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

Janka Medová, Kristína Ovary Bulková and Soňa Čeretková
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Janka Medová: Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia
Kristína Ovary Bulková: Department of School Education, Faculty of Humanities, Tomas Bata University, Štefánikova 5670, 760 01 Zlín, Czech Republic
Soňa Čeretková: Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia

Mathematics, 2020, vol. 8, issue 12, 1-20

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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