ABSTRACT
In situations that we studied earlier in this volume, such at the understanding of inclusion relationships in a set of flowers (Chapter 5),1 the problem remained indeterminate, because at any age a bouquet can easily be made out of daisies and roses. To study our question in a decidable fashion, we chose to have children compare two sets of seriable elements. Set A was additive in form (sticks 2,4, 6, 8, and 10 cmlong); setBwas exponential (2, 4, 8,16, and 32 cm). The required actions took place in two phases. Phase 1 was simply exploratory: freely arranging the two sets, which were presented out of order. Phase 2 was more genuinely constructive; it consisted of making a continuation for each series once it was arranged in the form of a "staircase." After each phase, children were asked to describe similarities and differences.
