The Dialectic between Embodied Experiences and Mathematical Concepts

In their article, Saxe, de Kirby, Kang, Le, and Schneider [this issue] address a crucial issue in children’s mathematical development: how to understand the dialectic between everyday (embodied experiences) and scientific concepts (verbally defined, specialized disciplinary vocabulary). In other words, how can we conceptualize the interplay between bottom-up and top-down learning processes in a classroom community? Although this issue was identified by Vygotsky [1987] 80 years ago, detailed descriptions of its microgenesis 1 are rare. In addition to articulating the dynamics of this dialectic, Saxe and his colleagues demonstrate how it was used to support students’ understanding of several mathematics concepts that have been shown to be difficult to learn (e.g., equivalent fractions). To illustrate their analytic approach, Saxe et al. draw from a corpus of data collected over 19 lessons in one fifth-grade classroom located in California. Despite their single case study design, they argue that the process by which they conceptualized students’ learning could generalize to other classrooms and other content areas. To support this claim, they mention Saxe’s previous research in culture and cognition