Board # 36 : Engineering Faculty Perspectives on Student Mathematical Maturity

Brian E Faulkner; Geoffrey L Herman; Katherine Earl

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Conference: 2017 ASEE Annual Conference & Exposition
Location: Columbus, Ohio
Publication Date: June 24, 2017
Start Date: June 24, 2017
End Date: June 28, 2017
Conference Session: NSF Grantees Poster Session
Tagged Topic: NSF Grantees Poster Session
Page Count: 10
DOI: 10.18260/1-2--27839
Permanent URL: https://peer.asee.org/27839
Download Count: 439

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 teaching assistant professor with the Deprartment of Computer Science at the University of Illinois at Urbana-Champaign. He also has a courtesy appointment as 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, conceptual change and development in engineering students, and change in faculty beliefs about teaching and learning. He serves as the Publications Chair for the ASEE Educational Research and Methods Division.

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Katherine Earl

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Katherine Earl is a graduate student in the Department of Education's Counseling Psychology Program at the University of Illinois at Urbana-Champaign; earl2@illinois.edu.

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Abstract

Mathematics coursework causes significant engineering student attrition. Many students drop out of engineering before even taking their first engineering course, due to failing a prerequisite mathematics course. If the mathematics prerequisites fail so many engineering students, it is prudent to understand what exactly those students ought to be gaining by taking these courses. When asked what their students gain from the math course sequence, many engineering faculty respond that it is not technique mastery, but “mathematical maturity” that matters. We conducted a qualitative thematic analysis of 25 interviews with engineering faculty from 11 disciplines who taught engineering courses that list part of the core engineering mathematics sequence as a direct prerequisite. We examine which mathematical skills, habits, and attitudes constitute “mathematical maturity” for engineering students according to these engineering faculty. We constructed an initial coding scheme from literature on mathematical epistemology, mathematical competencies, and symbol sense, with additional codes allowed to emerge during coding by two researchers.

Some of the findings of this study are presented here. 1) Faculty emphasize that students forget much mathematical content before encountering its applications in engineering courses. Many blame the fact that the engineering application of mathematical content may not come for years after the math course, and the engineering curriculum provides little reinforcement of math skills in the intervening semesters. This issue is particularly acute for complex numbers. 2) Engineering faculty are profoundly ignorant of what is currently being taught in mathematics classrooms. Many confess that they don’t know what is being taught at their own university, in the prerequisites for their own classes. Mismatched expectations may result. 3) Faculty repeatedly stressed that “mathematics is the language of engineering”, but don’t see their students holding the same view. Faculty find their students ability to use mathematics for the communication of precise, intricate ideas inadequate. 4) Faculty observe that students have excessive expectations of the certainty of mathematical knowledge. Faculty see students use excessive decimal digits, react with frustration to rough order-of-magnitude estimation or when presented with imperfect models. Faculty state that novice students seem to expect problem solving to not involve any kind of uncertainty, experimentation, or failure.

These results shed more light on the alignment of the current standard mathematics curriculum with the needs of the engineering students and faculty. This project exists in the context of a larger project examining mathematical education for engineering students and adoption of literature-supported curricula and pedagogy.

Citation
Format

Faulkner, B. E., & Herman, G. L., & Earl, K. (2017, June), Board # 36 : Engineering Faculty Perspectives on Student Mathematical Maturity Paper presented at 2017 ASEE Annual Conference & Exposition, Columbus, Ohio. 10.18260/1-2--27839

TY - CPAPER
AB - Mathematics coursework causes significant engineering student attrition. Many students drop out of engineering before even taking their first engineering course, due to failing a prerequisite mathematics course. If the mathematics prerequisites fail so many engineering students, it is prudent to understand what exactly those students ought to be gaining by taking these courses. When asked what their students gain from the math course sequence, many engineering faculty respond that it is not technique mastery, but “mathematical maturity” that matters. We conducted a qualitative thematic analysis of 25 interviews with engineering faculty from 11 disciplines who taught engineering courses that list part of the core engineering mathematics sequence as a direct prerequisite. We examine which mathematical skills, habits, and attitudes constitute “mathematical maturity” for engineering students according to these engineering faculty. We constructed an initial coding scheme from literature on mathematical epistemology, mathematical competencies, and symbol sense, with additional codes allowed to emerge during coding by two researchers.

Some of the findings of this study are presented here. 1) Faculty emphasize that students forget much mathematical content before encountering its applications in engineering courses. Many blame the fact that the engineering application of mathematical content may not come for years after the math course, and the engineering curriculum provides little reinforcement of math skills in the intervening semesters. This issue is particularly acute for complex numbers. 2) Engineering faculty are profoundly ignorant of what is currently being taught in mathematics classrooms. Many confess that they don’t know what is being taught at their own university, in the prerequisites for their own classes. Mismatched expectations may result. 3) Faculty repeatedly stressed that “mathematics is the language of engineering”, but don’t see their students holding the same view. Faculty find their students ability to use mathematics for the communication of precise, intricate ideas inadequate. 4) Faculty observe that students have excessive expectations of the certainty of mathematical knowledge. Faculty see students use excessive decimal digits, react with frustration to rough order-of-magnitude estimation or when presented with imperfect models. Faculty state that novice students seem to expect problem solving to not involve any kind of uncertainty, experimentation, or failure.

These results shed more light on the alignment of the current standard mathematics curriculum with the needs of the engineering students and faculty. This project exists in the context of a larger project examining mathematical education for engineering students and adoption of literature-supported curricula and pedagogy.

AU - Brian E Faulkner
AU - Geoffrey L Herman
AU - Katherine Earl
CY - Columbus, Ohio
DA - 2017/06/24
PB - ASEE Conferences
TI - Board # 36 : Engineering Faculty Perspectives on Student Mathematical Maturity
UR - https://peer.asee.org/27839
DO - 10.18260/1-2--27839
ER -