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

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2017 ASEE Annual Conference & Exposition


Columbus, Ohio

Publication Date

June 24, 2017

Start Date

June 24, 2017

End Date

June 28, 2017

Conference Session

Mathematics Division Technical Session 3

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Paper Authors


Emre Tokgoz Quinnipiac University

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Emre Tokgoz is currently an Assistant Professor of Industrial Engineering at 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.

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Hazal Ceyhan

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Decision making for finding an exact or approximate solution of a definite integral can be challenging for Riemann integral learners. A conceptual cross section of calculus and numerical methods/analysis courses is approximation of definite integrals that cannot be determined exactly by using the existing integral formulas. Therefore, understanding the meaning of integral approximation and deciding whether approximation or exact solution should be used for solving an integral question are important aspects of engineering education for solving challenging real life problems. In this study, Science-Technology-Engineering-Mathematics (STEM) students’ preferences to use an exact or an approximate solution to solve a definite integral problem is analyzed.

Undergraduate and graduate students’ who were enrolled to a Numerical Methods or Numerical Analysis course at a large Midwest university during a particular semester in the United States participated to this IRB approved research. The responses of the students to a written questionnaire and the follow up video recorded interviews are used for qualitative and quantitative analysis of the research question. Qualitative interview responses were used for analyzing students’ decision making process. The schema development idea of Piaget and Garcia (1989) is employed for qualitative analysis of the students’ responses to the research question. The results indicated participants’ weakness in deciding to approximate the solution and majority of the participants’ trying to determine an exact solution to the problem. Realization of the need for a numerical method/analysis approach to solve a definite integral observed to be a conceptual challenge for both undergraduate and graduate students.

Tokgoz, E., & Ceyhan, H. (2017, June), Integral Concept and Decision Making: Do the STEM Majors Know When to Use Numerical Methods for Integral Approximation? Paper presented at 2017 ASEE Annual Conference & Exposition, Columbus, Ohio. 10.18260/1-2--28543

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