Getting a Grip on Variability
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Getting a Grip on Variability Richard Lehrer1
· Leona Schauble1 · Panchompoo Wisittanawat1
Received: 27 March 2020 / Accepted: 17 July 2020 © Society for Mathematical Biology 2020
Abstract Because science is a modeling enterprise, a key question for educators is: What kind of repertoire can initiate students into the practice of generating, revising, and critiquing models of the natural world? Based on our 20 years of work with teachers and students, we nominate variability as a set of connected key ideas that bridge mathematics and science and are fundamental for equipping youngsters for the posing and pursuit of questions about science. Accordingly, we describe a sequence for helping young students begin to reason productively about variability. Students first participate in random processes, such as repeated measure of a person’s outstretched arms, that generate variable outcomes. Importantly, these processes have readily discernable sources of variability, so that relations between alterations in processes and changes in the collection of outcomes can be easily established and interpreted by young students. Following these initial steps, students invent and critique ways of visualizing and measuring distributions of the outcomes of these processes. Visualization and measure of variability are then employed as conceptual supports for modeling chance variation in components of the processes. Ultimately, students reimagine samples and inference in ways that support reasoning about variability in natural systems. Keywords Education · Modeling variability · Random processes · Sampling variability · Informal inference Given the diversity of the sciences and the many goals and forms of scientific practice, science education needs to be driven by a coherent vision of what is most worthwhile for students to learn. Moreover, that vision not only should encompass ultimate goals, but must also include an account of how instruction from the earliest grades can provide a strong foundation for ideas that may not come to fruition until years later. We start from the premise that science is inherently a modeling enterprise (Nersessian 2008; National Research Council 2012; Windschitl et al. 2008), a premise that leads to the question: What kind of conceptual repertoire best initiates students into the modeling game (Hestenes 1982)? We have been pursuing this question for the past 20 years in
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partnership with participating school districts in three different states. Elsewhere we describe how we introduce children to inventing and revising models as conceptual means for understanding the functioning of natural systems (Lehrer and Schauble 2019). Here, we focus attention on a set of conceptual core ideas that have proven to be especially powerful in children’s developing modeling repertoire. In particular, we seek to describe and illustrate how variability and the associated idea
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