Using a Definition to Find the First Derivative of Functions: Misconceptions and Remediation at the Collegiate Level

Abstract

The aim of this research was to study and investigate first year university calculus students’ misconceptions 
about how to use the definition of limit to find the first derivative of functions and then remediate these 
misconceptions by using APOS theory (Action, Process, Object, and Schema). Students (n = 82 female 
and male) were selected based on their performance in the first semester of university, i.e., purposive 
selection. Data obtained in the pretest indicated five types of misconceptions students had in handling 
the first derivative by finding the limit of function by the definition method. The researcher conducted a 
remedial plan on the concept of conjugates using APOS theory as an intervention for the remedy and 
recovery. The result of the post-test showed improvement and progress in the students’ achievement, so 
the intervention was effective by using APOS Theory. The researcher recommended using APOS for similar 
situations