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Autor/inn/en | Gál-Szabó, Zsófia; Bede-Fazekas, Ákos |
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Titel | Formalization of Odometer Thinking and Indices for the Classification of Combinatorial Strategies |
Quelle | In: International Electronic Journal of Mathematics Education, 15 (2020) 1, (16 Seiten)Infoseite zur Zeitschrift
PDF als Volltext |
Sprache | englisch |
Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
ISSN | 1306-3030 |
Schlagwörter | Mathematics Instruction; Problem Solving; Classification; Learning Strategies; Thinking Skills; Models; Measurement; Foreign Countries; Graphs; Equations (Mathematics); Mathematical Formulas; Hungary Mathematics lessons; Mathematikunterricht; Problemlösen; Classification system; Klassifikation; Klassifikationssystem; Learning methode; Learning techniques; Lernmethode; Lernstrategie; Denkfähigkeit; Analogiemodell; Messverfahren; Ausland; Grafische Darstellung; Equations; Mathematics; Gleichungslehre; Mathematische Formel; Ungarn |
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. (As Provided). |
Anmerkungen | International Electronic Journal of Mathematics Education. Suite 124, Challenge House 616 Mitcham Road, CR0 3AA, Croydon, London, UK. Tel: +44-208-936-7681; e-mail: iejme@iejme.com; Web site: https://www.iejme.com |
Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
Update | 2020/1/01 |