Development of time, speed, and distance concepts.

The rule-assessment approach was used to examine 5-, 8-, 11-, and 20-year-olds understanding of the concepts of time, speed, and distance. Parallel tasks were developed for the three concepts that allowed specification of whether children were relying on time, speed, distance, end point, end time, beginning point, or beginning time cues in making their judgments. It was found that 5-year-olds understood all three concepts in the same way: Whichever train ended farther ahead on the tracks was said to have traveled for the longer time, at the faster speed, and for the greater distance. Twenty-year-olds, at the other extreme, understood all three concepts as distinct and separate ideas. The transitional period was marked by specific confusions among the three concepts: Time was regularly confused with distance, distance was confused with time, and speed was confused with distance and to some extent with end point. Both speed and distance concepts appeared to be mastered well before the concept of time. In 1928, Albert Einstein posed a question to Jean Piaget: In what order do children acquire the concepts of time and speed? The question was prompted by an issue within physics. Newtonian mechanics viewed time as a fundamental notion and denned speed in terms of it (velocity = distance/time). Relativity theory, by contrast, denned time and speed in terms of each other (and in relation to fixed points), with neither con-cept viewed as the more basic. Einstein wanted to know which concept children understood first, whether understanding of each was intuitive or derived, and how initial understanding of one concept influenced subsequent understanding of the other. Almost 20 years later, Piaget published a two-volume, 500-page reply to Einsteins query (Piaget, 1946a/1969; 1946b/1970). The evolution of the concepts of speed and abso-lute linear time had proved to be consider-We wish to express our thanks to C. Paul Clark,