A good diagram is valuable despite the choice of a mathematical approach to problem solving
written by
Alexandru Maries and
Chandralekha Singh
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solution. We conducted an investigation in which 118 students in an algebra-based introductory physics course were subjected to two different interventions during the problem solving in recitation quizzes throughout the semester. Here, we discuss the problem solving performance of students in different intervention groups for two problems involving standing waves in tubes, one which was given in a quiz and the other in a midterm exam. These problems can be solved using two different methods, one involving a diagrammatic representation and the other involving mostly mathematical manipulation of equations. In the quiz, students were either (1) asked to solve the problem in which a partial diagram was provided or (2) explicitly asked to draw a diagram. A comparison group was not given any instruction regarding diagrams. Students in group (1), who were given the partial diagram, could not use that partial diagram by itself to solve the problem. The partial diagram was simply intended as a hint for students to complete the diagram and follow the diagrammatic approach. However, we find an opposite effect, namely, that students given this diagram were less likely to draw productive diagrams and performed worse than students in the other groups. Moreover, we find that students who drew a productive diagram performed better than those who did not draw a productive diagram even if they primarily used a mathematical approach. Interviews with individual students who were asked to solve the problem provided further insight.
Physics Education Research Conference 2013
Part of the PER Conference Invited Paper series Portland, OR: July 17-18, 2013 Pages 31-34
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<a href="https://www.compadre.org/portal/items/detail.cfm?ID=13089">Maries, Alexandru, and Chandralekha Singh. "A good diagram is valuable despite the choice of a mathematical approach to problem solving." Paper presented at the Physics Education Research Conference 2013, Portland, OR, July 17-18, 2013.</a>
AIP Format
A. Maries and C. Singh, presented at the Physics Education Research Conference 2013, Portland, OR, 2013, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13089&DocID=3624).
AJP/PRST-PER
A. Maries and C. Singh, A good diagram is valuable despite the choice of a mathematical approach to problem solving, presented at the Physics Education Research Conference 2013, Portland, OR, 2013, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13089&DocID=3624>.
APA Format
Maries, A., & Singh, C. (2013, July 17-18). A good diagram is valuable despite the choice of a mathematical approach to problem solving. Paper presented at Physics Education Research Conference 2013, Portland, OR. Retrieved December 13, 2017, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13089&DocID=3624
Chicago Format
Maries, Alexandru, and Chandralekha Singh. "A good diagram is valuable despite the choice of a mathematical approach to problem solving." Paper presented at the Physics Education Research Conference 2013, Portland, OR, July 17-18, 2013. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13089&DocID=3624 (accessed 13 December 2017).
MLA Format
Maries, Alexandru, and Chandralekha Singh. "A good diagram is valuable despite the choice of a mathematical approach to problem solving." Physics Education Research Conference 2013. Portland, OR: 2013. 31-34 of PER Conference Invited Paper. 13 Dec. 2017 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13089&DocID=3624>.
BibTeX Export Format
@inproceedings{
Author = "Alexandru Maries and Chandralekha Singh",
Title = {A good diagram is valuable despite the choice of a mathematical approach to problem solving},
BookTitle = {Physics Education Research Conference 2013},
Pages = {31-34},
Address = {Portland, OR},
Series = {PER Conference Invited Paper},
Month = {July 17-18},
Year = {2013}
}
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%A Alexandru Maries
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