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., & Simon, M. A. (2004). Distinguishing two stages of mathematics conceptual learning. International Journal of Science and Mathematics Education, 2, 287-304.