Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies
Zsófia Gál-Szabó 1 2 * , Ákos Bede-Fazekas 3 4
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1 Doctoral School of Education, University of Szeged, Szeged, HUNGARY2 MTA-SZTE Science Education Research Group, Szeged, HUNGARY3 MTA Centre for Ecological Research, Institute of Ecology and Botany, Vácrátót, HUNGARY4 MTA Centre for Ecological Research, GINOP Sustainable Ecosystems Group, Tihany, HUNGARY* Corresponding Author

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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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

INT ELECT J MATH ED, 2020, Volume 15, Issue 1, Article No: em0546

https://doi.org/10.29333/iejme/5882

Publication date: 21 Aug 2019

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