This content will become publicly available on January 6, 2027

Title: Development and assessment of early counting-based cardinal concepts
The purpose of the present research was to evaluate two different theo- retical perspectives of cardinality and counting development. According to one perspective, the cardinality concept underlying meaningful 1-to- 1-counting (“How many...?”) provides the basis for the later develop- ment of a more advanced cardinality concept that underlies meaningful counting-out (“Give n...”). According to another, a single cardinality concept underlies the development of both meaningful 1-to-1 counting and counting out a specified number of items. Thirty preschoolers 38- to 51-months-olds were pretested. Seven children who were develop- mentally ready for cardinality training were individually trained and re- tested. Overall, the evidence of the pre- and post-testing was more consistent with stepwise cardinality and counting development. For example, some children constructed the basic cardinality concept and achieved meaningful counting without understanding the more advanced cardinality concept and achieving meaningful counting out.  more » « less
Award ID(s):
2201039
PAR ID:
10708321
Author(s) / Creator(s):
; ; ;
Editor(s):
Lehalle, Henri; Tijus, Charles
Publisher / Repository:
Cairn.info for Presses Universitaires de France
Date Published:
Journal Name:
Enfance
Volume:
n° 254
Issue:
4
ISSN:
0013-7545
Page Range / eLocation ID:
549 to 559
Subject(s) / Keyword(s):
Cardinality principle counting give-n task, mathematics
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract How do young children develop a concept of equity? Infants prefer dividing resources equally and expect others to make such distributions. Between the ages of 3–8, children begin to exhibit preferences to avoid inequitable outcomes in their distributions, dividing resources unequally if the result of that distribution is a more equitable outcome. Four studies investigated children’s developing preferences for generating equitable distributions, focusing on the mechanisms for this development. Children were presented with two characters with different amount of resources, and then a third character who will distribute more resources to them. Three- to 8-year-olds were asked whether the third character should give an equal number of resources to the recipients, preserving the inequity, or an unequal number to them, creating an equitable outcome. Starting at age 7, children showed a preference for equitable distributions (Study 1, N = 144). Studies 2a (N = 72) and 2b (N = 48) suggest that this development is independent of children’s numerical competence. When asked to take the perspective of the recipient with fewer resources, 3- to 6-year-olds were more likely to make an equitable distribution (Study 3, N = 122). These data suggest that social perspective taking underlies children’s prosocial actions, and supports the hypothesis that their spontaneous capacity to take others’ perspectives develops during the early elementary-school years. 
    more » « less
  2. null (Ed.)
    How do young children develop a concept of equity? Infants prefer dividing resources equally and expect others to make such distributions. Between the ages of 3–8, children begin to exhibit preferences to avoid inequitable outcomes in their distributions, dividing resources unequally if the result of that distribution is a more equitable outcome. Four studies investigated children’s developing preferences for generating equitable distributions, focusing on the mechanisms for this development. Children were presented with two characters with different amount of resources, and then a third character who will distribute more resources to them. Three- to 8-year-olds were asked whether the third character should give an equal number of resources to the recipients, preserving the inequity, or an unequal number to them, creating an equitable outcome. Starting at age 7, children showed a preference for equitable distributions (Study 1, N = 144). Studies 2a (N = 72) and 2b (N = 48) suggest that this development is independent of children’s numerical competence. When asked to take the perspective of the recipient with fewer resources, 3- to 6-year-olds were more likely to make an equitable distribution (Study 3, N = 122). These data suggest that social perspective taking underlies children’s prosocial actions, and supports the hypothesis that their spontaneous capacity to take others’ perspectives develops during the early elementary-school years. 
    more » « less
  3. The general aim of the research was to conduct a rare test of the efficacy of hypothetical learning progressions (HLPs) and a basic assumption of basing instruction on HLPs, namely teaching each successive level is more efficacious than skipping lower levels and teaching the target level directly. The specific aim was evaluating whether counting-based cardinality concepts unfold in a stepwise manner. The research involved a pretest—delayed-posttest design with random assignment of 14 preschoolers to two conditions. The experimental intervention was based on an HLP for cardinality development (first promoting levels that presumably support and are necessary for the target level and then the target knowledge). The active-control treatment entailed a Teach-to-Target approach (first promoting irrelevant cardinality knowledge about recognizing written numbers and then directly teaching the same target-level goals with the same explicit instruction and similar games). A mix of quantitative and qualitative analyses indicated HLP participants performed significantly and substantially better than Teach-to-Target participants on target-level concept and skill measures. Moreover, the former tended to make sensible errors, whereas the latter generally responded cluelessly. 
    more » « less
  4. English, Lyn (Ed.)
    The basis for meaningful one-to-one counting is the cardinality principle (CP): The last number word used in counting a collection indicates its total. A popular view is that CP development builds on subitizing: the immediate association and labeling of a small collection with a number word. Simon etal. (2021) challenged the theoretical rationale and supporting evidence of this view, arguing in part that subitizing does not provide an adequate conceptual basis for constructing CP knowledge. The present review entails an examination of the theoretical role of subitizing in the construction of the CP and an evaluation of the evidence supporting it. 
    more » « less
  5. Children’s early understanding of mathematics provides a foundation for later success in school. Identifying ways to enhance mathematical instruction is crucial to understanding the ideal ways to promote academic success. Previous work has identified mathematical language (i.e., the words and concepts related to early mathematical development such as more, same, or similar) as a key mechanism that can be targeted to improve children’s development of early numeracy skills (e.g., counting, cardinality, and addition). Current recommendations suggest a combination of numeracy instruction and quantitative language instruction to promote numeracy skills. However, there is limited direct support of this recommendation. The goal of the proposed study is to compare the unique and combined effects of each type of instruction on children’s numeracy skills in the context of picture book reading. We randomly assigned 234 children (ages 3–5) to one of four conditions where they worked with trained project staff who read picture books targeting: (a) quantitative language only (e.g., more or less), (b) numeracy only (e.g., cardinality, addition), (c) combined [quantitative language + numeracy], or (d) nonnumerical (active control) picture books. Results revealed no significant effects of the quantitative language only or numeracy only conditions, but mixed effects of the combined condition. These findings indicate that more work is needed on how mathematical language and numeracy instruction should best be delivered to preschool children. 
    more » « less