What counts? Sources of knowledge in children’s acquisition of the successor function

Schneider, Rose M.; Sullivan, Jess; Guo, Kaiqi; Barner, David

doi:10.31234/osf.io/vu47r

Cited by 3 publications

(3 citation statements)

References 5 publications

(17 reference statements)

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“…This difference suggests that subset‐knowers’ ability to label Unit Task addition events is likely not due to reasoning about an isomorphism between count list successor relations and set operations. However, consistent with previous findings (Schneider et al, 2021), in a separate GLMM we found no difference in accuracy between these two tasks for CP‐knowers ( β = 0.33, p =0.11). While CP‐knowers’ equivalent performance on these tasks is compatible with Structure Mapping, given this group's chance performance for sets of 4 and 5, and the small size of this effect ( d =0.26) it is possible that such a mapping is fragile at this point in development and may not be deployed by all children.…”

Section: Methodssupporting

confidence: 92%

“…Although we might expect lower Next Number performance in comparison to the Unit Task due to response format (free response vs. two‐alternative forced‐choice), we address this issue by exploring whether performance on these tasks differs as a function of CP‐knower status, which would suggest a difference in numerical knowledge, rather than response format. Previous work finds a strong correlation between these two tasks among older CP‐knowers, and this correlation remains when both tasks use an open‐ended response format (Schneider, Sullivan, Guo, & Barner, 2021).…”

Section: Methodsmentioning

confidence: 90%

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Starting small: exploring the origins of successor function knowledge

Schneider

Pankonin

Schachner

et al. 2021

Developmental Science

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Although most U.S. children can accurately count sets by 4 years of age, many fail to understand the structural analogy between counting and numberthat adding 1 to a set corresponds to counting up 1 word in the count list. While children are theorized to establish this Structure Mapping coincident with learning how counting is used to generate sets, they initially have an item-based understanding of this relationship, and can infer that, e.g, adding 1 to "five" is "six", while failing to infer that, e.g., adding 1 to "twenty-five" is "twenty-six" despite being able to recite these numbers when counting aloud. The item-specific nature of children's successes in reasoning about the relationship between changes in cardinality and the count list raises the possibility that such a Structure Mapping emerges later in development, and that this ability does not initially depend on learning to count. We test this hypothesis in two experiments and find evidence that children can perform item-based addition operations before they become competent counters. Even after children learn to count, we find that their ability to perform addition operations remains item-based and restricted to very small numbers, rather than drawing on generalized knowledge of how the count list represents number. We discuss how these early item-based associations between number words and sets might play a role in constructing a generalized Structure Mapping between counting and quantity.

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Section: Methodssupporting

confidence: 92%

Section: Methodsmentioning

confidence: 90%

Starting small: exploring the origins of successor function knowledge

Schneider

Pankonin

Schachner

et al. 2021

Developmental Science

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“…However, knowledge of the cardinality principle alone does not guarantee a child's understanding of the successor function for all numbers. It takes CP-knowers approximately two years to learn the specific successor of every number in their count list, and to learn that all numbers have a successor--learning that is aided by their experience with simple n+1 addition facts in early elementary school (Cheung et al, 2017;R. M. Schneider et al, 2020).…”

Section: The Real Preschoolers Of Orange Countymentioning

confidence: 99%

The real preschoolers of Orange County: Early number learning in a diverse group of children

Sarnecka¹,

Negen²,

Scalise³

et al. 2021

Preprint

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The authors assessed a battery of number skills in a sample of over 500 preschoolers, including bothmonolingual and bilingual/multilingual learners from households at a range of socio-economic levels.Receptive vocabulary was measured in English for all children, and also in Spanish for those who spoke it.The first goal of the study was to describe entailment relations among numeracy skills: Findings indicatedthat transitive and intransitive counting were jointly required for understanding cardinality; that cardinalityand knowledge of written number symbols were both required for using number lines. The study’s secondgoal was to describe relations between symbolic numeracy and language context (i.e., monolingual vs.bilingual contexts), separating these from well-documented socio-economic influences such as householdincome and parental education: Language context had only a modest effect on numeracy, with nodifferences detectable on most tasks. However, a difference did appear on the scaffolded number-line task,where bilingual learners performed slightly better than monolinguals. The third goal of the study was to findout whether symbolic number knowledge for one subset of children (Spanish/English bilingual learnersfrom low-income households) differed when tested in their home language (Spanish) vs. their language ofpreschool instruction (English): Findings indicated that children performed as well or better in English thanin Spanish for all measures, even when their receptive vocabulary scores in Spanish were higher than inEnglish.

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