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

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. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
Slovak Research and Development AgencySlovak Research and Development Agency [APVV-15-0368]; Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic; VEGAVedecka grantova agentura MSVVaS SR a SAV (VEGA) [1/0815/18]; Ministry of Education, Youth and Sports of the Czech RepublicMinistry of Education, Youth & Sports - Czech Republic [RO60201015025]
Ministerstvo Školství, Mládeže a Tělovýchovy, MŠMT: RO60201015025; Ministerstvo školstva, vedy, výskumu a športu Slovenskej republiky; Agentúra na Podporu Výskumu a Vývoja, APVV: APVV-15-0368; Vedecká Grantová Agentúra MŠVVaŠ SR a SAV, VEGA: 1/0815/18