Evaluation of Mathematical Building Blocks Impacting STEM Majors’ Ability to Solve Conceptual Power Series Questions

Emre Tokgoz

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Conference: 2024 Fall ASEE Mid-Atlantic Section Conference
Location: Farmingdale State College, NY, New York
Publication Date: October 25, 2024
Start Date: October 25, 2024
End Date: November 5, 2024
Conference Session: Technical Sessions 3
Tagged Topic: Professional Papers
Page Count: 13
DOI: 10.18260/1-2--49437
Permanent URL: https://peer.asee.org/49437
Download Count: 49

Paper Authors

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Emre Tokgoz SUNY - Farmingdale State College orcid.org/0000-0002-3417-9825

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Emre Tokgoz is a faculty of Department of Computer Security at SUNY - Farmingdale. His research interests in STEM education include understanding and proposing improvement ideas for advanding undergraduate and graduate students' conceptual mathematics, engineering, computing, and cybersecurity knowledge.

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Abstract

Solving power series questions in calculus requires demonstration of the associated sub-concept knowledge and the ability to progress from one content to another for deriving the desired outcome. In this building blocks of calculus concepts, furthering algebraic question solutions is a process of advancing from one sub-concept to another. For instance, a student who is trying to solve a question that requires to determine the derivative of a function’s power series term-by-term would need to know how to apply derivative formulas term-by-term, be able to simplify and calculate algebraic expressions, and demonstrate cognitive ability to design a solution that integrates sub-concepts simultaneously. Failing to advance the solution in one of the sub-concepts as a part of the traditional paper-pencil solutions would be a failure in determination of the entire solution. The goal of this research is to investigate the impact of any sub-concept that impacts STEM students’ responses to the research question. This investigation requires to focus on the building blocks of several concepts to determine a solution to a power series and differentiation related question by demonstrating an understanding of concepts such as algebraic and derivative calculations, power series, infinity, factorials, and functions’ equality. Written responses of 18 senior undergraduate and graduate mathematics and engineering students’ responses to a power series research question are initially collected after attaining Institutional Review Board approval. A follow-up video recorded interview with each participant is conducted upon the written response collection. The data is analyzed by introducing a new evaluation method called Conceptual Learning Distribution (CLD) along with the application of Triangulation evaluation introduced by the author on the same data set. Qualitative (participants’ interview responses) and quantitative (statistics used after applying APOS theory) results are evaluated in this work by using the written questionnaire and video recorded interview responses. STEM educators and researchers can benefit from the results attained from this work by possibly adapting the CLD as a method of student performance evaluation and apply it as a research methodology for determining comprehension levels of mathematical concepts.

Citation
Format

Tokgoz, E. (2024, October), Evaluation of Mathematical Building Blocks Impacting STEM Majors’ Ability to Solve Conceptual Power Series Questions Paper presented at 2024 Fall ASEE Mid-Atlantic Section Conference, Farmingdale State College, NY, New York. 10.18260/1-2--49437

TY  - CPAPER
AB  - Solving power series questions in calculus requires demonstration of the associated sub-concept knowledge and the ability to progress from one content to another for deriving the desired outcome. In this building blocks of calculus concepts, furthering algebraic question solutions is a process of advancing from one sub-concept to another. For instance, a student who is trying to solve a question that requires to determine the derivative of a function’s power series term-by-term would need to know how to apply derivative formulas term-by-term, be able to simplify and calculate algebraic expressions, and demonstrate cognitive ability to design a solution that integrates sub-concepts simultaneously. Failing to advance the solution in one of the sub-concepts as a part of the traditional paper-pencil solutions would be a failure in determination of the entire solution. The goal of this research is to investigate the impact of any sub-concept that impacts STEM students’ responses to the research question. This investigation requires to focus on the building blocks of several concepts to determine a solution to a power series and differentiation related question by demonstrating an understanding of concepts such as algebraic and derivative calculations, power series, infinity, factorials, and functions’ equality.
 
Written responses of 18 senior undergraduate and graduate mathematics and engineering students’ responses to a power series research question are initially collected after attaining Institutional Review Board approval. A follow-up video recorded interview with each participant is conducted upon the written response collection. The data is analyzed by introducing a new evaluation method called Conceptual Learning Distribution (CLD) along with the application of Triangulation evaluation introduced by the author on the same data set. Qualitative (participants’ interview responses) and quantitative (statistics used after applying APOS theory) results are evaluated in this work by using the written questionnaire and video recorded interview responses. STEM educators and researchers can benefit from the results attained from this work by possibly adapting the CLD as a method of student performance evaluation and apply it as a research methodology for determining comprehension levels of mathematical concepts.

AU  - Emre Tokgoz
CY  - Farmingdale State College, NY, New York
DA  - 2024/10/25
PB  - ASEE Conferences
TI  - Evaluation of Mathematical Building Blocks Impacting STEM Majors’ Ability to Solve Conceptual Power Series Questions
UR  - https://peer.asee.org/49437
DO  - 10.18260/1-2--49437
ER  -