Using Knowledge Space Theory to Delineate Critical Learning Paths in Calculus

Abstract

This study examined the effects of using tutorials in pre-calculus content on college students’ performance in Calculus 1 as measured by the levels of conceptual development delineated through critical learning paths based on their achievement scores and quizzes. Our main objective is to provide evidence that a strong grounding in pre-calculus concepts is necessary for students’ success in Calculus and beyond. We employed Knowledge Space Theory (KST) to analyze data collected on a set of calculus questions that reflect different levels of conceptual development. These calculus questions were given to a group of students enrolled in calculus classes at a Southeastern urban university in the United States. Three tests were examined and the knowledge states were extracted for each test (using Visual Basic software) and knowledge trees were constructed (using an R package) to determine students’ critical learning paths. The findings of this study revealed that critical learning paths supported evidence that a strong foundation in Precalculus is necessary for students’ success in Calculus and beyond. Juxtaposing the succession of knowledge states and critical learning paths reflected student understanding of the basic calculus concepts and proposed a systematic approach to supplemental enrichment and remediation. https://doi.org/10.26803/ijlter.19.3.8