University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on several IRB approved pedagogical studies to observe undergraduate and graduate mathematics and engineering students' calculus and technology knowledge since 2011. His other research interests include nonlinear optimization, financial engineering, facility allocation problem, vehicle routing problem, solar energy systems, machine learning, system design, network analysis, inventory systems, and Riemannian geometry. Miss Hazal CeyhanMaking 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.

Quinnipiac University. He completed a Ph.D. in Mathematics and another Ph.D. in Industrial and Systems Engineering at the University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on several IRB approved pedagogical studies to observe undergraduate and graduate mathematics and engineering students' calculus and technology knowledge since 2011. His other research interests include nonlinear optimization, financial engineering, facility allocation problem, vehicle routing problem, solar energy systems, machine learning, system design, network analysis, inventory systems, and Riemannian geometry.