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Two mathematical models of cognitive development are investigated. One model assumes that cognitive growth proceeds by stages, and the other assumes that cognitive growth is continuous. Both models make predictions concerning the percentages of the population at different cognitive levels. In the stage model, the cognitive level is identified with the stage, and in the continuous learning model, the cognitive level is defined by attainment above a given threshold and below the next highest threshold. The models are applied to three large‐scale experimental studies which categorize adolescents according to their Piagetian stage, namely a study by Lawson & Renner (1974) in the USA, a study by Shayer & Wylam (1978) in England, and a study by Shemesh, Eckstein & Lazarowitz (1992) in Israel. In all cases, the fit of the stage model to the experimental data was better than the fit of the continuous learning model.
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Eckstein et al. (1992) studied this question.
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