Multimedia Instructional Resources that Support Students’ Reasoning with Quantities

Aaron Weinberg
Ithaca College

Mathematically modeling physical phenomena in STEM fields requires conceptualizing these phenomena in terms of quantities (measurable attributes of objects) and relationships between them. In mathematics, reasoning about quantities is essential for developing productive notions of rates of change and accumulation—the foundations of calculus. The natural sciences also rely on the process of quantification to model and explore the relationships between objects as they interact within physical systems. In this workshop, we will begin by sharing a few scenarios that highlight the importance of conceptualizing systems in terms of quantities and quantitative relationships. We will introduce the central ideas of quantitative reasoning in the context of mathematics, and provide opportunities for participants to brainstorm examples of quantities and quantitative reasoning in other disciplines. Then, we will share examples of instructional videos from the Calculus Videos Project that demonstrate ways to represent measurable attributes of objects and to support students’ quantitative reasoning as part of the instructional materials and design. Finally, we will provide opportunities for participants to discuss the design of instructional materials and visualizations that could be used to help students in their own disciplines reason about systems quantitatively.