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

2016 ◽  
Author(s):  
Pierina Cheung ◽  
Miriam Rubenson ◽  
David Barner
Keyword(s):  
Natural Number ◽  
Word Learning ◽  
Number Word ◽  
Successor Function ◽  
Developmental Transition

Recent accounts of number word learning posit that when children learn toaccurately count sets (i.e., become "cardinal principle" or "CP" knowers),they have a conceptual insight about how the count list implements thesuccessor function - i.e., that every natural number *n *has a successordefined as *n+1* (Carey, 2004, 2009; Sarnecka & Carey, 2008). However,recent studies suggest that knowledge of the successor function emergessometime after children learn to accurately count, though it remainsunknown when this occurs, and what causes this developmental transition. Wetested knowledge of the successor function in 100 children aged 4 through 7and asked how age and counting ability are related to: (1) children'sability to infer the successors of all numbers in their count list, and (2)knowledge that *all *numbers have a successor. We found that children donot acquire these two facets of the successor function until they are about5.5 or 6 years of age - roughly 2 years after they learn to accuratelycount sets and become CP-knowers. These findings show that acquisition ofthe successor function is highly protracted, providing the strongestevidence yet that it cannot drive the cardinal principle induction. Wesuggest that counting experience, as well as knowledge of recursivecounting structures, may instead drive the learning of the successorfunction.

scholarly journals Counting to Infinity: Does learning the syntax of the count list predict knowledge that numbers are infinite?

2020 ◽  
Author(s):  
Junyi Chu ◽  
Pierina Cheung ◽  
Rose M. Schneider ◽  
Jess Sullivan ◽  
David Barner
Keyword(s):  
Natural Number ◽  
Recursive Function ◽  
Implicit Knowledge ◽  
Successor Function ◽  
Counting Rule ◽  
Number Words ◽  
The Us ◽  
Counting Range ◽  
Per Se

By around the age of 5½, many children in the US judge that numbers never end, and that it is always possible to add +1 to a set. These same children also generally perform well when asked to label the quantity of a set after 1 object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: every natural number, n, has a successor, n+1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language-specific counting routines (e.g., the rules in English that represent base 10 structure). We tested 4- and 5-year-old children’s knowledge of counting with three tasks, which we then related to (1) children’s belief that 1 can always be added to any number (the successor function), and (2) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge wasn’t directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as four years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end.

scholarly journals Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners

2016 ◽  
Vol 88 ◽  
pp. 162-186 ◽  
Author(s):  
Mathieu Le Corre ◽  
Peggy Li ◽  
Becky H. Huang ◽  
Gisela Jia ◽  
Susan Carey
Keyword(s):  
Word Learning ◽  
English Learners ◽  
Number Word ◽  
Early Number

scholarly journals Do Children Use Language Structure to Discover the Recursive Rules of Counting?

2019 ◽  
Author(s):  
Rose M. Schneider ◽  
Jess Sullivan ◽  
Franc Marušič ◽  
Rok Žaucer ◽  
Priyanka Biswas ◽  
...  
Keyword(s):  
Natural Number ◽  
Task Performance ◽  
Mathematical Knowledge ◽  
Analytic Approach ◽  
Successor Function ◽  
Recursive Structure ◽  
Critical Step ◽  
Language Structure ◽  
Foundational Principle ◽  
Linguistic Rules

We test the hypothesis that children acquire the successor function — a foundational principle stating that every natural number n has a successor n+1 — by learning the productive linguistic rules that govern verbal counting. Previous studies report that speakers of languages with less complex count list morphology have greater counting and mathematical knowledge at earlier ages in comparison to speakers of more complex languages (e.g., Miller & Stigler, 1987). Here, we tested whether differences in count list transparency affected children’s acquisition of the successor function in three languages with relatively transparent count lists (Cantonese, Slovenian, and English) and two languages with relatively opaque count lists (Hindi and Gujarati). We measured 3.5- to 6.5-year-old children’s mastery of their count list’s recursive structure with two tasks assessing productive counting, which we then related to a measure of successor function knowledge. While the more opaque languages were associated with lower counting proficiency and successor function task performance in comparison to the more transparent languages, a unique within-language analytic approach revealed a robust relationship between measures of productive counting and successor knowledge in almost every language. We conclude 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 counting transparency.

scholarly journals Why is number word learning hard? Evidence from bilingual learners.

2016 ◽  
Author(s):  
Katherine Wagner ◽  
Pierina Cheung ◽  
Katherine Kimura ◽  
David Barner
Keyword(s):  
Word Learning ◽  
The Other ◽  
Number Word ◽  
Bilingual Learners ◽  
Specific Language ◽  
Number Words ◽  
Two Factors ◽  
Partial Transfer ◽  
Hard Evidence ◽  
Positive Integers

Young children typically take between 18 months and 2 years to learn themeanings of number words. In the present study, we investigated thisdevelopmental trajectory in bilingual preschoolers to examine the relativecontributions of two factors in number word learning: (1) the constructionof numerical concepts, and (2) the mapping of language specific words ontothese concepts. We found that children learn the meanings of small numberwords (i.e., one, two, and three) independently in each language,indicating that observed delays in learning these words are attributable todifficulties in mapping words to concepts. In contrast, children generallylearned to accurately count larger sets (i.e., five or greater)simultaneously in their two languages, suggesting that the difficulty inlearning to count is not tied to a specific language. We also replicatedprevious studies that found that children learn the counting procedurebefore they learn its logic – i.e., that for any natural number, n, thesuccessor of n in the count list denotes the cardinality n+1. Consistentwith past studies, we find that knowledge of this successor principleexhibits partial transfer between languages, suggesting that the logic ofthe positive integers may not be stored in a language-specific format. Weconclude that delays in learning the meanings of small number word aremainly due to language-specific processes of mapping words to concepts,whereas the logic and procedures of counting appear to be learned in aformat that is independent of a particular language and thus transfersrapidly from one language to the other in development.

scholarly journals Quantity implicature and access to scalar alternatives in language acquisition

2015 ◽  
pp. 525
Author(s):  
Alan Clinton Bale ◽  
Neon Brooks ◽  
David Barner
Keyword(s):  
Language Acquisition ◽  
Word Learning ◽  
Number Word ◽  
Scalar Implicature ◽  
Scalar Implicatures ◽  
Relevant Alternatives ◽  
Knowing That

When faced with a sentence like "Some of the toys are on the table," adults, but not preschoolers, compute a scalar implicature, taking the sentence to imply that not all the toys are on the table. This paper explores the hypothesis that children fail to compute scalar implicatures because they lack knowledge of the relevant scalar alternatives to words like "some." Four-year-olds were shown pictures in which three out of three objects fit a description (e.g., three animals reading), and were asked to evaluate statements that relied on context-independent alternatives (e.g., knowing that "all" is an alternative to "some" for the utterance "Some of the animals are reading") or contextual alternatives (e.g., knowing that the set of all three visible animals is an alternative to a set of two for the utterance "Only the cat and the dog are reading"). Children failed to reject the false statements containing context-independent scales even when the word "only" was used (e.g., "only some"), but correctly rejected equivalent statements containing contextual alternatives (e.g., "only the cat and dog"). These results support the hypothesis that children’s difficulties with scalar implicature are due to a failure to generate relevant alternatives for specific scales. Consequences for number word learning are also discussed.

scholarly journals Parallel individuation supports numerical comparisons in preschoolers (in press)

2017 ◽  
Author(s):  
Pierina Cheung
Keyword(s):  
Word Learning ◽  
Number System ◽  
Number Word ◽  
Approximate Number System ◽  
Numerical Comparisons ◽  
Subject Design ◽  
Tentative Evidence ◽  
Numerical Operations

While the approximate number system (ANS) has been shown to represent relations between numerosities starting in infancy, little is known about whether parallel individuation – a system dedicated to representing objects in small collections – can also be used to represent numerical relations between collections. To test this, we asked preschoolers between the ages of 2 ½ and 4 ½ to compare two arrays of figures that either included exclusively small numerosities (< 4) or exclusively large numerosities (> 4). The ratios of the comparisons were the same in both small and large numerosity conditions. Experiment 1 used a between-subject design, with different groups of preschoolers comparing small and large numerosities, and found that small numerosities are easier to compare than large ones. Experiment 2 replicated this finding with a wider range of set sizes. Experiment 3 further replicated the small-large difference in a within-subject design. We also report tentative evidence that non- and 1-knowers perform better on comparing small numerosities than large numerosities. These results suggest that preschoolers can use parallel individuation to compare numerosities, possibly prior to the onset of number word learning, and thus support previous proposals that there are numerical operations defined over parallel individuation (e.g., Feigenson & Carey, 2003).

scholarly journals Why is number word learning hard? Evidence from bilingual learners

2015 ◽  
Vol 83 ◽  
pp. 1-21 ◽  
Author(s):  
Katie Wagner ◽  
Katherine Kimura ◽  
Pierina Cheung ◽  
David Barner
Keyword(s):  
Word Learning ◽  
Number Word ◽  
Bilingual Learners ◽  
Hard Evidence

scholarly journals Accessing the unsaid: The role of scalar alternatives in children’s pragmatic inference

2016 ◽  
Author(s):  
David Barner ◽  
Neon Blue Brooks ◽  
Alan Bale
Keyword(s):  
Word Learning ◽  
Number Word ◽  
Scalar Implicature ◽  
Knowing That ◽  
Pragmatic Inference

When faced with a sentence like, “Some of the toys are on the table”,adults, but not preschoolers, compute a scalar implicature, taking thesentence to imply that not all the toys are on the table. This paperexplores the hypothesis that children fail to compute scalar implicaturesbecause they lack knowledge of relevant scalar alternatives to words like“some”. Four-year-olds were shown pictures in which three out of threeobjects fit a description (e.g., three animals reading), and were asked toevaluate statements that relied on context-independent alternatives (e.g.,knowing that all is an alternative to some for the utterance “Some of theanimals are reading”) or contextual alternatives (e.g., knowing that theset of all three visible animals is an alternative to a set of two for theutterance “Only the cat and the dog are reading”). Children failed toreject the false statements containing context-independent scales even whenthe word only was used (e.g., only some), but correctly rejected equivalentstatements containing contextual alternatives (e.g., only the cat and dog).These results support the hypothesis that children’s difficulties withscalar implicature are due to a failure to generate relevant alternativesfor specific scales. Consequences for number word learning are alsodiscussed.

scholarly journals Quantity implicature and access to scalar alternatives in language acquisition

2010 ◽  
Vol 20 ◽  
pp. 525 ◽  
Author(s):  
Alan Clinton Bale ◽  
Neon Brooks ◽  
David Barner
Keyword(s):  
Language Acquisition ◽  
Word Learning ◽  
Number Word ◽  
Scalar Implicature ◽  
Scalar Implicatures ◽  
Relevant Alternatives ◽  
Knowing That

When faced with a sentence like "Some of the toys are on the table," adults, but not preschoolers, compute a scalar implicature, taking the sentence to imply that not all the toys are on the table. This paper explores the hypothesis that children fail to compute scalar implicatures because they lack knowledge of the relevant scalar alternatives to words like "some." Four-year-olds were shown pictures in which three out of three objects fit a description (e.g., three animals reading), and were asked to evaluate statements that relied on context-independent alternatives (e.g., knowing that "all" is an alternative to "some" for the utterance "Some of the animals are reading") or contextual alternatives (e.g., knowing that the set of all three visible animals is an alternative to a set of two for the utterance "Only the cat and the dog are reading"). Children failed to reject the false statements containing context-independent scales even when the word "only" was used (e.g., "only some"), but correctly rejected equivalent statements containing contextual alternatives (e.g., "only the cat and dog"). These results support the hypothesis that children’s difficulties with scalar implicature are due to a failure to generate relevant alternatives for specific scales. Consequences for number word learning are also discussed.

scholarly journals Does Grammatical Structure Accelerate Number Word Learning? Evidence from Learners of Dual and Non-Dual Dialects of Slovenian

PLoS ONE ◽  
2016 ◽  
Vol 11 (8) ◽  
pp. e0159208 ◽  
Author(s):  
Franc Marušič ◽  
Rok Žaucer ◽  
Vesna Plesničar ◽  
Tina Razboršek ◽  
Jessica Sullivan ◽  
...  
Keyword(s):  
Word Learning ◽  
Number Word ◽  
Grammatical Structure
Sign in / Sign up

Export Citation Format

Share Document