International Electronic Journal of Mathematics Education

Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Gál-Szabó Z, Bede-Fazekas Á. Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies. INT ELECT J MATH ED. 2020;15(1), em0546. https://doi.org/10.29333/iejme/5882
APA 6th edition
In-text citation: (Gál-Szabó & Bede-Fazekas, 2020)
Reference: Gál-Szabó, Z., & Bede-Fazekas, Á. (2020). Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies. International Electronic Journal of Mathematics Education, 15(1), em0546. https://doi.org/10.29333/iejme/5882
Chicago
In-text citation: (Gál-Szabó and Bede-Fazekas, 2020)
Reference: Gál-Szabó, Zsófia, and Ákos Bede-Fazekas. "Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies". International Electronic Journal of Mathematics Education 2020 15 no. 1 (2020): em0546. https://doi.org/10.29333/iejme/5882
Harvard
In-text citation: (Gál-Szabó and Bede-Fazekas, 2020)
Reference: Gál-Szabó, Z., and Bede-Fazekas, Á. (2020). Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies. International Electronic Journal of Mathematics Education, 15(1), em0546. https://doi.org/10.29333/iejme/5882
MLA
In-text citation: (Gál-Szabó and Bede-Fazekas, 2020)
Reference: Gál-Szabó, Zsófia et al. "Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies". International Electronic Journal of Mathematics Education, vol. 15, no. 1, 2020, em0546. https://doi.org/10.29333/iejme/5882
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Gál-Szabó Z, Bede-Fazekas Á. Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies. INT ELECT J MATH ED. 2020;15(1):em0546. https://doi.org/10.29333/iejme/5882

Abstract

Students’ solutions of enumerative combinatorial problems may be assessed along two main dimensions: the correctness of the solution and the method of enumeration. This study looks at the second dimension with reference to the Cartesian product of two sets, and at the ‘odometer’ combinatorial strategy defined by English (1991). Since we are not aware of any algorithm-based methods suitable for analysing combinatorial strategies on a large-scale sample, in this study we endeavour to formalize the odometer strategy and recommend a method of algorithm-based classification of solutions according to the strategy used. In the paper (1) odometer thinking is described using a formula based on its definition, and (2) constancy and cyclicity are characterized using mathematical formulae, which are then used to describe odometer thinking in a computationally efficient manner (‘odometricality’). Our hypothesis, i.e. that odometer thinking may be approximated by the odometricality index, is successfully tested on a random sample of automatically generated solutions (n=10,000) by calculating the correlation between odometricality and the formal measure of odometer thinking. Finally, we offer a method (and R script) for classifying strategy use.

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