This investigation was concerned with developmental changes in problemsolving strategies as reflected in children's solutions to permutation problems. In addition to the usual product measure of problem-solving efficiency (number of unrepeated arrangements), measures of strategies reflecting the experimental procedure of holding variables constant (holding initial marks constant, in this case) and degree of development of rule systems reflecting mathematical group properties were developed. Sixteen boys and 16 girls at each of three age levels (12, 15, and 18) homogeneous with respect to socioeconomic and ability level, were administered four permutation tasks that varied with respect to representational level and degree of task structure within an element set. Analysis of these data revealed two major nonexclusive problem-solving strategies which increased with age: (a) one reflecting mathematical group structure and (b) one of holding initial marks constant while permuting the remainder. In addition, the data indicated differential developmental trends in the usual product score as compared to the strategy scores. Stimulus variables had a complex effect on strategy selection and suggest significant sex as well as age differences. The implications of these data for further research on developmental strategies in problem solving and cognitive theory are presented.
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