Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

Medová, Janka; Bulková, Kristína Ovary; Čeretková, Soňa

doi:10.3390/math8122257

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Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

by

Janka Medová

^1,*

,

Kristína Ovary Bulková

^2,* and

Soňa Čeretková

¹

Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia

²

Department of School Education, Faculty of Humanities, Tomas Bata University, Štefánikova 5670, 760 01 Zlín, Czech Republic

^*

Authors to whom correspondence should be addressed.

Mathematics 2020, 8(12), 2257; https://doi.org/10.3390/math8122257

Submission received: 30 October 2020 / Revised: 14 December 2020 / Accepted: 18 December 2020 / Published: 21 December 2020

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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Abstract

Algebraic thinking, combinatorial thinking and reasoning skills are considered as playing central roles within teaching and learning in the field of mathematics, particularly in solving complex open-ended mathematical problems Specific relations between these three abilities, manifested in the solving of an open-ended ill-structured problem aimed at mathematical modeling, were investigated. We analyzed solutions received from 33 groups totaling 131 students, who solved a complex assignment within the mathematical contest Mathematics B-day 2018. Such relations were more obvious when solving a complex problem, compared to more structured closed subtasks. Algebraic generalization is an important prerequisite to prove mathematically and to solve combinatorial problem at higher levels, i.e., using expressions and formulas, therefore a special focus should be put on this ability in upper-secondary mathematics education.

Keywords: mathematical problem solving; combinatorial thinking; reasoning; mathematical proof; algebraic generalization

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MDPI and ACS Style

Medová, J.; Bulková, K.O.; Čeretková, S. Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest. Mathematics 2020, 8, 2257. https://doi.org/10.3390/math8122257

AMA Style

Medová J, Bulková KO, Čeretková S. Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest. Mathematics. 2020; 8(12):2257. https://doi.org/10.3390/math8122257

Chicago/Turabian Style

Medová, Janka, Kristína Ovary Bulková, and Soňa Čeretková. 2020. "Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest" Mathematics 8, no. 12: 2257. https://doi.org/10.3390/math8122257

APA Style

Medová, J., Bulková, K. O., & Čeretková, S. (2020). Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest. Mathematics, 8(12), 2257. https://doi.org/10.3390/math8122257

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

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