An Analysis of STEM Students’ Integral and Area Under the Curve Knowledge

Abstract

STEM students' ability to combine a concept's possible image that can be structured mentally, and its definition based on their integral knowledge is important particularly for area and integral related engineering applications. Detailed oriented application to the solution under certain conditions is also important; for instance, the relationship between integral calculation and area under the curve needs to be treated carefully in calculations. The data analyzed in this work was collected from 24 STEM students at a mid-sized Northeastern university that either enrolled or completed the second 4-credit course in the United States during 2020 and 2021 years. The participants completed a questionnaire and had gone through video recorded interviews to explain their written questionnaire responses by following an Institutional Review Board (IRB) process attained for the research. Action-Process-Object-Schema (APOS) theory is used for evaluation of the research question, along with the concept image and concept definition approach of Dreyfus et. al [1]. The written responses alone were not sufficient neither for APOS classification nor for concept image and concept definition application in which case video recorded interviews helped with this classification of the participants. The results indicated the need for designing more interactive calculus assignments, exercises, and quizzes for concepts that require better mental construction of such concepts by involving participants actively as a part of the questions asked in assignments, exercises, and quizzes.