ABSTRACT
Mter studying the remembrance of additive seriations (Chapters I to 2), we thought it important to establish the generality of our findings by an analysis of the memory of serial multiplications involving the ordination, in two dimensions, of objects differing in two seriable characteristics, for instance, size and colour. The simplest and at the same time the most comprehensive model is a support (cardboard) on which the elements have been seriated from left to right according to variations in one of these characteristics (e.g. a gradation of colours from light pink to dark red) and from top to bottom according to variations in their other characteristic (e.g. decreases in size). With this type of arrangement (Figure 23), only the two diagonals and the lines parallel to them represent seriations of both characteristics at once (e.g. Nos. 1, 6, 11, 16; 4, 7, 10, 13; 2, 7, 12; 5, 10, 15; 3, 6, 9; 8, 11, 14; 2, 5; 9, 14; 12, 15; 3, 8), while the horizontal rows and vertical columns consist of elements differing in only one of the two characteristics. For the purposes of serial multiplication, the child must bear these semi-equivalences in mind, since he cannot reconstruct or remember the model by means of the diagonals alone.
