Proceedings

  • This paper is an attempt to suggest features of future statistics education in the light of the emerging paradigms of science, education and mathematics. The paper consists of three sections; an introduction clarifying the context and limitations of the present paper, an explanation of the included concepts and the conclusions about some features of the future statistics education in the light of the studied emerging paradigms. These features included the integration of statistics education through an "applied" approach to problems, rejecting linearity, concentrating on conceptual frameworks and "conditional prediction", and emphasizing the study of probability and the way to deal with the results of statistical analyses.

  • Statistics in Action (STAC) is a course designed to explain the processes involved in a survey. The course was designed by Statistics Sweden (SCB) for their internal staff. SCB has bilateral agreements with Statistics South Africa (Stats SA) and one of the initiatives of this partnership is the STAC course. Seven STAC courses were presented at Stats SA during the period 1997 to 2001. On each occasion two consultants from SCB presented the course. In 1998 and 2001 facilitators from Stats SA co-presented the course. The size of the groups ranged from 15-20 participants. Since its inception in South Africa a total of 115 employees from Stats SA and two each from the Department of Justice and the Department of Labour were trained. This paper attempts to establish the usefulness of the course and to determine if it has enhanced the participants' knowledge of the survey process. Should the course be continued at Stats SA? Can the course serve as an instrument to address statistical literacy within the National Statistics System (NSS)?

  • The findings reported in this article came from a study which took place in an introductory college-level statistics course and which adopted a nontraditional approach to statistics instruction that had variation as its central tenet. The conjecture driving the study was that poor understanding of statistical concepts might be the result of instructional neglect of variation and that instruction which puts emphasis on building student intuitions about variation and its relevance to statistics should also lead to improved comprehension of other statistical concepts. The results of the study point to a number of critical junctures and obstacles to the conceptual evolution of variation. The article discusses one of those critical junctures and obstacles, the understanding of histograms.

  • This paper reports on research that created a controlled environment for interviewing individual students on the topic of sampling, allowing for cognitive conflict from other students. At various points in the interview the student was shown video extracts with contrasting views to those expressed and ask for a reaction. Outcomes are discussed with respect to (a) the outcomes for 37 students, in terms of their reaction to the cognitive conflict presented, and (b) the methodology, in terms of modeling cognitive aspects of a classroom environment in a controlled setting.

  • Theoretical frameworks for analyzing teacher subject-matter knowledge in specific mathematical domains are rare. In this paper we propose a theoretical framework for teacher subject-matter knowledge and understanding about probability. The framework comprises of seven aspects: essential features, the strength of probability, different representations and models, alternative ways of approaching, basic repertoire, different forms of knowledge and understanding, and knowledge about mathematics. We explain the importance of each aspect for teacher knowledge of probability, discuss its possible nature and illustrate our claims with specific examples.

  • Our paper describes a suite of studies involving students' statistical thinking in Grades 1 through 8. In our key studies (Jones et al., 2000, Mooney, in press), we validated Frameworks that characterised students' thinking on four processes: describing, organizing, representing, and analyzing and interpreting data. These studies showed that the students' thinking was consistent with the four cognitive levels postulated in a general developmental model. We also report on two teaching experiments, with primary students (Jones et al., 2001; Wares et al., 2000) that used the Framework to inform instruction. Teaching experiment results showed that children produced fewer idiosyncratic descriptions of data, possessed intuitive knowledge of center and spread and were constrained in analysis and interpretation by knowledge of data context.

  • 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.

  • Models for statistical modes of thinking and problem solving have been developed, and continue to be developed, by teachers and researchers. The purpose of these models range from helping to understand how individual students solve problems to developing instruments for educational research. These models have arisen with particular perspectives and primary uses in mind. In this paper we compare and contrast some statistical thinking models originating from statistics education research (Ben-Zvi & Friedlander, 1997; Jones, Thornton, Langrall, Mooney, Perry & Putt, 2000) with some models arising from the discipline of statistics and sub-disciplines (Wild & Pfannkuch, 1999; Hoerl & Snee, 2001). Drawing upon models from both these areas we discuss issues that include their development and use, how they might illuminate one another and what we can learn from them.

  • In this paper we describe the main ideas in a theoretical model that was developed for mathematics education research and is also applicable to statistics education. This model takes into account the three basic dimensions of teaching and learning processes: epistemic dimension (concerning the nature of statistical knowledge), cognitive dimension (concerning subjective knowledge) and instructional dimension (related to interaction patterns between the teacher and the students in the classroom). These theoretical notions are justified and applied to analyse a teaching process for the median in the introductory training of teachers.

Pages