Distinguishing Two Stages of Mathematics Conceptual Learning
In this theoretical article, we distinguish two stages of learning a new mathematical concept – participatory and anticipatory. We use a recently developed mechanism for explaining mathematical conceptual learning – reflection on activity-effect relationship – as well as von Glasersfeld’s tripartite model of a scheme, to explain qualitative distinctions between the two stages. We use this distinction to explain why instructional interventions (including inquiry-based approaches) may not bring about the intended instructional goals.
Tzur, R., and Simon, M. A. (2003). Distinguishing Two Stages of Mathematics Conceptual Learning. In F.-L. Lin & C.-J. Guo (Eds.), Proceedings of the International Conference on Science and Mathematics Learning. Taipei, Taiwan R.O.C.: National Taiwan Normal University.