Task design to promote students’ covariational reasoning: A multi-theoretical approach
Heather Lynn Johnson, University of Colorado Denver, U.S.A.
Secondary students have many opportunities to learn key mathematical concepts, such as rate and function. However, rate and function remain difficult concepts to teach and learn. To address this challenge, I have developed dynamic computer environments and tasks to provide students opportunities to use covariational reasoning. When students use covariational reasoning, they can conceive of variation in measurable attributes of related objects. I share theoretically based design principles underlying a freely available Ferris wheel dynamic computer environment (https://illuminations.nctm.org/Activity.aspx?id=6908) and related task sequence. I explicate a multi-theoretical approach used to design within and across the task sequence. Marton’s variation theory underpins design across tasks in the sequence. Thompson’s theory of quantitative reasoning underpins design within each task in the sequence. To illustrate the efficacy of the Ferris wheel dynamic computer environment and task sequence, I provide evidence of secondary students’ advances in covariational reasoning. I discuss implications for the design of dynamic computer environments and tasks to promote students’ use of covariational reasoning.
Johnson, H. L. (2017, October). Task design to promote students’ covariational reasoning: A multi-theoretic approach. Universität Bremen Mathematisches Kolloquium. Bremen, Germany