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Educating Students To Question, Test, And Verify Problem Solutions

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2004 Annual Conference


Salt Lake City, Utah

Publication Date

June 20, 2004

Start Date

June 20, 2004

End Date

June 23, 2004



Conference Session

Improving Mechanics of Materials Classes

Page Count


Page Numbers

9.495.1 - 9.495.17

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Paper Authors

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Jr., Hartley T. Grandin Hartley T. Grandin,

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Joseph Rencis University of Arkansas

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session 2468

Educating Students to Question, Test and Verify Problem Solutions

Joseph J. Rencis, Hartley T. Grandin, Jr.

Mechanical Engineering Department Worcester Polytechnic Institute, Worcester, MA 01609-2280, USA

Abstract This paper assumes the importance of educating our engineering students to question, test and verify “answers” to all of their problem solutions. It presents an approach currently practiced by the authors in teaching an introductory mechanics of materials course. In problem solving, emphasis is placed on: (1) writing the governing equations in symbolic form with a bare minimum of algebraic manipulation, (2) solving the equations with a commercially available, student choice, computer equation solver and (3) most importantly, developing and implementing test case scenarios to verify the validity of the problem solution. There are three major advantages to this approach. First, the development of the equations in symbolic form requires the students to focus more on the physics of the problem. Second, the use of the computer equation solvers eliminates tedious and often error prone algebraic manipulation. Third, the test case scenarios suggested for verification of the “answer” force the student to consider limiting, “known result”, solutions of the problem. Throughout the course, the students apply this approach to homework and project activities. Initially they are given the test scenarios, but, with practice, they learn to create their own. This paper presents two example problems to demonstrate the approach.


In a homework assignment, the ultimate goal for a majority of undergraduate engineering students is simply to obtain the “answer” in the back of the book. A common approach is to search the textbook chapter for the applicable formula or equation and immediately insert numbers and calculate an answer. This approach is often successful with problems that require few equations, especially if the equations can be solved sequentially or are easily manipulated to isolate the unknown variable. The unfortunate aspect of this is that students may spend very little time focusing on the basic fundamental physics of the problem and, generally, no time at all on the very important verification of the “answer”! As problems become more complex, with increased numbers of simultaneous equations, such as with statically indeterminate problems, this approach is laborious and fraught with opportunities for equation manipulation errors. As a result, introductory course instruction and textbooks do not involve these types of problems. This paper presents the authors’ attempt to prepare the student for problems of greater complexity with emphasis not only on the physics of the problem, but also on the verification of the “answer”. These two issues are stressed in activities in-class (examples, quizzes and tests)

Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education

Grandin, J. H. T., & Rencis, J. (2004, June), Educating Students To Question, Test, And Verify Problem Solutions Paper presented at 2004 Annual Conference, Salt Lake City, Utah.

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2004 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015