Skip to main content
SpringerLink
Log in

Problem Posing: A Possible Pathway to Mathematical Modelling

  • Chapter
  • First Online:
Teaching Mathematical Modelling: Connecting to Research and Practice

Abstract

Problem posing is an important component of learning mathematics as is problem solving, and it is an essential part of mathematical modelling. This chapter reports two small studies conducted in a Year 1–2 class and a Year 3–4 class, respectively. The purpose of each study was to examine the extent to which the use of real world artefacts provide a stimulus for young students to pose problems that can be investigated using mathematical modelling. The students in both studies had no prior experience in problem posing. However, they generated a range of problems linked to the real world albeit some in a superficial sense, whereas others gave genuine rise to mathematical modelling.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
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

  • Bonotto, C. (2008). On the relationships between informal out-of-school mathematics and formal in-school mathematics in the development of abstract mathematical knowledge [regular lecture]. In M. Niss (Ed.) ICME10 2004, Proceedings of tenth international congress on Mathematical Education [CD]. Roskilde: IMFUFA.

    Google Scholar 

  • Bonotto, C. (2010a). Realistic mathematical modeling and problem posing. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical competencies (pp. 399–408). New York: Springer.

    Chapter  Google Scholar 

  • Bonotto, C. (2010b). How it is possible to make real-world mathematics more visible: Some results from two Italian projects. In A. Araújo, A. Ferandes, A. Azevedo, & J. F. Rodrigues (Eds.), Conference proceedings of EIMI 2010; Educational interfaces between mathematics an industry (pp. 107–116). Lisbon/Bedford: Centro Internacional de Matemática/COMAP.

    Google Scholar 

  • Brown, S., & Walter, M. (2005). The art of problem posing (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Cai, J., & Hwag, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behaviour, 21, 401–421.

    Article  Google Scholar 

  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt für Didaktik der Mathematik, 37(3), 149–158.

    Article  Google Scholar 

  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183–217.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • English, L. D. (2003). Engaging students in problem posing in an inquiry-oriented mathematics classroom. In F. K. Lester Jr. & R. I. Charles (Eds.), Teaching mathematics through problem solving, Prekindergarten-Grade 6 (pp. 187–196). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • English, L. D., Fox, J. L., & Watters, J. J. (2005). Problem posing and solving with mathematical modelling. Teaching Children Mathematics, 12(3), 156–163.

    Google Scholar 

  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.

    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(5), 521–539.

    Article  Google Scholar 

  • Stillman, G. (in press). Problem finding and problem posing for mathematical modelling. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling—From theory to practice. Singapore: World Scientific.

    Google Scholar 

  • Whitin, D. (2004). Building a mathematical community through problem posing. In R. Rubinstein & G. W. Bright (Eds.), Perspectives on the teaching of mathematics (pp. 129–140). Reston, VA: NCTM.

    Google Scholar 

  • Whitin, D. J. (2006). Problem posing in the elementary classroom. Teaching Students Mathematics, 13(1), 14–18.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Education VIC | Faculty of Education, Australian Catholic University, Melbourne, Australia

    Ann Downton

Authors
  1. Ann Downton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ann Downton .

Editor information

Editors and Affiliations

  1. Education VIC | Faculty of Education, Australian Catholic University, Ballarat, Victoria, Australia

    Gloria Ann Stillman

  2. Faculty of Education, University of Hamburg, Hamburg, Germany

    Gabriele Kaiser

  3. Department of Mathematics, University of Kassel, Kassel, Germany

    Werner Blum

  4. Education VIC | Faculty of Education, Australian Catholic University, Melbourne, Victoria, Australia

    Jill P. Brown

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Downton, A. (2013). Problem Posing: A Possible Pathway to Mathematical Modelling. In: Stillman, G., Kaiser, G., Blum, W., Brown, J. (eds) Teaching Mathematical Modelling: Connecting to Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6540-5_45

Download citation

Publish with us

Policies and ethics

Search

Navigation