The Development of Children's Problem Solving in a Gears Task: A Problem Space Perspective

I examined two contexts of development in children's problem solving: (1) the macro‐context of different age cohorts (8–9 vs 11–12 years of age); and (2) the micro‐context of an approximately one‐hour experimental session. Twenty subjects (even divided across sexes and these two age groups) were individually presented a collection of variously sized gears, a board onto which these gears could be easily attached and rotated, and a knob. Each subject was asked to find all solutions, in which two marked gears were turning the same way, and to represent these solutions graphically. Subjects applied four different problem spaces to the task: the Euclidean, the Kinematic, the Dynamic, and the Topological. The Arithmetic Modifier could be applied to any of these problem spaces, resulting in a numerical characterization of the gear constructions and/or production strategies. The 11–12's tended to shift problem spaces adaptively; the 8–9's seldom did so. Analysis of the pathways of transition between the problem spaces revealed a complex picture of partial or complete incorporation, and substitution.