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Drawing physical insight from mathematics via extreme case reasoning
written by
Mark Eichenlaub, Deborah Hemingway, and Edward F. Redish
Students often get stuck in problem solving, ignoring their physical intuition in favor of plug-and-chug or pattern-matching approaches. We suggest that examining the extreme cases is a useful way of moving students towards more expert-like problem solving. Based on a case study, we show that novice students can quickly learn to use extreme cases productively in problem-solving. In reasoning about extreme cases, students blend conceptual and mathematical cognitive resources. At the same time, they can generate new and creative uses for extreme-case reasoning, here recasting it from a tool for evaluating answers to one for generating them. Extreme case reasoning may prove a valuable instructional goal at the introductory level.
Physics Education Research Conference 2016
Part of the PER Conference series Sacramento, CA: July 20-21, 2016 Pages 108-111
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![]() <a href="https://www.per-central.org/items/detail.cfm?ID=14206">Eichenlaub, M, D. Hemingway, and E. Redish. "Drawing physical insight from mathematics via extreme case reasoning." Paper presented at the Physics Education Research Conference 2016, Sacramento, CA, July 20-21, 2016.</a>
![]() M. Eichenlaub, D. Hemingway, and E. Redish, , presented at the Physics Education Research Conference 2016, Sacramento, CA, 2016, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14206&DocID=4558).
![]() M. Eichenlaub, D. Hemingway, and E. Redish, Drawing physical insight from mathematics via extreme case reasoning, presented at the Physics Education Research Conference 2016, Sacramento, CA, 2016, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14206&DocID=4558>.
![]() Eichenlaub, M., Hemingway, D., & Redish, E. (2016, July 20-21). Drawing physical insight from mathematics via extreme case reasoning. Paper presented at Physics Education Research Conference 2016, Sacramento, CA. Retrieved February 10, 2025, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14206&DocID=4558
![]() Eichenlaub, M, D. Hemingway, and E. Redish. "Drawing physical insight from mathematics via extreme case reasoning." Paper presented at the Physics Education Research Conference 2016, Sacramento, CA, July 20-21, 2016. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14206&DocID=4558 (accessed 10 February 2025).
![]() Eichenlaub, Mark, Deborah Hemingway, and Edward F. Redish. "Drawing physical insight from mathematics via extreme case reasoning." Physics Education Research Conference 2016. Sacramento, CA: 2016. 108-111 of PER Conference. 10 Feb. 2025 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14206&DocID=4558>.
![]() @inproceedings{
Author = "Mark Eichenlaub and Deborah Hemingway and Edward F. Redish",
Title = {Drawing physical insight from mathematics via extreme case reasoning},
BookTitle = {Physics Education Research Conference 2016},
Pages = {108-111},
Address = {Sacramento, CA},
Series = {PER Conference},
Month = {July 20-21},
Year = {2016}
}
![]() %A Mark Eichenlaub %A Deborah Hemingway %A Edward F. Redish %T Drawing physical insight from mathematics via extreme case reasoning %S PER Conference %D July 20-21 2016 %P 108-111 %C Sacramento, CA %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14206&DocID=4558 %O Physics Education Research Conference 2016 %O July 20-21 %O application/pdf ![]() %0 Conference Proceedings %A Eichenlaub, Mark %A Hemingway, Deborah %A Redish, Edward F. %D July 20-21 2016 %T Drawing physical insight from mathematics via extreme case reasoning %B Physics Education Research Conference 2016 %C Sacramento, CA %P 108-111 %S PER Conference %8 July 20-21 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14206&DocID=4558 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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