The challenge of proportion: does it require rethinking of the measurement paradigm?

We are developing an approach to teaching important proportionality-based concepts to first grade students in a way that supports students' future progress in the domain. We consider the proportionality between magnitudes as a basic relationship behind multiple cases, usually described mathematically as ratio or rate. The core of our strategy is the modelling of a situation of proportionality and its transformations by creating a compound unit. The key action is coordinated measurement (co-measurement): students work in pairs, and each student is in charge of changing one of two magnitudes, while preserving proportionality. Based on our successful experiments in Grades 2–6, we incorporate shared responsibility work organization ("joint actions") and the idea of compound unit into Davydov's mathematics curriculum for the first grade. We built a new module based on Davydov's idea about the role of rule-mediated counting by sets. In this paper, we present the results of our study, showing that first graders can learn the idea of compound unit and work with two magnitudes of different kinds while preserving proportionality. [ABSTRACT FROM AUTHOR]