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Abstract

This study was designed as a test for two neo-Piagetian theories. More specifically, this research examined the relationships between the development of proportional reasoning strategies and three cognitive variables from Pascual-Leone's and Case's neo-Piagetian theories. A priori hypotheses linked the number of problems students worked until they induced a proportional reasoning strategy to the variables of M-space, degree of field dependence, and short-term storage space. The subjects consisted of students enrolled in Physical Science I, a science course for nonscience majors at the University of Southern Mississippi. Of the 34 subjects in the study, 23 were classified as concrete operational on the basis of eight ratio tasks. Problems corresponding to five developmental levels of proportional reasoning (according to Piagetian and neo-Piagetian theory), were presented by a microcomputer to the 23 subjects who had been classified as concrete operational. After a maximum of 6 hours of treatment, 17 of the 23 subjects had induced ratio schemata at the upper formal level (IIIB), while the remaining subjects used lower formal level (IIIA) schemata. The data analyses showed that neither M-space and degree of field-dependence, either alone or in combination, nor short-term storage predicted the number of problems students need to do until they induce an appropriate problem-solving strategy. However, there were significant differences in the short-term storage space of those subjects who mastered ratio problems at the highest level and those who did not. Also, the subjects' degree of field-dependence was not a predictor of either the ability to transfer problem-solving strategies to a new setting or the reuse of inappropriate strategies. The results of this study also suggest that short-term storage space is a variable with high correlations to a number of aspects of learning such as transfer and choice of strategy after feedback.