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Analysis of STEM Majors’ Calculus Knowledge by Using APOS Theory on a Quotient Function Graphing Problem

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2015 ASEE Annual Conference & Exposition


Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015





Conference Session

Mathematics Division Technical Session 2

Tagged Division


Page Count


Page Numbers

26.213.1 - 26.213.12



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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 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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Abstract: Success in many engineering and mathematics courses is tied to well-developed calculus knowledge.Several important calculus concepts used in STEM courses include limit, first derivative, second derivative, andasymptote. In this article, undergraduate and graduate engineering and mathematics students’ ability to transform analgebraic function to its geometric representation is analyzed. Participants were either enrolled or recently (twoweek period) completed a Numerical Methods/Analysis course during the data collection period. Video recordedand written responses to graphing a quotient function are analyzed by using Action-Process-Object-Schema (APOS)theory. Participants are asked to sketch the graph of the given quotient function after calculating its limiting values,first derivative, second derivative and asymptotes. Qualitative and quantitative results indicated Mathematicsmajors’ higher success rate among all the participants.

Tokgoz, E. (2015, June), Analysis of STEM Majors’ Calculus Knowledge by Using APOS Theory on a Quotient Function Graphing Problem Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.23552

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