Developing a plan for solving a problem: A representational shift

Research analyzing transitions from lower to higher levels of problem solving has focused either on quantitative increments in processing demands (Case, 1984; Klahr & Robinson, 1981) or on qualitative shifts in the organization of representations (Fischer & Pipp, 1984; Piaget, 1976). This study is concerned with distinguishing the value of these two approaches to problem solving through a microgenetic analysis of children's initial attempts to solve the Tower of Hanoi problem. As suggested by Siegler and Crowley (1991), a microgenetic approach is particularly useful in determining the process of cognitive change. One-hundred and thirty-six children, ages 6 through 8 years, were presented with the standard three-disc problem and allowed 3 minutes to complete it. The quality of the children's performance was analyzed by noting the positioning of the first move, the number and location of illegal moves, and the frequency and location of optimal moves. The results indicate that qualitative shifts in children's representation of the problem space are a crucial aspect of successful performance.