Publication Date


Date of Final Oral Examination (Defense)


Type of Culminating Activity


Degree Title

Master of Science in Mathematics Education



Major Advisor

Laurie Cavey, Ph.D.


Sasha Wang, Ph.D.


Margaret T. Kinzel, Ph.D.


The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus.

A major finding of this study is that students can be successful in a first-year calculus course without demonstrating a process level understanding of function at the beginning of the course. In general, a positive correlation between understanding of function and success in calculus was found.

An item-by-item analysis of the two questionnaires revealed that students demonstrated competence, relative to their measured understanding of function, with items that are typically presented in standard mathematics courses taken prior to calculus, such as when provided a function as an algebraic rule and asked to calculate the value of the function. Also, students tended to justify decisions for solutions based on criteria not necessarily related to the definition of function. This however, appeared to have little impact on the level of success a student was able to achieve in calculus.