Markovian interpretations of conservation learning.

Abstract

A general theory of how children learn conservation concepts is presented. In contrast to earlier attempts to explain conservation learning, which are highly content-specific, the present theory assumes that there are several formally equivalent routes whereby a conservation concept can be acquired. The acquisition process is described at an abstract level in terms of a rule-sampling system. This description implies a three-state Markov model with identifiable parameters. Three experiments designed to test the model's quantitative predictions about conservation learning experiments are reported. The data generated by these experiments are used both to assess goodness of fit and to test several hypotheses about parameter invariance. It is shown that the theory provides sensible and testable explanations of some empirical phenomena that have traditionally been of interest to conservation learning researchers. Three specific phenomena-age changes in susceptibility to conservation training, stage effects in learning, and transfer of training-are given detailed consideration. Likelihood ratio procedures are developed for testing the theory's predictions in these three areas.The conservation concepts of middle childhood are without doubt the most extensively studied class of phenomena in the literature on human concept development. Given the enormity of the data base, it is not surprising that in addition to Piaget's original work, a number of other theories of how children acquire conservation concepts have appeared. They are sufficiently numerous that some writers have been prompted to formulate classification schemes based on their common properties (e.g., Beilin, 1978). One scheme that seems to cover most extant theories is: specific experience models, perceptual readiness models, and cognitive readiness models.

Catastrophe Analysis of Discontinuous Development

“…This latter point is also of importance with regard to Markov models of Brainerd (1979) and the transition model of Pascual-Leone (1970). In Molenaar (1986) is explained why such models do not test discontinuities.…”

“…In catastrophe theory qualitative changes in quantitative behavior are modelled in a way clearly distinguished from not only (non-linear) regression models but also from Markov chains models (Brainerd, 1979) and special formulations of Rasch models (Wilson, 1989).…”

Characterizing sequence knowledge using online measures and hidden Markov models

“…Markov models have been applied in many areas, including recall and recognition (Kintsch & Morris, 1965), paired associate learning (Nicolson, 1982), and conservation learning (Brainerd, 1979). In a Markov model, the response patterns associated with each state are such that we can determine with certainty in which state a subject is by his or her response.…”

Issues with a Rule-Sampling Theory of Conservation Learning from a Structuralist Point of View

“…Indeed, a structuralist theory is not performance-oriented, but is ultimately about growing competence. Brainerd [1979] also identifies certain parameters in his Mar kovian state transition model as being re flective of competence. Specifically, an agedependent increase in the values of these parameters would indicate a growing propor tion of conservation rules in the set of rulesto-bc-sampled.…”

“…The evolving forms of interpattern ing, then, are conformable to stagewise devel opment. As to the ontogenesis of conserva tion, Brainerd [1979] has proposed a rule sampling theory of conservation learning. The rules which figure in Brainerd' s theoreti cal model can be conceived of as instances of particular cognitive operations.…”