Functions, operations, and décalage in the development of transitivity

The hypothesis that some attempts to reduce the performance demands of concrete operational tasks may have allowed children to solve those tasks with preoperational functions was tested by administering two previously used versions of the transitivity task for length and weight to 120 children 6 to 9 years of age. In the standard Piagetian version of the task, comparison objects were presented only two at a time, with no correlation between length or weight and spatial position. In the alternate version, objects were ordered in space by length or weight, but placed too far apart for differences in length to be seen. As predicted: (a) the standard version was solvable only through an operational composition of premise relations, but the alternate version allowed children to recode length or weight as a function of spatial position; (b) the functional solution was easier and developed at an earlier age than the operational solution for length as for weight. In addition, the decalage between length and weight was found to result from children's tendency to infer weight as a function of size rather than from an operational composition of premis e relations.