Evaluation of engineering & mathematics majors' Riemann integral definition knowledge by using APOS theory

Abstract

In this study senior undergraduate and graduate mathematics and engineering students' conceptual knowledge of Riemann's definite integral definition is observed by using APOS (Action-Process-Object-Schema) theory. Seventeen participants of this study were either enrolled or recently completed (i.e. 1 week after the course completion) a Numerical Methods or Analysis course at a large Midwest university during a particular semester in the United States. Each participant was asked to complete a questionnaire consisting of calculus concept questions and interviewed for further investigation of the written responses to the questionnaire. The research question is designed to understand students' ability to apply Riemann's limit-sum definition to calculate the definite integral of a specific function. Qualitative (participants' interview responses) and quantitative (statistics used after applying APOS theory) results are presented in this work by using the written questionnaire and video recorded interview responses. Participants are asked to calculate the definite integral of the function f(x) = x2 on the interval [1, 2] by using the limit definition of Riemann integral. Missing conceptual knowledge of the participants in calculus are observed when they were incapable of determining the solution to the problem.