Abstract The aim of the study was to establish the interrelationship amongst a variety of individual differences and performance when children were learning mathematics from intrinsic programmed instruction presented in teaching machines. In order to investigate the reliability of such inter‐relationships in different environments, a replicate rather than a large sample design was used. The sample consisted of six groups of children from four secondary schools (minimum N = 50). Various measures of intelligence, reading ability, personality trait, mathematical attainment, attitude and speed of progress were assessed and intercorrelated. Principal component analysis was done for each of the six groups. One of the components, usually the first, was one of maturation with high item correlations for age, intelligence, attainment, speed of progress, errors and gain in mathematical attainment measures. The children who most benefited from intrinsic programmed instruction were those who would most have benefited from conventional instruction. Attitude measures were found to be independent of maturational factors and were related to sex and personality traits. However, the major differences in component structure between samples suggested that reactions to, and achievement from, programmed instruction were more related to the way programmed instruction was organised in the various schools than to individual differences in age, intelligence and personality.
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