Even in its prime, psychology showed an interest in early arithmetic, witness E. L. Thorndike's book The Psychology of Arithmetic published in 1922. Conversely, the teaching of arithmetic has always reflected the psychological theories in vogue at the time. Anyone over 50 remembers the endless hours spent in school reciting sums in unison to memorize them. We were then applying one of the principles of Thorndike's theory of associationism, the “law of exercise,” thereby increasing the specific stimulus-response link (Mayer, 1977). Cognitive psychology today recognizes that higher mental processes are involved in the learning of early arithmetic, that is, the acquisition of the fundamental conceptual schemes of number and additive structures.

This contemporary view is expressed in the work of the International Group for the Psychology of Mathematics Education (PME). The need for more sophisticated theories can be illustrated by the notion of number, which fails to be described in terms of classical concept formation theory since it cannot be defined in terms of attributes or in terms of examples and nonexamples. Instead, number is now viewed as a conceptual scheme, that is, a network of related knowledge together with all the problem situations in which it can be used. Much of our research is also embedded in an epistemological framework, both in the general sense of the growth of knowledge and in the more restricted sense of genetic epistemology, which takes into account the development and maturation of the child.