Undergraduate STEM Students’ Comprehension of Function Series and Related Calculus Concepts

Emre Tokgoz; Elif Naz Tekalp; Hasan Alp Tekalp

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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 3
Tagged Division: Mathematics
Page Count: 14
DOI: 10.18260/1-2--37950
Permanent URL: https://strategy.asee.org/37950
Download Count: 252

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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 mathematics and engineering students’ calculus and technology knowledge since 2010. 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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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 a 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 in with Dr. Emre Tokgoz.

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Hasan Alp Tekalp

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Abstract

Series expansion of functions is frequently used as a part of teaching and research in STEM fields, therefore understanding and improving STEM students’ series knowledge is important for improving STEM education. There is little attention given to pedagogical research on understanding STEM students’ function series expansion comprehension and their ability to solve related calculus problems. The results attained in this work is expected to help for determining and developing a successful method of teaching Taylor series after weaknesses of the students are investigated. We use the same research question used in [Reference] to continue investigating undergraduate STEM students’ ability to respond to the following set of power series questions:

Q. In a few sentences legibly answer each of the following questions (a) through (d).

a) Describe the difference, if any, that exists between e^x and 1 + x/1! + x^2/2! b) Describe the difference, if any, that exists between e^1 + e^1*((x-1))/1! + e^1 *〖(x-1)〗^2/2! and e^2 + e^2 * ((x-1))/1! + e^2 *〖(x-1)〗^2/2! c) Describe the difference, if any that exists between the infinite series ∑_(n=0)^∞*x^n/n! and the infinite series ∑_(n=0)^∞*〖e^2 * (x-2)^n/n!〗 d) Describe the difference, if any that exists between finite series ∑_(n=0)^k*x^n/n! and the infinite series ∑_(n=0)^∞*x^n/n!

Empirical data is collected for evaluating STEM students’ comprehension of the series concept that requires knowledge of several calculus concepts. This empirical data collected from 20 undergraduate STEM students received IRB approval at a mid-sized university located at the Northeast side of the United States. The research participants are compensated for their written and video recorded oral interview responses to the research question. Participating students’ written questionnaire responses and the follow-up video recorded interviews are analyzed qualitatively and quantitatively by using the Action-Process-Object-Schema (APOS) theory. Asiala et al. applied APOS to mathematical topics in 1996, and this theory was explained as the combined knowledge of a student in a specific subject based on Piaget’s philosophy from 1970s. The qualitative data consisted of the transcription of the video recorded interviews while the quantitative analysis was the statistical analysis of the data. Calculus concepts that needed to be known by the participants to answer the research question (i.e. calculus sub-concepts) such as basic algebra, finite and infinite power series approximation, center concept of Taylor series, and limit of functions are also investigated and analyzed in this work. The numerical analysis of the collected data and the corresponding participant responses are also displayed.

Citation
Format

Tokgoz, E., & Tekalp, E. N., & Tekalp, H. A. (2021, July), Undergraduate STEM Students’ Comprehension of Function Series and Related Calculus Concepts Paper presented at 2021 ASEE Virtual Annual Conference Content Access, Virtual Conference. 10.18260/1-2--37950

TY  - CPAPER
AB  - Series expansion of functions is frequently used as a part of teaching and research in STEM fields, therefore understanding and improving STEM students’ series knowledge is important for improving STEM education. There is little attention given to pedagogical research on understanding STEM students’ function series expansion comprehension and their ability to solve related calculus problems. The results attained in this work is expected to help for determining and developing a successful method of teaching Taylor series after weaknesses of the students are investigated. We use the same research question used in [Reference] to continue investigating undergraduate STEM students’ ability to respond to the following set of power series questions: 

Q. In a few sentences legibly answer each of the following questions (a) through (d).

a) Describe the difference, if any, that exists between e^x and 1 + x/1! +  x^2/2! 
b) Describe the difference, if any, that exists between e^1 + e^1*((x-1))/1! + e^1 *〖(x-1)〗^2/2!  and 
e^2 + e^2 * ((x-1))/1! + e^2  *〖(x-1)〗^2/2!
c) Describe the difference, if any that exists between the infinite series ∑_(n=0)^∞*x^n/n! and the infinite series ∑_(n=0)^∞*〖e^2 * (x-2)^n/n!〗
d) Describe the difference, if any that exists between finite series ∑_(n=0)^k*x^n/n!  and the infinite series ∑_(n=0)^∞*x^n/n!

Empirical data is collected for evaluating STEM students’ comprehension of the series concept that requires knowledge of several calculus concepts. This empirical data collected from 20 undergraduate STEM students received IRB approval at a mid-sized university located at the Northeast side of the United States. The research participants are compensated for their written and video recorded oral interview responses to the research question. Participating students’ written questionnaire responses and the follow-up video recorded interviews are analyzed qualitatively and quantitatively by using the Action-Process-Object-Schema (APOS) theory. Asiala et al.  applied APOS to mathematical topics in 1996, and this theory was explained as the combined knowledge of a student in a specific subject based on Piaget’s philosophy from 1970s. The qualitative data consisted of the transcription of the video recorded interviews while the quantitative analysis was the statistical analysis of the data. Calculus concepts that needed to be known by the participants to answer the research question (i.e. calculus sub-concepts) such as basic algebra, finite and infinite power series approximation, center concept of Taylor series, and limit of functions are also investigated and analyzed in this work. The numerical analysis of the collected data and the corresponding participant responses are also displayed. 

AU  - Emre Tokgoz
AU  - Elif Naz Tekalp
AU  - Hasan Alp Tekalp
CY  - Virtual Conference
DA  - 2021/07/26
PB  - ASEE Conferences
TI  - Undergraduate STEM Students’ Comprehension of Function Series and Related Calculus Concepts
UR  - https://strategy.asee.org/37950
DO  - 10.18260/1-2--37950
ER  -