Development of concepts of interrelationships among duration, distance, and speed

The main purpose of this study was to clarify the developmental processes o f understanding of interrelationships among the three concepts, duration, d istance, and speed. In Experiment 1, five developmental phases were found b ased on data of 222 four- to eleven-year-old children. In the first phase, children displayed an implicit understanding of the direct relationships be tween duration and distance, and between distance and speed. This phase was most common among 4-year-olds. Second, children occasionally understood th e inverse relation between duration and speed. Third, all of the two direct relations and the inverse relation were almost correctly understood, altho ugh the third dimension was still rather ignored. Fourth, children made the ir judgements based on the duration-distance-speed system, but were not ful ly conscious of it. Finally, children judged consciously based on this syst em. About half of the 11-year-olds reached this phase. In Experiment 2, 29 children repeatedly participated in the same experiment six or eight times once a year till 6th grade. Generally, their understanding developed along the process that emerged in Experiment 1, although there was facilitation o f a transfer from the coordination of two-by-two relations to the duration- distance-speed system, Theoretical and educational implications of these fi ndings were discussed.