ABSTRACT
Conservation of length when objects undergo a change of position does not yet imply any understanding of Euclidean metrics. A judgment of equality between sites which become vacant in the course of changes of position and those which are newly occupied does not entail subdivision or the construction of a unit of measurement. How do children pass from qualitative conservation to the measurement of length? The detailed analysis of that transition must be preceded by a further study devoted to the conservation of length in which the subject is asked to compare the lengths of equal objects, some of which are rectilinear while others are bent at various angles. In ch. IV, §1, we reported an experiment in which children were asked to compare two shapes of unequal length, one of which was curvilinear while the other was rectilinear, but with the pair so arranged that their extremities coincided. This experiment was followed by another in which the test-objects were both rectilinear and equal in length but their arrangement was staggered. The question remains how children will respond when asked to compare two objects which are identical in length if these are first presented as rectilinear shapes in exact alignment, and then one of them is distorted in one way or another. Will the conservation of length be delayed in this situation, or will this special situation and measurement in general prove tractable as soon as conservation has been achieved? More generally, what is the process leading from conservation to measurement? The present experiment, like that of spontaneous measurement in ch. II, deals with problems of measuring, but the situation has been so devised as to take into account what has since been learned of the role of the coordination of sites in the conservation of distance and length.
