Abstract
In design research instructional design and research are interrelated, “the design of classroom learning environment serves as the context for research and, conversely, ongoing and retroactive analyses are conducted in order to inform the improvement of design” (Cobb et al., 2011, p. 75). The design of mathematical tasks or learning sequences of exercise and their analysis is a central component of research in mathematics education and ties together learning trajectories and design research.
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References
Baroody, A. J., Cibulskis, M., Lai, M. L., & Li, X. (2004). Comments on the use of learning trajectories in curriculum development and research. Mathematical Thinking and Learning, 6(2), 227–260.
Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89.
Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127–166.
Cobb, P., Gravemeijer, K., & Yackel, E. (2011). An introduction: Symbolizing and instructional design-developing instructional sequences to support students’ mathematical learning. In A. Sfard, E. Yackel, & K. Gravemeijer (Eds.), A journey in mathematics education research. New York, NY: Springer.
Confrey, J., & Maloney, A. (2010, June). The construction, refinement, and early validation of the equipartitioning learning trajectory. In Proceedings of the 9th International Conference of the Learning Sciences-Volume 1 (pp. 968–975). Chicago, IL: International Society of the Learning Sciences.
Confrey, J., Maloney, A. P., & Corley, A. K. (2014). Learning trajectories: A framework for connecting standards with curriculum. ZDM, 46(5), 719–733.
Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128.
Jaworski, B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning. Teaching, Journal of Mathematics Teacher Education, 9, 187–211.
Lamon, S. (2007). Rational numbers and proportional reasoning: Towards a thoeretical framework for research. In F. K. Lester (Ed.), Second edition of research on mathematics teaching and learning (pp. 629–667). Greenwich, CT: NCTM.
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 114–145.
Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104.
Steffe, L. P. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 6(2), 129–162.
Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction toward a theory of teaching. Educational Researcher, 41(5), 147–156.
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Baker, W., Czarnocha, B. (2016). Two Learning Trajectories. In: Czarnocha, B., Baker, W., Dias, O., Prabhu, V. (eds) The Creative Enterprise of Mathematics Teaching Research. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-549-4_28
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DOI: https://doi.org/10.1007/978-94-6300-549-4_28
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