Abstract
Over the last two decades, researchers have shown increased interest in problem posing in mathematics professional development. In the context of teaching mathematics, problem posing can entail asking questions during classroom interactions to assess student understanding, modifying existing problems to adjust the difficulty level of a task, and creating problems to meet instructional objectives. In this chapter, we review the research conducted between 1990 and 2012 on problem posing in mathematics methods courses in elementary teacher education. Despite the range of foci, goals, and theoretical perspectives in the literature, we describe ways in which problem posing has been investigated in the preservice teacher population. Despite the paucity of empirical studies, we were able to group these studies into three distinct categories: (a) problem posing as a skill integral to the practice of teaching mathematics; (b) problem posing as an activity separate from teaching; and (c) problem posing as a tool to assess an outcome variable (for researchers) or as a tool for teaching or assessing the development of preservice teachers’ knowledge or beliefs. Implications for mathematics teacher educators that stem from the review of the literature are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.
Ball, D. L., & Bass, H. (2001). Making mathematics reasonable in school. In G. Martin (Ed.), Research compendium for the principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Ball, D. L., & Forzani, F. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497–511.
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of Teacher Education, 59(5), 389–407.
Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall, & J. A. Ross (Eds.), Proceedings of the Twenty-Sixth Annual Meeting of the North American Chapter of the International Group for Psychology of Mathematics Education (Vol. 2, pp. 773–782). Toronto, ON: PMENA.
Bragg, L., & Nicol, C. (2008). Designing open-ended problems to challenge preservice teachers’ views on mathematics and pedagogy. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education and 20th Conference of the North-American Chapter (Vol. 2, pp. 256–270). Morelia, Mexico: PME.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dortrecht, The Netherlands: Kluwer.
Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Hillsdale, NJ: Erlbaum.
Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21, 401–421.
Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA, 6(4), 135–146.
Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243–270.
Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.
Dewey, J. (1933). How we think. Boston, MA: D.C. Heath and Company.
Dewey, J. (1934). Art as experience. New York, NY: Perigree.
English, L. (1997). Development of seventh-grade students’ problem posing. In E. Pehkonen (Ed.), 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 241–248). Lahti, Finland: PME.
English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.
Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380–392.
Gonzales, N. A. (1996). Problem formulation: Insights from student generated questions. School Science and Mathematics, 96(3), 152–157.
Hawkins, D. (2000). The roots of literacy. Boulder, CO: University Press of Colorado.
Hiebert, J., Carpenter, T. R., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., … Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
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: Lawrence Erlbaum.
Leung, S. S. (1994). On analyzing problem posing processes: A study of prospective elementary teachers differing in mathematics knowledge. In J. P. da Ponte, & J. F. Matos (Eds.), Proceedings of the 18th International Conference of the International Group for the Psychology of Mathematics Education (pp. 168–175). Lisbon, Portugal: PME.
Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5–24.
Livy, S., & Vale, C. (2011). First-year pre-service teachers’ mathematical content knowledge: Methods of solution for a ratio question. Mathematics Teacher Education and Development, 13(2), 22–43.
Martin, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Erlbaum.
National Council of Teachers of Mathematics. (1989). Principles and standards for school mathematics. Reston, VA: Author.
Newell, A., & Simon, H. A. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45, 1080–1110.
Nicol, C., & Bragg, L. A. (2009) Designing problems: What kinds of open-ended problems do preservice teachers pose? In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 225–232). Thessaloniki, Greece: PME.
Osana, H. P., Cooperman, A., Adrien, E., Rayner, V., Bisanz, J., Watchorn, R., & Sherman LeVos, J. (2012, April). Examining teacher knowledge and classroom practices during inquiry teaching on the equal sign. Paper presented at the American Educational Research Association, Vancouver, Canada.
Osana, H., & Royea, D. (2011). Obstacles and challenges in preservice teachers’ explorations with fractions: A view from a small-scale intervention study. The Journal of Mathematical Behavior, 30(4), 333–352.
Pirie, S. (2002). Problem posing: What can it tell us about students’ mathematical understanding? (ERIC Accession No. ED 471 760).
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. A. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York, NY: Macmillan.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–31.
Sierpinska, A., & Osana, H. (2012). Analysis of tasks in pre-service elementary teacher education courses. Research in Mathematics Education, 14(2), 109–135.
Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem posing and problem solving. Zentralblatt für Didaktik der Mathematik, 29(3), 75–80.
Simon, M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24(3), 233–254.
Sinclair, N. (2004). The roles of the aesthetic in mathematical inquiry. Mathematical Thinking and Learning, 6(3), 261–284.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press.
Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks, CA: Sage.
Ticha, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In V. Durand-Guerrier, S. Soury-Lavergne, F. Arzarello, & 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.
Tirosh, D., & Graeber, A. O. (1990). Evoking cognitive conflict to explore preservice teachers’ thinking about division. Journal for Research in Mathematics Education, 21, 98–108.
Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175.
Vacc, N. (1993). Questioning in the mathematics classroom. Arithmetic Teacher, 41(2), 88–91.
Van Zoest, L., & Stockero, S. (2008). Synergistic scaffolds as a means to support preservice teacher learning. Teaching and Teacher Education, 24(8), 2038–2048.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.
Wilson, S., & Berne, J. (1999). Teacher learning and acquisition of professional knowledge: An examination of contemporary professional development. In A. Iran-Nejad & D. Pearson (Eds.), Review of research in education (pp. 173–209). Washington, DC: American Educational Research Association.
Zazkis, R., & Campball, S. (1996). Divisibility and multiplicative structure of natural numbers: Preservice teachers’ understanding. Journal for Research in Mathematics Education, 27, 540–563.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Osana, H.P., Pelczer, I. (2015). A Review on Problem Posing in Teacher Education. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_23
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6258-3_23
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6257-6
Online ISBN: 978-1-4614-6258-3
eBook Packages: Humanities, Social Sciences and LawEducation (R0)