ABSTRACT
Naturally, what is most important is establishing how the child, whether or not he thinks this reconstruction is possible, would explain it in terms of the inversion of the arithmetic operations that were being carried out. In the other, they built a big cube out of 8 little cubes whose positions were interchangeable. Being asked to compare the three tasks, and inventing series of commutative or non-commutative operations, encouraged reflections about order. The pieces were each a distinct color and varied in size but could be seriated by their cross-sectional areas. Each piece could be fitted precisely to the next, which allowed the child to observe one and only one order in which they could be threaded onto the shaft. The subject can note through a pseudo-empirical abstraction the order imposed on the parts of the mushroom by his ordering action; in other words, he can read off the result of the serial chaining action from the objects themselves.
