The development and assessment of counting-based cardinal number concepts

Baroody, Arthur J.; Lai, Meng-Lung

doi:10.1007/s10649-022-10153-5

Cited by 8 publications

(6 citation statements)

References 37 publications

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“…Based on these considerations and others detailed in Baroody et al (2017) and Baroody and Lai (2022), we propose an alternative course of verbal cardinality development summarized in Table 1. This model diverges from the conventional wisdom regarding Phase 1 in that it posits successive development of small-n recognition and creation-a proposition that is tested by the present analysis.…”

Section: Theoretical Argumentmentioning

confidence: 87%

“…This model diverges from the conventional wisdom regarding Phase 1 in that it posits successive development of small-n recognition and creation-a proposition that is tested by the present analysis. For evidence supporting the sequential development of analogous subphases for Phase 2, see and Baroody and Lai (2022).…”

Section: Theoretical Argumentmentioning

confidence: 97%

“…This developmental difference has been explained in terms of the additional performance factors required to count out a specified number of items(Resnick & Ford, 1981) or its new conceptual demands(Fuson, 1988; but cf. Sarnecka & Carey, 2008; seeBaroody & Lai, 2022, for a review).…”

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confidence: 99%

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The development and assessment of early cardinal-number concepts

et al. 2023

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Number-recognition tasks, such as the how-many task, involve set-to-word mapping, and number-creation tasks, such as the give-n task, entail word-to-set mapping. The present study involved comparing sixty 3-year-olds’ performance on the two tasks with collections of one to three items over three time points about 3 weeks apart. Inconsistent with the sparse evidence indicating equivalent task performance, an omnibus test indicated that success differed significantly by task (and set size but not by time). A follow-up analysis indicated that the hypothesis that success emerges first on the how-many task was, in general, significantly superior to the hypothesis of simultaneous development. It further indicated the how-many-first hypothesis was superior to a give-n-first hypothesis for sets of three. A theoretical implication is that set-to-word mapping appears to develop before word-to-set mapping, especially in the case of three. A methodological implication is that the give-n task may underestimate a key aspect of children’s cardinal understanding of small numbers. Another is that the traditional give-n task, which requires checking an initial response by one-to-one counting, confounds pre-counting and counting competencies.

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Section: Theoretical Argumentmentioning

confidence: 87%

Section: Theoretical Argumentmentioning

confidence: 97%

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The development and assessment of early cardinal-number concepts

et al. 2023

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“…Our findings support the conclusion that children who do not yet use counting to track cardinality already understand fundamental aspects about the structure of the number system (as laid out by Barner, 2017). We know from previous research that a child who does not yet know the cardinal principle and only knows the cardinalities for a few numbers, say up to three, already knows (1) how numbers "one, two, three" go in order in the number sequence (Litkowski et al, 2020;Wynn, 1990), (2) how this number sequence can be applied to sets in the act of counting (even though they do not yet functionally understand the cardinal principle) (Gordon et al, 2019;Cheung et al, 2022, Baroody & Lai, 2022 and ( 3) how numbers "one, two, three" each represent a unique cardinality of a set one = |{a}|, two = |{a, b}| and three = |{a, b, c}| (Le Corre & Carey, 2007). Our findings together with previous research suggest they additionally have access to reasoning about set-based operations (Schneider et al, 2022a).…”

Section: Children Learn the Successor Function Alongside The Cardinal...mentioning

confidence: 99%

Children’s early understanding of the successor function

Wege¹,

Inglis²,

Gilmore³

2023

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Children learn the cardinalities of the first numbers one, two, three and four before they learn how counting tracks cardinality for all numbers. It may be that when children start to understand counting, they also discover the structure of the number system. At this stage they may understand that the cardinality of a set is the last number assigned after counting each item (cardinal principle) and that each number represents the cardinality of the set created by adding one to an empty set for every count it takes to reach that number (successor function). We tested this by assessing children’s early understanding of the successor function in relation to their cardinality knowledge. Children who were not yet cardinal principle knowers demonstrated understanding of the successor function within the limits of their cardinality knowledge. Our findings suggest that children have some structural knowledge of the number system before learning how counting tracks cardinality. We discuss how continued counting practice may eventually allow children to expand this knowledge across all numbers.

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“…task or the "what's on this card?" task (Baroody & Lai, 2022;Mou et al, 2021;Marchand et al, 2022) or other insights into the principles that guide meaningful counting (Jara-Ettinger et al, 2016;Schneider et al, 2022, Schneider et al, 2021Davidson et al, 2012, Cheung et al, 2017.…”

Section: Implications For the Knower-level Frameworkmentioning

confidence: 99%

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

Wege¹,

Bourque²,

Merkley³

et al. 2022

Preprint

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The Give-N (give-a-number) task has become a popular assessment of children’s number word learning since Wynn’s (1990; 1992) seminal work 30 years ago. Using the Give-N task, numerous studies have shown that children learn the first few number words slowly and effortfully, before they understand how counting represents number. We conducted a systematic review of studies using the Give-N task to provide an overview of the task’s theoretical and methodological significance and document variations in its administration and scoring. We found quite a lot of variation in how the task has been used and interpreted in the literature. Such variations include, for example, whether children are asked to count on every trial, whether the study adopts a titration method, the type of stimuli used, and the scoring criteria used for knower-level classifications. Moving forward with theory and methodology for research in children’s acquisition of number words and counting requires 1) reflection on the limitations of classifying children’s performance on the Give-N task in the knower-level framework and 2) consistent reporting of Give-N methodology.

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The development and assessment of counting-based cardinal number concepts

Cited by 8 publications

References 37 publications

The development and assessment of early cardinal-number concepts

The development and assessment of early cardinal-number concepts

Children’s early understanding of the successor function

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

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