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Problem Posing in Primary School Teacher Training

  • Alena Hošpesová
  • Marie Tichá
Part of the Research in Mathematics Education book series (RME)

Abstract

The chapter reports results of a survey whose aim was to contribute to research in the area of problem posing in teacher training. The core of the research project was empirical survey with qualitative design. Preservice and in-service teachers were posing problems in the environment of fractions and reflected on this activity in writing. Analysis of the posed problems and participants’ reflections were to answer the following questions: (a) What shortcomings can be identified in the posed problems? (b) How are the posed problems perceived by preservice and in-service teachers? (c) What relations are there between quality of the posed problems and perception of this activity by their authors?

Keywords

Problem posing Primary school mathematics teachers Improvement of subject didactic competence 

Notes

Acknowledgement

Elaboration of the chapter was supported by RVO 67985840.

References

  1. Bandura, A. (1997). Self-efficacy. The exercise of control. New York, NY: W. H. Freeman.Google Scholar
  2. Behr, M., Lesh, R., Post, T., & Silver, E. A. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91–125). New York, NY: Academic.Google Scholar
  3. Bromme, R. (1994). Beyond subject matter: A psychological topology of teachers’ professional knowledge. In R. Biehler et al. (Eds.), Didactics of mathematics as a scientific discipline (pp. 73–88). Dordrecht, The Netherlands: Kluwer.Google Scholar
  4. Cai, J., & Brooke, M. (2006). New perspectives of looking back in mathematical problem solving. Mathematics Teaching, 196, 42–45.Google Scholar
  5. Cai, J., & Cifarelli, V. (2005). Exploring mathematical exploration: How do two college students formulate and solve their own mathematical problems? FOCUS on Learning Problems in Mathematics, 27(3), 43–72.Google Scholar
  6. English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183–217.CrossRefGoogle Scholar
  7. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dodrecht, The Netherlands: Reidel.Google Scholar
  8. Gavora, P. (2010). Slovak preservice teacher self-efficacy: theoretical and research considerations. The New Educational Review, 21(2), 17–30.Google Scholar
  9. Harel, G., Koichu, B., & Manaster, A. (2006). Algebra teachers’ ways of thinking characterizing the mental act of problem posing. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 241–248). Prague, Czech Republic: Charles University.Google Scholar
  10. Hošpesová, A., & Tichá, M. (2010). Reflexion der aufgabenbildung als weg zu erhöhung der lehrerprofesionalität. In C. Böttinger, K. Bräuning, M. Nührenbörger, R. Schwarzkopf, & E. Söbbeke (Eds.), Mathematik im Denken der Kinder; Anregung zur mathematik-didaktischen Reflexion (pp. 122–126). Seelze, Germany: Klett/Kalmeyer.Google Scholar
  11. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Hillsdale, NJ: Erlbaum.Google Scholar
  12. Klafki, W. (1967). Studie k teorii vzdělání a didaktice (Studien zur Bildungstheorie und Didaktik). Praha, Czech Republic: SPN.Google Scholar
  13. Koman, M., & Tichá, M. (1998). On travelling together and sharing expenses. Teaching Mathematics and its Applications, 17(3), 117–122.CrossRefGoogle Scholar
  14. Lamon, S. (2006). Teaching fractions and ratios for understanding (2nd ed.). Mahwah, NJ: Erlbaum.Google Scholar
  15. Pittalis, M., Christou, C., Mousolides, N., & Pitta-Pantazi, D. (2004). A structural model for problem posing. In M. J. Hoines & A. J. Bishop (Eds.), Proceedings of 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 49–56). Bergen, Norway: PME.Google Scholar
  16. Polya, G. (2004). How to solve it: A new aspect of mathematical method (with a new foreword by John H. Conway). Princeton, NJ: Princeton University Press.Google Scholar
  17. Ponte, J. P., & Henriques, A. (2013). Problem posing based on investigation activities by university students. Educational Studies in Mathematics, 83(1), 145–156.CrossRefGoogle Scholar
  18. Prediger, S. (2006). Continuities and discontinuities for fractions: a proposal for analysing in different levels. In J. Novotná et al. (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 377–384). Praha, Czech Republic: PME.Google Scholar
  19. Selter, C. (1997). Instructional design for teacher education. In M. Beishuizen, K. P. E. Gravenmeijeer, & E. C. D. M. van Lieshout (Eds.), The role of contexts and models in the development of mathematical strategies and procedures (pp. 55–77). Utrecht, The Netherlands: Freudenthal Institute.Google Scholar
  20. Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.CrossRefGoogle Scholar
  21. Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129–135.Google Scholar
  22. Singer, F. M., Ellerton, N. F., Cai, J., & Leung, E. (2011). Problem posing in mathematics learning and teaching: A research agenda. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 137–166). Ankara, Turkey: PME.Google Scholar
  23. Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar
  24. Švaříček, R., & Šeďová, K. (2007). Kvalitativní výzkum v pedagogických vědách. (Qualitative research in education.) Praha: Portál.Google Scholar
  25. Tichá, M., & Hošpesová, A. (2006). Qualified pedagogical reflection as a way to improve mathematics education. Journal for Mathematics Teachers Education, 9, 129–156. (Special Issue: Inter-relating theory and practice in mathematics teacher education).Google Scholar
  26. Tichá, M., & Hošpesová, A. (2010). Problem posing and development of pedagogical content knowledge in preservice teacher training. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 1941–1950). Lyon, France: Institut National de Recherche Pédagogique.Google Scholar
  27. Tichá, M., & Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143.Google Scholar
  28. Tichá, M. (2003). Following the path of discovering fractions. In J. Novotná (Ed.), Proceedings of SEMT’03 (pp. 17–27). Praha, Czech Republic: United Kingdom PedF.Google Scholar
  29. Toluk-Ucar, Z. (2008). Developing preservice teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25, 166–175.CrossRefGoogle Scholar
  30. Webster’s Encyclopedic Unabridged Dictionary of the English Language (1996). New York, NY: Gramercy Books.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of South BohemiaČeské BudějoviceCzech Republic
  2. 2.Institute of Mathematics of the Academy of Sciences of the Czech RepublicUniversity of South BohemiaPragueCzech Republic

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