Verna M. Adams

The Interaction of Field Independence with Discovery Learning in Mathematics

This study tested the hypothesis that students with a field-independent cognitive style would learn most about numeration systems if they had minimum guidance and maximum opportunity for discovery through the use of manipulative materials. Field-dependent students were expected to perform best with maximum guidance and a symbolic treatment. Data were gathered on 46 prospective elementary school teachers who had been randomly assigned to the two treatment groups. Multiple regression analysis revealed a significant disordinal interaction for one of two achievement measures. The interaction supported the hypothesis that field-independent students achieve most in a discovery treatment, and field-dependent students learn best in expository instruction.

Individual Differences in Cognitive Style and Discovery Approaches to Learning Mathematics.

AbstractIn order to test the hypothesis that field independence would interact with level of guidance, students in five mathematics classes were randomly assigned to either a low guidance or a high guidance treatment group for a week of instruction. Both treatments used an inductive sequence of instruction on the topic of networks. Students were assessed on two aptitudes, field independence and general reasoning. Achievement was significantly better (p > .05) in the high guidance group than the low guidance group on both the posttest and the retention test. No significant interactions with the aptitude variables were found.

Locus of Control and Mathematics Instruction: Three Exploratory Studies.

The relationship between locus of control and three dimensions of discovery learning was investigated in a series of studies. Mathematics students were randomly assigned to treatments that differed in level of guidance, inductive or deductive sequencing, or use of small groups. A significant aptitude-treatment interaction occurred between locus of control and small-group instruction on the topic of networks. The other studies did not produce significant interactions, although varying the level of guidance did produce a trend in the predicted direction. Using inductive or deductive sequences of instruction did not appear to interact with locus of control.

The Interaction of Field Independence with Small-Group Instruction in Mathematics

This study tested the hypothesis that the cognitive style of field independence would interact with treatments that dif fered in the use of small groups as opposed to individual in struction. Students (N = 111) were assessed on field inde pendence and general ability and randomly assigned to treatments for a week of instruction. Achievement was measured by an immediate posttest and a delayed retention test, and student ratings of instruction were obtained. There was a significant (p < .05) interaction with measures of field independence when achievement was the dependent variable, but not when student ratings were used. However, the interaction appeared to be due more to general ability than to cognitive style. Also, students gave significantly higher ratings to small-group instruction.