A Computational Analysis of Conservation

An approach to modeling cognitive development with a generative connectionist algorithm is described and illustrated with a new model of conservation acquisition. Among the conservation phenomena captured with this model are acquisition, the problem size effect, the length bias effect, and the screening effect. The simulations suggest novel explanations for sudden jumps in conservation performance (based on new representations of conservation transformations) and for the problem size effect (based on an analog representation of number). The simulations support the correlation-learning explanation of length bias (that length correlates with number during number altering transformations). Some conservation phenomena that so far elude computational modeling attempts are also discussed along with their prospects for capture. Suggestions are made for theorizing about cognitive development as well as about conservation acquisition. A variety of classic puzzles about cognitive development are addressed in the light of this model and similar models of other aspects of cognitive development. One of the mainstays of research on cognitive development is conservation. Conservation involves a belief in the continued quantitative equivalence of two physical quantities over a transformation that only appears to alter one of the quantities. A well known conservation problem presents the child with two identical rows of evenly spaced objects. An example of such a row is portrayed in the first line of Table 1. Once the child agrees that two such rows have the same number of objects, the experimenter transforms one of the rows, e.g., by spreading out the items thereby elongating the row, as shown in the fourth line of Table 1. Then the experimenter asks the child whether the two rows still have the same amount or whether one of them now has more. Piaget (1965) and many subsequent researchers found that young children, below about six or seven years of age, respond that one of the two rows, usually the longer row, now has more than the other. This seemed somewhat surprising given that quantities of items in the two rows were still identical. In contrast, children older than six or seven years respond that the two rows still have equal amounts, i.e., they conserve the equivalence of the two amounts over the elongating transformation. Table 1 Example Transformations with Constant Density Transformation Length Density Row Pre-transformation 2 2 o o o o Add 2.5 2 o o o o o Subtract 1.5 2 o o o Elongate 4 1 o o o o Compress 1.33 3 o o o o