Distribution : a Resource for Understanding Error and Natural Variation

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 PlantsTM, 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.”