An Analysis of Conceptual Integral Knowledge of STEM Majors

Abstract

Importance of integral in STEM applications is well-known however the corresponding pedagogical research for understanding undergraduate and graduate students' comprehension of integral concepts has not been studied comprehensively. Students' pedagogical integral knowledge can be evaluated from different perspectives. One aspect of such an evaluation is by stating the limit definition of definite integral for a specific function and asking students to determine the function as well as the integral bounds. Another way can be asking students to calculate a given integral by applying the limit definition of integral. In this study, seventeen senior undergraduate and graduate STEM students' written questionnaire and interview responses to two definite integral questions are collected and evaluated. These participants were either enrolled or completed a Numerical Methods or Analysis course at a large Midwest university during a particular semester in the United States. Qualitative data is displayed by using sample interview responses of the participants. Quantitative and qualitative responses are incorporated into the Action-Process-Object-Schema (APOS) theory classification for the specific questions. Participants are asked to explain their written questionnaire responses during the interviews. Concluding remarks with suggestions to the mathematics educators are provided for designing exercise and assignment questions in the conclusion and future work section.