Class-Inclusion Developmental Levels and Logical Necessity

Abstract

The relation between class inclusion developmental stages and the logical necessity of the judgments provided by the children is not yet strongly established. 192 children from grades 2 to 6 showing three different levels of class-inclusion answers (failure, correct answer based upon counting, correct answer based upon logical reasons) were submitted to one out of four different necessity tasks. In these tasks, children were required (1) to solve class-inclusion problems when the use of empirical means of verification was prevented; (2) to maintain their inclusion judgment despite a modification of the initial display; (3) to discover the B = A relationship in initial displays or through modification; and (4) to understand the impossible (B <A) and possible relationships (B > A, B = A). Results indicate (1) that subjects using logical reasons differ from those using counting in only one specific situation, the ability to reject the impossible case, while subjects who fail class-inclusion problems also fail all necessity tasks, (2) that the four necessity tasks are not equally difficult, suggesting a gradual mastery of these problems, and (3) that the necessity tasks are more difficult than the usual class-inclusion problems. Results are discussed with reference to the two kinds of generalization process (inductive and constructive) hypothesized by Piaget and Henriques (1978).