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An Exploratory Analysis of the Representation of a Mathematical Structure in Students’ Cognitive Structures1

The study investigated learning of mathematical structure. Eighth grade students (N = 87) were assigned randomly to read either a programmed text on probability (experimental group) or one on prime numbers (control group). The subject matter structure of the probability text was mapped with the method of directed graphs. Structure in students’ memories, cognitive structures, was investigated using a word association technique. Cognitive structure and achievement data were gathered at pretest, posttest, and retention test. The directed graphs provided an interpretable map of subject matter structure. Experimental students learned and retained the content structure but the control students did not. A comparison of word association, achievement, and attitude data indicated that learning of structure may differ from learning measured by achievement tests.