Relationships Among Performances on Three Formal Operations Tasks

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Abstract
Twenty-eight male and female seventh grade students who ranged widely in mathematical ability were administered three formal operations tasks in individual interviews (chemical combinations, bending rods, balance beam). Objective notes on task performances were made during the interviews and later categorized into Piagetian concrete and formal levels of intellectual development by two independent raters. Responses on each task ranged from early concrete to fully formal operational. Correlation coefficients among performance on tasks ranged from .60 to .70. The tasks were found to have a very high degree of internal homogeneity (HR = .66). A principal components analysis yielded one factor which accounted for 76.6% of the variance. These results support the hypothesis that these tasks require use of the same or a unified set of cognitive parameters.