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

The main purpose of this study was to clarify the developmental processes of understanding of interrelationships among the three concepts, duration, distance, and speed. In Experiment 1, ” ve developmental phases were found based on data of 222 four- to eleven-year-old children. In the ” rst phase, children displayed an implicit understanding of the direct relationships between duration and distance, and between distance and speed. This phase was most common among 4-year-olds. Second, children occasionally understood the inverse relation between duration and speed. Third, all of the two direct relations and the inverse relation were almost correctly understood, although the third dimension was still rather ignored. Fourth, children made their judgements based on the duration-distance-speed system, but were not fully conscious of it. Finally, children judged consciously based on this system. 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 of a transfer from the coordination of two-by-two relations to the duration-distance-speed system. Theoretical and educational implications of these ” ndings were discussed.