Even at young ages, children self-report experiencing math anxiety, which negatively relates to their math achievement. Leveraging a large dataset of first and second grade students' math achievement scores, math problem solving strategies, and math attitudes, we explored the possibility that children's math anxiety (i.e., a fear or apprehension about math) negatively relates to their use of more advanced problem solving strategies, which in turn relates to their math achievement. Our results confirm our hypothesis and, moreover, demonstrate that the relation between math anxiety and math problem solving strategies is strongest in children with the highest working memory capacity. Ironically, children who have the highest cognitive capacity avoid using advanced problem solving strategies when they are high in math anxiety and, as a result, underperform in math compared with their lower working memory peers.

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assistance with the study and Booil Jo and Jane P. Kim for advice on statistical analysis. We also thank Kristen Pilner Blair for assistance with the development of the Restaurant Game as part of number sense training program and Valentin Iovene for contributing to the development of reverse meta-analysis tool.

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Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low—compared to high—math anxious individuals perform better when they activate this network less—a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently.

The odd–even effect in numerical processing has been explained as the easier processing of even numbers compared with odd numbers. We investigated this effect in Sudoku puzzles, a reasoning problem that uses numbers but does not require arithmetic operations. Specifically, we asked whether the odd–even effect occurred with Sudoku puzzles and whether individual differences in working memory (WM), aging, and experience with Sudoku modulated this effect. We manipulated the presence of odd and even numbers in Sudoku puzzles, measured WM with the Wisconsin Card Sorting Test and backward digit span task, tested older and younger adults, and collected Sudoku experience frequency. Performance on Sudoku was more accurate for even puzzles than odd ones. Younger, experienced, and higher-WM participants were more accurate on Sudoku, but these individual difference variables did not interact with the odd–even effect. Odd numbers may impose more cognitive load than even numbers, but future research is needed to examine how age, experience, or WM may influence the odd–even effect.

Mathematical knowledge is constructed hierarchically from basic understanding of quantities and the symbols that denote them. Discrimination of numerical quantity in both symbolic and non-symbolic formats has been linked to mathematical problemsolving abilities. However, little is known of the extent to which overlap in quantity representations between symbolic and non-symbolic formats is related to individual differences in numerical problem solving and whether this relation changes with different stages of development and skill acquisition. Here we investigate the association between neural representational similarity (NRS) across symbolic and non-symbolic quantity discrimination and arithmetic problem-solving skills in early and late developmental stages: elementary school children (ages 7-10 years) and adolescents and young adults (AYA, ages 14-21 years). In children, cross-format NRS in distributed brain regions, including parietal and frontal cortices and the hippocampus, was positively correlated with arithmetic skills. In contrast, no brain region showed a significant association between cross-format NRS and arithmetic skills in the AYA group. Our findings suggest that the relationship between symbolic-non-symbolic NRS and arithmetic skills depends on developmental stage. Taken together, our study provides evidence for both mapping and estrangement hypotheses in the context of numerical problem solving, albeit over different cognitive developmental stages.