Mathematical Problem Posing pp 433-447 | Cite as

# Problem Posing in Primary School Teacher Training

## 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

- Bandura, A. (1997).
*Self-efficacy. The exercise of control*. New York, NY: W. H. Freeman.Google Scholar - 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 - 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 - Cai, J., & Brooke, M. (2006). New perspectives of looking back in mathematical problem solving.
*Mathematics Teaching, 196*, 42–45.Google Scholar - 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 - English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities.
*Educational Studies in Mathematics, 34*, 183–217.CrossRefGoogle Scholar - Freudenthal, H. (1983).
*Didactical phenomenology of mathematical structures*. Dodrecht, The Netherlands: Reidel.Google Scholar - Gavora, P. (2010). Slovak preservice teacher self-efficacy: theoretical and research considerations.
*The New Educational Review, 21*(2), 17–30.Google Scholar - 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 - 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 - 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 - Klafki, W. (1967).
*Studie k teorii vzdělání a didaktice (Studien zur Bildungstheorie und Didaktik)*. Praha, Czech Republic: SPN.Google Scholar - Koman, M., & Tichá, M. (1998). On travelling together and sharing expenses.
*Teaching Mathematics and its Applications, 17*(3), 117–122.CrossRefGoogle Scholar - Lamon, S. (2006).
*Teaching fractions and ratios for understanding*(2nd ed.). Mahwah, NJ: Erlbaum.Google Scholar - 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 - 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 - 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 - 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 - 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 - 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 - Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing.
*Teaching Children Mathematics, 12*(3), 129–135.Google Scholar - 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 - Streefland, L. (1991).
*Fractions in realistic mathematics education: A paradigm of developmental research*. Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar - Švaříček, R., & Šeďová, K. (2007). Kvalitativní výzkum v pedagogických vědách. (Qualitative research in education.) Praha: Portál.Google Scholar
- 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 - 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 - Tichá, M., & Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing.
*Educational Studies in Mathematics, 83*(1), 133–143.Google Scholar - 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 - Toluk-Ucar, Z. (2008). Developing preservice teachers understanding of fractions through problem posing.
*Teaching and Teacher Education, 25*, 166–175.CrossRefGoogle Scholar - Webster’s Encyclopedic Unabridged Dictionary of the English Language (1996). New York, NY: Gramercy Books.Google Scholar