PUZZLES – A CREATIVE WAY OF DEVELOPMENT OF LOGICAL THINKING

Authors

  • Eva Milková University of Hradec Králové

Keywords:

Logical Thinking, Enjoyable Teaching and Learning, Puzzles, Graph Theory, Combinatorial Optimization, Multimedia Application

Abstract

Logical thinking of students should be enhanced at all levels of their studies. There are many possibilities how to achieve it. In the paper one possible way within the subjects “Discrete Mathematics” and “Discrete Methods and Optimization” dealing with graph theory and combinatorial optimization will be presented. These mathematical disciplines are powerful tools for teachers allowing them to develop logical thinking of students, increase their imagination and make them familiar with solutions to various problems. Thanks the knowledge gained within the subjects students should be able to describe various practical situations with the aid of graphs, solve the given problem expressed by the graph, and translate the solution back into the initial situation. Student engagement is crucial for successful education. Practical tasks and puzzles attract students to know more about the explained subject matter and to apply gained knowledge. There are an endless number of enjoyable tasks, puzzles and logic problems in books like “Mathematics is Fun”, in riddles magazines and on the Internet. In the paper, as an inspiration, four puzzles developing logical thinking appropriate to be solved using graph theory and combinatorial optimization will be introduced. On these puzzles of different level of difficulty the students’ ability to find out the appropriate graph-representation of the given task and solve it will be discussed as well. The author of the paper has been prepared with her students various multimedia applications dealing with objects appropriate to subject matter for more than 15 years. In the paper we also discuss a benefit of multimedia applications used as a support of subjects “Discrete Mathematics” and “Discrete Methods and Optimization”.

References

Albrecht, K. (1984) Brain Building: Easy Games to Develop Your Problem Solving Skills, Prentice Hall.

Biggs, N.L., Lloyd, K.E., Wilson, R.J. (1976) Graph theory 1736-1936, Oxford: Clarendon Press.

Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C. (2009) Introduction to Algorithms, London: The MIT Press.

Huba, T., Pestún, I., Huba, M. (2011) ‘Learning by pleasure – powered paraglider and others UAVs control’, Proceedings of 14th International Conference on Interactive Collaborative Learning (ICL2011) - 11th International Conference Virtual University (vu'11), Slovenská technická univerzita, Bratislava, Slovakia, pp. 548 – 552.

Hubálovský, Š. (2010) ‘Modelling of real kinematics situation as a method of the system approach to the algorithm development thinking’, International journal of applied mathematics and informatics, vol. 4, no. 4, pp. 83-91.

Hubálovský, Š., Musílek, M. (2010) ‘Automatic cryptoanalysis of the monoalphabetical substitution as a method of the system approach in the algorithm development thinking’, International journal of applied mathematics and informatics, vol. 4, no. 4, pp. 92-102.

Matoušek, J., Nešetřil, J. (1998) Invitation to Discrete Mathematics, Oxford: Clarendon Press.

Milková, E. (2009) ‘Constructing Knowledge in Graph Theory and Combinatorial Optimization’, WSEAS TRANSACTIONS on MATHEMATICS, vol. 8, no. 8, pp. 424-434.

Milková, E. (2010a) ‘Nalezení všech nejkratších cest mezi dvěma vrcholy’, Matematika Fyzika Informatika, vol. 19, no. 9, pp. 559-566.

Milková, E. (2010b) ‘BFS Tree and x-y Shortest Paths Tree’, Proceedings of International Conference on Applied Computer Science (ACS), WSEAS Press, Malta, pp. 391-395.

Nowak, J., Gowin, D. (1984) Learning how to learn, Cambridge University Press.

Pascual, R. (2010) ‘Enhancing project-oriented learning by joining communities of practice and opening spaces for relatedness’, Europ. J. Eng. Education, vol. 35, no. 1, pp. 3-16.

Pražák P. (2010) ‘Recursively Defined Sequences and CAS’, Proceedings of International Conference on Educational Technologies (EDUTE’10), WSEAS Press, Tunisia, pp. 58-61.

Skiena, S. S. (1998) The Algorithm Design Manual, Springer-Verlag.

Šitina, J. (2010) Grafové algoritmy – vizualizace, Hradec Králové: University of Hradec Králové.

Vejmola, S. (1986) Konec záhady hlavolamů, Prague: Státní pedagogické nakladatelství.

Williams, R. (2005) "e-Learning Strategy: What’s in the Blend? ", In: Proceedings of the 4th European Conference on e-Learning, Amsterdam, Nederland: ACL, pp. 245-51.

Additional Files

Published

2011-12-30

How to Cite

Milková, E. (2011) ’PUZZLES – A CREATIVE WAY OF DEVELOPMENT OF LOGICAL THINKING’, Journal on Efficiency and Responsibility in Education and Science, vol. 4, no. 4, pp. 207–218 Retrieved from https://www.eriesjournal.com/index.php/eries/article/view/48.

Issue

Section

Review study