## Research Projects - Learning and Teaching at the Physics-Mathematics Interface

PI: Thompson

Collaborators

- Michael E. Loverude, California State University – Fullerton
- Warren M. Christensen, North Dakota State University
- Joseph F. Wagner, Xavier University (Mathematics & Statistics)

Sponsored in part by NSF grant PHY-1405726 (Division of Mathematical and Physical Sciences)

- Current graduate student: Benjamin Schermerhorn
- Contact John R. Thompson by email for more information

This project will investigate the development of students’ mathematical understanding in the context of learning physics, particularly while solving challenging upper-division physics problems. The project team will conduct an integrated program of research, curriculum development, and assessment of topics covering a typical sophomore- or junior-level course in mathematical methods. The broad goals are to conduct research on student resources, study the process of transfer from mathematics to physics and the coevolution of knowledge in the two disciplines, and develop a set of Math / Physics tasks suitable for instruction, research, and assessment materials that will integrate challenging math content with topics covered in upper-division physics core courses.

Examples of current research topics:

- Student construction and use of multivariable coordinate system differential elements in vector calculus

(B. P. Schermerhorn) - The role of the differential in the context of the sign of “backwards” integrals
- Vectors and vector states in quantum mechanics