Van Deventer MST: Isomorphic math and physics vector representations

Joel Van Deventer
Comparing student performance on isomorphic math and physics vector representations
Unpublished MST thesis, University of Maine, August, 2008.

We designed isomorphic mathematics and physics free-response vector quizzes to evaluate student understanding of vectors in both contexts. Questions are identical, with only the context of the question changing in each case. To validate our test, we carried out task-based interviews with introductory physics students completing a semester’s instruction. We used our results from the interviews to develop a multiple-choice version of the vector quizzes which was then administered to introductory physics students before and after instruction. Overall, student performance on these isomorphic vector tasks is similar before instruction, different after an initial lecture on vectors in a math context, and different after a semester of instruction in our introductory mechanics course. In general student performance on the math vector tasks, after an initial lecture on vectors in an abstract context, seems to be indicative of performance on the physics vector tasks after a semester of instruction. No general trends were found relating to either the context dependence of the student performance or the responses distributions between individual math and physics isomorphic tasks. We find many students inconsistently apply vector manipulation tools and incompletely apply procedures across different vector tasks and contexts.

Recommended Citation

Deventer, Joel Van, "Comparing Student Performance on Isomorphic Math and Physics Vector Representations" (2008). Electronic Theses and Dissertations. 1348.

http://digitalcommons.library.umaine.edu/etd/1348

Van Deventer and Wittmann on math and physics vectors

J. Van Deventer and M.C. Wittmann
Comparing Student Use of Mathematical and Physical Vector Representations
Physics Education Research Conference Proceedings 2007.

Research has shown that students have difficulties with vectors in college introductory physics courses and high school physics courses; furthermore, students have been shown to perform worse on a vector task with a physical context when compared to the same task in a mathematical context. We have used these results to design isomorphic mathematics and physics free-response vector test questions to evaluate student understanding of vectors in both contexts. To validate our test, we carried out task-based interviews with introductory physics students. We used our results to develop a multiple-choice version of the vector test which was then administered to introductory physics students. We report on our test, giving examples of questions and preliminary findings.

©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 208-211
2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820935