Calculus Instructors' Responses to Prior Knowledge Errors

Abstract

This study investigates the responses to prior knowledge errors that Calculus I instructors make when assessing students. Prior knowledge is operationalized as any skill or understanding that a student needs to successfully navigate through a Calculus I course. A two part qualitative study consisting of student exams and instructor interviews was employed to examine how instructors approach prior knowledge mistakes when they are evaluating students. Analysis of these interviews revealed that calculus instructors agree that algebra and trigonometry are essential components of prior knowledge within a calculus course. Additionally, perceived inconsistencies in instructor grading were reconciled using a sensible system framework.