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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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Sharing scenarios facilitate division performance in preschoolers.
Understanding division is critical for later mathematical achievement. Yet division concepts are difficult to grasp and are often not explicitly taught until middle childhood. Given the structural similarity between sharing and division, we investigated whether contextualizing division problems as sharing scenarios improved preschool-aged children’s abilities to solve them, as compared with other arithmetic problems which do not share structural similarities with sharing. Preschoolers (N = 113) completed an addition, subtraction, and division problem in either a sharing context that presented arithmetic via contextualized sharing scenarios, or a comparable, linguistically-matched non-social context (randomly assigned). Children were assessed on their formal, verbal responses and their informal, non-verbal, action-based responses (abilities to solve the problems using manipulatives) to these arithmetic problems. Most critically, context predicted children’s performance on the division, but not the addition or subtraction trial, supporting a structural link between sharing and division. Results also revealed that children’s action-based responses to the arithmetic problems were much more accurate than their verbal ones. Results are discussed in terms of the conceptual link between division and sharing.
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- Award ID(s):
- 1920725
- PAR ID:
- 10233025
- Date Published:
- Journal Name:
- Cognitive development
- Volume:
- 56
- ISSN:
- 0885-2014
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/https://doi.org/10.1016/j.cogdev.2020.100954
