná. As a feature of the research was supported in Bogdan and Biklen (1994), Roesch (1996), Rosa (2009) and Silva and Menezes (2005). At first it was used diagnostic test called pre-test in order to analyze prior student performance in relation to the basic contents of Statistics . After the application was developed a didactic sequence that included basic contents of Statistics was developed . During application of the sequence, there was a more effective participation of students, this is, showed greater involvement and interest in the content covered, since they could collect, organize and tabulate data. Based on the results of student performance after application it is possible to infer that the instructional sequence was effective as acquiring the knowledge of statistical concepts, thus contributing to the development of reasoning skills, thinking and statistical literacy . As a final product of this research, presents an education booklet teacher support containing a didactic sequence with basic content Statistics facing the final years of basic school, which is appended to this dissertation.

Statistically skilled workers are highly demanded in today's world, which means we need high-quality statistics education. There has been a continuously increased enrollment of statistics students. At the college level, introductory statistics courses are typically taught by professors who often hold a strong qualification in mathematics but may lack formal training in statistics education and statistical analysis. Existing literature claims that a unique way of thinking--statistical thinking or reasoning--is essential when teaching statistics, especially at the introductory level. To elaborate and expand on the issue of statistical thinking, a qualitative study was conducted on 15 mathematics teachers from a local community college to discuss differences between statistics and mathematics as academic disciplines and exemplify two types of thinking--statistical thinking and mathematical thinking--among mathematics teachers who teach college-level introductory statistics. Additionally, the study also inspected mathematics teachers' pedagogical ideas influenced by each type of thinking, some of which were recognized as "pedagogically powerful ideas" that transcend students' conceptual understanding about statistics. The study consisted of two online questionnaires and one interview. In the two online questionnaires, participants explored and rated five technology options for teaching statistics and self-evaluated their technology, pedagogy, and content knowledge. During the interview, participants solved nine statistical problems designed to elicit statistical thinking and addressed pertinent pedagogical questions related to each problem's statistical concept. A framework that hypothesizes aspects of mathematics teachers' statistical thinking and mathematical thinking in statistics was created, summarizing the prominent differences in problem-solving, variability, context, data production, transnumeration, and probabilistic thinking. Select responses from participating mathematics teachers were provided as examples of each type of thinking. Furthermore, it was revealed that mathematics teachers with a different type of thinking tended to cover different statistical topics, deliver the same statistical concept in different ways, and assess students' knowledge with different emphases and standards. This study's results have implications: if statistics is to be taught by mathematics teachers, statistical thinking is required to implement pedagogically powerful ideas for furthering meaningful statistical learning and to unveil the differences between statistics and mathematics.