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Designing Non-routine Mathematical Problems as a Challenge for High Performing Prospective Teachers

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Research Advances in the Mathematical Education of Pre-service Elementary Teachers

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

Designing non-routine mathematical problems is a challenging task, even for high performing prospective teachers in elementary teacher education, especially when these non-routine problems concern knowledge at the mathematical horizon (HCK). In an experimental setting, these prospective teachers were challenged to design non-routine HCK problems. Interaction with peers, feedback from experts, analyzing HCK problems to find criteria, building a repertoire of prototypes, a cyclic design process, experts who are themselves struggling in designing problems were the most important and effective aspects of the learning environment to rise from this explorative study.

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References

  • Bain, K. (2004). What the best college teachers do. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.

    Google Scholar 

  • Borasi, R., Fonzi, J., Smith, C. F., & Rose, B. J. (1999). Beginning the process of rethinking mathematics instruction: a professional development program. Journal of Mathematics Teacher Education, 2, 49–78.

    Google Scholar 

  • Brixler, B. A. (2007). The effects of scaffolding student’s problem-solving process via question prompts on problem solving and intrinsic motivation in an online learning environment. University Park, PA: The Pennsylvania State University.

    Google Scholar 

  • Feldhusen, J. F. (2005). Giftedness, talent, expertise, and creative achievement. In R. J. Sternberg, & J. E. Davidson, Conceptions of Giftedness (pp. 64–79). Cambridge: Cambridge University Press.

    Google Scholar 

  • Frey, N., & Fisher, D. (2010). Motivation Requires a Meaningful Task. English Journal, 100(1), 30–36.

    Google Scholar 

  • Heller, K. A., Perleth, C., & Lim, T. K. (2005). The Munich Model of Giftedness Designed to Identify and Promote Gifted Students. In R. J. Sternberg, & J. E. Davidson, Conceptions of Giftedness (pp. 147–170). Cambridge: Cambridge University Press.

    Google Scholar 

  • Kantowski, M. G. (1977). Processes involved in Mathematical Problem Solving. Journal for Research in Mathematics Education, 8, 163–180.

    Google Scholar 

  • Keller, J. M. (2010). Motivational Design for Learning and Performance. The ARCS Model Approach. New York/Dordrecht/Heidelberg/London: Springer.

    Google Scholar 

  • Kool, M., & Keijzer, R. (2015). Excellent student teachers of a Dutch teacher education institute for primary education develop their ability to create mathematical problems. In G. Makrides (Red.), EAPRIL Conference Proceedings (November 26–28, 2014 Nicosia, Cyprus) (pp. 160–177). Nicosia, Cyprus: EAPRIL.

    Google Scholar 

  • Scager, K. (2013). Hitting the high notes. Challenge in teaching honours students. Utrecht: Utrecht University.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

    Google Scholar 

  • Simon, M. A. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education 26(2), 114–145.

    Google Scholar 

  • Subotnik, R. F., & Jarvin, L. (2005). Beyond expertise. In R. J. Sternberg, & J. E. Davidson, Conceptions of giftedness (pp. 343–357). Cambridge: Cambridge University Press.

    Google Scholar 

  • Swan, K., Holmes, A., Vargas, J. D., Jennings, S., Meier, E., & Rubenfeld, L. (2002). Situated Professional Development and Technology Integration: The CATIE Mentoring Program. Journal of Technology and Teacher Education, 10(2), 169–190.

    Google Scholar 

  • Van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (Red.). (2006). Educational design research. London: Routledge.

    Google Scholar 

  • Van Geert, P., & Steenbeek, H. W. (2005). The dynamics of scaffolding. New Ideas in Psychology, 23, 115–128.

    Google Scholar 

  • Van Tassel-Baska, J. (1993). Theory and research on curriculum development for the gifted. In K. A. Heller, F. J. Mönks, & A. H. Passow, International handbook of research and development of giftedness and talent (pp. 365–386). Oxford: Pergamon.

    Google Scholar 

  • Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to Solve Mathematical Application Problems: A Design Experiment With Fifth Graders. Mathematical Thinking and Learning, 1(3), 195–229.

    Google Scholar 

  • Yin, R. K. (2009). Case Study Research: Design and Methods. Fourth Edition. Thousand Oaks, CA: SAGE Publications.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Hogeschool Utrecht, Instituut Theo Thijssen, Padualaan 97, 3584 CH, Utrecht, The Netherlands

    Marjolein Kool

  2. Hogeschool iPabo, Jan Tooropstraat 136, 1061 AD, Amsterdam, The Netherlands

    Ronald Keijzer

Authors
  1. Marjolein Kool
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  2. Ronald Keijzer
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Corresponding author

Correspondence to Marjolein Kool .

Editor information

Editors and Affiliations

  1. Department of Education, University of Oxford, Oxford, United Kingdom

    Gabriel J. Stylianides

  2. Graduate School of Education, Utsunomiya University, Utsunomiya, Tochigi, Japan

    Keiko Hino

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Kool, M., Keijzer, R. (2018). Designing Non-routine Mathematical Problems as a Challenge for High Performing Prospective Teachers. In: Stylianides, G., Hino, K. (eds) Research Advances in the Mathematical Education of Pre-service Elementary Teachers. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68342-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-68342-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68341-6

  • Online ISBN: 978-3-319-68342-3

  • eBook Packages: EducationEducation (R0)

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