Espoused Faculty Epistemologies for Engineering Mathematics: Towards Defining “Mathematical Maturity” for Engineering

Brian E Faulkner; Geoffrey L Herman

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Conference: 2016 ASEE Annual Conference & Exposition
Location: New Orleans, Louisiana
Publication Date: June 26, 2016
Start Date: June 26, 2016
End Date: June 29, 2016
ISBN: 978-0-692-68565-5
ISSN: 2153-5965
Conference Session: NSF Grantees Poster Session I
Tagged Topic: NSF Grantees Poster Session
Page Count: 11
DOI: 10.18260/p.26735
Permanent URL: https://peer.asee.org/26735
Download Count: 398

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Paper Authors

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Brian E Faulkner University of Illinois, Urbana-Champaign

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Brian Faulkner is a graduate student at the University of Illinois at Urbana Champaign. His interests include teaching of modeling, engineering mathematics, textbook design, and engineering epistemology.

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Geoffrey L Herman University of Illinois, Urbana-Champaign orcid.org/0000-0002-9501-2295

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Dr. Geoffrey L. Herman is a visiting assistant professor with the Illinois Foundry for Innovation in Engineering Education at the University of Illinois at Urbana-Champaign and a research assistant professor with the Department of Curriculum & Instruction. He earned his Ph.D. in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign as a Mavis Future Faculty Fellow and conducted postdoctoral research with Ruth Streveler in the School of Engineering Education at Purdue University. His research interests include creating systems for sustainable improvement in engineering education, promoting intrinsic motivation in the classroom, conceptual change and development in engineering students, and change in faculty beliefs about teaching and learning. He serves as the webmaster for the ASEE Educational Research and Methods Division.

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Abstract

Successful experiences in mathematics courses during the first two years of college are critical to students’ persistence and learning in their engineering studies. Many core engineering courses require long prerequisite chains, delaying students’ deeper engagement in engineering topics and providing many deterrents for student persistence in engineering even before students take their engineering courses. The disconnect between the mathematics sequence and engineering courses makes it harder for students to perceive how their mathematics knowledge supports their engineering learning and for students to transfer and apply their mathematics knowledge to their engineering coursework. Further, with the lack of engagement with engineering tasks and learning early in the curriculum, students fail to develop identities as engineers that support students’ persistence when learning becomes more challenging. The negative effects of these disconnects are amplified for at-risk populations such as women, minorities, and students from low socio-economic status in engineering, increasing attrition of these populations even though they may perform better. These challenges dictate that we need to better understand what engineering faculty believe about the interplay between engineering and mathematics and how those beliefs shape curriculum and teaching practices.

Initial inquiries into the structure of engineering curriculum revealed that faculty frequently claimed that the prerequisite chains were needed to promote students’ “mathematical maturity.” To better understand how to improve engineering curricula, we are engaging faculty to understand their espoused and practiced definitions of “mathematical maturity.” We hope to identify mismatches between these two definitions to identify avenues for change and improvement in mathematics instruction for engineering.

Epistemological beliefs about knowledge have been shown to strongly affect student outcomes in mathematics and consequently their performance and persistence in engineering. Furthermore, the epistemology of teachers has been shown to influence what is learned by students. We will compare the espoused beliefs of engineering faculty about mathematics instruction in engineering to Gainsburg’s concept of ‘skeptical reverence’ describing the mathematical epistemology of veteran practicing engineers. We are interviewing faculty who teach courses that depend on the calculus sequence as a direct prerequisite to describe their espoused epistemologies about mathematics knowledge and instruction. These interviews are being analyzed using qualitative methods with an a priori coding scheme. We are simultaneously exploring faculty’s teaching practices and curricula to explore how those epistemologies are practiced. The results of this study can inform the construction of integrated engineering mathematics courses or how faculty teach and use mathematics in their engineering courses.

Citation
Format

Faulkner, B. E., & Herman, G. L. (2016, June), Espoused Faculty Epistemologies for Engineering Mathematics: Towards Defining “Mathematical Maturity” for Engineering Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.26735

TY  - CPAPER
AB  - Successful experiences in mathematics courses during the first two years of college are critical to students’ persistence and learning in their engineering studies. Many core engineering courses require long prerequisite chains, delaying students’ deeper engagement in engineering topics and providing many deterrents for student persistence in engineering even before students take their engineering courses. The disconnect between the mathematics sequence and engineering courses makes it harder for students to perceive how their mathematics knowledge supports their engineering learning and for students to transfer and apply their mathematics knowledge to their engineering coursework. Further, with the lack of engagement with engineering tasks and learning early in the curriculum, students fail to develop identities as engineers that support students’ persistence when learning becomes more challenging. The negative effects of these disconnects are amplified for at-risk populations such as women, minorities, and students from low socio-economic status in engineering, increasing attrition of these populations even though they may perform better. These challenges dictate that we need to better understand what engineering faculty believe about the interplay between engineering and mathematics and how those beliefs shape curriculum and teaching practices.

Initial inquiries into the structure of engineering curriculum revealed that faculty frequently claimed that the prerequisite chains were needed to promote students’ “mathematical maturity.” To better understand how to improve engineering curricula, we are engaging faculty to understand their espoused and practiced definitions of “mathematical maturity.” We hope to identify mismatches between these two definitions to identify avenues for change and improvement in mathematics instruction for engineering.

Epistemological beliefs about knowledge have been shown to strongly affect student outcomes in mathematics and consequently their performance and persistence in engineering. Furthermore, the epistemology of teachers has been shown to influence what is learned by students. We will compare the espoused beliefs of engineering faculty about mathematics instruction in engineering to Gainsburg’s concept of ‘skeptical reverence’ describing the mathematical epistemology of veteran practicing engineers. We are interviewing faculty who teach courses that depend on the calculus sequence as a direct prerequisite to describe their espoused epistemologies about mathematics knowledge and instruction. These interviews are being analyzed using qualitative methods with an a priori coding scheme. We are simultaneously exploring faculty’s teaching practices and curricula to explore how those epistemologies are practiced. The results of this study can inform the construction of integrated engineering mathematics courses or how faculty teach and use mathematics in their engineering courses. 

AU  - Brian E Faulkner
AU  - Geoffrey L Herman
CY  - New Orleans, Louisiana
DA  - 2016/06/26
PB  - ASEE Conferences
TI  - Espoused Faculty Epistemologies for Engineering Mathematics: Towards Defining “Mathematical Maturity” for Engineering 
UR  - https://peer.asee.org/26735
DO  - 10.18260/p.26735
ER  -