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Evaluation of Engineering & Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS Theory

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

June 29, 2016





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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 a 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 an IRB approved pedagogical study to observe undergraduate and graduate mathematics and engineering students’ calculus and technology knowledge in 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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In this study senior undergraduate and graduate mathematics and engineering students’ conceptual knowledge of Riemann’s definite integral definition is observed by using APOS theory. Seventeen participants of this study were either enrolled or recently (i.e. 1 week) completed a Numerical Methods or Analysis course at a large Midwest university during a particular semester in the United States. Each participant was asked to complete a questionnaire consisting of calculus concept questions and interviewed for further investigation of the written responses to the questionnaire. The research question is designed to understand students’ ability to apply Riemann’s limit-sum definition to calculate the definite integral of a specific function. Qualitative (participants’ interview responses) and quantitative (statistics used after applying APOS theory) results are presented in this work by using the written questionnaire and video recorded interview responses. Participants are asked to calculate the definite integral of the function f(x) = x2 on the interval [1, 2] by using the limit definition of Riemann integral. Missing conceptual knowledge of the participants’ in calculus are observed when they were incapable of determining the solution to the problem.

Tokgoz, E. (2016, June), Evaluation of Engineering & Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS Theory Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.26777

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