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.
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.
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.
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.
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.
Frey, N., & Fisher, D. (2010). Motivation Requires a Meaningful Task. English Journal, 100(1), 30–36.
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.
Kantowski, M. G. (1977). Processes involved in Mathematical Problem Solving. Journal for Research in Mathematics Education, 8, 163–180.
Keller, J. M. (2010). Motivational Design for Learning and Performance. The ARCS Model Approach. New York/Dordrecht/Heidelberg/London: Springer.
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.
Scager, K. (2013). Hitting the high notes. Challenge in teaching honours students. Utrecht: Utrecht University.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
Simon, M. A. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education 26(2), 114–145.
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.
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.
Van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (Red.). (2006). Educational design research. London: Routledge.
Van Geert, P., & Steenbeek, H. W. (2005). The dynamics of scaffolding. New Ideas in Psychology, 23, 115–128.
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.
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.
Yin, R. K. (2009). Case Study Research: Design and Methods. Fourth Edition. Thousand Oaks, CA: SAGE Publications.
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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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