A Mathematics Educator Walks into a Physics Class: Identifying Math Skills in Students’ Physics Problem-Solving Practices

Abstract

One of the main goals of lower division “service” mathematics courses is to provide STEM-intending students with opportunities to engage in activities and contexts that can support their efforts to apply the mathematical ideas they are learning to successive major courses. The Mathematics Association of America has supported many mathematicians’ efforts to ask partner discipline faculty what topics and habits of mind they feel should be covered in mathematics classes to prepare them for their subsequent classes. We add to this work with a twist: Instead of asking physics faculty what they want students to know, we analyzed videos that students in an introductory physics class created so that we could ask ourselves what mathematical practices were most and least prevalent in the students’ physics problem-solving efforts. A qualitative analysis of the results, which we present here, indicated that most students were proficient in math practices involving problem setup and that the majority were able to apply mathematical concepts such as trigonometry and the solving of algebraic equations. However, only 44% of the student groups concluded their explanations by discussing answer reasonability and only 18% conducted a unit analysis to determine if their answers were applicable to the context of the problems assigned, even though both of these elements are important components of the overall sensemaking process. This report presents examples that illustrate these results and concludes with implications for teaching both entry-level mathematics and physics courses by modeling productive problem-solving and sensemaking practices.