June 14, 2015
June 14, 2015
June 17, 2015
Educational Research and Methods
26.795.1 - 26.795.13
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.
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
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