THE INFLUENCES OF AGE, INTELLIGENCE, AND TRAINING ON THE ACQUISITION OF A FORMAL OPERATIONAL CONCEPT (RULE-USAGE, PROBLEM-SOLVING, GIFTEDNESS).

Individual differences in problem-solving have been studied from both information-processing and developmental psychology perspectives. The purpose of the present research was to use an information-processing approach to investigate the effects of both age and intelligence on the performances by young persons on experimental tasks which required systematic application of appropriate solution rules. Eighty 10- and 15-year-old subjects were assigned to one of eight groups on the bases of their ages, sex, and intelligence levels. The testing condition was the same for all groups. Stimulus materials consisted of a two-pan balance and a variety of different-density cubes. Subjects' responses to the materials were their predictions of equilibrium or imbalance. Correct solutions required understanding of the physical science concepts of volume and density, and the mathematics concept of proportionality. From analysis of variance performed on the data, it was found that males and females did not differ in their abilities to problem-solve. The highly-intelligent subjects had a greater frequency of correct responses in both age groups, and the older subjects outperformed younger subjects. The equilibrium problems presented in the study were of six separate types, and the interaction effects in the data revealed that the six types were of varying levels of difficulty. It was in the analyses of the subjects' patterns of responses to the several types that the most theoretically interesting results appeared. Examination of the response patterns led to assignment of the respondents to categories of probable rule-usage. The less sophisticated problem-solvers did not take density into account and consistently relied on their knowledge of the volume concept in making their decisions. Solvers functioning at higher rule-levels were able to consider density as well before making their predictions, although a substantial number failed to use cues present in the experiment to reckon the respective densities correctly. Fully-functional problem-solvers gave responses which showed their mastery of the mathematics of proportionality. Twenty-four subjects participated in a second experiment which was a short demonstration-oriented training study providing feedback, although the algorithm for correct problem solution was not directly taught. Results were discussed in terms of the efficacy of the rule-usage model