scholarly journals How children interface number words with perceptual magnitudes

2020 ◽  
Author(s):  
Denitza Dramkin ◽  
Darko Odic
Keyword(s):  
Individual Differences ◽  
Number Word ◽  
General Process ◽  
Estimation Performance ◽  
Number Words ◽  
Verbal Estimation ◽  
Length And Area ◽  
Perceptual Systems ◽  
Symbolic Number

How do children map symbolic number words to continuous and noisy perceptual magnitudes? We explore how 5- to 12-year-olds attach novel units to number, length, and area by examining whether verbal estimation performance is primarily predicted by access to number words, the precision of children’s underlying perceptual systems, or a more general process in structurally aligning number words with perceptual magnitudes. We find that from age five onward, children can readily form novel mappings between number words and perceptual magnitudes, including dimensions they have no experience estimating in (e.g., length, area), and even when faced with completely novel units (e.g., mapping a collection of three dots to “one” unit for number). Additionally, estimation performance was poorly predicted by the noise in their underlying perceptual magnitudes and number word access. Instead, we show that individual differences in children’s abilities to translate continuous perceptual signals into discrete categories underlie verbal estimation performance.

scholarly journals Cross-linguistic patterns in the acquisition of quantifiers

2016 ◽  
Vol 113 (33) ◽  
pp. 9244-9249 ◽  
Author(s):  
Napoleon Katsos ◽  
Chris Cummins ◽  
Maria-José Ezeizabarrena ◽  
Anna Gavarró ◽  
Jelena Kuvač Kraljević ◽  
...  
Keyword(s):  
Cultural Practices ◽  
Number Word ◽  
Negative Concord ◽  
Number Words ◽  
Word Acquisition ◽  
Linguistic Patterns ◽  
Specific Meaning ◽  
Specific Factors ◽  
And Gender ◽  
Perceptual Systems

Learners of most languages are faced with the task of acquiring words to talk about number and quantity. Much is known about the order of acquisition of number words as well as the cognitive and perceptual systems and cultural practices that shape it. Substantially less is known about the acquisition of quantifiers. Here, we consider the extent to which systems and practices that support number word acquisition can be applied to quantifier acquisition and conclude that the two domains are largely distinct in this respect. Consequently, we hypothesize that the acquisition of quantifiers is constrained by a set of factors related to each quantifier’s specific meaning. We investigate competence with the expressions for “all,” “none,” “some,” “some…not,” and “most” in 31 languages, representing 11 language types, by testing 768 5-y-old children and 536 adults. We found a cross-linguistically similar order of acquisition of quantifiers, explicable in terms of four factors relating to their meaning and use. In addition, exploratory analyses reveal that language- and learner-specific factors, such as negative concord and gender, are significant predictors of variation.

scholarly journals Language, procedures, and the non-perceptual origin of number word meanings

2017 ◽  
Vol 44 (3) ◽  
pp. 553-590 ◽  
Author(s):  
DAVID BARNER
Keyword(s):  
Building Blocks ◽  
Independent Learning ◽  
Learning Problems ◽  
Number Word ◽  
Word Meanings ◽  
Number Words ◽  
Perceptual Representations ◽  
Children First ◽  
Positive Integers ◽  
Perceptual Systems

AbstractPerceptual representations of objects and approximate magnitudes are often invoked as building blocks that children combine to acquire the positive integers. Systems of numerical perception are either assumed to contain the logical foundations of arithmetic innately, or to supply the basis for their induction. I propose an alternative to this framework, and argue that the integers are not learned from perceptual systems, but arise to explain perception. Using cross-linguistic and developmental data, I show that small (~1–4) and large (~5+) numbers arise both historically and in individual children via distinct mechanisms, constituting independent learning problems, neither of which begins with perceptual building blocks. Children first learn small numbers using the same logic that supports other linguistic number marking (e.g. singular/plural). Years later, they infer the logic of counting from the relations between large number words and their roles in blind counting procedures, only incidentally associating number words with approximate magnitudes.

Language, procedures, and the non-perceptual origin of natural number concepts

2016 ◽  
Author(s):  
David Barner
Keyword(s):  
General Framework ◽  
Ad Hoc ◽  
Building Blocks ◽  
Number Words ◽  
Linguistic Markers ◽  
Logical Foundations ◽  
Large Numbers ◽  
Perceptual Representations ◽  
Positive Integers ◽  
Perceptual Systems

Perceptual representations – e.g., of objects or approximate magnitudes –are often invoked as building blocks that children combine with linguisticsymbols when they acquire the positive integers. Systems of numericalperception are either assumed to contain the logical foundations ofarithmetic innately, or to supply the basis for their induction. Here Ipropose an alternative to this general framework, and argue that theintegers are not learned from perceptual systems, but instead arise toexplain perception as part of language acquisition. Drawing oncross-linguistic data and developmental data, I show that small numbers(1-4) and large numbers (~5+) arise both historically and in individualchildren via entirely distinct mechanisms, constituting independentlearning problems, neither of which begins with perceptual building blocks.Specifically, I propose that children begin by learning small numbers(i.e., *one, two, three*) using the same logical resources that supportother linguistic markers of number (e.g., singular, plural). Several yearslater, children discover the logic of counting by inferring the logicalrelations between larger number words from their roles in blind countingprocedures, and only incidentally associate number words with perception ofapproximate magnitudes, in an *ad hoc* and highly malleable fashion.Counting provides a form of explanation for perception but is not causallyderived from perceptual systems.

Numerical symbols as explanations of human perceptual experience

2018 ◽  
Author(s):  
David Barner
Keyword(s):  
Perceptual Experience ◽  
Number Words ◽  
The World ◽  
Symbolic Systems ◽  
Perceptual Systems

Why did humans develop precise systems for measuring experience, like numbers, clocks, andcalendars? I argue that precise representational systems were constructed by earlier generationsof humans because they recognized that their noisy perceptual systems were not capturingdistinctions that existed in the world. Abstract symbolic systems did not arise from perceptualrepresentations, but instead were constructed to describe and explain perceptual experience. Byanalogy, I argue that when children learn number words, they do not rely on noisy perceptualsystems, but instead acquire these words as units in a broader system of procedures, whosemeanings are ultimately defined by logical relations to one another, not perception.

scholarly journals Verbal estimation of the magnitude of time, number, and length

2020 ◽  
Author(s):  
R. S. Ogden ◽  
F. R. Simmons ◽  
J. H. Wearden
Keyword(s):  
Processing System ◽  
Visual Displays ◽  
Verbal Responses ◽  
Physical Length ◽  
Estimation Performance ◽  
Verbal Estimation ◽  
The Mean ◽  
The Way

AbstractPerformance similarities on tasks requiring the processing of different domains of magnitude (e.g. time, numerosity, and length) have led to the suggestion that humans possess a common processing system for all domains of magnitude (Bueti and Walsh in Philos Trans R Soc B 364:1831–1840, 2009). In light of this, the current study examined whether Wearden’s (Timing Time Percept 3:223–245, 2015) model of the verbal estimation of duration could be applied to verbal estimates of numerosity and length. Students (n = 23) verbally estimated the duration, number, or physical length of items presented in visual displays. Analysis of the mean verbal estimates indicated the data were typical of that found in other studies. Analysis of the frequency of individual verbal estimates produced suggested that the verbal responses were highly quantized for duration and length: that is, only a small number of estimates were used. Responses were also quantized for number but to a lesser degree. The data were modelled using Wearden’s (2015) account of verbal estimation performance, which simulates quantization effects, and good fits could be obtained providing that stimulus durations were scaled as proportions (0.75, 1.06, and 0.92 for duration, number, and length, respectively) of their real magnitudes. The results suggest that despite previous reports of similarities in the processing of magnitude, there appear to be differences in the way in which the underlying representations of the magnitudes are scaled and then transformed into verbal outputs.

scholarly journals The association between number magnitude and space is dependent on notation: Evidence from an adaptive perceptual orientation task

2019 ◽  
Vol 5 (1) ◽  
pp. 38-54
Author(s):  
Tianwei Gong ◽  
Baichen Li ◽  
Limei Teng ◽  
Zijun Zhou ◽  
Xuefei Gao ◽  
...  
Keyword(s):  
Judgment Task ◽  
Snarc Effect ◽  
Number Word ◽  
Reaction Time Difference ◽  
Number Words ◽  
Number Magnitude ◽  
Spatial Response ◽  
Orientation Task ◽  
Arabic Digits ◽  
Perceptual Orientation

Research on adults' numerical abilities suggests that number representations are spatially oriented. This association of numbers with spatial response is referred to as the SNARC (i.e., spatial–numerical association of response codes) effect. The notation-independence hypothesis of numeric processing predicts that the SNARC effect will not vary with notation (e.g., Arabic vs. number word). To test such assumption, the current study introduced an adaptive experimental procedure based on a simple perceptual orientation task that can automatically smooth out the mean reaction time difference between Arabic digits and traditional Chinese number. We found that the SNARC effect interacted with notation, showing a SNARC effect for Arabic digits, but not for verbal number words. The results of this study challenged the commonly held view that notation does not affect numerical processes associated with spatial representations. We introduced a parallel model to explain the notation-dependent SNARC effect in the perceptual orientation judgment task.

scholarly journals Inversion effects on mental arithmetic in English- and Polish-speaking adults

2019 ◽  
Vol 73 (1) ◽  
pp. 91-103
Author(s):  
Carolin Annette Lewis ◽  
Julia Bahnmueller ◽  
Marta Wesierska ◽  
Korbinian Moeller ◽  
Silke Melanie Göbel
Keyword(s):  
Mental Arithmetic ◽  
Word Formation ◽  
Place Value ◽  
Number Word ◽  
Problem Size ◽  
Number Range ◽  
Number Words ◽  
Language Groups ◽  
Addition Problem ◽  
The Cost

In some languages the order of tens and units in number words is inverted compared with the symbolic digital notation (e.g., German 23 → “ dreiundzwanzig,” literally: “ three-and-twenty”). In other languages only teen-numbers are inverted (e.g., English 17 → “ seventeen”; Polish 17 → “ siedemnaście” literally “ seventeen”). Previous studies have focused on between group comparisons of inverted and non-inverted languages and showed that number word inversion impairs performance on basic numerical tasks and arithmetic. In two independent experiments, we investigated whether number word inversion affects addition performance within otherwise non-inverted languages (Exp. 1: English, Exp. 2: Polish). In particular, we focused on the influence of inverted ( I; English: teen-numbers ⩾ 13, Polish: numbers 11–19) and non-inverted ( N) summands with sums between 13 and 39. Accordingly, three categories of addition problems were created: N + N, N + I, and I + I with problem size matched across categories. Across both language groups, we observed that problems with results in the 20 and 30 number range were responded to faster when only non-inverted summands were part of the problems as opposed to problems with one or two inverted summands. In line with this, the cost of a carry procedure was the largest for two inverted summands. The results support the notion that both language-specific and language-invariant aspects contribute to addition problem-solving. In particular though, regarding language-specific aspects, the results indicate that inverted number word formation of teens influences place-value processing of Arabic digits even in otherwise non-inverted languages.

The Number Language used by Preschool Children and their Mothers in the Context of Cooking

1996 ◽  
Vol 21 (1) ◽  
pp. 16-20 ◽  
Author(s):  
Jennifer M. Young-Loveridge
Keyword(s):  
Preschool Children ◽  
Mathematics Learning ◽  
Free Play ◽  
Number Word ◽  
Word Use ◽  
Number Words ◽  
Degree Of Control ◽  
The Relationship ◽  
Play Context

The present study was designed to explore the spontaneous use of number language by preschool children and their mothers in the context of cooking. The results show that preschool children use a variety of number words in this context. Mothers made substantially greater use of number words than did their children, possibly because the cooking context required a greater degree of control by the adult than would have been the case in a free-play context. Many instances of number-word use by mothers and by children went unacknowledged by their conversational partners. Although the relationship between children's number word use and that of their mothers was relatively weak (r=.34), there was a considerably stronger relationship between the numbers of reciprocal numeracy episodes and children's number-word use (r=.59). These findings support the idea that contingent responsiveness by adults is important for enhancing children's mathematics learning.

scholarly journals Electrophysiological Evidence for the Involvement of the Approximate Number System in Preschoolers' Processing of Spoken Number Words

2014 ◽  
Vol 26 (9) ◽  
pp. 1891-1904 ◽  
Author(s):  
Michal Pinhas ◽  
Sarah E. Donohue ◽  
Marty G. Woldorff ◽  
Elizabeth M. Brannon
Keyword(s):  
Number System ◽  
Number Word ◽  
Word Knowledge ◽  
Approximate Number System ◽  
Word Comprehension ◽  
Number Words ◽  
Visual Objects ◽  
Number Representations ◽  
Word Onset ◽  
Neural Underpinnings

Little is known about the neural underpinnings of number word comprehension in young children. Here we investigated the neural processing of these words during the crucial developmental window in which children learn their meanings and asked whether such processing relies on the Approximate Number System. ERPs were recorded as 3- to 5-year-old children heard the words one, two, three, or six while looking at pictures of 1, 2, 3, or 6 objects. The auditory number word was incongruent with the number of visual objects on half the trials and congruent on the other half. Children's number word comprehension predicted their ERP incongruency effects. Specifically, children with the least number word knowledge did not show any ERP incongruency effects, whereas those with intermediate and high number word knowledge showed an enhanced, negative polarity incongruency response (Ninc) over centroparietal sites from 200 to 500 msec after the number word onset. This negativity was followed by an enhanced, positive polarity incongruency effect (Pinc) that emerged bilaterally over parietal sites at about 700 msec. Moreover, children with the most number word knowledge showed ratio dependence in the Pinc (larger for greater compared with smaller numerical mismatches), a hallmark of the Approximate Number System. Importantly, a similar modulation of the Pinc from 700 to 800 msec was found in children with intermediate number word knowledge. These results provide the first neural correlates of spoken number word comprehension in preschoolers and are consistent with the view that children map number words onto approximate number representations before they fully master the verbal count list.

scholarly journals Ontogenetic origins of human integer representations

2019 ◽  
Author(s):  
Susan Carey ◽  
David Barner
Keyword(s):  
Number Word ◽  
Second Phase ◽  
Word Meanings ◽  
Hume’S Principle ◽  
Number Words ◽  
Number Representations ◽  
Exact Counting ◽  
Counting Algorithms ◽  
Numerical Magnitudes ◽  
Two Phases

Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children’s understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume’s principle (that 1-to-1 correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role.

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