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Conceptual Power Series Knowledge of STEM Majors

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2018 ASEE Annual Conference & Exposition


Salt Lake City, Utah

Publication Date

June 23, 2018

Start Date

June 23, 2018

End Date

July 27, 2018

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 the Director and 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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Taylor series expansion of functions has important applications in engineering, mathematics, physics, and computer science; therefore observing responses of graduate and senior undergraduate students to Taylor series questions appears to be the initial step for understanding students’ conceptual cognitive reasoning. These observations help to determine and develop a successful teaching methodology after weaknesses of the students are investigated. Pedagogical research on understanding mathematics and conceptual knowledge of physics majors’ power series was conducted in various studies ([1-10]); however, to the best of our knowledge, Taylor series knowledge of engineering majors was not investigated prior to this study. In this work, the ability of graduate and senior undergraduate engineering and mathematics majors responding to a set of power series questions are investigated. Written questionnaire responses of participating students and the follow-up interviews to have a better understanding of these written responses are analyzed qualitatively and quantitatively by using the Action-Process-Object-Schema (APOS) theory. Samples of the student responses to the written questionnaire and the transcribed interview data are displayed throughout this work. Written and oral interview data collected from participating STEM majors indicated a well-established knowledge of approximation, a poor knowledge of the meaning of center concept that takes place in the Taylor series expansion of functions, and a well-established knowledge of infinity as a part of infinite series concept.

Tokgoz, E. (2018, June), Conceptual Power Series Knowledge of STEM Majors Paper presented at 2018 ASEE Annual Conference & Exposition , Salt Lake City, Utah. 10.18260/1-2--30216

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