Training Effects on the Development and Generalization of Piagetian Logical Operations and Knowledge of Number

The effects of two training sequences on the development of logical operations and number were investigated. Four-year-old children were randomly as­ signed and trained for 8 weeks in one of three conditions: logical foundations (classification and seriation), number skills (counting), and control. Each of the experimental treatments was based on either of two broad perspectives: the logical foundations model of Piagetian theorists and a skills integration model. Instruments measuring number abilities and logical operations were designed as pre- and posttest measures. Findings were that (a) both experi­ mental groups significantly outperformed the control group on both tests, (b) the number skills group significantly outperformed the logical foundations group on the number test, and (c) there was no significant difference between the experimental groups on the logical operations test. Results are discussed in terms of their implications for developmental psychology and education. Theory and research in the early devel­ opment of number and logic can be catego­ rized along two major lines (Carpenter, 1980; Reese & Overton, 1970): the logical foun­ dations model and a skills integration model. The logical foundations model of Piaget ex­ plains the development of number in terms of a synthesis of classification and asym­ metrical relations operations (Piaget, 1952). In this view, significant conceptual compe­ tence regarding number is not achieved until operational competence is att~ined. Skills