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Qualitative and Quantitative Analysis of University Students’ Ability to Relate Calculus Knowledge to Function Graphs

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2020 ASEE Virtual Annual Conference Content Access


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Publication Date

June 22, 2020

Start Date

June 22, 2020

End Date

June 26, 2021

Conference Session

Mathematics Division Technical Session 5: From Functions to Big Data–A Hands-on Challenge

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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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Hasan Alp Tekalp


Elif Naz Tekalp

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My name is Elif Naz Tekalp. I am a junior industrial engineering student at Quinnipiac University. I also have mathematics and general business minor. I am interested in the role of mathematics in engineering education and professional life. I was very passionate about the research that I participated with my Dr. Emre Tokgoz.

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Berrak Seren Tekalp Quinnipiac University

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My name is Berrak Seren Tekalp, I am from Turkey, and I am a junior in Industrial Engineering at Quinnipiac University. I have a mathematics and a general business minor. Beginning in my sophomore year, I’ve done many academic types of research with my professors. In these projects, I have used advanced features within the IBM SPSS Statistics and Excel programs. I am a hard and reliable worker. I have been able to expand my communication skills, and through my time as an active member of multiple student organizations and engineering groups at Quinnipiac. I’ve led numerous meetings and club projects. I am comfortable with working in teams.

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It is the nature of engineering and mathematics educators to find out about engineering students’ success in answering calculus questions, particularly the questions that involve more than one calculus concept that requires to know other calculus concepts. Efforts have been made in understanding engineering students’ ability to respond calculus questions in Science-Technology-Engineering-Mathematics (STEM) fields that require knowledge of more than one calculus concept (Ref) and more research results are added every year to these results for understanding students’ approach to solve these problems. New teaching styles are designed to serve STEM students better by using these results. Empirical data collected on university students’ answers to conceptual calculus questions is the key to measure university students’ success in answering conceptual calculus questions with multiple underlying calculus concepts. For instance, understanding the calculus aspect of a function’s graph in two-dimensional space would require the knowledge of first and second derivatives, limit calculations, horizontal and vertical asymptotes, and the ability to connect all these concepts’ answers to be able to answer the question correct. The research methodology explained in this work received IRB approval at a university located on the Northeast side of the United States. The participants were undergraduate engineering students from three different disciplines: Civil, Industrial, and Mechanical Engineering. The quantitative data collected consisted of numerical responses of the research participants to parts (a) – (h) of the question related to a variety of different calculus concepts. We used Action-Process-Object-Schema (APOS) theory to analyze 19 undergraduate engineering students’ ability to respond to a calculus question that has multiple parts requiring the conceptual knowledge of first and second derivatives, limit calculations, horizontal and vertical asymptotes. Action-Process-Object-Schema (called APOS) theory is applied to mathematical topics (mostly functions) by Asiala, Brown, DeVries, Dubinsky, Mathews, and Thomas in 1996, and they explained this theory as the combined knowledge of a student in a specific subject based on Piaget‘s philosophy from 1970s. The collected qualitative data consisted of the transcription of the participants’ video recorded follow-up interviews; the purpose of the follow-up interviews was to explore the depth of students’ conceptual knowledge on the research question. The quantitative analysis of the question consisted of probabilistic results as well as the correlation analysis of the correct responses attained for parts (a) – (h) of the question. Overall, qualitative and quantitative analysis of the data indicated strong horizontal and vertical asymptote knowledge of participants while the main weakness appeared to be determining the domains of the function when the first derivative of the function is positive and negative.

Tokgoz, E., & Tekalp, H. A., & Tekalp, E. N., & Tekalp, B. S. (2020, June), Qualitative and Quantitative Analysis of University Students’ Ability to Relate Calculus Knowledge to Function Graphs Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--35113

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