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AbstractThis study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain‐specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain‐general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief‐laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief‐neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real‐life referents) develops later than the ability to reason about belief‐inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8

AbstractWe determined the relative importance of the so‐called approximate number system (ANS), symbolic number comparison (SNC) and verbal and spatial short‐term and working memory (WM) capacity for mathematics achievement in 1,254 Grade 2, 4 and 6 children. The large sample size assured high power and low false report probability and allowed us to determine effect sizes precisely. We used reading decoding as a control outcome measure to test whether findings were specific to mathematics. Bayesian analysis allowed us to provide support for both null and alternative hypotheses. We found very weak zero‐order correlations between ANS measures and math achievement. These correlations were not specific to mathematics, became non‐significant once intelligence was considered and ANS measures were not selected as predictors of math by regression models. In contrast, overall SNC accuracy and spatial WM measures were reliable and mostly specific predictors of math achievement. Verbal short‐term and WM and SNC reaction time were predictors of both reading and math achievement. We conclude that ANS tasks are not suitable as measures of math development in school‐age populations. In contrast, all other cognitive functions we studied are promising markers of mathematics development.

AbstractWe determined how various cognitive abilities, including several measures of a proposed domain‐specific number sense, relate to mathematical competence in nearly 100 9‐year‐old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo‐spatial short‐term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short‐term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non‐verbal intelligence measures were also non‐significant predictors when added to our model. Number sense variables were non‐significant predictors in the model and they were also non‐significant predictors when entered into regression analysis with only a single visuo‐spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular 'number sense'. We suggest an 'executive memory function centric' model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

AbstractWe studied whether the origins of math anxiety can be related to a biologically supported framework of stress induction: (un)controllability perception, here indicated by self‐reported independent efforts in mathematics. Math anxiety was tested in 182 children (8‐ to 11‐year‐olds).Latent factor modelingwas used to test hypotheses on plausible causal processes and mediations within competing models in quasi‐experimental contrasts. Uncontrollability perception in mathematics, or (in)dependence of efforts, best fit the data as an antecedent of math anxiety. In addition, the relationship of math anxiety with gender was fully mediated by adaptive perception of control (i.e. controllability). That is, young boys differ from girls in terms of their experience of control in mathematics learning. These differences influence math anxiety. Our findings are consistent with recent suggestions in clinical literature according to which uncontrollability makes women more susceptible to fear and anxiety disorders.A video abstract of this article can be viewed athttp://www.youtube.com/watch?v=I4b_47Y-e_U