Acquiring the cardinal knowledge of number words: A conceptual replication

Abstract

Understanding the way in which counting represent numerosities was shown to be a long-lasting process. As shown in the Give-a-number task, acquiring the meanings of verbal number words goes through successive developmental stages in which children first learn the cardinal meanings of small number words one at a time before generalizing the cardinal principle they have induced from the first three number words to all number words within their counting range. This acquisition would take about a year, and would be completed by the age of 3 ½ years. The aim of the present study was to provide a conceptual replication of the developmental sequence described in Wynn’s study nearly 30 years ago using the Give-a-number task. A first cross-sectional study was conducted on 213 Belgian children aged between 39 and 74 months using the Give-a-number task to examine the developmental pattern and the influence of age on this acquisition. The time span of acquisition was examined in a second study in which 34 children were tested five times every months between the age of 36 to 52 months. Results showed that acquiring the cardinal meanings of number words spread out over a protracted period, far more extended than assumed by Wynn. Furthermore, children do not generalize all-at-once to large number words, the cardinal knowledge they learned on small number words. Rather, number words were found to be learned one at a time in a really progressive manner. Results were discussed with regard to their implications for the existing theories and in relation with other tasks assessing the acquisition of verbal number symbols.

Early number word learning: Associations with domain-general and domain-specific quantitative abilities

“…In addition, our finding also suggests that children’s age is a consistent predictor of children’s cardinal number development. This finding echoes with many previous findings showing that children’s cardinal number knowledge increased with age (e.g., Rousselle and Vossius, 2021 ). The age-related change is possibly related to the growing experiences with counting in everyday play and activities ( Gallistel and Gelman, 1992 ).…”

Children’s early understanding of the successor function

“…Their knowledge of the structure of the number system is hence limited at four and they lack insight into the set operations that relate numbers beyond four to each other, e.g., that six is exactly one more than five which is one more than four. To expand their knowledge of the structure of the number system to larger numbers, cardinal principle knowers may need further practice with the exact order of the number sequence and the relation of numbers with each other (Barner, 2017;Buijsman, 2019;Speapen et al, 2018;Rousselle & Vossius, 2021).…”

Thirty years of the Give-N task: A systematic review, reflections, and recommendations

“…Wynn (1990) for instance scored children as Counters, even if they counted incorrectly, as long as they counted in response to the Give-N requests. Children who do not spontaneously count aloud may also be scored as Counters if they give items deliberately one by one or point at items one by one (Rousselle & Vossius, 2021). It may not always be obvious whether children are engaged in counting behaviour and reliable scoring can require laborious double coding of video recordings (Jara-Ettinger et al, 2016;Posid & Cordes, 2018).…”

“…For example, subset knowers have some knowledge about numbers beyond their knower-level and some of them also recognize the procedural aspect of the cardinal principle (Cheung et al, 2021;Gunderson, Spaepen, Gibson, Goldin-Meadow, & Levine, 2015;O'Rear, McNeil & Kirkland, 2020;Wagner, Chu, & Barner, 2019). On the other hand, cardinal principle knowers may still lack fundamental insights into the cardinal principle and the logic of counting (Jacobs, Flowers, & Jara-Ettinger, 2021;Jara-Ettinger et al, 2016;Le Corre, 2014;Schneider et al, 2022;Schneider et al, 2021;Davidson, Eng & Barner, 2012, Cheung et al, 2017Cheung et al, 2015;Krajcsi, 2022;Rousselle & Vossius, 2021). Taken together, these findings challenge the assumption of a sharp discontinuity that differentiates subset knowers from cardinal principle knowers.…”

“…After 30 years of knower-levels, a challenge for future research into children's number word and counting acquisition will be to disentangle how theories have been shaped by the methodology of the knower-level framework and vice versa. The detailed discussion of those theories is beyond the scope of this review (but see Carey & Barner, 2019;Broody & Lai, 2022;Cheung & Ansari, 2019;Kracsji 2021;Marchand et al, 2022;Rousselle & Vossius, 2021;Sarnecka, Goldman & Slusser, 2015;Sella et al, 2021;Simon, Della Volpe & Velamur., 2021), but our study highlights some open questions with theoretical implications that should be addressed in future studies. For example, can we reliably differentiate subset knowers from cardinal principle knowers?…”