Rationals and decimals as required in the school curriculum: Part 1: Rationals as measurement

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment, carried out jointly with his wife, Nadine, in her classroom at the École Jules Michelet, was to teach all of the material on rational and decimal numbers required by the national program with a carefully structured, tightly woven and interdependent sequence of “situations.” This article describes and discusses the first portion of that experiment.