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Assessing Critical Thinking in Mechanics in Engineering Education
Chris Papadopoulos1, Adeeb Rahman2, and Josh Bostwick3
Typically, mechanics education in engineering schools focuses on communicating explicit content to students, but deemphasizes the critical thought that underlies the discipline of mechanics. We give examples of the failure of students to apply basic principles of mechanics insolving problems. We develop assessment tools to measure critical thinking in student work, and how well mechanics textbooks engage students in critical analysis. Both tools focus on the treatment of three criteria that we judge to be fundamental, but which are commonly overlooked or undervalued – completeness of free body diagrams, consideration of physical dimension, and careful use ofcoordinates and sign conventions. Data collected from employing our assessment tools indicates that most of the time, students omit or misunderstand at least one critical idea when solving a problem, even when they obtain a correct answer. We also found that most of the textbooks surveyed had at least one major shortcoming pertaining to our criteria. Mechanics educators should vigorously emphasizefundamental aspects of mechanics, such as those that we suggest here, as a necessary (though insufficient) step to improve the ability of students to think critically and solve problems independently.

1. Introduction
Rooting Mechanics Education in Mechanics. The science of Mechanics provides the educational foundation for nearly all branches of engineering, due the importance of both (1) its explicitcontent and subject matter (e.g. the behavior of mechanisms and structures), and (2) its embodiment of analysis and rational thought (e.g. building equations, based on rational models, that describe physical phenomena). Our experience indicates that students and instructors in mechanics courses emphasize the explicit content, but at the expense of developing analytical technique. This view echoesSchafersman, who, though not a mechanician, writes of the need to develop critical thinking in education:
Perhaps you can now see the problem. All education consists of transmitting to students two different things: (1) the subject matter or discipline content of the course ("what to think"), and (2) the correct way to understand and evaluate this subject matter ("how to think"). We do anexcellent job of transmitting the content of our respective academic disciplines, but we often fail to teach students how to think effectively about this subject matter, that is, how to properly understand and evaluate it. [1]

While in the short run the narrower focus on content enables students to (sometimes) get answers to some problems fairly quickly, students often lack even a basic workingknowledge of how to apply principles of mechanics to approach general problems – even problems that
1 2

Assistant Professor, Dept. of Civil Engineering and Mechanics, UW-Milwaukee, cpapa@uwm.edu. Assistant Professor, Dept. of Civil Engineering and Mechanics, UW – Milwaukee, adeeb@uwm.edu. 3 Undergraduate Research and Teaching Assistant, Dept. of Civil Engineering and Mechanics and Dept. of Physics,UW – Milwaukee, bostwick@uwm.edu.

require only technique that they have already learned. We proffer that such shortcomings often result from the failure to carefully address fundamentals of mechanics in mechanics pedagogy4. Such fundamentals include the completeness of free body diagrams, the consideration of physical dimension, and the careful definition and use of coordinates and signconventions.

Consider, for example, a student who incorrectly derives the equation of an oscillating mass as

& m&− kx = 0 . The sign error in this equation may be, in the student’s mind, simply due to a x
minor algebraic error that is of little consequence – “it’s just a sign.” But it is likely that the source of this error lies not in careless algebra, but in misunderstanding, or not...
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