Literature Index

Recognizing the differences between three discrete distributions (Binomial, Hypergeometric and Negative Binomial) can be challenging for students. We present an activity designed to help students differentiate among these distributions. In addition, we present assessment results in the form of pre-and post-tests that were designed to assess the effectiveness of the activity. Pilot study results show promise that the activity may help students recognize the differences in these three distributions.

The studies we present investigate elementary students' reasoning about distributions in two contexts: (a) measurement and (b) naturally occurring variation. We first summarize an investigation in which fourth-graders measured the heights of a variety of objects and phenomena, including the school's flagpole, a pencil, and several launches of model rockets. Students noted that the measurements were distributed and that sources of error corresponded to differences in qualities of distribution, especially spread. Next, students investigated the distributions of measurements of height for rockets of different design, to learn whether and how they could be confident that rockets with rounded nose cones "really" went higher than those with pointed nose cones. We then turn to the naturally-occurring variation context, in which these same students (now fifth-graders) studied the growth of Wisconsin Fast Plants(tm), fast-growing members of the Brassica family that enable multiple cycles of classroom observation and experiment within a school year (life cycle is about 40 days). We recount how students became adept at using changing shapes of distributions to support plausible accounts of growth processes. Questions about what would be likely to happen "if we grew them again" motivated investigations of sampling, which, in turn, suggested choices of statistics to represent a sample distribution. Finally, students invented means for considering how one might know whether two different distributions of measures could reasonably be considered "really different."

There are many good reasons to incorporate thinking about diversity into a course, not the least of which is that it can have a real impact on student learning and cognitive development. In this webinar, we will explore both how the tools of statistics can help students better understand complex and controversial issues, and, in the other direction, how using these complex and controversial issues can help facilitate deeper learning of statistics.

This paper will report on the outcomes for international students from two different cohorts, undertaking equivalent courses. The two streams are differentiated by their course entry standards. The entry level for one stream is an academic ENTER score of 68 and an IELTS language score of 5.5 and for the other an academic ENTER score of 80 with an IELTS language score of 6.0 was needed. Each of these two cohorts' is taught in a different manner. The two cohorts of students have been tracked over a period of years and their educational outcomes compared. The tracking indicates that the student cohort with the lower entry level has achieved similar outcomes to that with the higher entry level. Can it be concluded that the similarity in outcomes can be attributed to teaching methodology?