scholarly journals Measuring Emerging Number Knowledge in Toddlers

2021 ◽  
Vol 12 ◽  
Author(s):  
Alex M. Silver ◽  
Leanne Elliott ◽  
Emily J. Braham ◽  
Heather J. Bachman ◽  
Elizabeth Votruba-Drzal ◽  
...  
Keyword(s):  
Cardinal Number ◽  
Choice Point ◽  
Number Word ◽  
Word Knowledge ◽  
Infants And Toddlers ◽  
Number Words ◽  
Exact Number ◽  
Correct Image ◽  
Rule Out ◽  
Number Knowledge

Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers (N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss.

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 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.

Approximate number word knowledge before the cardinal principle

2015 ◽  
Vol 130 ◽  
pp. 35-55 ◽  
Author(s):  
Elizabeth A. Gunderson ◽  
Elizabet Spaepen ◽  
Susan C. Levine
Keyword(s):  
Number Word ◽  
Word Knowledge

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 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.

scholarly journals Semantic Access in Number Word Translation

2008 ◽  
Vol 55 (2) ◽  
pp. 102-112 ◽  
Author(s):  
Wouter Duyck ◽  
Marc Brysbaert
Keyword(s):  
First Language ◽  
Number Word ◽  
Magnitude Effect ◽  
Number Words ◽  
Number Magnitude ◽  
Forward Translation ◽  
Semantic Access ◽  
Lexical Similarity ◽  
Word Translation ◽  
Dual Route Model

Abstract. The revised hierarchical model of bilingualism (e.g., Kroll & Stewart, 1994 ) assumes that second language (L2) words primarily access semantics through their first language (L1) translation equivalents. Consequently, backward translation from L2 to L1 should not imply semantic access but occurs through lexical wordform associations. However, recent research with Dutch-French bilinguals showed that both backward and forward translation of number words yields a semantic number magnitude effect ( Duyck & Brysbaert, 2004 ), providing evidence for strong form-to-meaning mappings of L2 number words. In two number-word translation experiments with Dutch-English-German trilinguals, the present study investigated whether semantic access in L1-L2 and L1-L3 number-word translation depends on lexical similarity of the languages involved. We found that backward translation from these more similar language pairs to L1 still yields a semantic magnitude effect, whereas forward translation does not, in contrast with the Dutch-French results of Duyck and Brysbaert (2004) . We argue against a dual route model of word translation and suggest that the degree of semantic activation in translation depends on lexical form overlap between translation equivalents.

scholarly journals Language effects in early development of number writing and reading

2021 ◽  
Vol 7 (3) ◽  
pp. 368-387 ◽  
Author(s):  
Anna F. Steiner ◽  
Sabrina Finke ◽  
Francina J. Clayton ◽  
Chiara Banfi ◽  
Ferenc Kemény ◽  
...  
Keyword(s):  
Grade Level ◽  
Longitudinal Design ◽  
Number Word ◽  
Number Words ◽  
Language Effects ◽  
English Speaking ◽  
Linguistic Challenges ◽  
The Impact ◽  
Accuracy Rates ◽  
Specific Number

Reading and writing multidigit numbers requires accurate switching between Arabic numbers and spoken number words. This is particularly challenging in languages with number-word inversion such as German (24 is pronounced as four-and-twenty), as reported by Zuber, Pixner, Moeller, and Nuerk (2009, https://doi.org/10.1016/j.jecp.2008.04.003). The current study aimed to replicate the qualitative error analysis by Zuber et al. and further extended their study: 1) A cross-linguistic (German, English) analysis enabled us to differentiate between language-dependent and more general transcoding challenges. 2) We investigated whether specific number structures influence accuracy rates. 3) To consider both transcoding directions (from Arabic numbers to number words and vice versa), we assessed performance for number reading in addition to number writing. 4) Our longitudinal design allowed us to investigate transcoding development between Grades 1 and 2. We assessed 170 German- and 264 English-speaking children. Children wrote and read the same set of 44 one-, two- and three-digit numbers, including the same number structures as Zuber et al. For German, we confirmed that a high amount of errors in number writing was inversion-related. For English, the percentage of inversion-related errors was very low. Accuracy rates were strongly related to number syntax. The impact of number structures was independent of transcoding direction or grade level and revealed cross-linguistic challenges of transcoding multidigit numbers. For instance, transcoding of three-digit numbers containing syntactic zeros (e.g., 109) was significantly more accurate than transcoding of items with lexical zeros (e.g., 190). Based on our findings, we suggest adaptations of current transcoding models.

scholarly journals ASMĀ' AL-A'DĀD WA KINĀYĀTUHA FĪ AL-QUR'AN AL-KARĪM (DIRĀSAH TAHLĪLIYYAH NAHWIYYAH)

2021 ◽  
Vol 7 (2) ◽  
pp. 29
Author(s):  
Rezeka Ma'rifatul Mahmudah
Keyword(s):  
Content Analysis ◽  
Secondary Data ◽  
Data Sources ◽  
Primary Data ◽  
Number Word ◽  
Number Words ◽  
Library Research ◽  
Holy Quran ◽  
The Holy Quran ◽  
Analysis Design

In the types of words there is a chapter on numerals and their kinayah. It is widely used in Arabic, either in conversation or in Arabic texts. The purpose in this research is to describe the number words and their kinayah, as well as the form of the number word phrase and the position of the number word and its kinayah in the verse of the holy Quran. The type in this research is library research with a content analysis design (adapted from Krippendorf) because it is based on the data sources in this study in the form of documents. The primary data in this study was the holy Quran and the secondary data in this study were taken from books related to the research. And the results of this study, 1. Quantity of number word 37 words in the Quran 2. Quantity of kinayah number in the Quran 4 words 3. Quantity of  position number 17 verse in the Quran 4. Quantity of position kinayah number 6 verse in the Quran.

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