Cognitive Style and Mathematics Learning: The Interaction of Field Independence and Instructional Treatment in Numeration Systems

Abstract

The relationship between a cognitive style variable, field-dependence-independence, and instructional treatments that differed in two dimensions of discovery learning, level of guidance and level of abstraction, was investigated. The four treatments used either minimum or maximum guidance with or without manipulative materials. The 116 subjects, all prospective elementary teachers, were pretested and then randomly assigned to treatments. Students were tested for immediate achievement at both the concrete and symbolic level, and then retested 4 weeks later. There was a significant (p<.05p<.05) aptitude-treatment interaction between field-dependence-independence (measured by the Hidden Figures Test) and level of guidance on two of the four dependent variables. As predicted, field-independent students did better with minimum guidance, whereas field-dependent students excelled with maximum guidance. Although there was one interaction between field-dependence-independence and level of abstraction, the data showed no consistent pattern for this dimension.