Scientific Program > Topic 8 > Session 8B >
Presentation 8B3. Structuring Natural and Measurement Variation as Distribution in the Elementary Grades

Richard Lehrer (USA)
Leona Schauble (USA)


Presentation Abstract

Humans appear to have an inborn propensity to classify and generalize, activities that are fundamental to our understanding of the world. Yet, however one describes objects and events, their variability is at least as important as their similarity. In Full House, Stephen Jay Gould neatly drives home this point with his choice of a chapter subhead: "Variability as Universal Reality". Gould further notes that modeling natural systems often entails accounting for their variability. An example now widely familiar from both the popular and professional press is the account of how seemingly tiny variations in beak morphology led to dramatic changes in the proportions of different species of Galapagos finches as the environment fluctuated over relatively brief periods of time.

Because variability is so important for understanding a wide range of scientific phenomena, we aim to introduce students to concepts of distribution early in their education. One of our approaches is drawn from the history of statistics, where concepts of distribution arose in response to variation in astronomical measure. Accordingly, we introduce elementary-grade students to distribution as a way of structuring their measures of less celestial events, like the heights of flagpoles and the apogees of model rocket flights. In this context, center has a ready interpretation as "true" length (or best estimate) and spread is understood as an indicator of precision of measure. However, as in the history of statistics, the transition of concepts of distribution to the study of natural variation raises several important conceptual hurdles for students, despite the seemingly obvious relationships. Accordingly we compare and contrast fourth- and fifth-graders understandings of distribution in these two contexts. We focus especially on the role of sampling in helping students come to understand how distributions could be employed as signatures of growth processes, which provided a bridge from the worlds of measurement and natural variations.


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