Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive interviews were conducted to characterize their reasoning about mechanism and mathematical description of the systems of levers represented in the items. Participant item responses were modeled using item response theory and participant talk and gesture were coded according to developed analytic frameworks. Participants were elementary, middle, and high school students as well as college undergraduates, and adults without college education. The results suggest a relationship between participants’ tendencies to describe these systems mathematically and their mechanistic reasoning ability. Moreover, there are specific elements of mechanistic reasoning that are more highly associated with mathematical description. In addition, there is a relationship between a participant’s propensity to both mathematically describe and mechanistically trace mechanical systems.



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