This project team is investigating a new method for teaching and learning multivariable calculus in which students actively explore central ideas through measurement and conjecture. The intellectual merit of this approach rests on the use of physical models of multivariable functions with a dry-erase surface and accompanying instruments that allow students to draw, measure, and grasp concepts geometrically. Through a marriage of the "flipped classroom" and collaborative learning, student teams work through activity sheets to investigate key ideas and relationships before a formal introduction in lecture. The project team conjectures that discovery learning with the physical models builds geometric understanding of multivariable calculus, imbues meaning in the algebraic formulas, improves performance and attitudes, and improves understanding of scientific applications. To disseminate its findings and exercise the project's broader impact, the PI team is conducting summer workshops with dozens of faculty, previously recruited from high schools, two- and four-year colleges and universities. Participants learn how about effective use of the surfaces and during the subsequent academic year all participants teach multivariable calculus using the surfaces, as well as arrange a control class at their respective institutions for comparison. Written assessments and clinical interviews are being used to compare learning outcomes between students using the surfaces and students receiving traditional instruction.
