Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic and non-symbolic approximate division. Subjects were presented with non-symbolic (dot array) or symbolic (Arabic numeral) dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children (Experiment 1 N = 89, Experiment 2 N = 42) and adults (Experiment 3 N = 87) were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System (ANS) acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction.
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Neural representational similarity between symbolic and non‐symbolic quantities predicts arithmetic skills in childhood but not adolescence
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 problem‐solving 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.
more » « less- NSF-PAR ID:
- 10445815
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Developmental Science
- Volume:
- 24
- Issue:
- 6
- ISSN:
- 1363-755X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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