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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The purpose of this study was to compare student achievement and satisfaction in online versus traditional introductory statistics courses. The sample studied were undergraduates at a small liberal arts school enrolled in introductory statistics over a period of six semesters. There were a few significant findings in student achievement in the overall sample and other meaningful results were found when assessing nursing and business majors specifically. Student satisfaction results between the two formats were inconclusive. Future studies on this topic can include hybrid education data in addition to online and traditional to see if there are any differences in achievement or student satisfaction in that population. Another possible study could be done regarding achievement in students who took preparatory training prior to enrolling in an online course.

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

In the last three decades, there has been a significant growth in the number of undergraduate students taking introductory statistics. As a result, there is a need by universities and community colleges to find well-qualified instructors and graduate teaching assistants to teach the growing number of statistics courses. Unfortunately, research has shown that even teachers of introductory statistics struggle with concepts they are employed to teach. The data presented in this research sheds light on the statistical knowledge of graduate teaching assistants (GTAs) and community college instructors (CCIs) in the realm of probability by analyzing their work on surveys and task-based interviews on the p-value. This research could be useful for informing professional development programs to better support present and future teachers of statistics.

The low grades that students score in some statistical units in Kenyan universities is of great concern and has evoked research interest in the teaching of some of the units and the students’ learning of the statistical content. The aim of the study was to investigate the difficulties undergraduate students experience in the learning of bivariate normal distribution in a Kenyan university. The research also aimed to answer the following research questions on the difficulties undergraduate students encounter in the learning of bivariate normal distribution. The first research question was based on the reasons why students find learning of bivariate normal distribution difficult and the second research question was to find the reasons why students experience such difficulties in learning bivariate normal distribution. The target population for this study included lecturers teaching statistics in the university, and second- and third- year students enrolled or who have previously completed the probability and statistics III unit, where the bivariate normal distribution content is covered. In selecting students for the study, the simple random sampling technique was employed while convenient sampling was used to select lecturers who participated in the study. A mixed methods design was adopted for this study where both quantitative and qualitative data was collected. A total of 175 students and six lecturers participated in this research study. All students who participated in the study did a bivariate normal distribution test (Appendix 1) designed by the researcher and then filled in a questionnaire (Appendix 2). The lecturers who participated in the study filled in an open-ended questionnaire (Appendix 3). The results showed that undergraduate students have difficulties in learning bivariate normal distribution. This is because most of them could neither state the bivariate normal distribution nor solve any of the application questions on the content. The students find it difficult to learn and comprehend the bivariate normal distribution equation with its many parameters and constants of the two random independent variables. The results also showed that students could not state the normal distribution equation nor could they solve questions on the normal distribution, which forms the foundational knowledge required for effective learning of the bivariate normal distribution content. ii Based on the results, the study recommended that emphasis should be placed on the basic and foundational knowledge of the normal distribution content and its applications before teaching bivariate normal distribution in probability and statistics III. In addition, it is recommended that all students should be involved in the learning of basic content to enable them to understand all parameters and constants in the equations and their applications. The study also recommends that lecturers revise the foundational knowledge and content related to the bivariate normal distribution before introducing and teaching the bivariate normal distribution content. This study also recommends that the university should consider a change of curriculum by teaching the bivariate normal distribution, as an introductory course to the unit under the multivariate distributions in statistics, in third year of the students’ studies. ; ; / Mathematics Education / M. Sc. (Mathematics Education)

The aim of this study was to validate an instrument that can be used by instructors or social scientist who are interested in evaluating statistics anxiety. The psychometric properties of the English version of the Statistical Anxiety Scale (SAS) was examined through a confirmatory factor analysis of scores from a sample of 323 undergraduate social science majors enrolled in colleges and universities in the United States. In previous studies, the psychometric properties of the Spanish and Italian versions of the SAS were validated; however, the English version of the SAS had never been assessed. Inconsistent with previous studies, scores on the English version of the SAS did not produce psychometrically acceptable values of validity. However, the results of this study suggested the potential value of a revised two-factor model SAS to measure statistics anxiety. Additionally, the Attitudes Towards Statistics (ATS) scale was used to examine the convergent and discriminant validities of the two-factor SAS. As expected, the correlation between the two factors of the SAS and the two factors of the ATS uncovered a moderately negative correlation between examination anxiety and attitudes towards the course. Additionally, the results of a structural regression model of attitudes towards statistics as a predictor of statistics anxiety suggested that attitudes towards the course and attitudes towards the field of statistics moderately predicts examination anxiety with attitudes towards the course having the greatest influence. It is recommended that future studies examine the relationship between attitudes towards statistics, statistics anxiety, and other variables such as academic achievement and instructional style.