Research

  • The concept of statistical variation in a probability distribution is closely connected to the concept of sample space in a probability task. One must have some sense of the possible outcomes in a probability task in order to predict the likely variation range that will occur during repeated trials of that probability task. A survey version of a NAEP probability task was given to 652 mathematics students in grades 6 - 12 to obtain information on students' understanding of the sample space. Subsequently 28 students from grades 8-12 were given an interview version that included a simulation of the task. Survey results indicate that a higher percentage of students taking advanced mathematics correctly answered the probability task than was predicted by the NAEP data. Results of the interviews suggest that students who at first thought incorrectly about the probability task were likely to change their minds after seeing the variation in results of sets of repeated trials of the task.

  • Students in the same statistics course learn different things, and view the role of the lecturer in different ways. We report on empirical research on students' conceptions of learning statistics, their expectations of teaching, and the relationship between them. The research is based on interviews, analysed using a qualitative methodology, with statistics students studying for a mathematics degree. Students expressed a range of conceptions of learning in statistics and a range of views of their lecturers' teaching. Looking at what students expect of teachers and their views of their own learning provides an opportunity for teachers to develop teaching practices that challenge students to move towards more integrated conceptions of statistics learning.

  • We desired to improve student learning in our introductory, algebra-based statistical methods course. Marketing claims as well as anecdotal evidence suggested that electronic forms of educational material improve student learning. Some recent empirical evidence presented in the statistical literature uses both qualitative and quantitative data to evaluate computer-based learning aids. In order to contribute to evaluation of educational technology we designed an experiment to evaluate the use of ActivStats Multimedia Educational Software (on CD) and CyberStats Introduction to Statistics (on the web). Specifically, we assessed how the use of these two forms of educational material in the statistics laboratory portion of our course impacted student learning and attitudes. Implications of these results are discussed as well as lessons learned for designing future experiments.

  • Traditionally, the concept of sampling distribution has been seen as fundamental to an understanding of introductory statistical inference. As a result many computer packages have been developed which offer activities intended to support the development of this concept. However, we need to recognise that the concept of sampling distribution is complex and multi-faceted, with many different mathematical and symbolic representations possible. Computer simulations of the sampling distribution tend to address only the empirical representation of this concept, and leave the linking of representations to the user. And it is the development of these links which is critical to the development of understanding in statistical inference. This paper reports some results of a study analysing the role of the computer-based technology in the development of understanding of sampling distribution.

  • As statistical education evolves as a discipline more research involving the examination of statistical reasoning across disciplines is anticipated. For example, statistical investigations can cross into areas of scientific reasoning quite easily. In both situations, research questions are posed; data are collected, analyzed, graphed and interpreted. Instead of integrating statistics in the curriculum there is still a division of labour, whereby math educators are responsible for the teaching of statistics, and science teachers the teaching of scientific inquiry. Cross-disciplinary relationships need to be further examined in terms of our definitions of statistical reasoning and how we assess learning and problem-solving across disciplines. Two case studies will be contrasted to reveal the differences between statistical reasoning in a middle school science classroom and a mathematics classroom.

  • Teacher educators have a concern about the level of mathematical (including statistical) content knowledge of students who enter teacher education programs. Many students have knowledge of certain statistical procedures but lack a real understanding of those procedures such as why and when some should be used in preference to others. This paper reports on a study into the statistical knowledge of primary (elementary) teacher education students. An open-ended task (using a small multi-variate data set) was given to the students and required them to examine and report any interesting features in the data. Aspects of the students' level of 'data sense' was evaluated through an investigation of the statistical procedures that they used in relation to the report which they produced on what the data showed.

  • This project is based the epistemological reflection of the teacher about the stochastic' ideas in elementary education. It considers the European term stochastics meaning "probability and statistics". Throughout the study of mistakes and difficulties in learning and experiencing situations that permit the reflection about stochastics, the teaching and resources' methods and its practical use, the teacher will find different ways in its pedagogical practice to widen its professional development. In this world of information that we live, it's important to have the knowledge of the probability of facts to make decisions, to do forecasts and to acquire more ability to think about the uncertainties, because more and more the population has more access to social and economical issues on which the graphics and tables provide the survey results. So, based on these facts, our project has a main question. Which transformations the process of reflection about teaching of statistics and probability will bring to the training and practice of teachers? To answer this question, we are developing a qualitative research, defining the category in analysis of the empirical material, for the analysis of the interviews, the videos and the reports of the participant teachers. There are five teachers and two group coordinators participating in this research. The group has been working for two years and so far the results are very significant. We believe that the conclusions of this project will present relevant contributions not only for the research in statistics education, but also for the practice and development of the teachers.

  • A large experiment, investigating to what extent the use of real data and/or technology and/or pedagogical methods favour student's learning of statistics concepts, was carried out in Italy. The experiment has been monitored both from the side of pupils and teachers. This paper shows the findings from the teachers' point of view, through the analysis of their professional profile, attitudes towards statistics and opinions on its teaching before and after the experiment. The study reveals that, as teachers' training was in mathematics, they taught statistics with a mathematical approach, instead of "teaching statistics as a respectable subject" (Moore, 1992, p.14). The experiment produced a further more significant result, as it produced a substantial modification of teachers' perception of the approach to adopt for teaching statistics.

  • Here we present a report of a study carried out with six high school teachers who participated in a workshop of simulation activities using Fathom -dynamic software for teaching statistics-. At the end of eight weekly work sessions of three hours each, participant teachers were asked to answer a questionnaire related to their opinions about aspects of using the technique of simulation in teaching. We analyzed their answers bearing in mind four general aspects: the role of simulation in teaching; the different steps to follow in a simulation; the complexity of starting situations; and the most important concepts which take part in simulation activities. The results show that teachers deem as important only certain aspects of simulation but neglect others, which are also fundamental in teaching.

  • With ever increasing demands on limited resources, universities are looking for ways to utilise their resources more efficiently. At Swinburne University of Technology, in the statistics component of the psychology course, we have developed a set of materials which allow students to work independently, rather than attending lectures and tutorials. This means fewer students attend tutorials and we can give those that need it more individual assistance. A major concern with this strategy is that students might choose to work independently for inappropriate reasons. This study explores the differences in performance between students who choose to attend lectures and those who opt for independent study, and seeks to identify factors which explain these differences. The research is based on a number of questionnaires collected throughout the semester and analysed in conjunction with the students' results.

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