ABSTRACT
The operation often described as an 'arrangement' is the permutation of n things taken all or r at a time. It is therefore not a multiplicative operation in the same sense as those described in Chapters 7 to 9, though it may be called a multiplication in the broader sense because it involves a squaring operation. In fact a permutation is a seriation of all the possible seriations or ordinations of the elements. Our main reason for examining the memory of such structures is therefore that they involve a higher operational level than the multiplication of classes or relations (and serial ones in particular). Thus, while simple, or first power, multiplications can be performed by children as soon as they have reached the level of so-called 'concrete' operations (seven to eight years), i.e. of operations based on step-by-step 'groupings', permutations call for a grasp of higher structures based on hypothetico-deductive, or 'formal', thought, i.e. on propositional operations with a combinatorial function, and these are not normally grasped until the age of eleven to twelve years. Hence, we thought it important to establish whether or not the memory of such structures (perceived but not constructed by the subjects themselves) obeys the same laws as that governing the structures we have been discussing, i.e. whether or not it, too, does not become perfected until the corresponding operation can be performed.
