## Abstract

This article reports the findings of classroom research exploring the potential of posing challenging mathematical problems situated in real-world financial contexts to activate mathematical knowledge, skills and reasoning. The Organisation for Economic Cooperation and Development (OECD) Programme for International Student Assessment (PISA) 2012 mathematical literacy assessment framework (OECD, 2013) provided theoretical framing for the study, which examined the use of a “financial dilemma” titled *Shopping for shoes* in a Year 5/6 composite class in a suburban Australian primary school. The social and mathematical dimensions of the task, together with a particular lesson structure, successfully engaged 10 to 12-year-old students in exploring mathematics through a financial problem-solving experience. The findings reveal that students’ notions of friendship and fairness guided the way they *formulated* the problem and *employed* mathematics. Strategies intended to encourage students to *interpret* the alignment and reasonableness of their social and mathematical thinking against the problem context were critical to the lesson.

### Similar content being viewed by others

## References

Anderson, T., & Shattuck, J. (2012). Design-based research: A decade of progress in education research?

*Educational Researcher, 41*(1), 16–25. doi:10.3102/0013189X11428813.Australian Securities & Investments Commission (2014).

*National financial literacy strategy 2014–2017*. Retrieved from http://www.financialliteracy.gov.au/media/546585/report-403_national-financial-literacy-strategy-2014-17.pdf.Sullivan, P., Mousley, J., & Jorgensen, R. (2009). Tasks and pedagogies that facilitate mathematical problem solving. In B. Kaur (Ed.),

*Mathematical problem solving*(pp.17-42). Association of Mathematics Educators: Singapore / USA / UK World Scientific Publishing.Sawatzki, C. (2013). What financial dilemmas reveal about students' social and mathematical understandings. In V. Steinle, L. Ball, & C. Bardini (Eds.),

*Mathematics education: yesterday, today and tomorrow, Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia*(pp.602-609). Melbourne, Australia: MERGA.Sawatzki, C. (2014). Connecting Social and Mathematical Thinking: The Use of “Real world” Contexts. In J. Anderson, M. Cavanagh & A. Prescott (Eds.),

*Curriculum in focus: Research guided practice, Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia*(pp.557-564). Sydney, Australia: MERGA.Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2014)

*.*Supporting teachers in structuring mathematics lessons involving challenging tasks.*Journal of Mathematics Teacher Education, 18*(2), 123-140. doi:10.1007/s10857-014-9279-2.Sawatzki, C. (2016). Lessons in financial literacy task design: Authentic, imaginable, useful.

*Mathematics Education Research Journal, 29*(1), 25-43. doi:10.1007/s13394-016-0184-0.Boaler, J. (1994). When do girls prefer football to fashion? An analysis of female underachievement in relation to ‘realistic’ mathematics context.

*British Educational Research Journal, 20*, 551–564.Borasi, R. (1986). On the nature of problems.

*Educational Studies in Mathematics, 17*(2), 125–141. doi:10.1007/BF00311517.Citibank Australia (2009).

*Australian primary school students show it’s not all doom and gloom they understand how to save money*. Retrieved from https://www.citibank.com.au/AUGCB/APPS/portal/loadPage.do?path=/info/sub_det/aboutus_news_20090309.htmandtabId=home.Cobb, P., Stephan, M, McClain, K., & Gravemeijer, K. (2011). Participating in classroom mathematical practices. In E. Yackel, K., Gravemeijer, & A. Sfard (Eds.),

*A journey in mathematics education research*(pp.117–163). The Netherlands: Springer. doi:10.1007/978-90-481-9729-3_3.Commonwealth Bank Foundation (2006).

*Australian financial literacy assessment*. Retrieved from http://www.commbank.com.au/about-us/download-printed-forms/AFLA-2006-report.pdf.Csíkos, C., Kelemen, R., & Verschaffel, L. (2011). Fifth-grade students’ approaches to and beliefs of mathematics word problem solving: a large sample Hungarian study.

*ZDM - The International Journal on Mathematics Education, 43*, 561–571.Draper, R. J. (2002). School mathematics reform, constructivism, and literacy: A case for literacy instruction in the reform-oriented math classroom.

*Journal of Adolescent and Adult Literacy, 45*(6), 520–529 Retrieved from http://www.jstor.org/stable/40014740.Dweck, C. S. (2000).

*Self-theories: Their role in motivation, personality, and development*. Philadelphia, PA: Psychology Press.Goos, M., Dole, S., & Geiger, V. (2011). Improving numeracy education in rural schools: A professional development approach.

*Mathematics Education Research Journal, 23*(2), 129–148. doi:10.1007/s13394-011-0008-1.Gravemeijer, K. (1997). Solving word problems: A case of modelling?

*Learning and Instruction, 7*(4), 389–397.Jablonka, E. (2003). Mathematical literacy. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kirkpatrick, & F. K. S. Leung (Eds.),

*Second international handbook of mathematics education*(pp. 75–102). Dordrecht, The Netherlands: Kluwer.Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction.

*Journal for Research in Mathematics Education, 44*(4), 646–682.Kelly, A. E. (2006). Quality criteria for design research: Evidence and commitments. In J. van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.),

*Educational design research*(pp. 107–118). New York, NY: Routledge.Lappan, G., Fey, T., Fitzgerald, W. M., Friel, S., & Phillips, E. D. (2006).

*Connected mathematics 2: Implementing and teaching guide*. Boston, MA: Pearson, Prentice Hall.Mandell, L., & Klein, L. (2007). Motivation and financial literacy.

*Financial Services Review, 16*(2), 105–116.McKenney, S., & Reeves, T. C. (2013). Systematic review of design-based research progress: Is a little knowledge a dangerous thing?

*Educational Researcher, 42*(2), 97–100. doi:10.3102/0013189X12463781.Ministerial Council for Education, Early Childhood Development and Youth Affairs [MCEECDYA] (2005).

*National consumer and financial literacy framework*(Revised 2009). Retrieved from http://www.curriculum.edu.au/verve/_resources/National_Consumer_Financial_Literacy_Framework_FINAL.pdf.Organisation for Economic Co-operation and Development [OECD] (2006).

*Assessing scientific, reading and mathematical literacy: A framework for PISA 2006*. Paris, France: OECD Publishing. doi:10.1787/9789264026407-en.Organisation for Economic Cooperation and Development [OECD] (2012).

*OECD INFE Guidelines on Financial Education in Schools*. Retrieved from http://www.oecd.org/daf/fin/financial-education/2012%20Schools%20Guidelines.pdf.Organisation for Economic Cooperation and Development [OECD] (2013).

*PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy*. OECD Publishing. doi:10.1787/9789264190511-en.Peled, I. (2008). Who is the boss? The roles of mathematics and reality in problem solving. In J. Vincent, R. Pierce, & J. Dowsey (Eds.),

*Connected maths*(pp. 274–283). Melbourne, Australia: Mathematical Association of Victoria.Smith, M. S., & Stein, M. K. (2011).

*Five practices for orchestrating productive mathematical discussions*. Reston, VA: National Council of Teacher of Mathematics.Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents.

*Journal of Mathematical Behaviour, 24*(3–4), 341–350.Stacey, K. (2015). The real world and the mathematical world. In K. Stacey & R. Turner (Eds.),

*Assessing mathematical literacy: The PISA experience*(pp. 57–84). Cham, Switzerland: Springer International Publishing.Thomson, S. (2014).

*Financing the future: Australian students’ results in the PISA 2012 Financial Literacy assessment*. Victoria, Australia: Australian Council for Educational Research (ACER). Retrieved from http://www.acer.edu.au/files/PISA_2012_Financial_Literacy.pdfVan den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage.

*Educational Studies in Mathematics, 54*, 9–35. doi:10.1023/B:EDUC.0000005212.03219.dc.Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics.

*For the Learning of Mathematics, 2*, 2–9.Vasquez, O. A. (2006). Cross-national explorations of sociocultural research on learning.

*Review of Research in Education, 30*, 33–64 Retrieved from http://www.jstor.org/stable/4129769.Verschaffel, L. (2002). Taking the modeling perspective seriously at the elementary school level: Promises and pitfalls (Plenary lecture). In A. Cockburn & E. Nardi (Eds.),

*Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education*. (Vol. 1, pp. 64–82). Norwich, UK: School of Education and Professional Development, University of East Anglia.Verschaffel, L., & De Corte, E. (1993). A decade of research on word-problem solving in Leuven: Theoretical, methodological and practical outcomes.

*Educational Psychology Review, 5*, 239–256.Verschaffel, L., & De Corte, E. (1997). Word problems: A vehicle for promoting authentic mathematical understanding and problem solving in the primary school? In T. Nunes & P. Bryant (Eds.),

*Learning and teaching mathematics: An international perspective*(pp. 69–97). Hove, UK: Psychology Press.Verschaffel, L., deCorte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems.

*Learning and Instruction, 4*, 273–294.Wyndhamn, J., & Säljö, R. (1997). Word problems and mathematical reasoning—A study of children’s mastery of reference and meaning in textual realities.

*Learning and Instruction, 7*, 361–382.Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics.

*Journal for Research in Mathematics Education, 27*, 458–477.Zbiek, R. M., & Conner, A. (2006). Beyond motivation: exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics.

*Educational Studies in Mathematics, 63*(1), 89–112. doi:10.1007/s10649-005-9002-4.

## Author information

### Authors and Affiliations

### Corresponding author

## Rights and permissions

## About this article

### Cite this article

Sawatzki, C., Sullivan, P. Shopping for Shoes: Teaching Students to Apply and Interpret Mathematics in the Real World.
*Int J of Sci and Math Educ* **16**, 1355–1373 (2018). https://doi.org/10.1007/s10763-017-9833-3

Received:

Accepted:

Published:

Issue Date:

DOI: https://doi.org/10.1007/s10763-017-9833-3