Date of Award

Spring 1-1-2018

Document Type


Degree Name

Master of Arts (MA)

First Advisor

Eric Stade

Second Advisor

David Grant

Third Advisor

Katherine Stange


Previous research has demonstrated that students enrolled in calculus courses continue to struggle with old algebra ideas along with new calculus-specific concepts. In this study we seek to investigate student thinking around the sequencing of mathematical processes (SMP) by examining student work in a one-semester university calculus course. Our results indicate that students enrolled at the calculus level continue to struggle with algebraic order of operations in addition to making new mistakes with respect to the commutativity of differentiation and other operations; these errors are often evidenced in student failure to apply the product, quotient, or chain rules. We examine these SMP mistakes through the theoretical lenses of APOS theory, conceptual and procedural thinking, and structural and operational thinking. In addition, we look at two student sense-making strategies - using demarcating symbols and naming differentiation rules - to explore whether these are correlated with student propensity to make SMP-type errors.