Research

During the three years 1978-1981 a research project based at Loughborough in the East Midlands region of England investigated probability concepts of 11-16 year olds. A test of twenty-six questions was administered to a stratified sample of 2930 pupils from comprehensive mixed schools. These pupils were also given a test of general reasoning ability. the project's findings have been summarized in a 40 page booklet which includes all the test questions and analyses of responses. Nearly all test items, displayed an improvement in performance with increasing chronological age and with intellectual ability. Items requiring only the comparison of two direct quantities were well done by all ages tested (11 to 16 years), but those requiring comparison of two ratios were very poorly done, especially below the age of 15 years. This contrast is exemplified by the results for the two items. In this article we shall look at the development and test results of just one of the questions used.

Twentieth-century psychologists have been pessimistic about teaching reasoning, prevailing opinion suggesting that people may possess only domain-specific rules, rather than abstract rules; this would mean that training a rule in one domain would not produce generalization to other domains. Alternatively, it was thought that people might possess abstract rules (such as logical ones) but that these are induced developmentally through self-discovery methods and cannot be trained. Research suggests a much more optimistic view: even brief formal training in inferential rules may enhance their use for reasoning about everyday life events. Previous theorists may have been mistaken about trainability, in part because they misidentified the kind of rules that people use naturally.

The main aim of our research has been to contribute to an elucidation of the following problem: from what age, and in what sense, is it possible to speak of an intuition of chance and probability in the child? Taking Piaget's view as our starting-point, we have assumed that the central feature is that of the relationship between the possible and the necessary. At the same time, we have looked at other aspects which seemed likely to throw light on the problem as a whole: (a) Probability can be expressed either as a prediction of a single isolated event (without specifying the hypothetical multiplicity of its origin), of as a prediction of several events - which may be repetitions of a single event, or a succession of different events. We therefore need to know to what extent children of different ages understand the concept of relative frequency, and the extent to which this enters into their understanding of probabilistic situations. (b) How far is the child able to abstract a common probabilistic structure from different specific contexts and situations? It seemed important to us to include series of events described by unequal probabilities. Reprinted from Enfance 2 (1967), 193 - 206.

In order to investigate the nature of probabilistic reasoning, we devised two experimental problems, each of which involved two hope questions (long- and short-term). We will present the two standard problems along with the Bayesian solution. Then we will discuss a number of features of the solution by applying it to a variety of situations. After describing how our subjects reasoned about the standard problems, we will present a didactic device we developed to make the search problem more conducive to resolution. Finally, we will explore subjects' ability to transfer the lesson learned from the didactic device to the analogous wait problem.