Number Of Words Research Articles

Pygmies, Bushmen, and savage numbers – a case study in a sequence of bad citations

There is a prevalent claim in the literature examining the history of numbers and the development of number words that some African group (“Bushmen” or “Pygmies”) counts in a particular way, where their numerals are of the form 1, 2, 3, 2+2, 2+2+1, etc. Numerous forms of this claim are traced back to their original sources through an extensive search of the available literature. The author argues that the different forms can be traced back to two early sources, which have been misquoted and bastardized along the way.

The Numerical Ratio Effect for Digits and Number Words: the Lack of Individual Differences

The Numerical Ratio Effect for Digits and Number Words: the Lack of Individual Differences

Utilization of aluminium helically corrugated twisted tape inserts for heat transfer enhancement of turbulent flow

In a single stage unstable run with the assist of helically corrugated tube, the increment of convective hotness shift has been examined. In a coaxial duct hotness evaporator, results of slope-to-breadth proportion and costal-extent to breadth proportion of spirally fluted ducts on the hotness exchange improvement, thermic presentation part and isothermal friction are finding and concluded. In a huge amount of unstable liquid move in which Reynolds number between 4500 and 63,000. In smooth tube the heat shift and thermal production is less than the corrugated tube. In test range heat exchange rate is increase in a huge range. Therefore, due to constraint drop output tells in corrugated tube the value of friction factor occurs from 1.4 to 1.9 times on the plane tube. Besides, due to experimental data on the basis curve fitting of relations of the Nusselt number, abrasion part and thermic presentation part in words of slope proportion, costal-extent proportion, Reynolds number, and Prandtl number for the fluted duct are find. Now a days heat transfer enhancement is the major problem in industries. In this present work a technique has been used to enhance the heat transfer.

The classifiability scale

Abstract In many languages, nouns need a numeral classifier to combine with number words or quantifiers. Even though languages may have an elaborate system of numeral classifiers, there usually are exceptional nouns that combine directly with number words. This paper deals with the following questions: Which nouns trigger a numeral classifier when counted? Which nouns are more likely to occur without an additional classifier in a numeral context? Data from 32 languages reveal a classifiability scale of nouns depending on their semantics. The more animate a noun, the more likely is the occurrence of a classifier. With inanimate nouns, classifiers often may or must be omitted. The investigation extends to units, with units of time being much more likely to be accompanied by a numeral classifier than other units. These findings are surprising in the light of the predominant view that numeral classifiers are individuating units in languages where nouns appear to be uncountable mass nouns. I discuss several approaches, of which animacy and the form-frequency correspondence principle are most promising.

Social identity, precision and charity: when less precise speakers are held to stricter standard

Recent has begun to show systematic connections between social information and pragmatic reasoning. These findings raise the question of whether social information shapes comprehenders' assessments of the correctness of linguistic description in light of a single known and determined fact. We explore this question by testing the impact of speaker identity on T(ruth)-V(alue) J(udgment)s based on the interpretation of number words. We find that imprecise statements from speakers socially expected to be less precise – i.e. “Chill" ones – are rejected at a higher rate, and thus held to more stringent evaluation standards, than those from speakers socially expected to speak more precisely – i.e. “Nerdy" ones. We explain the new finding by appealing to the idea that, by virtue of generally being perceived to be more precise, Nerdy speakers are granted higher epistemic credibility than Chill ones. The emerging picture is one in which TVJ assessments are affected by social considerations in a different way from other experimental tasks, suggesting a nuanced interplay between social information and different interpretation tasks and processes

Arithmetic thinking as the basis of children's generative number concepts

Predominant psychological theories of number acquisition posit that children acquire natural number concepts as they acquire the successor principle, or the knowledge that every natural number is succeeded by another natural number that is exactly-one more than it. However, exactly how children acquire the successor principle remains largely unexplained. Recently developed ideas within this family of theories posit that an abstract recursive successor function is acquired from the recursive structure of number words; however, the types of recursion underlying the successor function and number words are distinctively different (one is a self-referential function and the other is a self-embedded structure), making it difficult to theorize how one type triggers the acquisition of another. Moreover, our analysis of the literature questions if the knowledge about the successor principle is even empirically measurable. Here, we argue that number acquisition is a process of understanding a generative rule that governs the system of natural numbers and point out that the successor principle is not the only generative rule that governs the natural number system. We propose an alternative hypothesis that generative number concepts emerge from children's realization about how the combinatorial rules of numerals allow arithmetic (specifically additive and multiplicative) representations of quantity. Importantly, under addition and multiplication—which are historically rooted in concatenation and grouping of physical objects—natural numbers are mathematically closed. As a corollary, the system of infinitely generative natural numbers is conceptualized. This new theoretical framework allows the construction of novel empirical questions and testable hypotheses based on the formalized rules of numerical syntax and numeration systems, and therefore opens a new avenue for studying later stages of children's acquisition of number concepts.

Phonological activation improves semantic access provided by Arabic digits and number words.

Arabic digits (e.g., "6") and number words (e.g., "", "six", " ") are the two main formats in which numbers can be represented. Although phonology plays a crucial role in the semantic accessing of alphabetic words and Chinese characters, whether it is involved in the processing of different numerical notations, which have been shown to be dissociable from characters, is still unknown. Using a parity judgment task, two experiments were performed by manipulating the phonological relationship between a prime and a target. The primes were Tibetan or Chinese characters and the targets were presented either as number words (Experiment 1) or as Arabic digits (Experiment 2). The results revealed that phonology affected semantic access for both number words and Arabic digits. Additionally, semantic access for Tibetan number words was more susceptible to phonological information. The results for Arabic digits followed the same pattern for Tibetan primes. Further, language proficiency also affected the role of phonology in number processing. Participants with low language proficiency relied more on phonological encoding when processing the numbers. The results suggest that phonology is crucial for semantic access of different numerical notations.

The approximate number system cannot be the leading factor in the acquisition of the first symbolic numbers

When learning the meaning of symbolic numbers, children learn the numbers up to 4 sequentially. A prominent account of this learning process proposes that the increasing sensitivity of the preverbal approximate number system (ANS) allows for reliable discrimination of increasingly large neighboring numbers, which, consequently, leads to the sequential acquisition of the first symbolic numbers. In this work, a more complete quantitative description of this account is provided. This description is based on the mathematical model of the ANS and on additional relevant parameter values reported in the literature. The quantitative description demonstrates that, in the time period during which children learn the meaning of the first number words, the improvement of ANS sensitivity cannot provide the assumed changes in the discriminability of these numbers. The present result challenges the role of the ANS as a leading factor in the acquisition of the first symbolic numbers.

An Investigation of the Frequency of Time and Number Words Used in Informal Conversations with Children

An Investigation of the Frequency of Time and Number Words Used in Informal Conversations with Children

Early number word learning: Associations with domain-general and domain-specific quantitative abilities.

Cardinal number knowledge-understanding "two" refers to sets of two entities-is a critical piece of knowledge that predicts later mathematics achievement. Recent studies have shown that domain-general and domain-specific skills can influence children's cardinal number learning. However, there has not yet been research investigating the influence of domain-specific quantifier knowledge on children's cardinal number learning. The present study aimed to investigate the influence of domain-general and domain-specific skills on Mandarin Chinese-speaking children's cardinal number learning after controlling for a number of family background factors. Particular interest was paid to the question whether domain-specific quantifier knowledge was associated with cardinal number development. Specifically, we investigated 2-5-year-old Mandarin Chinese-speaking children's understanding of cardinal number words as well as their general language, intelligence, approximate number system (ANS) acuity, and knowledge of quantifiers. Children's age, gender, parental education, and family income were also assessed and used as covariates. We found that domain-general abilities, including general language and intelligence, did not account for significant additional variance of cardinal number knowledge after controlling for the aforementioned covariates. We also found that domain-specific quantifier knowledge did not account for significant additional variance of cardinal number knowledge, whereas domain-specific ANS acuity accounted for significant additional variance of cardinal number knowledge, after controlling for the aforementioned covariates. In sum, the results suggest that domain-specific numerical skills seem to be more important for children's development of cardinal number words than the more proximal domain-general abilities such as language abilities and intelligence. The results also highlight the significance of ANS acuity on children's cardinal number word development.

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., “two”), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.

A shared numerical magnitude representation evidenced by the distance effect in frequency-tagging EEG

Humans can effortlessly abstract numerical information from various codes and contexts. However, whether the access to the underlying magnitude information relies on common or distinct brain representations remains highly debated. Here, we recorded electrophysiological responses to periodic variation of numerosity (every five items) occurring in rapid streams of numbers presented at 6 Hz in randomly varying codes—Arabic digits, number words, canonical dot patterns and finger configurations. Results demonstrated that numerical information was abstracted and generalized over the different representation codes by revealing clear discrimination responses (at 1.2 Hz) of the deviant numerosity from the base numerosity, recorded over parieto-occipital electrodes. Crucially, and supporting the claim that discrimination responses reflected magnitude processing, the presentation of a deviant numerosity distant from the base (e.g., base “2” and deviant “8”) elicited larger right-hemispheric responses than the presentation of a close deviant numerosity (e.g., base “2” and deviant “3”). This finding nicely represents the neural signature of the distance effect, an interpretation further reinforced by the clear correlation with individuals’ behavioral performance in an independent numerical comparison task. Our results therefore provide for the first time unambiguously a reliable and specific neural marker of a magnitude representation that is shared among several numerical codes.

Verbal counting and the timing of number acquisition in an indigenous Amazonian group.

Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words.

Direct intracranial recordings in the human angular gyrus during arithmetic processing.

The role of angular gyrus (AG) in arithmetic processing remains a subject of debate. In the present study, we recorded from the AG, supramarginal gyrus (SMG), intraparietal sulcus (IPS), and superior parietal lobule (SPL) across 467 sites in 30 subjects performing addition or multiplication with digits or number words. We measured the power of high-frequency-broadband (HFB) signal, a surrogate marker for regional cortical engagement, and used single-subject anatomical boundaries to define the location of each recording site. Our recordings revealed the lowest proportion of sites with activation or deactivation within theAG compared to other subregions of the inferior parietal cortex during arithmetic processing. The few activated AG sites were mostly located at the border zones between AG and IPS, or AG and SMG. Additionally, we found that AG sites were more deactivated in trials with fast compared to slow response times. The increase or decrease of HFB within specific AG sites was the same when arithmetic trials were presented with number words versus digits and during multiplication as well as addition trials. Based on our findings, we conclude that the prior neuroimaging findings of so-called activations in the AG during arithmetic processing could have been due to group-based analyses that might have blurred the individual anatomical boundaries of AG or the subtractive nature of the neuroimaging methods in which lesserdeactivations compared to the control condition have been interpreted as "activations". Our findings offer a new perspective with electrophysiological data about the engagement of AG during arithmetic processing.

Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding.

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude.

Syntactic chunking reveals a core syntactic representation of multi-digit numbers, which is generative and automatic

Representing the base-10 structure of numbers is a challenging cognitive ability, unique to humans, but it is yet unknown how precisely this is done. Here, we examined whether and how literate adults represent a number’s full syntactic structure. In 5 experiments, participants repeated number-word sequences and we systematically varied the order of words within each sequence. Repetition on grammatical sequences (e.g., two hundred ninety-seven) was better than on non-grammatical ones (hundred seven two ninety). We conclude that the participants represented the number’s full syntactic structure and used it to merge number words into chunks in short-term memory. Accuracy monotonously improved for sequences with increasingly longer grammatical segments, up to a limit of ~ 4 words per segment, irrespectively of the number of digits, and worsened thereafter. Namely, short chunks improved memorization, whereas oversized chunks disrupted memorization. This chunk size limit suggests that the chunks are not based on predefined structures, whose size limit is not expected to be so low, but are created ad hoc by a generative process, such as the hierarchical syntactic representation hypothesized in Michael McCloskey’s number-processing model. Chunking occurred even when it disrupted performance, as in the oversized chunks, and even when external cues for chunking were controlled for or were removed. We conclude that the above generative process operates automatically rather than voluntarily. To date, this is the most detailed account of the core representation of the syntactic structure of numbers—a critical aspect of numerical literacy and of the ability to read and write numbers.

Transcoding counts: Longitudinal contribution of number writing to arithmetic in different languages

Number writing involves transcoding from number words (e.g., “thirty-two”) to written digit strings (32) and is an important unique predictor of arithmetic. The existing longitudinal evidence about the relation between transcoding and arithmetic is mostly language specific. In languages with number word inversion (e.g., German), the order of tens and units is transposed in spoken number words compared with Arabic numbers. This makes transcoding more challenging than in languages without number word inversion (e.g., English). In the current study, we aimed to understand whether the contribution of number writing to the development of arithmetic is similar in languages with and without number word inversion. German-speaking children (n = 166) and English-speaking children (n = 201) were followed over the first 3 years of primary school. In a series of multiple linear regressions, we tested whether number writing of multi-digit numbers was a significant unique predictor of arithmetic after controlling for well-known non-numerical predictors (nonverbal reasoning and working memory) and numerical predictors (symbolic and nonsymbolic magnitude comparison). Number writing in Grade 1 predicted arithmetic in Grades 1, 2, and 3 over and above the other predictors. Crucially, number writing performance was of comparable importance for arithmetic development in German- and English-speaking children. Our findings extend previous evidence by showing that transcoding predicts the development of arithmetic skills during the first 3 years of primary school in languages with and without number word inversion.

Environmental influences on mathematics performance in early childhood.

Math skills relate to lifelong career, health, and financial outcomes. Individuals' own cognitive abilities predict math performance and there is growing recognition that environmental influences including differences in culture and variability in math engagement also impact math skills. In this Review, we summarize evidence indicating that differences between languages, exposure to math-focused language, socioeconomic status, attitudes and beliefs about math, and engagement with math activities influence young children's math performance. These influences play out at the community and individual level. However, research on the role of these environmental influences for foundational number skills, including understanding of number words, is limited. Future research is needed to understand individual differences in the development of early emerging math skills such as number word skills, examining to what extent different types of environmental input are necessary and how children's cognitive abilities shape the impact of environmental input.

Opportunities for recognising, assessing, and providing online support among elementary school students with dyscalculia

Mathematics is present throughout our lives. Already in infancy, children become acquainted with quantities and the differentiation of quantities (Starkey & Cooper, 1995; Huntley et al., 2000; Csépe et al., 2007, 2008). According to von Aster and Shalev (2007), the quantitative core system (cardinality) develops in infancy. An infant is capable of subitising, estimating, and comparing the quantities of a small number of items. After learning from their environment in early childhood, children perceive quantities and then understand the strategy needed for counting and are able to count verbally. They use different classifications to determine the quantities. Kindergarten prepares the knowledge needed for the application of the concept of numbers and lays the foundations for the concept of operations. As a continuation of knowledge acquisition of knowledge, in primary school the establishment of a unified and broad foundation takes place with a focus on the development and consolidation of the concept of numbers and operations. Number words representing quantities are associated with digits, therefore school children express them with symbols without the presence of quantities (von Aster & Shalev, 2007; Jármi, 2013, p. 50). This developmental process allows for the learning of written operation performance in the lower grades, while the internal number line (analogous quantity representation) develops in the child, which strengthens spatial thinking. In the initial stage of the lower school grades, active knowledge acquisition dominates, which is the first level of abstraction of mathematical activities. In the grades that follow, the constantly and spirally repeating, expanding nature of knowledge strengthens the fourth level of abstraction, i.e., the independent application of symbols.

The Relations between Cardinal Number Knowledge and Quantifier Comprehension

ABSTRACT How does linguistic structure affect children’s developing cardinal number knowledge? The bootstrapping theory proposes that children might use syntactic information provided by known words such as quantifiers to bootstrap the meanings of unfamiliar words such as number words. Prior studies of numeral and quantifier development have indicated that the bootstrapping mechanism that children can use to discover numeral meanings might work differently in different languages. Nevertheless, support for this conclusion remains preliminary. The present study explored this hypothesis through an investigation of the possible relations between cardinal number knowledge and quantifier comprehension in Mandarin Chinese-speaking children. Notably, in contrast with previous studies, this study also offered a glimpse into children’s receptive vocabulary development and its relation with cardinal number knowledge and quantifier comprehension. Results showed that cardinal number knowledge did not seem to be correlated with quantifier comprehension (both “exact” and “non-exact” quantifiers) when controlling for such covariates as children’s age, gender, parent education, and family income. Moreover, children’s receptive vocabulary size explained a significant amount of variance in their quantifier knowledge over and above children’s age, gender, parent education, and family income, but not in their cardinal number development over and above these covariates. These results provide further evidence for the hypothesis that while the bootstrapping mechanism may facilitate number word learning in children speaking languages like English, it might play a lesser role in children speaking classifier languages such as Mandarin Chinese. Implications for the role that general receptive vocabulary plays in the acquisition of number words and quantifiers are also discussed.