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Developing a Mathematical Modelling Task for All Students

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Mathematical Modelling and Applications

Abstract

This chapter describes an authentic mathematical modelling task designed by a learning support teacher for a Year 7 pre-algebra class co-taught with a regular Year 7 grade mathematics teacher. The task integrated two parts of the Year 7 mathematics curriculum: area and percent. Students were asked to calculate the cost of decorating (flooring and painting) the inside of their dream house. Using prices from a local building supply store, students had to decide what type of flooring and wall covering they could afford. Using a constructivist framework, this chapter provides an overview of authentic task development and the role such tasks play for students who struggle with mathematics, particularly students with special needs.

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References

  • Auger, W. F., & Rich, S. J. (2007). Curriculum theory and methods: Perspectives on learning and teaching. Mississauga: Wiley.

    Google Scholar 

  • Beswick, K. (2011). Putting context in context: An examination of the evidence of the benefits of ‘contextualized’ tasks. International Journal of Science and Mathematics Education, 9, 367–390.

    Article  Google Scholar 

  • Brewer, J., & Daane, C. J. (2002). Translating constructivist theory into practice in primary-grades mathematics. Education, 123(2), 416–426.

    Google Scholar 

  • Felton, M., Anhalt, C., & Cortez, R. (2015). Going with the flow: Challenging students to make assumptions. Mathematics Teaching in the Middle School, 20(6), 342–349.

    Article  Google Scholar 

  • Fyfe, E., Rittle-Johnson, B., & DeCaro, M. (2012). The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters. Journal of Educational Psychology, 104(4), 1094–1108.

    Article  Google Scholar 

  • Kramarski, B., Mevarech, Z., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49, 225–250.

    Article  Google Scholar 

  • Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2002). Model development sequences. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 35–58). Mahwah: Erlbaum.

    Google Scholar 

  • Math Forum. (2015). Mathematics education: Constructivism in the classroom. Retrieved from http://mathforum.org/mathed/constructivism.html. Accessed 15 Sept 2015.

  • McDuffie, A., Wohlhuter, K., & Breyfogle, M. L. (2011). Tailoring tasks to meet students’ needs. Mathematics Teaching in the Middle School, 16(9), 550–555.

    Google Scholar 

  • National Governors Association Center for Best Practice and the Council of Chief of State School Officers. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practice and the Council of Chief of State School Officers.

    Google Scholar 

  • Piaget, J. (1972). The psychology of the child. New York: Basic Books.

    Google Scholar 

  • Piaget, J. (1990). The child’s conception of the world. New York: Littlefield Adams.

    Google Scholar 

  • Sartawi, A., Alsawaie, O., Dodeen, H., Tibi, S., & Alghazo, I. (2012). Predicting mathematics achievement by motivation and self-efficacy across gender and achievement levels. Interdisciplinary Journal of Teaching & Learning, 2(2), 59–77.

    Google Scholar 

  • Small, M. (2010). Beyond one right answer. Educational Leadership, 68(1), 28–32.

    Google Scholar 

  • Vincent, J., & Stacey, K. (2008). Do mathematics textbooks cultivate shallow teaching? Applying the TIMSS video study criteria to Australian eighth-grade mathematics textbooks. Mathematics Education Research Journal, 20(1), 81–106.

    Article  Google Scholar 

  • Voltz, D., Sims, M., & Nelson, B. (2010). Connecting teachers, students, and standards. Retrieved from http://www.ascd.org/publications/books. Accessed 15 Apr 2015.

  • Vos, P. (2013). Assessment of modelling in mathematics examination papers: Ready-made models and reproductive mathematising. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modeling: Connecting to research and practice (pp. 479–488). Dordrecht: Springer.

    Chapter  Google Scholar 

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Correspondence to Edel Reilly .

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Reilly, E. (2017). Developing a Mathematical Modelling Task for All Students. In: Stillman, G., Blum, W., Kaiser, G. (eds) Mathematical Modelling and Applications. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-62968-1_37

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  • DOI: https://doi.org/10.1007/978-3-319-62968-1_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62967-4

  • Online ISBN: 978-3-319-62968-1

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