• Eva Patáková Charles University in Prague



Quality of mathematical problems, Self-evaluative comments, Problem posing, Expert – specialist – novice comparison


The research presented in the article consists of two parts. Firstly, opinions on mathematical problem quality are explored within four groups of participants (novices, specialists and experts in problem posing; high school students who never posed their own problems). Secondly, self-reflections written by the participants who have some experience in problem posing (novices, specialists and experts) are explored and compared with the general view of problem quality received in the first part of the research. The more experienced problem posers have more requirements on problem quality (both as general requirements and within their own work on posing problems). There is a slight decrease in ability to notice important features of mathematical problem quality after the first experience in problem posing. Experts lay stress on mathematical features of the problem whilst novices and specialists more on problem – student interaction.


  • Kotásek, J. et al. (2012) National programme for the development of education in the Czech Republic: White paper, Prague: Tauris.

  • Patáková, E. (2013a) ‘The quality of mathematical problems – how we evaluate it’. In Kvasnička, R. (Ed.), Proceedings of the 10th International Conference Efficiency and Responsibility in Education, Prague: Czech University of Life Sciences, pp. 488-496.

  • Patáková, E. (2013b) ‘Teachers’ Problem Posing in Mathematics’, Procedia – Social and Behavioral Sciences, Elsevier Ltd, Forthcoming.

  • Pelczer, I., Gamboa, F. (2009) ‘Problem Posing: Comparison between Experts and Novices’, Proceedings of the 18th International Conferrence of the International Group for the Psychology of Mathematics Education, Atlanta, pp. 353-360.

  • Stehlíková, N. (2000) ‘Analýza písemného řešení žáka, jedna z možných technologií’. In Novotná, J. (Ed.), Analýza řešení slovních úloh. Prague: PedF UK, pp. 98-117.

  • Stoyanova, E., Ellerton, N.F. (1996). ‘A framework for research into students’ problem posing’. In P. Clarkson (Ed.), Technology in Mathematics Education. Melbourne: Mathematics Education Research Group of Australasia, pp. 518-525.

  • Tarhan, L., Ayar-Kayali, H., Urek, R., Acar, B. (2008) ‘Problem-based learning in 9th grade chemistry class: Intermolecular forces’, Research in Science Education, vol. 38, no. 3, pp. 285–300.

  • Vondrová, N., Žalská, J. (2012) ‘Do student teachers attend to mathematics specific phenomena when observing mathematics teaching on video?’, Orbis scholae, vol. 6, no. 2, pp. 85–101.

  • Zhou, C. (2012) ‘Teaching Engineering Students Creativity: A Review of Applied Strategies’, Journal on Efficiency and Responsibility in Education and Science, vol. 5, no. 2, pp. 99–114.

  • Zhouf, J. (2010) Tvorba matematických problémů pro talentované žáky, Prague: PedF UK.

  • Additional Files



    How to Cite

    Patáková, E. (2013) ’THE QUALITY OF MATHEMATICAL PROBLEMS - EVALUATION AND SELF-EVALUATION’, Journal on Efficiency and Responsibility in Education and Science, vol. 6, no. 3, pp. 143–154.



    Research Paper