Summer Research Project with Dr. Danielle Champney

Project description

This summer I will be delving more deeply into some existing data that I have collected (with colleagues) on how students use their calculus and physics backgrounds to reason about math tasks that require approximation. Students’ ideas about approximation and ‘good approximations’ are often heavily context dependent, but not always in predictable ways. For example, Students’ phrases such as “pure mathematical reasoning … that’s like not normal reasoning” and “in physics, you use a calculator. Math, you don’t,” abound, and the dialogue around them has interesting things to say about students’ perceptions of mathematics and what it means to do mathematics. With our approximation tasks, many students indicated that strategies like plugging in numbers or comparing graphs seemed “too easy” and “there ought to be an algebraic way to do it.” This sharply contrasts with the mathematicians and math graduate students we interviewed, who solved our tasks with exactly those methods. This has opened up space for us to think more deeply about students’ perceptions of how the disciplines use approximation, and to expand this study to other STEM contexts that use similar ideas (e.g. chemistry).

After quickly orienting to some of the prior work that we have done, I hope to spend time this summer analyzing the existing data set for additional themes of interest, as well as designing an extension of the study that could be carried out next year. If you are interested in (a) exploring how people learn and perceive common themes across physics, mathematics, chemistry, and other STEM disciplines, (b) thinking critically about students’ problem solving process across these themes, and/or (c) if you would like some experience with the process of designing a math education study that will be implemented in the coming year, then please let me know by sending me a little about yourself and why you might like to work on this project. I also welcome questions, and would be happy to send you some (short) papers if you want to get a feel for the type of work that I will be doing!