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Shopping for Shoes: Teaching Students to Apply and Interpret Mathematics in the Real World

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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.

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  • 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.

    Article  Google Scholar 

  • Australian Securities & Investments Commission (2014). National financial literacy strategy 2014–2017. Retrieved from

  • 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.

    Article  Google Scholar 

  • Borasi, R. (1986). On the nature of problems. Educational Studies in Mathematics, 17(2), 125–141. doi:10.1007/BF00311517.

    Article  Google Scholar 

  • Citibank Australia (2009). Australian primary school students show it’s not all doom and gloom they understand how to save money. Retrieved from

  • 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

  • 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.

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia, PA: Psychology Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gravemeijer, K. (1997). Solving word problems: A case of modelling? Learning and Instruction, 7(4), 389–397.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Mandell, L., & Klein, L. (2007). Motivation and financial literacy. Financial Services Review, 16(2), 105–116.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Ministerial Council for Education, Early Childhood Development and Youth Affairs [MCEECDYA] (2005). National consumer and financial literacy framework (Revised 2009). Retrieved from

  • 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

  • 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.

    Google Scholar 

  • Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematical discussions. Reston, VA: National Council of Teacher of Mathematics.

    Google Scholar 

  • Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. Journal of Mathematical Behaviour, 24(3–4), 341–350.

    Article  Google Scholar 

  • 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

  • Van 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.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 2, 2–9.

    Google Scholar 

  • Vasquez, O. A. (2006). Cross-national explorations of sociocultural research on learning. Review of Research in Education, 30, 33–64 Retrieved from

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Verschaffel, L., deCorte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4, 273–294.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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Correspondence to Carly Sawatzki.

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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).

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