Analysis of STEM Students’ Ability to Respond to Algebra, Derivative, and Limit Questions for Graphing a Function

Emre Tokgoz; Samantha Eddi Scarpinella; Michael Giannone

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Conference: 2021 ASEE Virtual Annual Conference Content Access
Location: Virtual Conference
Publication Date: July 26, 2021
Start Date: July 26, 2021
End Date: July 19, 2022
Conference Session: Mathematics Division Technical Session 2
Tagged Division: Mathematics
Page Count: 11
DOI: 10.18260/1-2--36685
Permanent URL: https://strategy.asee.org/36685
Download Count: 421

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Paper Authors

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Emre Tokgoz Quinnipiac University

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Emre Tokgoz is currently the Director and an Associate 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 STEM 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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Samantha Eddi Scarpinella Quinnipiac University

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Michael Giannone Quinnipiac University

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Michael Giannone is currently a Senior at Quinnipiac University majoring in Industrial Engineering. He currently has been accepted to Pennsylvania State University to pursue a Master's in Industrial Engineering. Michael is interested in working either in the Healthcare of Manufacturing industry. Michael has worked at Pratt and Whitney located in East Hartford, CT as well as Crash Safety located in East Hampton, CT. Both of these experiences has helped him strengthen his knowledge in data analytics and optimization. One of Michael’s biggest interests in Ergonomics and Human Factors which he plans to purse later in his career.

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Abstract

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 and improving engineering students’ ability to respond calculus questions in Science-Technology-Engineering-Mathematics (STEM) fields that require knowledge of more than one calculus concept ([3]-[6]) 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 correctly answer the question. The research methodology explained in this work received IRB approval at a university located on the Northeastern side of the United States. The participants are 18 engineering undergraduate engineering students from different disciplines and backgrounds. The quantitative data collected consisted of written responses of the research participants to parts (a) – (e) of the question related to a variety of different calculus concepts. 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. Action-Process-Object-Schema (APOS) theory and another theory developed in [4] are used for analysis of 18 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 theoretical method introduced in [4] for analysis of collected responses of participants designed for measuring success per participant per 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) – (e) of the question. Overall, qualitative and quantitative analysis of the data indicated strong horizontal and vertical asymptote as well as second derivative knowledge of participants while the main weakness appeared to be determining the graph of the function when the first derivative of the function is positive and negative.

Citation
Format

Tokgoz, E., & Scarpinella , S. E., & Giannone, M. (2021, July), Analysis of STEM Students’ Ability to Respond to Algebra, Derivative, and Limit Questions for Graphing a Function Paper presented at 2021 ASEE Virtual Annual Conference Content Access, Virtual Conference. 10.18260/1-2--36685

TY  - CPAPER
AB  - 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 and improving engineering students’ ability to respond calculus questions in Science-Technology-Engineering-Mathematics (STEM) fields that require knowledge of more than one calculus concept ([3]-[6]) 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 correctly answer the question. 
The research methodology explained in this work received IRB approval at a university located on the Northeastern side of the United States. The participants are 18 engineering undergraduate engineering students from different disciplines and backgrounds. The quantitative data collected consisted of written responses of the research participants to parts (a) – (e) of the question related to a variety of different calculus concepts. 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. Action-Process-Object-Schema (APOS) theory and another theory developed in [4] are used for analysis of 18 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 theoretical method introduced in [4] for analysis of collected responses of participants designed for measuring success per participant per 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) – (e) of the question. Overall, qualitative and quantitative analysis of the data indicated strong horizontal and vertical asymptote as well as second derivative knowledge of participants while the main weakness appeared to be determining the graph of the function when the first derivative of the function is positive and negative. 

AU  - Emre Tokgoz
AU  - Samantha Eddi Scarpinella 
AU  - Michael Giannone
CY  - Virtual Conference
DA  - 2021/07/26
PB  - ASEE Conferences
TI  - Analysis of STEM Students’ Ability to Respond to Algebra, Derivative, and Limit Questions for Graphing a Function
UR  - https://strategy.asee.org/36685
DO  - 10.18260/1-2--36685
ER  -