** NSF Proposal Summary
DUE-1323800 **

9/13–8/16; $649,293

** PARADIGMS IN PHYSICS: REPRESENTATIONS OF PARTIAL DERIVATIVES **

*Corinne A. Manogue, Tevian Dray, David Roundy, & Emily H. van Zee*

** Overview **

This proposal continues the joint work of two very successful projects: The Paradigms in Physics Project, a complete redesign of the physics major, now in its sixteenth year, and the Vector Calculus Bridge Project, an effort to “bridge the gap” between the mathematics and physics of vector calculus, now in its twelfth year. Curricular materials produced by these projects, including group activities, instructor's materials, and three published and one online textbook are currently in use at OSU and a number of other institutions.

The next phase of this project looks at representations of the quantification of change, particularly partial derivatives, across many STEM disciplines, with the goal of aiding students in moving toward the robust and multi-faceted understandings typical of STEM professionals. The project will include strands that explore the ways in which STEM experts use and represent change, that develop and test curricular materials for middle-division math and physics courses, that establish students' initial and ongoing levels of understanding as they progress through the curricular materials, and that make these curricular materials freely available online to the education community.

** Intellectual Merit **

This project will advance knowledge within physics and mathematics education as well as across other science, technology, and engineering fields that engage undergraduates in learning how to use partial derivatives to model changing quantities in complex environments. Success in upper-level undergraduate and graduate courses in these fields requires understanding what partial derivatives are and how to use them. Drawing upon expertise in mathematics, physics, and education, the team is tracing learning trajectories from what novice students write, draw, and say when encountering partial derivatives in upper-level courses through various representations experts use as they identify and interpret ways that variables change under different circumstances. In analyzing such data, the team is extending and adapting ways of thinking from other fields, such as identifying the different “epistemic games” students and experts “play” when solving problems involving partial derivatives. Based on such research, the curricular materials will include prompts for encouraging metacognition, ways to help students become aware of their own thought processes while transferring their emerging expertise from one context to another.

Led by the PIs of the Paradigms and Bridge projects, the team includes curriculum developers, education researchers, and recent adopters of curriculum materials from previous projects. This team has published 29 papers and 3 books based on previous grants in this ongoing project.

** Broader Impact **

This project will directly impact mathematics and physics education at the middle-division undergraduate level by providing classroom-tested curricular materials and associated instructor resources to the education community through existing, proven online resources (an activities wiki and textbook). Mathematics materials will support learning trajectories in multiple STEM disciplines, not just mathematics and physics. The addition of the new materials will make the existing resources easier to adopt by providing more complete coverage, in line with most common course structures. The project structure itself provides a model of how to advance STEM education holistically, combining an influential national advisory committee with a local interdisciplinary panel of experts drawn from affiliates in OSU's new Center for Research in Lifelong STEM Learning. All of these experts were chosen in part because of their potential to use the intellectual results of the work synergistically in their own related projects.