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Designing Software for Mathematical Engagement through Modeling

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Mathematics Education and Technology-Rethinking the Terrain

Part of the book series: New ICMI Study Series ((NISS,volume 13))

Abstract

The framing theory guiding the work described here is that mathematics learning is facilitated through long-term student engagement in collaborative projects, integration of sustained emphasis on content knowledge, deep engagement of student interests, and support for student experience and progress, and commitment to learning through interactive microworlds that foster modeling and collaboration. We describe two case studies of software design/implementation, one an animation environment, and the other a game and game-design microworld. We describe each case in some detail, and compare the projects’ affordances, constraints, and design lessons, and persisting challenges.

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Notes

  1. 1.

    In fact the Lunar Lander was designed to form part of materials within the BBC Jam initiative.

  2. 2.

    Three levels of the software are planned, if funding permits. The first is described herein; the second adds 3D perspective and lighting and the third adds in acoustics and sound.

References

  • Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23–38.

    Article  Google Scholar 

  • Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. H. Clements, J. Sarama & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 267–298). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89.

    Article  Google Scholar 

  • Confrey, J. (1990). What constructivism implies for teaching. In C. Maher, R. Davis & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (4th ed., pp. 107–124). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Confrey, J. (2006). The evolution of design studies as methodology. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 135–152). New York: Cambridge University Press.

    Google Scholar 

  • Confrey, J., & Maloney, A. (1999). Interactive diagrams. Ithaca, NY: McGraw-Hill.

    Google Scholar 

  • Confrey, J., & Maloney, A. (2006). Graphs ‘n glyphs: Unpublished software.

    Google Scholar 

  • Confrey, J., & Maloney, A. (2007a). Research-design interactions in building function probe software. In M. K. Heid (Ed.), Research on technology and the teaching and learning of mathematics. Greenwich, CT: Information Age Publishing Inc.

    Google Scholar 

  • Confrey, J., & Maloney, A. (2007b). A theory of mathematical modelling in technological settings. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study. New York: Springer.

    Google Scholar 

  • Confrey, J., Castro-Filho, J., Maloney, A., & Wilhelm, J. (1999). Interactive diagrams to address key student conceptions in mathematics. Science Education and Technology, 231–236.

    Google Scholar 

  • Gravemeijer, K., Lehrer, R., van Oers, B., & Verschaffel, L. (Eds.). (2004). Symbolizing, modeling and tool use in mathematics education. Dordrecht: Kluwer.

    Google Scholar 

  • Hall, R. C. (1999). Case studies of math at work: exploring design-oriented mathematical practices in school and work. Final Report to the National Science Foundation.

    Google Scholar 

  • Harel, I. (1988). Software design for learning: children’s constructions of meanings for fractions and logo programming. MIT Media Laboratory, Cambridge, MA.

    Google Scholar 

  • Harel, I., & Papert, S. (1991). Constructionism. Norwood, NJ: Ablex Publishing.

    Google Scholar 

  • Hoyles, C. (1993). Microworlds/schoolworlds: the transformation of an innovation. In C. Keitel & K. Ruthven (Eds.), Learning from computers: mathematics education and technology. New York: Springer-Verlag.

    Google Scholar 

  • Hoyles, C., Sutherland, R., & Noss, R. (1991). Evaluating a computer-based microworld: what to pupils learn and why. Paper presented at the 15th Conference of the International Group for the Psychology of Mathematics Education, Assisi.

    Google Scholar 

  • Hoyles, C., Noss, R., Adamson, R., Lower, S., & Gurtner, J.-L. (2002). Face-to-face and online collaboration: appreciating rules and adding complexity. International Journal of Continuing Engineering Education and Lifelong Learning, 12(5/6), 521–539.

    Article  Google Scholar 

  • Jolly, E. J., Campbell, P. B., & Perlman, L. (2004). Engagement, capacity and continuity: a trilogy for student success. GE Foundation.

    Google Scholar 

  • Kafai, Y. B. (1995). Computer game design as a context for children’s learning. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Kahn, K., Sendova, E., Sacristán, A. I., & Noss, R. (2005). Making infinity concrete by programming never-ending processes. Paper presented at the 7th International Conference on Technology and Mathematics Teaching, Bristol, UK.

    Google Scholar 

  • Kalas, I. (2007). Gauges: dynamic tools for exploratory learning. Paper presented at the Logo 07, Slovakia.

    Google Scholar 

  • Krause, E. F. (1975). Taxicab geometry. Philippines: Addison-Wesley.

    Google Scholar 

  • Latour, B. (1990). Drawing things together. In M. Lynch & S. Woolgar (Eds.), Representation in scientific practice. Cambridge, MA: MIT Press.

    Google Scholar 

  • Lave, J., & Wenger, E. (2002). Legitimate peripheral participation in communities of practice. In M. R. Lea & K. Nicoll (Eds.), Distributed learning: social and cultural approaches to practice (pp. 56–63). London: Routledge/Falmer.

    Google Scholar 

  • Lehrer, R., & Schauble, L. (2000). Modeling in mathematics and science. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 5, pp. 101–159). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Lehrer, R., & Schauble, L. (2006). Cultivating model-based reasoning in science education. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 371–388). Cambridge: Cambridge University Press.

    Google Scholar 

  • Lehrer, R., Strom, D., & Confrey, J. (2002). Grounding metaphors and inscriptional resonance: children’s emerging understanding of mathematical similarity. Cognition and Instruction, 20(3), 359–398.

    Article  Google Scholar 

  • Miller, C. S., Lehman, J. F., & Koedinger, K. R. (1999). Goals and learning in microworlds. Cognitive Science, 23(3), 305–336.

    Article  Google Scholar 

  • Missouri Department of Elementary and Secondary Education. (2004). Mathematics grade-level expectations. Retrieved 10 November, 2006, from http://dese.mo.gov/divimprove/curriculum/GLE/Math%20GLE%20FINAL%20-%20ALL%20SECTIONS.DOC.

  • Mor, Y., & Noss, R. (2008). Programming as mathematical narrative. International Journal of Continuing Engineering Education and Life-Long Learning, 18(2), 214–233.

    Article  Google Scholar 

  • Mor, Y., Noss, R., Hoyles, C., Kahn, K., & Simpson, G. (2006). Designing to see and share structure in number sequences. International Journal for Technology in Mathematics Education, 13(2), 65–78.

    Google Scholar 

  • Murnane, R. J., & Levy, F. (1998). Standards, information, and the demand for student achievement. Federal Reserve Bank of New York Economic Policy Review, 4(1), 117–124.

    Google Scholar 

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: learning cultures and computers. Dordrecht: Kluwer.

    Google Scholar 

  • Noss, R., & Hoyles, C. (2006). Exploring mathematics through construction and collaboration. In R. K. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 389–405). Cambridge: Cambridge University Press.

    Google Scholar 

  • Noss, R., Bakker, A., Hoyles, C., & Kent, P. (2007). Situating graphs as workplace knowledge. Educational Studies in Mathematics, 65(3), 367–384.

    Article  Google Scholar 

  • Papert, S. (1980). Mindstorms: children, computers and powerful ideas. New York: Basic Books.

    Google Scholar 

  • Papert, S. (1991). Situating constructionism. In I. Harel & S. Papert (Eds.), Constructionism. Stamford, CT: Ablex Publishing.

    Google Scholar 

  • Papert, S. (1996). An exploration in the space of mathematics educations. International Journal of Computers for Mathematical Learning, 1(1), 95–123.

    Google Scholar 

  • Rosas, R., Nussbaum, M., Cumsillea, P., Marianov, V., Correaa, M., Floresa, P., et al (2003). Beyond Nintendo: design and assessment of educational video games for first and second grade students. Computers & Education, 40, 71–94.

    Article  Google Scholar 

  • Roschelle, J., Kaput, J. J., & Stroup, W. (2000). Simcalc: accelerating student engagement with the mathematics of change. In M. J. Jacobsen & R. B. Kozma (Eds.), Innovations in science and mathematics education: advanced designs for technologies of learning (pp. 47–75). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Research in Mathematics Education, 26, 114–145.

    Google Scholar 

  • Simpson, G., Hoyles, C., & Noss, R. (2005). Designing a programming-based approach for modelling scientific phenomena. Journal of Computer Assisted Learning, 21, 143–158.

    Article  Google Scholar 

  • Simpson, G., Hoyles, C., & Noss, R. (2007). Exploring the mathematics of motion through construction and collaboration. Journal of Computer Assisted Learning, 22, 1–23.

    Google Scholar 

  • Weir, S. (1987). Cultivating minds: a Logo casebook. New York: Harper and Row.

    Google Scholar 

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Confrey, J. et al. (2009). Designing Software for Mathematical Engagement through Modeling. In: Hoyles, C., Lagrange, JB. (eds) Mathematics Education and Technology-Rethinking the Terrain. New ICMI Study Series, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0146-0_3

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