We have empirically assessed the distribution of published effect sizes and estimated power by analyzing 26,841 statistical records from 3,801 cognitive neuroscience and psychology papers published recently. The reported median effect size was D = 0.93 (interquartile range: 0.64–1.46) for nominally statistically significant results and D = 0.24 (0.11–0.42) for nonsignificant results. Median power to detect small, medium, and large effects was 0.12, 0.44, and 0.73, reflecting no improvement through the past half-century. This is so because sample sizes have remained small. Assuming similar true effect sizes in both disciplines, power was lower in cognitive neuroscience than in psychology. Journal impact factors negatively correlated with power. Assuming a realistic range of prior probabilities for null hypotheses, false report probability is likely to exceed 50% for the whole literature. In light of our findings, the recently reported low replication success in psychology is realistic, and worse performance may be expected for cognitive neuroscience.

Developmental dyscalculia is thought to be a specific impairment of mathematics ability. Currently dominant cognitive neuroscience theories of developmental dyscalculia suggest that it originates from the impairment of the magnitude representation of the human brain, residing in the intraparietal sulcus, or from impaired connections between number symbols and the magnitude representation. However, behavioral research offers several alternative theories for developmental dyscalculia and neuro-imaging also suggests that impairments in developmental dyscalculia may be linked to disruptions of other functions of the intraparietal sulcus than the magnitude representation. Strikingly, the magnitude representation theory has never been explicitly contrasted with a range of alternatives in a systematic fashion. Here we have filled this gap by directly contrasting five alternative theories (magnitude representation, working memory, inhibition, attention and spatial processing) of developmental dyscalculia in 9–10-year-old primary school children. Participants were selected from a pool of 1004 children and took part in 16 tests and nine experiments. The dominant features of developmental dyscalculia are visuo-spatial working memory, visuo-spatial short-term memory and inhibitory function (interference suppression) impairment. We hypothesize that inhibition impairment is related to the disruption of central executive memory function. Potential problems of visuo-spatial processing and attentional function in developmental dyscalculia probably depend on short-term memory/working memory and inhibition impairments. The magnitude representation theory of developmental dyscalculia was not supported.

BackgroundMathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies.MethodsFour-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires.ResultsNo gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys.ConclusionsOur study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because there is evidence that MA develops during the primary school years. Furthermore, our study showed no gender difference in mathematics performance, despite girls reporting higher levels of MA. These results might suggest that girls may have had the potential to perform better than boys in mathematics however their performance may have been attenuated by their higher levels of MA. Longitudinal research is needed to investigate the development of MA and its effect on mathematics performance.

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory), in which MA and mathematics performance can influence one another in a vicious cycle.

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