Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay

Elena Polotskaia; Annie Savard; Viktor Freiman

doi:10.12973/eurasia.2015.1325a

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Elena Polotskaia ¹ ^* , Annie Savard ², Viktor Freiman ³

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¹ Université du Québec en Outaouais² McGill University³ Université de Moncton^* Corresponding Author

Abstract

This essay proposes a reflection on the learning difficulties and teaching approaches associated with word problem solving. We question the development of word problem solving skills in the early grades of elementary school. We are trying to revive the discussion for two reasons. First, the knowledge in question—reversibility of arithmetic operations and flexibility of mathematical thinking—is the key element in elementary mathematics. Second, we hope to create a shift in the understanding of this knowledge development in students. Using the folk tale “The Three Little Pigs” as a metaphor, we analyze difficulties students experience while learning to solve word problems involving addition and subtraction. We formulate a hypothesis about the cognitive duality of word problem solving. This hypothesis explains a number of well-known learning difficulties and suggests teaching principles that could help avoid developmental obstacles and pitfalls within the teaching/learning process.

Keywords

additive word problems
elementary mathematics
knowledge development
thinking duality
problem solving

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2015, Volume 11, Issue 2, 251-261

https://doi.org/10.12973/eurasia.2015.1325a

Publication date: 02 Apr 2015

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How to cite this article

APA

Polotskaia, E., Savard, A., & Freiman, V. (2015). Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 251-261. https://doi.org/10.12973/eurasia.2015.1325a

Vancouver

Polotskaia E, Savard A, Freiman V. Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay. EURASIA J Math Sci Tech Ed. 2015;11(2):251-61. https://doi.org/10.12973/eurasia.2015.1325a

AMA

Polotskaia E, Savard A, Freiman V. Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay. EURASIA J Math Sci Tech Ed. 2015;11(2), 251-261. https://doi.org/10.12973/eurasia.2015.1325a

Chicago

Polotskaia, Elena, Annie Savard, and Viktor Freiman. "Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay". Eurasia Journal of Mathematics, Science and Technology Education 2015 11 no. 2 (2015): 251-261. https://doi.org/10.12973/eurasia.2015.1325a

Harvard

Polotskaia, E., Savard, A., and Freiman, V. (2015). Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), pp. 251-261. https://doi.org/10.12973/eurasia.2015.1325a

MLA

Polotskaia, Elena et al. "Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay". Eurasia Journal of Mathematics, Science and Technology Education, vol. 11, no. 2, 2015, pp. 251-261. https://doi.org/10.12973/eurasia.2015.1325a