Skip to main content
SpringerLink
Log in

A Review on Problem Posing in Teacher Education

  • Chapter
Book cover Mathematical Problem Posing

Part of the book series: Research in Mathematics Education ((RME))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.

    Google Scholar 

  • 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.

    Google Scholar 

  • Ball, D. L., & Forzani, F. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497–511.

    Article  Google Scholar 

  • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dortrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA, 6(4), 135–146.

    Google Scholar 

  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243–270.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dewey, J. (1933). How we think. Boston, MA: D.C. Heath and Company.

    Google Scholar 

  • Dewey, J. (1934). Art as experience. New York, NY: Perigree.

    Google Scholar 

  • 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.

    Google Scholar 

  • English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gonzales, N. A. (1996). Problem formulation: Insights from student generated questions. School Science and Mathematics, 96(3), 152–157.

    Article  Google Scholar 

  • Hawkins, D. (2000). The roots of literacy. Boulder, CO: University Press of Colorado.

    Google Scholar 

  • 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.

    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: Lawrence Erlbaum.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Martin, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Newell, A., & Simon, H. A. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45, 1080–1110.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Pirie, S. (2002). Problem posing: What can it tell us about students’ mathematical understanding? (ERIC Accession No. ED 471 760).

    Google Scholar 

  • 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.

    Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–31.

    Article  Google Scholar 

  • Sierpinska, A., & Osana, H. (2012). Analysis of tasks in pre-service elementary teacher education courses. Research in Mathematics Education, 14(2), 109–135.

    Article  Google Scholar 

  • Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem posing and problem solving. Zentralblatt für Didaktik der Mathematik, 29(3), 75–80.

    Article  Google Scholar 

  • Simon, M. A. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24(3), 233–254.

    Article  Google Scholar 

  • Sinclair, N. (2004). The roles of the aesthetic in mathematical inquiry. Mathematical Thinking and Learning, 6(3), 261–284.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks, CA: Sage.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175.

    Article  Google Scholar 

  • Vacc, N. (1993). Questioning in the mathematics classroom. Arithmetic Teacher, 41(2), 88–91.

    Google Scholar 

  • Van Zoest, L., & Stockero, S. (2008). Synergistic scaffolds as a means to support preservice teacher learning. Teaching and Teacher Education, 24(8), 2038–2048.

    Article  Google Scholar 

  • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.

    Google Scholar 

  • 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.

    Google Scholar 

  • Zazkis, R., & Campball, S. (1996). Divisibility and multiplicative structure of natural numbers: Preservice teachers’ understanding. Journal for Research in Mathematics Education, 27, 540–563.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Education, Concordia University, Montréal, QC, Canada

    Helena P. Osana

  2. Department of Mathematics and Statistics, Concordia University, Montréal, QC, Canada

    Ildiko Pelczer

Authors
  1. Helena P. Osana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ildiko Pelczer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Helena P. Osana .

Editor information

Editors and Affiliations

  1. Department of Educational Sciences, University of Ploiesti, Bucharest, Romania

    Florence Mihaela Singer

  2. Department of Mathematics, Illinois State University, Normal, Illinois, USA

    Nerida F. Ellerton

  3. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    Jinfa Cai

Rights and permissions

Reprints 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

Publish with us

Policies and ethics

Search

Navigation