Teaching Combinatorial Principles Using Relations through the Placemat Method

Viliam Ďuriš, Gabriela Pavlovičová, Dalibor Gonda and Anna Tirpáková
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Viliam Ďuriš: Department of Mathematics, Faculty of Natural Sciences, Constantine The Philosopher University in Nitra, Tr. A. Hlinku 1, 94901 Nitra, Slovakia
Gabriela Pavlovičová: Department of Mathematics, Faculty of Natural Sciences, Constantine The Philosopher University in Nitra, Tr. A. Hlinku 1, 94901 Nitra, Slovakia
Dalibor Gonda: Department of Mathematical Methods and Operations Research, Faculty of Management Science and Informatics, University of Žilina, Univerzitná 1, 01001 Žilina, Slovakia
Anna Tirpáková: Department of Mathematics, Faculty of Natural Sciences, Constantine The Philosopher University in Nitra, Tr. A. Hlinku 1, 94901 Nitra, Slovakia

Mathematics, 2021, vol. 9, issue 15, 1-13

Abstract: The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach.

Keywords: combinations; variations; permutations; the product rule; the sum rule; combinatorics; P and NP problems; relational education; high school; research; talented children; placemat method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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