On Engineering Students’ Algorithm Insight and Math Manipulation Abilities: A Review

Document Type

Conference Proceeding

Publication Date

4-1-2008

Publication Title

Proc. of the ASEE SE Section Regional Conference

Abstract

Abstract - Deficiencies in algorithm insight and mathematics manipulation abilities in college students have been the focus of recent education initiatives because they may be critical factors in students’ problem-solving development. This problem has been systematically studied by Redish and Tuminaro for Physics-major students, but has not yet been investigated for other science and engineering majors. The works of Redish et al. are discussed on their relevance to engineering education: they identified six different types of difficulties with assigning meaning to the mathematics in problem context; four of them apply to engineering problem solving. Their work on identifying the most common student problem-solving schemes is reviewed. This paper also discusses the work of the author and colleagues on the disconnection between the classic math teaching with “x and y” to the use of other variable names in engineering courses. Students lack adequate training on solving actual applied-math problems in context, because they largely use “formula pattern matching” instead of relating data and unknowns to implied concepts, and because they interpret data by relating it to symbols with which they are familiar. Initiatives (i.e., curricula and class content changes) and available teaching tools to overcome such deficiencies are reviewed, and recommendations for their use are made. It is concluded that there is a substantial body of knowledge that attempts to understand students’ math manipulation abilities, but experiences on application of such knowledge in the classroom are scarce. The author believes that the knowledge reviewed can help develop teaching environments and interventions to more effectively teach some engineering subjects.

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