Understanding of exact equality emerges after and builds on symbolic number knowledge
Bibliographic Data
| ID | 21306935 |
|---|---|
| Authors | Chi‐Chuan Chen (0000-0003-3659-8019, University of Illinois Urbana-Champaign, corresponding author), Chi-Chuan Chen, Daniel C Hyde (0000-0001-9888-5916, University of Illinois Urbana-Champaign) |
| Year | 2025 |
| Volume | 264 |
| Pages | 106226 |
| Publication date | 2025-11-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Cognition (JOURNAL) |
| Journal identifiers | ISSN: 0010-0277 • E-ISSN: 1873-7838 |
| Publisher | Elsevier BV (PUBLISHER) |
| DOI | 10.1016/j.cognition.2025.106226 |
| PMID | 40596802 |
| OpenAlex | W4411874132 |
| Language | EN |
| References cited | 49 |
Establishing whether two sets of objects have the same number of objects turns out to be surprisingly challenging for children even if they have some basic number word and counting knowledge. Here we study the relationship between understanding of exact equality of sets and symbolic number knowledge in preschool children (N = 208, Age = 2.89-5.09 years) at various stages of symbolic number word acquisition. We gave children two classic verbal symbolic number word knowledge tasks (Give-N, How Many?) and two comparable but non-verbal set-matching tasks in which they were asked to produce a set of objects that numerically matched a target set. We find strong evidence that symbolic number knowledge is related to but precedes set-matching for exact equality, both replicating and extending recent findings. Specifically, set-matching accuracy was better for children who understood symbolic number cardinality compared to those who did not, even after accounting for age and executive functions. Furthermore, this effect was seen across the range of set sizes tested (1-8), including smaller set sizes (1-4) typically thought to be within the cognitive limits to be compared for exact equality non-verbally. Finally, set-matching performance was below ceiling even at set sizes corresponding to individual children's specific level of symbolic number knowledge (N) as well as the preceding quantity (N-1). Together these results suggest that understanding of exact equality builds on symbolic number knowledge. More broadly, our results support the emerging view that understanding symbolic number cardinality is only one early step towards understanding the symbolic number system
Arithmetic · Cardinal number (linguistics) · Cardinality (data modeling) · Cognition · Cognitive psychology · Linguistics · Matching (statistics) · Numerical cognition · Set (abstract data type) · Statistics · The Symbolic · Cognitive and developmental aspects of mathematical skills · Computer Science · Mathematics · Mathematics Education and Teaching Techniques · Psychology · Reading and Literacy Development · Theoretical Computer Science
Children’s Counting and Concepts of Number
Executive function in early childhood
Children's acquisition of the number words and the counting system
Numerical Cognition Without Words
One, two, three, four, nothing more
Children's understanding of counting
Foundations of mathematics and literacy
How counting represents number
Preverbal and verbal counting and computation
Number as a cognitive technology
Core systems of number
Age differences in short-term retention of rapidly changing information.
Fitting Linear Mixed-Effects Models Using lme4
Counting and the ontogenetic origins of exact equality
Assessing the knower-level framework
Directionality in the interrelations between approximate number, verbal number, and mathematics in preschool-aged children
What Counts? Sources of Knowledge in Children’s Acquisition of the Successor Function
Comparing set-to-number and number-to-set measures of cardinal number knowledge in preschool children using latent variable modeling
Learning to represent exact numbers
Multiple cues for quantification in infancy
| Citation velocity | historical |
|---|---|
| Highly cited | No |