June 14, 2009
June 14, 2009
June 17, 2009
14.65.1 - 14.65.25
A Multicourse Effort for Instilling Systematic Engineering Problem Solving Skills Through the Use of a Mathematic Computer Aided Environment.
This paper describes a coordinated, multicourse effort at the Mechanical Engineering (ME) Department at Mississippi State University (MSU) to inculcate disciplined/systematic engineering problem solving skills through the use of mathematical worksheets such as those found in Mathcad. It is important to understand that the worksheets addressed here are not forms that are pre-designed for students to fill in the blanks. Students are required to solve problems in much the same manner they traditionally do with pencil and paper. These mathematical CAD programs include: a) word processing features that allow students to present their work in a professional manner, b) automatic recalculation and sophisticated graphing capabilities, which allow students to quickly fix their errors and perform parametric studies, c) symbolic and numerical processing which allows students to tackle more complex and realistic problems, and d) a large number of mathematical tools that greatly facilitate the analysis of engineering problems. Fully exploiting the above features require careful guidance so students can learn a systematic methodology that allows for a better understanding on how to approach and solve engineering problems. For ME students at MSU, these worksheets are required in three courses: Engineering Analysis, System Dynamics, and Energy Systems Design. A significant advantage to sequencing courses in this manner is that students spend more time (and effort) in engineering functions (formulation, verification, and validations) than in the arithmetic function (primarily accomplished by Mathcad). Details, examples, and assessment of effectiveness are discussed in the paper.
One important objective in engineering education is to inculcate in the students a systematic and practical approach to problem solving. Traditionally, this has been largely accomplished through the use of homework following guidelines for problem formulation and solution using engineering paper and handheld calculators. However, the widespread availability of laptops and user-friendly mathematical computer solvers is displacing the use of calculators in favor of worksheets from mathematical CAD programs such as Mathcad, Maple, etc. The features available in these programs include automatic recalculation, copy, pasting, and line editing of equations and text, symbolic processing, automatic handling of engineering units, and instantaneous graphic capabilities. Students can spend more time and effort in engineering functions such as problem formulation, solution, verification, and validation rather than recalculating results and plots each time a mistake is found or a parameter is perturbed.
On the other hand, without careful guidance, the use of these worksheets can quickly degenerate into careless and pointless use of equation solvers, displaying the solutions using a mismatch set of units, generating the wrong algebraic solutions, etc. Also, often, the software itself is not fully debugged and display erroneous results. Thus, the students must be carefully coached on the correct use of these mathematical worksheets. This is achieved by raising the expectations on
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