This study was designed to investigate individual differences in mathematical performance and in rates of development in mathematics at various levels of secondary schoolingo Inhelder and Piaget's (1958) theory of logical thinking in adolescents, together with Hamley's (1934) analysis of mathematical thought were used to construct a set of "predictor" tests. These together with reference tests for number and vocabulary, a standardised intelligence test (Raven's 1938 P.M.) and seven criterion tests in algebra, arithmetic and geometry at the levels of manipulation, concept understanding and problemsolving formed the battery of instruments used in the study.
The investigation was designed to explore the following research questions, the final results being assessed from various theoretical points of view.
(i) Within the limits of the test battery, what set of factors account for the observed individual differences on the mathematics tests and their inter-correlations?
(ii) In what way is the factorial structure of individual differences in mathematical performance, as measured by the criterion tests, modified by maturation and educational experiences?
(iii) What are the characteristic developmental functions in mathematical performance, what individual differences exist in these functions, and what are their correlates?
(iv) In terms of the factorial structure and the developmental functions, what are the characteristic differences between (a) boys and girls, (b) 'drop out' students and continuing students, ( c) "successful" students and "unsuccessful" students as judged by public examinations which act as selection barriers?
(v) For which variables do differences between classrooms contribute a significant amount of the variation? Sample A consisted of 383 first year students of average age 14.7 ye ars, chosen from 12 schools. Sample B contained 210 third year students from six schools. .....................................................................