Concrete–abstract–new-concrete: Freudenthal and Davydov in advancing embodied design framework: Twelfth Congress of the European Society for Research in Mathematics Education (CERME 12)

Freudenthal and Davydov-two giants of mathematics education research-had a similar sophisticated vision on the position of mathematical models and symbols in abstract-concrete dialectics. In our vertical analysis of those approaches, we integrate them in a spiral vision of mathematics learning. Starting from concrete enactment, students abstract previously latent aspects of their reality. Further, students fixate abstract ideas in mathematical artifacts, which in turn enable new concrete experiences. We show how local integration of two theoretical approaches can support an empirical analysis of embodied design for proportions and act as backing a design heuristic for embodied technologically supported activities.