The aim of the study was to investigate the effect of direct instruction on the ability to handle permutations and arrangements, as an example of a problem at the level of formal operations. 60 Bucharest school children, 20 aged 10 years, 20 aged 12 and 20 aged 14, tested individually, were first asked to estimate the number of possible permutations with 3, 4 and 5 objects. Results showed that these subjective estimates improved with age, with a threshold (or marked improvement) at age 12, though there was serious underestimating at all ages. A step-by-step teaching strategy using generative "tree diagrams" was then used. Even the 10-years-olds learned the use of the tree diagrams and the appropriate procedures for permutations and arrangements. Reprinted from The British Journal of Educational Psychology 40 (1970), Part 3.
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