Schermerhorn and Thompson on symbolic forms and differential length elements

Benjamin P. Schermerhorn and John R. Thompson

Students’ use of symbolic forms when constructing differential length elements

As part of an effort to examine students' understanding of the structure of non-Cartesian coordinate systems and the differential vector elements associated with these systems, students in junior-level electricity and magnetism (E&M) were interviewed in pairs. Students constructed differential length and volume elements for an unconventional spherical coordinate system. A symbolic forms analysis found that students invoked known as well as novel symbolic forms when building these vector expressions. Further analysis suggests that student difficulties were primarily conceptual rather than symbolic.

B. P. Schermerhorn and J. R. Thompson, Students’ use of symbolic forms when constructing differential length elements, 2016 PERC Proceedings [Sacramento, CA, July 20-21, 2016], edited by D. L. Jones, L. Ding, and A. Traxler, doi:10.1119/perc.2016.pr.073.

Christensen and Thompson on graphical slope and derivative representations

W.M. Christensen and J.R. Thompson
Investigating graphical representations of slope and derivative without a physics context
Phys. Rev. ST Physics Ed. Research 8, 023101 (2012).
http://link.aps.org/doi/10.1103/PhysRevSTPER.8.023101

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a physics context. As an extension from this work on students’ mathematical competency at the upper level in physics, we report on a preliminary investigation of mathematical understanding of fundamental concepts of slope and derivative among students in a third- semester multivariable calculus course. Among the first published findings of physics education research are investigations on students’ understanding of kinematics, with particular attention to graphical representations of position-, velocity-, and acceleration-versus-time graphs. Underlying these physical quantities are relationships that depend on derivatives and slopes. We report on our findings as we attempt to isolate students’ understanding of these mathematical concepts.