Integral Concept and Decision Making: Do the STEM Majors Know When to Use Numerical Methods for Integral Approximation?

摘要

Making the decision to solve a definite integral exactly or approximately can be a challenge for first time Riemann integral learners. A conceptual cross section between calculus and numerical methods/analysis courses is approximation of definite integrals that cannot be determined exactly by using existing methods. The realization of a need for a numerical method/analysis concept after determining that the definite integral cannot be solved exactly is another conceptual challenge that students can face. In this study, engineering and mathematics students' decision to determine an exact or approximate solution to a definite integral will be analyzed qualitatively and quantitatively. Participating students' responses to the research question are analyzed and the collected information is evaluated by using the schema development idea of Piaget et al. (1989). The research data consists of seventeen senior undergraduate and graduate mathematics and engineering students' responses to a research question who were either enrolled or recently completed (i.e. 1 week after course completion) a Numerical Methods/Analysis course at a large Midwest university during a particular semester in the United States. Missing conceptual knowledge of the participants is observed when they were incapable of determining the solution to the problem.