This project contributes to the joint work of two ongoing larger projects: The Paradigms in Physics Project, a complete redesign of the physics major, and the Vector Calculus Bridge Project, an effort to bridge the gap between the mathematics and physics of vector calculus.
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 multifaceted understandings typical of STEM professionals. The project includes strands that (1) explore the ways in which STEM experts use and represent change; (2) develop and test curricular materials for middle-division math and physics courses; and (3) establish students initial and ongoing levels of understanding as they progress through the curricular materials.
Intellectual Merit: This project is advancing 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. Based on such research, the curricular materials include prompts for encouraging 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.
Broader Impacts: This project directly impacts 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 a textbook. Mathematics materials support learning trajectories in multiple STEM disciplines, not just mathematics and physics. The addition of the new materials makes 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 research and curriculum development. The project includes an influential national advisory committee and a local interdisciplinary panel of experts drawn from affiliates in OSUs new Center for Research in Lifelong STEM Learning.
This team has published 29 papers and 3 books based on previous grants in this ongoing project. In addition, there is an ongoing series of faculty workshops to aid faculty in using the materials. The developments so far have been adopted and adapted in various forms by over 100 faculty at other institutions, and that number is increasing. Curricular materials produced by this project, including group activities, instructors materials, and publications, are all openly available on the project web site.
