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


  • Muneer Jebreel Karama


Misconceptions in mathematics, APOS theory; functions; intervention; calculus I; derivative by limit (definition); conjugate


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