Understanding STEM Students’ Conceptual Derivative Knowledge Through Analysis of Sub-concept Cognition

Emre Tokgoz

Download Paper | Permalink

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--49458
Permanent URL: https://peer.asee.org/49458
Download Count: 27

Paper Authors

biography

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

visit author page

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 advancing undergraduate and graduate students conceptual mathematics, engineering, computing, and cybersecurity knowledge.

visit author page

Download Paper | Permalink

Abstract

The derivative of mathematical functions is one of the central concepts in engineering applications, therefore investigating engineering students’ ways to understand the derivative concept and ability to respond derivative related questions is an interest of STEM educators and pedagogical researchers. The nature of a calculus question with multiple sub-concepts can make it a difficult task to solve the problem for students, therefore a closer look at STEM students’ missing conceptual knowledge through their responses to a complex calculus question and analyzing it pedagogically appears as a necessity to improve teaching practices. In this work, we use empirical data to analyze and evaluate engineering and mathematics students’ comprehension of the derivative concept. The empirical data is collected from 20 undergraduate STEM majors who were enrolled at a mid-sized university located on the Northeast side of the United States. This IRB approved research’s participants are compensated for their written responses to the following research question and the follow up video recorded oral interviews. Is h(x)=sin(|x|) a differentiable function for all real numbers in the domain? Please explain the domain of the function if it is differentiable. If it is not differentiable please explain why. The calculus sub-concepts used for evaluation included the following: • Differentiability. • Function domain. • Composition of functions. • Graph of a trigonometric function. • Absolute value function. There were two types of data collected during the research period: The first type, quantitative data, consisted of pre- and post-interview responses of the participants. The pre-interview written response was the solution of the participant to the question prior to the video recorded interview. The post-interview response was the written response of the participant during the oral interview in the case the participant wanted to add or change the existing answer. The oral interview was video recorded and conducted to ask more questions on written responses to investigate the research participants’ conceptual understanding of the research question related concepts. The research team used Action-Process-Object-Schema (APOS) theory as well as the concept image and concept definition of derivative to analyze the collected data. Asiala et al. applied the 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. Participants’ concept image and concept definition perception used by Tall (1981) is also used in this research for analysis of the data. The qualitative data consisted of the transcription of the video recorded interviews. Overall, qualitative and quantitative analysis of the data indicated participants’ weakness in establishing a connection between the concept image and concept definition of the derivative concept while the main weakness in sub-concept knowledge was observed to be the absolute value function knowledge to determine the derivative of the sine function. References 1. Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas K. (1997). A framework for research and curriculum development in undergraduate mathematics education. In J. Kaput, A. H. Schoenfeld, & E. Dubinsky (Eds.), Research in collegiate mathematics education II (p/. 1-32). Providence, RI: American Mathematical Society and Washington, DC: MAA. 2. Piaget, J. (1971). Psychology and epistemology. London: Routledge and Kegan Paul. 3. Tall, D. (1981) Concept image and concept definition in mathematics with particular reference to limits and continuity, Educational Studies in Mathematics, 12 (2), pp 151–169.

Citation
Format

Tokgoz, E. (2024, October), Understanding STEM Students’ Conceptual Derivative Knowledge Through Analysis of Sub-concept Cognition Paper presented at 2024 Fall ASEE Mid-Atlantic Section Conference, Farmingdale State College, NY, New York. 10.18260/1-2--49458

TY - CPAPER
AB - The derivative of mathematical functions is one of the central concepts in engineering applications, therefore investigating engineering students’ ways to understand the derivative concept and ability to respond derivative related questions is an interest of STEM educators and pedagogical researchers. The nature of a calculus question with multiple sub-concepts can make it a difficult task to solve the problem for students, therefore a closer look at STEM students’ missing conceptual knowledge through their responses to a complex calculus question and analyzing it pedagogically appears as a necessity to improve teaching practices.
In this work, we use empirical data to analyze and evaluate engineering and mathematics students’ comprehension of the derivative concept. The empirical data is collected from 20 undergraduate STEM majors who were enrolled at a mid-sized university located on the Northeast side of the United States. This IRB approved research’s participants are compensated for their written responses to the following research question and the follow up video recorded oral interviews.
Is h(x)=sin(|x|) a differentiable function for all real numbers in the domain? Please explain the domain of the function if it is differentiable. If it is not differentiable please explain why.
The calculus sub-concepts used for evaluation included the following:
• Differentiability.
• Function domain.
• Composition of functions.
• Graph of a trigonometric function.
• Absolute value function.
There were two types of data collected during the research period: The first type, quantitative data, consisted of pre- and post-interview responses of the participants. The pre-interview written response was the solution of the participant to the question prior to the video recorded interview. The post-interview response was the written response of the participant during the oral interview in the case the participant wanted to add or change the existing answer. The oral interview was video recorded and conducted to ask more questions on written responses to investigate the research participants’ conceptual understanding of the research question related concepts.
The research team used Action-Process-Object-Schema (APOS) theory as well as the concept image and concept definition of derivative to analyze the collected data. Asiala et al. applied the 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. Participants’ concept image and concept definition perception used by Tall (1981) is also used in this research for analysis of the data. The qualitative data consisted of the transcription of the video recorded interviews. Overall, qualitative and quantitative analysis of the data indicated participants’ weakness in establishing a connection between the concept image and concept definition of the derivative concept while the main weakness in sub-concept knowledge was observed to be the absolute value function knowledge to determine the derivative of the sine function.
References
1. Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., &amp;amp; Thomas K. (1997). A framework for research and curriculum development in undergraduate mathematics education. In J. Kaput, A. H. Schoenfeld, &amp;amp; E. Dubinsky (Eds.), Research in collegiate mathematics education II (p/. 1-32). Providence, RI: American Mathematical Society and Washington, DC: MAA.
2. Piaget, J. (1971). Psychology and epistemology. London: Routledge and Kegan Paul.
3. Tall, D. (1981) Concept image and concept definition in mathematics with particular reference to limits and continuity, Educational Studies in Mathematics, 12 (2), pp 151–169.
AU - Emre Tokgoz
CY - Farmingdale State College, NY, New York
DA - 2024/10/25
PB - ASEE Conferences
TI - Understanding STEM Students’ Conceptual Derivative Knowledge Through Analysis of Sub-concept Cognition
UR - https://peer.asee.org/49458
DO - 10.18260/1-2--49458
ER -