Foundations for the Mathematical Modeling of the First-year Introduction to Engineering Course Classification Scheme Using Abstract Mathematics

David Reeping; Kenneth J Reid

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Conference: 2015 ASEE Annual Conference & Exposition
Location: Seattle, Washington
Publication Date: June 14, 2015
Start Date: June 14, 2015
End Date: June 17, 2015
ISBN: 978-0-692-50180-1
ISSN: 2153-5965
Conference Session: Teaching and Learning Strategies II
Tagged Division: Educational Research and Methods
Tagged Topic: Diversity
Page Count: 13
Page Numbers: 26.795.1 - 26.795.13
DOI: 10.18260/p.24132
Permanent URL: https://peer.asee.org/24132
Download Count: 492

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Paper Authors

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David Reeping Ohio Northern University orcid.org/0000-0002-0803-7532

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David Reeping is a junior majoring in Engineering Education with a minor in Mathematics and an undergraduate research assistant. He is a Choose Ohio First scholar inducted during the 2012-2013 school year and the recipient of the Remsburg Creativity Award for 2013 and The DeBow Freed Award for outstanding leadership as an undergraduate student (sophomore male) in 2014. Also, he is a member of the freshman honorary society (Alpha Lambda Delta / Phi Eta Sigma) and the mathematics honorary society (Kappa Mu Epsilon). His research interests involve first year engineering course analysis, authentic projects and assessments, and K-12 engineering.

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Kenneth J Reid Virginia Tech

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Kenneth Reid is the Assistant Department Head for Undergraduate Programs and an Associate Professor in Engineering Education at Virginia Tech. He is active in engineering within K-12, serving on the TSA Boards of Directors and over 10 years on the IEEE-USA STEM Literacy Committee. He was awarded an IEEE-USA Professional Achievement Award in 2013 for designing the nation's first BS degree in Engineering Education. He was named NETI Faculty Fellow for 2013-2014, and the Herbert F. Alter Chair of Engineering (Ohio Northern University) in 2010. His research interests include success in first-year engineering, engineering in K-12, introducing entrepreneurship into engineering, and international service and engineering. He has written two texts in Digital Electronics, including the text used by Project Lead the Way.

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Abstract

Foundations of a Method for the Meaningful Comparison of First Year Engineering CoursesFirst year engineering programs tend to vary in structure at different universities, so rigorouscomparisons between programs are naturally difficult to make. The content of these first yearcourses is often a combination of the instructor’s preferences, learning outcomes dictated by theprogram, and accreditation outcomes. These courses tend to occupy their own sphere of contentand loosely relate to later classes or perhaps other “Introduction to Engineering” courses atdifferent universities. Through an NSF sponsored study, the Classification Scheme for First YearEngineering Courses was developed to enable comparison among courses and programs.Although the classification scheme was created with this application in mind, investigation intoprecise relationships between different engineering courses remains. Preliminary attempts atcomparisons took the form of radial plots where fundamental differences are visually apparentbetween courses. Difficulties with formally defining such differences and relationships betweenthe outcomes in the classification scheme and results prompted a study to develop amathematical method to make more rigorous comparisons.In order to better understand the way in which each piece of the courses corresponded with eachother, an axiom system was developed to generate the geometric plane and the figures thatrepresent the first year engineering courses, both of which were validated through mathematicalproof. This paper presents the foundational geometry that serves as the basis for the developmentof the mathematics to meaningfully compare courses in the first year and discussion on currentand future applications.One such application is the validation of an early hypothesis concerning the scheme itself: allfirst year engineering courses can be represented and grouped by using the classification scheme.Using a geometric argument and selected topics of set theory, it can be shown that mappings arepossible from one course to another where a single course is able to generate all other coursessimilar to the generator. This allows for “pockets” of sorts to be formed that enable appropriategrouping in relation to the hypothesis.To narrow the focus of this particular geometry to finding specific groups of courses, furtherrestrictions are necessary. The limitations on the formation of the shapes such that the course focican be determined will also be discussed.

Citation
Format

Reeping, D., & Reid, K. J. (2015, June), Foundations for the Mathematical Modeling of the First-year Introduction to Engineering Course Classification Scheme Using Abstract Mathematics Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.24132

TY  - CPAPER
AB  -     Foundations of a Method for the Meaningful Comparison of First Year                           Engineering CoursesFirst year engineering programs tend to vary in structure at different universities, so rigorouscomparisons between programs are naturally difficult to make. The content of these first yearcourses is often a combination of the instructor’s preferences, learning outcomes dictated by theprogram, and accreditation outcomes. These courses tend to occupy their own sphere of contentand loosely relate to later classes or perhaps other “Introduction to Engineering” courses atdifferent universities. Through an NSF sponsored study, the Classification Scheme for First YearEngineering Courses was developed to enable comparison among courses and programs.Although the classification scheme was created with this application in mind, investigation intoprecise relationships between different engineering courses remains. Preliminary attempts atcomparisons took the form of radial plots where fundamental differences are visually apparentbetween courses. Difficulties with formally defining such differences and relationships betweenthe outcomes in the classification scheme and results prompted a study to develop amathematical method to make more rigorous comparisons.In order to better understand the way in which each piece of the courses corresponded with eachother, an axiom system was developed to generate the geometric plane and the figures thatrepresent the first year engineering courses, both of which were validated through mathematicalproof. This paper presents the foundational geometry that serves as the basis for the developmentof the mathematics to meaningfully compare courses in the first year and discussion on currentand future applications.One such application is the validation of an early hypothesis concerning the scheme itself: allfirst year engineering courses can be represented and grouped by using the classification scheme.Using a geometric argument and selected topics of set theory, it can be shown that mappings arepossible from one course to another where a single course is able to generate all other coursessimilar to the generator. This allows for “pockets” of sorts to be formed that enable appropriategrouping in relation to the hypothesis.To narrow the focus of this particular geometry to finding specific groups of courses, furtherrestrictions are necessary. The limitations on the formation of the shapes such that the course focican be determined will also be discussed.
AU  - David Reeping
AU  - Kenneth J Reid
CY  - Seattle, Washington
DA  - 2015/06/14
PB  - ASEE Conferences
TI  - Foundations for the Mathematical Modeling of the First-year Introduction to Engineering Course Classification Scheme Using Abstract Mathematics
UR  - https://peer.asee.org/24132
DO  - 10.18260/p.24132
ER  -