Growth of cognitive abilities: Dynamic models and scaling

A dynamic model of cognitive growth, proposed by van Geert, has been extended in three different directions. (A) A term has been added to take into account external driving forces, that is, exposure to material to be learned. (B) A method has been developed to apply the model to cross-sectional studies. (C) Using ideas of Item Response Theory, a procedure has been developed to use the model to scale tests of cognitive abilities that consist of questions of varying difficulty. The model we use is an attempt to understand cognitive growth as the result of two driving forces: namely, the autocatalytic force proposed by van Geert that is due to processes internal to the person, while the other force is an external force and due to exposure to the material to be learned. Using the model, it is possible to derive a distribution function, g(d;t), that gives the fraction of correct responses by examinees of age t to questions of difficulty d. The model is tested by fitting the theoretical distribution function with the observed distribution of scores obtained by the testing of a large group of children ages 2 to 15 years on a Stanford-Binet test. (C) 2000 Academic Press.