Date of Award


Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Science (MS)




Robert Franzosa

Second Committee Member

Natasha Speer

Third Committee Member

William Bray


The purpose of this research was to understand the thought processes of students as they solve or attempt to solve questions about derivatives. I report on the common and uncommon inaccurate ideas students displayed as they completed conceptually based tasks about graphs of functions and their derivatives. Findings indicate that first semester calculus students have three main difficulties when attempting to sketch the first and second derivatives of a given graphical function. First, students have the tendency to sketch derivatives that represent opposite behavior of the original function. Second, proceeding left to right, many first derivative sketches begin correctly, but somewhere along the sketching process students become confused and the sketch ends up being incorrect. Lastly, many students express confusion about the second derivative and always sketch a linear function for the second derivative. Prior research in this area is reviewed and discussed, as well as the ramifications of this study and other research that would be beneficial in understanding students' qualitative comprehension of derivatives of graphical functions.