Poster #13 - Understanding of Exact Equality Emerges After and Builds on Symbolic Number Knowledge

• In Event: Poster Session 07

Abstract

Children have some capacity to establish the numerical equality sets of items before they have mastered counting, but these abilities appear to be limited to sets containing only a few items (< 4, Feigenson et al., 2004; Izard et al., 2014). Some propose that establishing exact numerical equality between larger sets has emerges jointly as a consequence of understanding counting and the associated cardinality principle (CP-knowledge, i.e., knowing how counting works; Sarnecka & Wright, 2013). However, both classic Piagetian number-conservation failures (Piaget, 1965) as well as more recent findings suggest that understanding of exact equality may not come with competency in counting and, instead, follows a more prolonged developmental trajectory (Schneider et al., 2022).
In this study, we further examine the emergence and relationship between of symbolic number knowledge and exact equality using two classic counting tasks (Give-N, How Many?), and two comparable nonverbal, non-symbolic set matching tasks (Nonverbal Give-N Matching; Non-verbal How Many? Matching) in a sample 201 preschool children (M = 3.87 years, SD = .19 years, range 2.89 – 5.09).
Analyzing the same set sizes (3, 4, 6, and 8) in our data as in Schneider et al, we replicated their finding that children’s exact non-symbolic set-matching accuracy is predicted by their CP-knowledge even after controlling for age (Fig 1). Further analyzing our data, including the full range of set sizes we tested (1-8), we found that children’s exact set-match accuracy lags behind their symbolic number knowledge. That is, children appear to acquire cardinal number knowledge of a given number (N) before they are able to accurately match sets of N items (Fig 2 ). This pattern suggests that understanding a given number word and how to use counting to enumerate a set with that number does not necessarily translate to being able to equate two sets of that number. We also find that accuracy in establishing exact equality for smaller numbers (1-3) is substantially improved in children who have mastered basic cardinal number knowledge relative to children who have not (Give-N abacus: t(377.04) = -5.099, p < 0.001; How Many? abacus: t(372.58) = -2.880, p = 0.004). This stands contrast to the assumption that exact equality can be achieved for smaller quantities through an earlier emerging non-verbal object tracking system ( Shusterman et al., 2017), and instead suggests that symbolic number knowledge may be necessary pre-requisite but still may not be sufficient for a complete understanding of exact equality of sets (Schneider et al., 2022).

Authors

• Chi-Chuan Chen, University of Illinois at Urbana-Champaign
  Presenting Author

• Daniel C. Hyde, University of Illinois at Urbana-Champaign