Getting a Grip on Variability

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.