Tim McCarty Ph.D Defense

Date: 7/10/2018
Time: 8:30AM-10:00AM
Place: 315 Armstrong Hall

Abstract: The differential is a symbol that is common in first- and second-year calculus. One might think that such a common mathematical symbol would be interpreted universally, but literature that addresses student interpretations of differentials suggeststhat this is not the case, and that many interpretations are possible. My dissertation explored the differential conceptualizations of experienced mathematicians. I interviewed ten expert mathematicians, discussing expressions which contained differentialsand auxiliary questions that asked the meaning of “differential,” the differences between and , and the interpretation of phrases used to describe infinitely small quantities. Not only did I find no overall formal concept image for the differential, but Ialso found many different and sometimes contrasting themes within each interview subject’s personal concept image. I have created a framework for categorizing the multiple conceptualizations I have found for the differentials themselves, as well as begun alist of ancillary themes that address possible thoughts about and uses of differentials. I conclude my dissertation with a list of teaching implications that might arise from the existence of multiple differential conceptualizations.

Everyone is invited.

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