Previous research (eg Barrouillet & Lepine, 2005; Cummings and Elkins, 1999) suggests that children with mathematical difficulties (MD) use inefficient problem solving strategies and lack computational fluency. This thesis extends existing research by investigating the cognitive and affective dimensions of mathematical difficulties in schoolchildren using a variety of methodological approaches. The principal aim is to identify the characteristics of children with MD and compare them with children of average ability, to identify the factors relevant to the learning of mathematics.In the existing literature (eg Baptist et. al., 2007), mathematical difficulties are primarily defined in terms of a cognitive deficit. However, learning may not only be a function of cognitive processes, and affective responses such as anxiety or attitude may play an important role in the learning of mathematics (Me Leod, 1994). To investigate the relative salience of these factors, an instrument to measure affective responses towards mathematics in schoolchildren was developed. This instrument was then utilised to investigate differences in maths anxiety, self efficacy, perceptions of the learning environment and attitudes towards the teacher between children with MD and children of average mathematical ability. In order to investigate the cognitive aspects of MD, dual task experiments were used to examine the role of subvocal rehearsal in arithmetic problem solving Mathematical problems were coupled with either a phonological or a neutral secondary task to find out how children with MD and average ability children use phonological working memory resources in arithmetic.The cognitive aspects of MD for the learning process were addressed by evaluating two different types of mathematics instruction. A protocol analysis illustrated how the format of instruction affected children's use of arithmetic problem solving strategies and how strategy usage was influenced by individual differences in information processing. Overall, the results suggest that the cognitive processing deficits of children with MD seem to result from inefficient problem-solving strategy usage which occupies cognitive resources, however, problem solving was improved via a direct instruction intervention which provided worked-out examples and model strategies. A follow-up analysis found that the interventions for children with MD would need to go beyond the learning of specific abilities in order to produce sustainable long-term effects on school achievement.
|Date of Award
|Martin Graff (Supervisor) & Peter Mayer (Supervisor)