Probability concepts in school pupils aged 11-16 years
The thesis begins with a survey of current teaching of probability and of research into probability concepts. The next part of the thesis reports an investigation into performance on probability items by candidates in the University of London GCE'0' Level Mathematics Multiple Choice Examination and in the East Midland Regional Examinations Board CSE Mathematics Examination. Analysis of multiple choice responses and examination scripts is described, investigating the extent of sex differences in probability. The main body of the thesis describes and discusses the development, administration and results of a probability concepts test, which was produced for the SSRC-sponsored 'Chance and Probability Concepts Project' (1978-81) under the direction of the author. The concepts test, which was administered to approximately 3000 pupils aged 11-16 years in mixed secondary and middle schools in the East Midlands, comprised items covering various elementary probabilistic, statistical and combinatoric concepts. The thesis then describes the establishment of a probability concepts hierarchy, supplementing the research of the Concepts in Secondary Mathematics and Science Project (Chelsea College, 1974-1979). Finally a detailed analysis of the test results is incorporated which considers probability conceptual development in relation to the variables age, intelligence, mathematical ability,and sex The main findings of the research are as follows: Probability concepts development is age-related but the most important single factor is the general intellectual ability of the subject. Mathematical ability is strongly related to test performance but this is largely attributable to its equally high correlation with intellectual ability. Sex differences exist, with boys generally superior, but these are of a minor nature. Some important conceptual ideas appear to be more highly developed in younger rather than older pupils, and in girls rather than boys. Most pupils do not attain Piaget's stage III (formal operations).