PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
What is a Differential? Ask Seven Mathematicians, Get Seven Different Answers
Page: 411
The symbol “𝑑𝑥” is one example of a differential, which is a calculus symbol that is found in a variety of settings and expressions. We wanted to explore how expert mathematicians think about differentials in some of these settings and expressions, in order to see what levels of consistency might appear among their views. To that end, we created an interview protocol that contained differentials in the contexts of derivatives, definite and indefinite integrals, and separable differential equations, interviewed seven mathematicians, and analyzed their responses using a form of thematic analysis. Overall, we found no instances of total agreement among all subjects, but did find several common and recurring themes, including some that were unexpected and not found in our previous studies.