**Title**: Promoting students’ smooth covariational reasoning

**Abstract**

Smooth covariational reasoning is an important form of reasoning for secondary and university students to develop and use. Yet, students may not necessarily engage in smooth covariational reasoning. Rather than positioning smooth covariational reasoning as a challenging form of reasoning out of reach for secondary students, I have investigated how students might use quantitative reasoning and smooth images of change when working in dynamic computer environments. Building from the work of mathematics education researchers, I led the development of a collection of Techtivities—free, accessible, digital media activities linking dynamic animations and graphs. Networking theories of different grain sizes–Thompson’s theory of quantitative reasoning and Marton’s variation theory—I intended students working on the Techtivities to have opportunities to engage in smooth covariational reasoning. Results are promising: Secondary students working with the Techtivities demonstrated smooth variational and covariational reasoning. To promote students’ smooth covariational reasoning, provide opportunities for students to (1) conceive of attributes as being possible to measure, (2) represent variation in each attribute, and (3) represent a relationship between attributes varying concurrently.

**Johnson, H. L.** (2017, December). Promoting students’ smooth covariational reasoning. *Mathematics Education Colloquium.* Tempe, Arizona: Arizona State University.