Study title

United Kingdom

Group

Individual

Study 1: The link between logical reasoning and mathematical ability The aim of the study was to investigate the relationships between mathematical performance and logical reasoning as measured by the ability to draw transitive inferences. In particular, we were interested in how much children were able to reason logically about problems where the believability and the logicality of conclusions were in conflict. The participants were forty-three 10-year-old children: 13 in the developmental dyscalculia (DD), 16 in the control, and 14 in the high maths ability group. Children were selected from a large sample of over 1000 children on the basis of extensive pre-testing on standardized measures of mathematical, reading and cognitive ability. Children in the DD and control groups were matched on IQ, working memory and reading ability, but DD children performed on the standardized maths tests at least 1 SD below the population mean. By contrast, high maths ability children performed at least 1 SD above the population mean. High maths ability children generally had higher IQs, and better working memory and reading skills than children in the other groups. We administered 12 reasoning problems: 4 with a belief-logic conflict, 4 with no conflict, and 4 with belief-neutral conclusions (where the conclusions were neither believable, nor unbelievable). Study 2: Electrophysiological investigation of the ratio-bias phenomenonIn the ratio-bias task participants are offered a choice between two lotteries (e.g., 1 winning event out of 10 vs. 9 winning events out of 100). Many individuals consistently choose the lottery with the greater number of potential successes, although it offers a smaller probability of success. This task was described as a problem eliciting a conflict between intuitive and rational (or Type 1 and 2) processes. According to dual-process theories, in the event of such conflict, Type 1 responses are automatically activated (i.e., all participants feel that a lottery with a higher number of winning events is more advantageous). However, these initial feelings can be overridden by conscious and effortful reasoning (i.e., understanding that ratios are important and not the absolute numbers). In our study we manipulated numerical congruency (i.e., whether a lottery with a higher absolute number of winning events also gives a higher chance of winning, based on the ratio of winning/non-winning events), perceptual congruency (whether the lottery where the overall surface area of winning events was larger also had the larger numerical proportion of winning events), and task difficulty (based on the difference between ratios). Accuracy and reaction times were recorded, as well as the activity of muscles in the thumbs of participants (using electromyography) which is indicative of response activation and inhibition processes. Twenty-two adults without mathematical difficulties participated in this experiment, and 540 trials were administered.