June 14, 2015
June 14, 2015
June 17, 2015
26.47.1 - 26.47.14
A Glimpse into How Students Solve Concept Problems in DynamicsAn examination of the most textbooks for the standard sophomore-level engineering dynamicscourse reveals that one of the primary learning objectives is to teach a systematic problem-solving process in which students construct mathematical models of a physical or engineeringsystem and then solve the resulting equations for the quantities of interest. McCracken andNewstetter (2001) characterize dynamics problem-solving as a process of transforming aproblem into a series of different representations. The first step is a process of transforming aproblem, originally in a textual and pictorial form found in the textbook, into a diagrammaticform, the Free Body Diagram which is sometimes accompanied by a mass-acceleration diagramor inertial response diagram. Then the diagrammatic representation is converted into a symbolicmathematical representation. Finally students are able to manipulate the symbolic modelmathematically to solve for quantities of interest.A key component of the modeling/problem-solving process is a strong conceptual understandingof the relevant physical processes involved. This allows the student to choose appropriatephysical principles and boundary conditions for the problems. Mazur (1996) described whatmany physics and engineering mechanics instructors are likely to feel as they see studentsdemonstrate that they are able to solve canonical textbook problems: they see it as an indicationthat students understand the course material.Intrigued by research from Halhoun and Hestenes (1985, 1987), however, Mazur tested hisstudents with a series of multiple choice concept questions. To an expert, the concept questionstend to look much simpler than the typical textbook questions. The need to perform calculationshas been stripped away. Some concept questions asked students to predict straightforward, butperhaps counterintuitive, consequences of Newton’s Third Law. Other concept questionsrequired students to think through a problem more deeply. However, a simple free body diagramand direct application of physical principles would yield the appropriate answer. To Mazur’ssurprise, his students scored significantly worse on the concept questions, compared to theproblem-solving questions. It is a result that I have been experiencing in my engineeringdynamics courses for the past several years as well.Mazur (1996) explains this discrepancy in terms of a shallow understanding of the problem-solving process that might be guided more by memorization than true understanding. However,he also reports an interesting quotation from a student: “… how should I answer these questions?According to what you taught us, or by the way I think about these things?” Anecdotally, I havereceived similar responses from students, and it might suggest that the problem might lie in hownovice students are unable to activate (or elicit) appropriate knowledge structures for the conceptproblems. Whereas an expert sees the full textbook problem and the concept problem asfundamentally similar, the novice, with more fragmented cognitive resources (Reddish, 2004)does not see how the techniques learned in the context of textbook problems can be applied toconcept problems.In this paper, I explore this idea further as I share recordings of students as they think throughand answer concept questions.
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