STEM majors' ability to relate integral and area concepts

Abstract

Area and integral concepts are interrelated under certain circumstances. In this work, senior undergraduate and graduate mathematics and engineering students' ability to combine concept image and concept definition based on their integral knowledge is observed. Seventeen participants of this study were either enrolled or completed a Numerical Methods/Analysis course at a large Midwest University during a particular semester. The participants completed a questionnaire and got interviewed to explain their written questionnaire responses. The questionnaire questions covered concepts such as functions, differentiation, function integrals, power series, and programming preferences of the participants. Action-Process-Object-Schema (APOS) theory of Asiala, Brown, DeVries, Dubinsky, Mathews and Thomas (1996) is considered initially for evaluation of the research question, however this theory is determined to be inappropriate for evaluating the research question. The data collected from the written questionnaire and video recorded interview responses are evaluated by using the concept image and concept definition approach of Dreyfus & Vinner (1989). In addition, Triad classification of the participants are determined to obtain the qualitative and quantitative results presented in this work.