A validity study of two paper‐pencil tests of concrete and formal operations

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Abstract
Two group paper‐pencil batteries, the Longeot (consisting of three subtests) and three puzzles (KLR) fromScience Teaching and the Development of Reasoning, were administered to 607 students from ninth and tenth grade mathematics and science classes. A subsample of 69 students was then administered three Inhelder tasks (chemicals, rods, and shadows). In general, the expected developmental trends were confirmed, with formal status being most difficult to attain on the Inhelder tasks and easiest to attain on the Longeot. The correlations between the KLR and Inhelder (0.61,p< 0.01) and the Longeot and Inhelder (0.55,p< 0.05) were moderately high. According to the method of Shayer (Note 2), it was found that each of five paper‐pencil subtests discriminates at or between the 2B (late concrete) and 3A (early formal) levels while the sixth subtest, the mealworm puzzle, was found to discriminate at the 3A level. This study indicates that either group battery may be useful in identifying transitional subjects. However, if a more stringent criterion of “formal” is needed, a “success” rate of four or five out of the six subtests may be required. Both group batteries are relatively easy to administer and score with a minimum of guidance, although the KLR scoring might need to be simplified for use by the practitioner. Sex differences found on the KLR and the Longeot are suggestive of the potential differential use of these tests by researchers investigating sex differences in achievement or aptitude.

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