Volba řešitelských strategií v závislosti na věku

Petr Eisenmann; Jiří Přibyl; Jarmila Novotná; Jiří Břehovský; Jiří Cihlář

doi:10.14712/18047106.432

Vol. 8 No. 2 (2017): sciED Research Reports

Choice of Heuristic Strategies with Respect to Age

Petr Eisenmann, ¹ Jiří Přibyl, ¹ Jarmila Novotná, ² Jiří Břehovský, ³ Jiří Cihlář, ¹

Katedra matematiky Přírodovědecká fakulta Univerzita J. E. Purkyně v Ústí nad Labem
Katedra matematiky a didaktiky matematiky, Pedagogická fakulta Univerzita Karlova
Katedra matematiky a didaktiky matematiky Fakulta přírodovědně-humanitní a pedagogická Technická univerzita v Liberci

DOI: https://doi.org/10.14712/18047106.432

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Eisenmann, P., Přibyl, J., Novotná, J., Břehovský, J., & Cihlář, J. (2017). Choice of Heuristic Strategies with Respect to Age. Scientia in Educatione, 8(2), 21-38. https://doi.org/10.14712/18047106.432

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Abstract

The paper reports on an experiment that was a part of a longitudinal research project entitled Development of culture of problem solving in mathematics carried out in Czech schools. The experiment involved 584 respondents aged 11–17. The experiment maps the distribution in pupils’ selection of heuristic strategies towards solving mathematical problems in case of different age groups of pupils. Pupils from the 6th and 8th grades of lower secondary and the Ist and IIIrd grade of upper secondary school were assigned three problems that could be solved effectively using heuristic strategies. Besides the success rate in solving the problems, attention was also paid to the manner in which the pupils managed to solve them. The results of the experiment show that the pupils tended to use some particular heuristic strategies despite the fact that they had not come across them in lessons. The occurrence of some of these strategies is independent of the age of pupils.

References

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Břehovský, J., Eisenmann, P., Ondrušová, J., Přibyl, J. & Novotná, J. (2013). Heuristic strategies in problem solving of 11-12-year-old pupils. In J. Novotná & H. Moraová (Eds.), Proceedings of Symposium on Elementary Maths Teaching SEMT ´13 (75–82). Praha: UK. Search in Google Scholar
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Eisenmann, P. & Přibyl, J. (2013). Systematické experimentování ve výuce matematiky. In Sborník příspěvků 6. konference Užití počítačů ve výuce matematiky (85–93). České Budějovice: Jihočeská univerzita v Českých Budějovicích. Search in Google Scholar
van den Heuvel-Panhuizen, M., Kolovou, A., & Robitzsch, A. (2013). Primary school students’ strategies in early algebra problem solving supported by an online game. Educational Studies in Mathematisc, 84(3), 281–307. Search in Google Scholar
Ho, S. T. & Lowrie, T. (2014). The model Metod: Students´performance and its effectiveness. The Journal of Matehematical Behavior, 35, 87–100. Search in Google Scholar
Iliada, E., 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 The International journal on Mathematics Education, 41(5), 605–618. Search in Google Scholar
Ishida, J. (2002): Students’ evaluation of their strategies when they find several solution methods. The Journal of Matehematical Behavior, 21(1), 49–56. Search in Google Scholar
Jiang, Ch., Hwang, S. & Cai, J. (2014). Chinese and Singaporean sixth-grade students’ strategies for solving probléme about speed. Educational Studies in Mathematics, 87(1), 27–50. Search in Google Scholar
Maláč, J. & Kurfürst, J. (1981). Zajímavé úlohy z učiva matematiky ZŠ. Praha: SPN. Search in Google Scholar
Molnár, J. et al. (1998–2001). Matematika 6–9: Učebnice s komentářem pro učitele. Olomouc: Prodos. Série učebnic pro základní školy. Search in Google Scholar
Novotná, J., Eisenmann, P. & Přibyl, J. (2015). Impact of heuristic strategies on pupils’ attitudes to problem solving. Journal on Efficiency and Responsibility in Education and Science, 8 (1), 15–23. Search in Google Scholar
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Pólya, G. (2004). How to Solve It: A New Aspect of Mathematical Method (Expanded Princeton Science Library ed.). Princeton: Princeton University Press. Search in Google Scholar
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Přibyl, J. & Ondrušová, J. (2014). Zavedení pomocného prvku – užitečná heuristická strategie. Matematika, fyzika, informatika, 23 (2), 95–105. Search in Google Scholar
Půlpán, Z. et al. (2007–2010). Matematika 6–9. Praha: SPN. Série učebnic pro základní školy. Search in Google Scholar
Schoenfeld, A. H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (334–370). New York: Macmillan. Search in Google Scholar

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[1] Boček, L. et al. (1993–1999). Matematika pro gymnázia. Praha: Prometheus. Série učebnic pro gymnázia. Search in Google Scholar

[2] Břehovský, J., Eisenmann, P., Ondrušová, J., Přibyl, J. & Novotná, J. (2013). Heuristic strategies in problem solving of 11-12-year-old pupils. In J. Novotná & H. Moraová (Eds.), Proceedings of Symposium on Elementary Maths Teaching SEMT ´13 (75–82). Praha: UK. Search in Google Scholar

[3] Bureš, J., Eisenmann, P. & Přibyl, J. (2016). Řešitelský obrázek jako efektivní cesta řešení úloh. Učitel matematiky, 24(2), 80–90. Search in Google Scholar

[4] Cihlář, J. & Zelenka, M. (1998). Matematika pro 8. ročník. Praha: Pythagoras Publishing, a. s. Search in Google Scholar

[5] Eisenmann, P., Novotná, J. & Přibyl, J. (2015). The heuristic strategy Introduction of an auxiliary element. D. Szarková, D. Richtáriková & Ľ. Balko (Eds.), Proceedings of 14th Conference on Applied Mathematics Aplimat 2015 (232–245). Bratislava: Slovak University of Technology in Bratislava. Search in Google Scholar

[6] Eisenmann, P., Novotná, J., Přibyl, J. & Břehovský, J. (2015). The development of a culture of problem solving with secondary students through heuristic strategies. Mathematics Education Research Journal, 27(4), 535–562. Search in Google Scholar

[7] Eisenmann, P. & Přibyl, J. (2013). Systematické experimentování ve výuce matematiky. In Sborník příspěvků 6. konference Užití počítačů ve výuce matematiky (85–93). České Budějovice: Jihočeská univerzita v Českých Budějovicích. Search in Google Scholar

[8] van den Heuvel-Panhuizen, M., Kolovou, A., & Robitzsch, A. (2013). Primary school students’ strategies in early algebra problem solving supported by an online game. Educational Studies in Mathematisc, 84(3), 281–307. Search in Google Scholar

[9] Ho, S. T. & Lowrie, T. (2014). The model Metod: Students´performance and its effectiveness. The Journal of Matehematical Behavior, 35, 87–100. Search in Google Scholar

[10] Iliada, E., 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 The International journal on Mathematics Education, 41(5), 605–618. Search in Google Scholar

[11] Ishida, J. (2002): Students’ evaluation of their strategies when they find several solution methods. The Journal of Matehematical Behavior, 21(1), 49–56. Search in Google Scholar

[12] Jiang, Ch., Hwang, S. & Cai, J. (2014). Chinese and Singaporean sixth-grade students’ strategies for solving probléme about speed. Educational Studies in Mathematics, 87(1), 27–50. Search in Google Scholar

[13] Maláč, J. & Kurfürst, J. (1981). Zajímavé úlohy z učiva matematiky ZŠ. Praha: SPN. Search in Google Scholar

[14] Molnár, J. et al. (1998–2001). Matematika 6–9: Učebnice s komentářem pro učitele. Olomouc: Prodos. Série učebnic pro základní školy. Search in Google Scholar

[15] Novotná, J., Eisenmann, P. & Přibyl, J. (2015). Impact of heuristic strategies on pupils’ attitudes to problem solving. Journal on Efficiency and Responsibility in Education and Science, 8 (1), 15–23. Search in Google Scholar

[16] Odvárko, O. et al. (1985–1988). Matematika pro střední odborné školy a studijní obory středních odborných učilišť 1.–6. část. Praha: SPN. Série učebnic pro střední odborné školy. Search in Google Scholar

[17] Pólya, G. (2004). How to Solve It: A New Aspect of Mathematical Method (Expanded Princeton Science Library ed.). Princeton: Princeton University Press. Search in Google Scholar

[18] Přibyl, J. & Eisenmann, P. (2014). Properties of problem solving strategies. In M. Houška, I. Krejčí & M. Flégl (Eds.), Proceedings of Efficiency and Responsibility in Education 2014 (623–630). Prague: Czech University of Life Sciences. Search in Google Scholar

[19] Přibyl, J. & Ondrušová, J. (2014). Zavedení pomocného prvku – užitečná heuristická strategie. Matematika, fyzika, informatika, 23 (2), 95–105. Search in Google Scholar

[20] Půlpán, Z. et al. (2007–2010). Matematika 6–9. Praha: SPN. Série učebnic pro základní školy. Search in Google Scholar

[21] Schoenfeld, A. H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (334–370). New York: Macmillan. Search in Google Scholar

Scientia in educatione

Choice of Heuristic Strategies with Respect to Age

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