A systematic study of children's ideas on motion of macroscopic objects was carried out with the participation of 631 subjects in Grades 2–12 (ages 7–8 through 17–18). An open-ended, four-part questionnaire was administered to the subjects. The responses were categorized according to the level of sophistication of the answer. The results were analyzed using a mathematical model that was first applied to the development of Piagetian stages (Eckstein & Shemesh, 1992, in press). For three of the questions, the responses change as the children mature, and it appears that the children pass through distinct, successive stages with respect to their conceptual understanding of these questions. The mathematical model predicts that the proportion of subjects at each stage is a linear combination of decreasing exponentials. The model fits the experimental data well. Characteristic times for transition between stages were calculated. If teaching strategies to overcome misconceptions are to be effective, then they must be appropriate to the particular misconception prevalent at each stage.