PROBLEM SOLVING IN SCHOOL MATHEMATICS BASED ON HEURISTIC STRATEGIES
Keywords:Problem Solving, Solving Strategies, Strategy of Analogy, Graphical Representation, Systematic Experimentation, Strategy of Reformulation, Way Back
The paper describes one of the ways of developing pupils’ creative approach to problem solving. The described experiment is a part of a longitudinal research focusing on improvement of culture of problem solving by pupils. It deals with solving of problems using the following heuristic strategies: Analogy, Guess – check – revise, Systematic experimentation, Problem reformulation, Solution drawing, Way back and Use of graphs of functions. Most attention is paid to the question whether short-term work, in this case only over the period of three months, can result in improvement of pupils’ abilities to solve problems whose solving algorithms are easily accessible. It also answers the question which strategies pupils will prefer and with what results. The experiment shows that even short-term work can bear positive results as far as pupils’ approach to problem solving is concerned.
Ball, D., Thames, M.H., Phelps, G. (2008) ‘Content knowledge for teaching. What makes it special?’, Journal of Teacher education, vol. 59, no. 5, pp. 389-407.
Brousseau, G. (1997) Theory of didactical situations in mathematics, Dordrecht: Kluwer Academic Publishers.
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.
Eisenmann, P., Novotná, J., Přibyl, J. (2013) ‘A Tool for Evaluation of Culture of Pupil Solving of Mathematical Problems‘, Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Kiel, vol. 5, p. 223.
Eisner, E.W. (1982) Cognition and Curriculum: A Basis for Deciding What to Teach, New York: Addison-Wesley Longman Limited.
Eysenck, M.W. (1993) Principles of Cognitive Psychology, Hove: Lawrence Erlbaum Associates Ltd.
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.
Kaufmann, G. (1985) ‘A theory of symbolic representation in problem solving’, Journal of Mental Imagery, vol. 9, no. 2, pp. 51-70.
Kopka, J. (2010) Ako riešiť matematické problémy, Ružomberok: Katolická univerzita v Ružomberku.
Kopka, J. (2013) Umění řešit matematické problémy. Praha: HAV – Hoza.
Maláč, J., Kurfürst, J. (1981) Zajímavé úlohy z učiva matematiky ZŠ, Praha: SPN.
Mullis, I.V.S., Martin, M.O., Foy, P., Arora, A. (2012) TIMSS 2011 international results in mathematics. Chestnut Hill: TIMSS & PIRLS International Study Center, Boston College.
Nesher, P., Hershkovitz, S., Novotná, J. (2003) ‘Situation Model, Text Base and What Else? Factors Affecting Problem Solving’, Educational Studies in Mathematics, vol. 52, no. 2, pp. 151-176.
Novotná, J. (2000) Analýza řešení slovních úloh, Praha: Univerzita Karlova, Pedagogická fakulta.
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, Prague, pp. 461-468.
OECD (2010) PISA 2009 Results: What Students Know and Can Do – Student Performance in Reading, Mathematics and Science (Volume I). Available from http://www.oecd.org/pisa/pisaproducts/48852548.pdf.
Polya, G. (1945) How to Solve It, Princeton: Princeton University Press.
Polya, G. (2004) How to solve it: a new aspect of mathematical method, Princeton: Princeton University Press.
Sanford, A.J. (1985) Cognition and Cognitive Psychology, Hillsdale, Weidenfeld & Nicolson Ltd. Sarrazy, B. and Novotná, J. (2013) ‘Mathematical creativity and highly able students: What can teachers do? An analysis of didactical regulations of different cognitive capacities in teaching and learning relational calculations to 9-10-year-old students’, Proceedings CERME 8. Available from http://www.cerme8.metu.edu.tr/wgpapers/WG7/WG7_Novotna.pdf.
Schoenfeld, A. (1985) Mathematical Problem Solving, London: Academic Press.
Stacey, K. (1991) ‘The effects on student’s problem solving behavior of long-term teaching through a problem solving approach’, Proceedings of the 15th conference of the international group for the psychology of mathematics education, vol. 3, pp. 278–285, Assisi.
Švec, V. (2012) ‘Experience: To teach or to reach?’, Proceedings of the 9th International Conference on Efficiency and Responsibility in Education, Prague, pp. 552-562.
Tichá, M., Hošpesová, A. (2006) ‘Qualified Pedagogical Reflection as a Way to Improve Mathematics Education’, Journal for Mathematics Teachers Education. Special Issue: InterRelating Theory and Practice in Mathematics Teacher Education, vol. 9, no. 2, pp. 129-156.
Zeitz, P. (2007) The Art and Craft of Problem Solving, John Wiley & Sons, Inc.
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