First-Year Non-STEM Majors’ Use of Definitions to Solve Calculus Tasks: Benefits of Using Concept Image over Concept Definition?

Abstract

Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial understanding denotes when the definition or the concept image has correct parts but essential parts are missing or incoherencies occur. Some students confused continuity with differentiability or perceived it as a graph not having holes, which is also reported by other studies. Another misconception that emerged is to perceive points on the x-axis as non-continuous. The partial understandings of asymptotes were related to the vertical asymptote as it was confused with a function property. Some students referred to the definitions when correctly solving some of the tasks and some students with coherent concept images were successful solving some of the tasks even when they did not refer to the definitions.