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Author ORCID Identifier



Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Sandra Madden

Second Advisor

Elizabeth McEneaney

Third Advisor

Harriet Pollatsek

Subject Categories

Curriculum and Instruction | Higher Education | Science and Mathematics Education


Multiple representations of the Fundamental Theorem of Calculus (FTC) are deemed essential to creating mathematical habits of mind, but not all classroom instruction includes them. This study articulates the relationship between college students’ experience with multiple representations of the FTC, gained through the enacted curriculum, and their use of multiple representations when problem solving or discussing the FTC. It suggests that students’ use of multiple representations directly relates to their curricular experience, which outweighs a student’s own inclination towards any particular representation. It further suggests that the relationship between classroom experience with a particular representation of the FTC, and its subsequent use in problem solving and discussion, is stronger for female students than for male students. Results in the literature indicate that female students tend to gravitate toward the representations they are exposed to through the enacted curriculum, while male students tend to be risk takers and may explore alternate representations. This study suggests that rich cognitive demand tasks that include multiple representations and are supported by an active learning environment help students develop a fuller understanding of the FTC. A mixed methods design is used, which includes lesson observations at three colleges, classroom assessments, and semi-structured think-aloud interviews with nine students – three from each college – as they problem-solve around the FTC. The study contributes to the existing literature on Calculus education by providing a more complete picture of the ways in which an enacted college curriculum that includes multiple representations of the FTC supports deeper learning and understanding of Calculus for all students, particularly female students.