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Background. Difficulty with arithmetic is a common problem. There is increasing evidence that arithmetical cognition is made up of multiple components, and that it is quite possible for children and adults to show strong discrepancies, in either direction, between the components. This suggested the desirability of developing interventions that assess and target children's weaknesses in specific components of numeracy. Aims. This paper reports two related studies of targeted interventions for children with mathematical difficulties. The aim was to develop intervention techniques, based on assessing and targeting specific strengths and weaknesses, and to assess their effectiveness. Sample. The first study, of the pilot Numeracy Recovery intervention programme, included 169 children aged 6 and 7. The second study, of the Catch Up Numeracy programme, included 246 children between the ages of 6 and 10, of whom 154 received the Catch Up intervention programme, 50 were given the same amount of time for non-targeted individualized mathematics work, and 42 children received no intervention, except for the usual school instruction. Both samples consisted of children, who had been identified by their teachers as having difficulties with arithmetic. Method. The first study took place in Oxford, and children were assessed on nine components of early numeracy. The project has since been adapted, under the name of Catch Up Numeracy, for wider use, and tested in 11 local authorities in the UK. The second study, which included 10 components of numeracy, involved teachers and teaching assistants receiving formal training from the Catch Up organization in delivering the programme. In both studies, following assessment, the children received weekly intervention (half an hour a week for approximately 30 weeks) in the components with which they had difficulty. The children were given standardized tests at the beginning and end of intervention. In the first study, the tests used were the Basic Number Skills subtest of the British Abilities Scales ; the Numerical Operations subtest of the Wechsler Objective Numerical Dimensions ; and the Arithmetic subtest of the Wechsler Intelligence Scale for Children . In the second study, the test used was the Basic Number Screening Test.