# IMPACT OF HEURISTIC STRATEGIES ON PUPILS’ ATTITUDES TO PROBLEM SOLVING

## Authors

• Jarmila Novotná Charles University in Prague
• Petr Eisenmann University of J. E. Purkyně Ústí nad Labem
• Jiří Přibyl University of J. E. Purkyně Ústí nad Labem

## Keywords:

Problem Solving, Solving Strategies, Guess – check – revise, Systematic experimentation, Introduction of an auxiliary element, Omitting a condition

## Abstract

The paper is a sequel to the article (Novotná et al., 2014), where the authors present the results of a 4-month experiment whose main aim was to change pupils’ culture of problem solving by using heuristic strategies suitable for problem solving in mathematics education. (Novotná et al., 2014) focused on strategies Analogy, Guess – check – revise, Systematic experimentation, Problem reformulation, Solution drawing, Working backwards and Use of graphs of functions. This paper focuses on two other heuristic strategies convenient for improvement of pupils’ culture of problem solving: Introduction of an auxiliary element and Omitting a condition. In the first part, the strategies Guess – Check – Revise, Working backwards, Introduction of an auxiliary element and Omitting a condition are characterized in detail and illustrated by examples of their use in order to capture their characteristics. In the second part we focus on the newly introduced strategies and analyse work with them in lessons using the tools from (Novotná et al., 2014). The analysis of results of the experiment indicates that, unlike in case of the strategy Introduction of an auxiliary element, successful use of the strategy Omitting a condition requires longer teacher’s work with the pupils. The following analysis works with the strategy Systematic experimentation, which seemed to be the easiest to master in (Novotná et al., 2014); we focus on the dangers it bears when it is used by pupils. The conclusion from (Novotná et al., 2014), which showed that if pupils are introduced to an environment that supports their creativity, their attitude towards problem solving changes in a positive way already after the period of four months, is confirmed.

## References

Brousseau, G., Novotná, J. (2008) ‘La culture scolaire des problèmes de mathématiques’, Les didactiques et leurs rapports à l‘ enseignement et à la formation. Quel statut épistémologique de leurs modèles et de leurs résultats?, Bordeaux, [CD ROM].

Břehovský, J., Eisenmann, P., Ondrušová, J., Přibyl, J., Novotná, J. (2013) ‘Heuristic Strategies in Problem Solving of 11-12-year-old pupils’, Proceedings of SEMT ´13, Prague, pp. 75-82.

Cihlář, J., Zelenka, M. (1998) Matematika 8, Praha: Pythagoras Publishing, a.s.

Elia, I., van den Heuvel-Panhuizen, M., Kolovou, A. (2009) Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, vol. 41, no. 5, pp. 605-618.

Fan, L., Zhu,Y. (2007) Representation of Problem-Solving Procedures: A Comparative Look at China, Singapore, and US mathematics textbooks. Educational Studies in Mathematics, vol. 66, no. 1, pp. 61-75.

Novotná, J., Eisenmann, P., Přibyl, J., Ondrušová, J., Břehovský, J. (2013) ‘Heuristic strategies in problem solving in school mathematics’, Proceedings of the 10th International Conference on Efficiency and Responsibility in Education (ERIE 2013), Prague, pp. 461-468.

Novotná, J., Eisenmann, P., Přibyl, J., Ondrušová, J., Břehovský, J. (2014) ‘Problem solving in school mathematics based on heuristic strategies’, Journal on Efficiency and Responsibility in Education and Science, vol. 7, no. 1, pp. 1-6.

Pólya, G. (2004) How to Solve It: A New Aspect of Mathematical Method (Expanded Princeton Science Library ed.). Princeton: Princeton University Press.

Wittmann, E.C. (1995) ‘Mathematics education as a „Design Science”’, Educational Studies in Mathematics, vol. 29, no. 4, pp. 355-374.

Zeitz, P. (2007) The Art and Craft of Problem Solving, New York: John Wiley & Sons, Inc.

2015-03-31

## How to Cite

Novotná, J., Eisenmann, P. and Přibyl, J. (2015) ’IMPACT OF HEURISTIC STRATEGIES ON PUPILS’ ATTITUDES TO PROBLEM SOLVING’, Journal on Efficiency and Responsibility in Education and Science, vol. 8, no. 1, pp. 15–23. https://doi.org/10.7160/eriesj.2015.080103

Research Paper