To infinity and beyond: Children generalize the successor function to all possible numbers years after learning to count

@article{Cheung2017ToIA,
  title={To infinity and beyond: Children generalize the successor function to all possible numbers years after learning to count},
  author={Pierina Cheung and Miriam Rubenson and David Barner},
  journal={Cognitive Psychology},
  year={2017},
  volume={92},
  pages={22-36}
}

Figures and Tables from this paper

Counting to Infinity: Does Learning the Syntax of the Count List Predict Knowledge That Numbers Are Infinite?
TLDR
How children discover this recursive function is explored, and whether it might be related to discovering productive morphological rules that govern language-specific counting routines, to suggest that children as young as 4 years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range.
Do children use language structure to discover the recursive rules of counting?
TLDR
It is concluded that learning productive rules of counting is a critical step in acquiring knowledge of recursive successor function across languages, and that the timeline for this learning varies as a function of counti list transparency.
Do children's number words begin noisy?
TLDR
Before children learn exact meanings for words like one, two, three, and four, they first acquire noisy preliminary meanings for these words, and there is no reliable evidence of preliminary meaning for larger meanings, so Give-a-Number cannot be used to readily identify signatures of the approximate number system.
Is thirty-two three tens and two ones? The embedded structure of cardinal numbers
TLDR
It is proposed that the syntax for building complex numerals, not the successor principle, represents a structural platform for numerical thinking in young children and regularity in numerical syntax facilitates the acquisition of generative properties of numbers.
Two roads to the successor axiom
TLDR
It is argued that when the authors look at children’s responses in interviews, the time when they learn the successor axiom and the intermediate learning stages they find themselves in, that there is an empirically viable alternative.
Language, procedures, and the non-perceptual origin of number word meanings*
  • D. Barner
  • Psychology
    Journal of Child Language
  • 2017
TLDR
It is argued that the integers are not learned from perceptual systems, but arise to explain perception, and small (~1–4) and large (~5+) numbers arise both historically and in individual children via distinct mechanisms, constituting independent learning problems.
...
...

References

SHOWING 1-10 OF 66 REFERENCES
Does learning to count involve a semantic induction?
How counting represents number: What children must learn and when they learn it
The development of language and abstract concepts: the case of natural number.
TLDR
It is suggested that 3-year-old children interpret number words by relating them to 2 distinct preverbal systems that capture only limited numerical information.
Why is number word learning hard? Evidence from bilingual learners
Pragmatic inference, not semantic competence, guides 3-year-olds' interpretation of unknown number words.
TLDR
Evidence is presented that some of children's apparent successes are best explained not by domain-specific semantic understanding of number but instead by language-general pragmatic abilities, suggesting that their judgments for numerals may not have relied on semantic knowledge that numerals have precise meanings.
Learning to Represent Exact Numbers - eScholarship
This article focuses on how young children acquire concepts for exact, cardinal numbers (e.g., three, seven, two hundred, etc.). I believe that exact numbers are a conceptual structure that was
The Role of the Number-After Rule in the Invention of Computational Shortcuts
How children invent a counting-on from the larger addend (COL) strategy is un-clear. An effort to understand how a child classified as mentally handicapped devised this strategy has suggested a
Children's understanding of counting
Levels of number knowledge during early childhood.
...
...