Literature Index

In this paper, we consider some combinatorial and statistical aspects of the popular Powerball lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the jackpot in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the expected value and the variance of the probability distribution for the dollar prize amount. In certain circumstances, the expected value is positive, which might suggest that it would be desirable to buy Powerball tickets. However, due to the extremely high coefficient of variation in this problem, we use the law of large numbers to show that we would need to buy an untenable number of tickets to be reasonably confident of making a profit. We also consider the impact of sharing the jackpot with other winners.

Statistics is a useful and necessary tool required by large numbers of pupils for their project work in other subject areas. But what are these pupils learning in their Mathematics lessons to back up all this practical statistical work? What can the Mathematics teacher provide to develop the necessary skills? Often little consideration is given to the QUALITY of the data collected and the most appropriate method of selecting a sample for a particular purpose. Should the Mathematics teacher consider sampling methods and help pupils to understand the need for a representative sample? Can the microcomputer be utilised for a more practical approach geared to the child's understanding?

This report discusses the task of implementing suggestions for statistical education.

Recent research has been aimed at finding out how precollege students think about variation, but very little research has been done with the prospective teachers of those students. Absent from the literature is an examination of the conceptions of variation held by elementary preservice teachers (EPSTs). This study addresses how EPSTs think about variation in the three contexts of sampling, data and graphs, and probability situations.<br><br>A qualitative study was undertaken with thirty students in an elementary teachers' mathematics course. The course included three classroom interventions comprised of activities promoting an exploration of variation in each of the three contexts. Written surveys were completed by all students both before and after the class interventions, and six students participated in pre and post interviews.<br><br>Collective results from the survey data, interview data, and class observations were used to describe components of an evolving framework useful for examining EPSTs' conceptions of variation. The three main aspects of the framework address how EPSTs reason in expecting, displaying, and interpreting variation. Each of the three aspects is further defined by different dimensions, which in turn have their own constituent themes. The depth in describing the evolving framework is a main contribution of this research.<br><br>Particular tasks created or modified for this research proved useful in examining EPSTs' conceptions of variation. One kind of task asked students to evaluate supposed results of experiments and decide if the results were genuine or not. Another kind of task provided specific arguments to which subjects could react. A third kind of task involved a comparison of data sets that were displayed using different types of graphs.<br><br>The framework was used to compare the thinking of the six interviewees from before to after the class interventions. Changes included richer conceptions of expectations of variation, more versatile understanding about displays of variation, and better interpretations of variation. The most notable changes were the overall depth in maturity of responses and an increased sophistication in communication during the post interview. Evidence suggests that the class interventions, and the survey and interview tasks, stimulated changes in the way students thought about variation.