Number Of Words Research Articles

The “How many?” task inadequately assesses the understanding of the cardinality principle

Once children have acquired the cardinality principle, they understand that the last number-word used in counting represents the total number of objects in a set. This principle is often assessed using the “How many?” task, which consists in asking “How many?” objects there are in a set after children have counted them. However, we show in this study that out of 188 kindergarteners (mean age: 4 ½ years), 42 (22,3 %) succeeded in repeating the last count word in the “How many?” task but failed to correctly apply the one-to-one correspondence principle during counting. Even when only the easiest countable sets were considered (i.e., linear and homogeneous collections or sets with a very limited number of objects), still more than 10 % of children from our sample repeated the last count word but failed to apply the one-to-one correspondence principle. Such developmental profile, in which children understand that the last word used in counting represents the total number of objects in a set but fail to grasp that each individual object must be associated with a single number word to determine this total, is not psychologically plausible. We conclude that the “How many?” task leads to an inaccurate assessment of the cardinality principle, in both its basic and more meaningful conception, in a non-negligible number of young children.

Introducing Mr. Three: Attention, Perception, and Meaning Selection in the Acquisition of Number and Color Words.

Children learn their first number words gradually over the course of many months, which is surprising given their ability to discriminate small numerosities. One potential explanation for this is that children are sensitive to the numerical features of stimuli, but don't consider exact cardinality as a primary hypothesis for novel word meanings. To test this, we trained 144 children on a number word they hadn't yet learned, and contrasted this with a condition in which they were merely required to attend to number to identify the word's referent, without encoding number as its meaning. In the first condition, children were trained to find a "giraffe with three spots." In the second condition, children were instead trained to find "Mr. Three", which also named a giraffe with three spots. In both conditions, children had to attend to number to identify the target giraffe, but, because proper nouns refer to individuals rather than their properties, the second condition did not require children to encode number as the meaning of the expression. We found that children were significantly better at identifying the giraffe when it had been labeled with the proper noun than with the number word. This finding contrasted with a second experiment involving color words, in which children (n = 56) were equally successful with a proper noun ("Mr. Purple") and an adjective ("the giraffe with purple spots"). Together, these findings suggest that, for number, but not for color, children's difficulty acquiring new words cannot be solely attributed to problems with attention or perception, but instead may be due to difficulty selecting the correct meaning from their hypothesis space for learning unknown words.

Neural evidence of core foundations and conceptual change in preschool numeracy.

Symbolic numeracy first emerges as children learn the meanings of number words and how to use them to precisely count sets of objects. This development starts before children enter school and forms a foundation for lifelong mathematics achievement. Despite its importance, exactly how children acquire this basic knowledge is unclear. Here we test competing theories of early number learning by measuring event-related brain potentials during a novel number word-quantity comparison task in 3-4-year-old preschool children (N=128). We find several qualitative differences in neural processing of number by conceptual stage of development. Specifically, we find differences in early attention-related parietal electrophysiology (N1), suggesting that less conceptually advanced children process arrays as individual objects and more advanced children distribute attention over the entire set. Subsequently, we find that only more conceptually advanced children show later-going frontal (N2) sensitivity to the numerical-distance relationship between the number word and visual quantity. The nature of this response suggested thatexact rather than approximate numerical meanings were being associated with number words over frontal sites. No evidence of numerical distance effects was observed over posterior scalp sites. Together these results suggest that children may engage parallel individuation of objects to learn the meanings of the first few number words, but, ultimately, create new exact cardinal value representations for number words that cannot be defined in terms of core, nonverbal number systems. More broadly, these results document an interaction between attentional and general cognitive mechanisms in cognitive development. RESEARCH HIGHLIGHTS: Conceptual development in numeracy is associated with a shift in attention from objects to sets. Children acquire meanings of the first few number words through associations with parallel attentional individuation of objects. Understanding of cardinality is associated with attentional processing of sets rather than individuals. Brain signatures suggest children attribute exact rather than approximate numerical meanings to the first few number words. Number-quantity relationship processing for the first few number words is evident in frontal but not parietal scalp electrophysiology of young children.

The expression of quantity in Oneida: a study in syntactic and semantic variation

Abstract One of the questions linguists try to answer is to what extent conceptual content is expressed similarly across languages. The null hypothesis is that languages express the same sorts of things but may differ in the particular morphological and syntactic constructions they use. This paper describes one semantic domain, quantification over objects in Oneida (Northern Iroquoian), where there is both variation in expression and variation in expressibility. Through a detailed and comprehensive description of quantificational expressions, we show that in Oneida quantification is pervasively and almost exclusively expressed by productive verb forms that are not number words; moreover, these verb forms head clauses (count clauses) adjoined to main clauses. We argue that to this morphosyntactic difference between Oneida and most languages corresponds a semantic difference, namely that in Oneida quantificational expressions denote properties of sets, whereas in most other languages they denote relations between sets (or between entities and sets), and this difference accounts for the systematic absence of proportional and partitive quantifiers in Oneida.

Evaluasi Peran Otoritas Jasa Keuangan dalam Pengawasan Implementasi Standar Audit 701 (2021)

The objectives of this study are to provide an overview of the benefits of communicating key audit matters (KAM) for OJK's oversight function, to identify findings related to KAM in United Kingdom and Malaysia, and how those regulators have responded to those findings, and to evaluate OJK's response related to KAM. This research is carried out by in-depth interviews with supervisors and analysts from the Directorate of Regulation and Development of the OJK Capital Market Sector. KAM communication provided benefits in OJK's supervisory function, among others, in determining the items to be reviewed in the Issuer's financial statements and in reviewing the audit responses stated in the auditor's report have been supported by the auditor's working papers. In carrying out their oversight function, the United Kingdom and Malaysia found, among others, that the average number of KAM and words in communicating KAM in the auditor's report continued to decline, the content of KAM of companies audited by Big 4 audit firms had more words for the same number of KAM, and the benefits of communicating KAM decreased because KAM disclosures were boilerplate. OJK's response in relation to the implementation of SA 701 (2021) is to draft OJK regulations related to KAM and to prepare a study related to the first-year implementation of SA 701 (2021). Based on these responses, it is reflected that OJK has an important role in the implementation support stage to ensure that the policy implementation runs well in the long term.

(Dis)similarities between non-symbolic and symbolic number representations: Insights from vector space models

Empirical evidence in support of a shared system for non-symbolic and symbolic number processing has been inconclusive. The current study aims to address this question in a novel way, specifically by testing whether the efficient coding principle based on co-occurrence of number symbols in natural language holds for both non-symbolic and symbolic number processing. The efficient coding principle postulates that perception is optimized when stimuli frequently co-occur in a natural environment. We hypothesized that both numerical ratios and co-occurrence frequencies of symbolic numbers would significantly influence participants' performance on a non-symbolic and symbolic number comparison task. To test this hypothesis, we employed latent semantic analysis on a TASA corpus to quantify number co-occurrence in natural language and calculate language similarity estimates. We engaged 73 native English speakers (mean age = 19.36, standard deviation = 1.83) with normal or corrected vision and no learning disorders in a number comparison task involving non-symbolic (dot arrays) and symbolic stimuli (Arabic numerals and English number words). Results showed that numerical ratios significantly predicted participants' performances across all number formats (ps < 0.001). Language similarity estimates derived from everyday language also predicted performance on the non-symbolic task and the symbolic task involving number words (ps < 0.007). Our results highlight the complex nature of numerical processing, pointing to the co-occurrence of number symbols in natural language as an auxiliary factor in understanding the shared characteristics between non-symbolic and symbolic number representations. Given that our study focused on a limited number range (5 to 16) and a specific task type, future studies should explore a wider range of tasks and numbers to further test the role of the efficient coding principle in number processing.

Playfulness and Kindergarten Children's Academic Skills: Executive Functions and Creative Thinking Processes as Mediators?

ABSTRACTThis study examined the direct and indirect relationships between playfulness (social and cognitive spontaneity), executive functions, convergent thinking, divergent thinking, and academic skills in Hong Kong Chinese kindergarten children. Participants were 181 second‐year (4 to 5 years) kindergarten children (45.9% boys) and their parents. Parents reported demographic information and children's playfulness and executive functions through a questionnaire. Children were administered behavioral assessments of convergent thinking, divergent thinking, Chinese word reading, and number word comparison at their kindergarten. Results from a path analytic model revealed the mediating roles of convergent and divergent thinking in the relationship between playfulness and number word comparison. In contrast, convergent thinking mediated the link between playfulness and Chinese word reading. Executive functions were positively related to playfulness but unrelated to children's academic skills. The findings suggest that playful children might develop better creative thinking processes, supporting their academic skills. Practically, the findings underscore the importance of play‐based learning in developing children's creativity and academic skills in the early years.

EXPRESS: Exploring 'phasic' vs. 'tonic' accounts of the effect of switch probability on the auditory attention switch cost.

Task-switching experiments have shown that the 'switch cost' (poorer performance for task switches than for repetitions) is smaller when the probability of a switch is high (e.g., 0.75) than when it is low (e.g., 0.25). Some theoretical accounts explain this effect in terms of top-down control deployed in advance of the task cue ('pre-cue reconfiguration'). We tested such accounts by manipulating the time available before the onset of the cue (the response-cue interval, RCI), reasoning that top-down pre-cue reconfiguration requires time and therefore its effect should increase with RCI. Participants heard a man and a woman simultaneously speaking number words and categorised the number (<5 vs. >5) spoken by the voice specified by a pictorial gender-related cue presented at an RCI of 100 ms or 2200 ms. The target voice switched with a probability of 0.25 or 0.75 (in separate sessions). In Experiment 1 RTs revealed a large effect of switch probability on the switch cost in the short RCI, which did not increase in the long RCI. Errors hinted at such an increase, but it did not receive clear statistical support and was disconfirmed by a direct and better powered replication in Experiment 2, which fully confirmed the RT pattern from Experiment 1. Thus, the effect of switch probability on the switch cost required little/no time following the response to emerge - it was already at full magnitude at a short RCI - challenging accounts that assume 'phasic' deployment of top-down task-set control in advance of the cue.

Numbers in Context: Cardinals, Ordinals, and Nominals in American English.

There are three main types of number used in modern, industrialized societies. Cardinals count sets (e.g., people, objects) and quantify elements of conventional scales (e.g., money, distance), ordinals index positions in ordered sequences (e.g., years, pages), and nominals serve as unique identifiers (e.g., telephone numbers, player numbers). Many studies that have cited number frequencies in support of claims about numerical cognition and mathematical cognition hinge on the assumption that most numbers analyzed are cardinal. This paper is the first to investigate the relative frequencies of different number types, presenting a corpus analysis of morphologically unmarked numbers (not, e.g., "eighth" or "21st") in which we manually annotated 3,600 concordances in the Corpus of Contemporary American English. Overall, cardinals are dominant-both pure cardinals (sets) and measurements (scales)-except in the range 1,000-10,000, which is dominated by ordinal years, like 1996 and 2004. Ordinals occur less often overall, and nominals even less so. Only for cardinals do round numbers, associated with approximation, dominate overall and increase with magnitude. In comparison with other registers, academic writing contains a lower proportion of measurements as well as a higher proportion of ordinals and, to some extent, nominals. In writing, pure cardinals and measurements are usually represented as number words, but measurements-especially larger, unround ones-are more likely to be numerals. Ordinals and nominals are mostly represented as numerals. Altogether, this paper reveals how numbers are used in American English, establishing an initial baseline for any analyses of number frequencies and shedding new light on the cognitive and psychological study of number.

Are “10 Grams of Protein” Better than “Ten Grams of Protein”? How Digits versus Number Words Influence Consumer Judgments

Abstract Numerical information can be communicated using different number formats, such as digits (“5”) or number words (“five”). For example, a battery product may claim to last for “5 hours” or “five hours.” And while these two formats are used interchangeably in the marketplace, it is not clear how they influence consumer judgments and behavior. Via six experimental studies, two online ad campaigns, and one large secondary dataset analysis, we find that digits, compared to number words, positively affect consumer behavior. We refer to this phenomenon as the number format effect. We further show that the number format effect occurs because consumers feel that digits (vs. number words) are the right way to present numerical information: digits lead to a sense of feeling right that then affects consumer behavior. Finally, we show that the number format effect is amplified when credibility of the source of information is low, and attenuated when source credibility is high. The current research advances knowledge of how numerical information influences consumer judgments and behavior and carries important implications for marketers and policymakers as they communicate numerical information to consumers.

Mapping skills between symbols and quantities in preschoolers: The role of finger patterns.

Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non-symbolic quantities. Preschool children (3-year-olds, N=113, Mage=40.8months, SDage=3.6months; 4-year-olds, N=103, Mage=52.9months, SDage=3.4months) both cardinality knowers and subset-knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence. RESEARCH HIGHLIGHTS: Children are more accurate in mapping between finger patterns and symbols (number words and Arabic digits) than in mapping finger patterns and quantities, indicating that fingers are processed holistically as symbolic codes. Children can map finger patterns to symbols above their corresponding cardinality level even in subset-knowers. Finger patterns may play a role in the process by which children learn to map symbols to quantities. Fingers patterns' use in the classroom context may be an adequate instructional and diagnostic tool.

Establishing a Material Description Table to Optimize Mandarin Proficiency for Indonesian Learners: An Applied Contrastive Analysis Perspective

Abstract. This study aims to elucidate the most contrasting differences between Mandarin and Indonesian language rules. Based on the analysis results, it is hoped that this can serve as a foundation for creating a learning media, namely a descriptive material table. The study reveals that the most contrasting rule lies in the Indonesian language auxiliary number words, which have no more than 30 auxiliary number words, whereas in Mandarin, or known as 量, there are over 200 such words. Additionally, there is a rule for constructing past tense sentences. In Indonesian, a word meaning “finished” is used to indicate the past, contrasting with Mandarin, which employs the particle “了”, which can also have different meanings according to different rules. Furthermore, there is a Numeral system rule where Indonesian simply translates numbers into letters, while Mandarin has specific and detailed rules; this clearly presents a contrasting difference. There is also a rule on reduplication, or in Mandarin termed 重叠, where the quantity of rules between the two languages is almost balanced, yet the functions of usage are vastly contrasting. Lastly, there is the rule of “离合词”, a Mandarin language rule that has no equivalent in Indonesian. The method employed is a mixed-method approach, along with a narrative elaboration model based on quantitative differences in the amount of data between Mandarin and Indonesian languages, which are then expounded upon qualitatively. The data source used is the Confucius Institute (孔子学院) recommended books: 标准教程 Standard Course HSK (Hanyu Shuping Kaoshi / Chinese Proficiency Tes) 1 - 6 下 (Part 2). Data analysis techniques include identification, classification, and presentation of the results of data analysis. The results of the research and presentation show that there is a big gap between Mandarin and Bahasa Indonesia linguistic tools, with each of the rules that bind it. Therefore, it is necessary to develop a learning media to reduce this gap.Keywords: Material description table, Applied Contrastive Analysis, Mandarin, Indonesian Learners.

Examining sources of language production switch costs amongst Tibetan-Chinese-English trilinguals

ABSTRACT The present study tested whether the switch costs of production-based language switching tasks by trilinguals are due to competition from outside language schemas or from within language systems. We recruited 90 Tibetan-Chinese-English trilinguals in 10th grade in a Tibetan middle school in China to name digits and number words using different stimuli valence. The study was divided into three experiments, one for each combination of two languages possible amongst Tibetan, Chinese and English. We observed the switch cost symmetrical patterns in the three experiments. The results suggest that the sources of switch cost are partially from outside competition between language schemas and partially from within language system. These results may contribute to our understanding of the language control mechanism between production-based and comprehension-based language switching tasks and language control mechanism of trilinguals with three orthographically different languages.

Love and hate do not modulate the attentional blink but improve overall performance

ABSTRACT How may feelings of love and hate impact people’s attention? We used a modified Attentional Blink (AB) task in which 300 participants were asked to categorise a name representing a person towards whom they felt either hate, love, or neutral (first target) plus identify a number word (second target), both embedded in a rapidly presented stream of other words. The lag to the second target was systematically varied. Contrary to our hypothesis, results revealed that both hated and loved names resulted in higher accuracy for the second target than neutral names, which was largely independent of lag. Also, there we observed no sustained transfer effects of love and hate onto neutral name trials. The findings differ from prior research on attentional blink and transient, non-personal, stimulus-driven emotions, suggesting that interpersonal feelings activate different attention-relevant mechanisms. Relevant to future research, we speculate that love and hate are motivators of goal-directed behaviour that facilitate subsequent information processing.

NYAYA-VAISESIKA ON NUMBER AND ITS PERCEPTION

The Nyaya and the Vaisesika system are two arthodox (astika) system of Indian Philosophy meaning they admit the Vedas as eternal and infallible that preexist the common era. In their early history, the Nayay and Vaisesika were two Independent system with their own respective metaphysics, epistemology, logic, ethics and solerious. Overtime, the Vaisesika system become so entwined with the Nyaya to the extent that until recently, there was he Independent history of the Vaisesika as a basic system. One reason for addverssing these two systems together is that share many important tents; both systems are committed to common – sense realism and pluralism in their ontology; believe in the creation of the world from material atmos that conjoin to generate. This world by the will of God and in accordance with the accumulated merits and demerits of individual agent. In my article I want to discuss about the Nyaya-vaisesika on number and its perception.The Nyaya-Vaisesika account of number is based on an analysis of our actual - cognitions like 'one', 'two', 'three', etc. They raised the different problems regarding number neither from their interest in mathematics nor from a logistic point of view. We use number words like 'one', 'two', 'three', etc, which in this view designate numbers one, two, three, etc. And numbers for them are as much qualifying features of substances as the qualities like colour, taste, etc. are. They hold a realistic view of number, but such realism should not be confused with Platonism, because numbers in their system are not eternal, timeless, self-subsistent entities known in a priori intuition. A peculiarity of the Nyaya-Vaisesika treatment of number should be noted. The number words like 'one' or 'two', do not refer to any single number like one or two. In fact they admit many ones many, twos many threes, etc.

The counting principle makes number words unique

Abstract Following Ariel (2021. Why it’s hard to construct ad hoc number concepts. In Caterina Mauri, Ilaria Fiorentini, &amp; Eugenio Goria (eds.), Building categories in interaction: Linguistic resources at work, 439–462. Amsterdam: John Benjamins), we argue that number words manifest distinct distributional patterns from open-class lexical items. When modified, open-class words typically take selectors (as in kinda table), which select a subset of their potential denotations (e.g., “nonprototypical table”). They are typically not modified by loosening operators (e.g., approximately), since even if bare, typical lexemes can broaden their interpretation (e.g., table referring to a rock used as a table). Number words, on the other hand, have a single, precise meaning and denotation and cannot take a selector, which would need to select a subset of their (single) denotation (??kinda seven). However, they are often overtly broadened (approximately seven), creating a range of values around N. First, we extend Ariel’s empirical examination to the larger COCA and to Hebrew (HeTenTen). Second, we propose that open-class and number words belong to sparse versus dense lexical domains, respectively, because the former exhibit prototypicality effects, but the latter do not. Third, we further support the contrast between sparse and dense domains by reference to: synchronic word2vec models of sparse and dense lexemes, which testify to their differential distributions, numeral use in noncounting communities, and different renewal rates for the two lexical types.

Weaker semantic priming effects with number words in the second language of math learning.

Bilinguals' exact number representations result from associations between language-independent Indo-Arabic digits ("5"), two verbal codes ("fünf" and "cinq") and a common, largely overlapping semantic representation. To compare the lexical and semantic access to number representations between two languages, we recruited a sample of balanced highly proficient German-French adult bilinguals. At school, those bilinguals learned mathematics in German for 6 years (LM1) and then switched to French (LM2) in 7th grade (12 years old) until 13th grade. After the brief presentation of primes (51 ms) consisting of Indo-Arabic digits or number words in German or French, an Indo-Arabic digits target had to be read in either German or French in an online study. Stimuli were numbers from 1 to 9, and we varied the absolute distance between primes and targets from 0 (i.e., 1-1) to 3 (1-4; as in Reynvoet et al., 2002). The priming distance effect (PDE) was used to measure the strength of numerical semantic association. We find comparable PDEs with Indo-Arabic digits and German number word primes, independently from the target naming language. However, we did not find a clear PDE with French number word primes, neither when naming targets in German, nor in French. The weaker PDE from LM2 compared to LM1 primes is interpreted as a weaker lexico-semantic association of LM2 number words. These results indicate a critical role of the LM1 and further emphasize the role of language in processing numbers. They might have important implications for designing bilingual school curricula. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Automorphic word maps and the Amit–Ashurst conjecture

Abstract In this article, we address the Amit–Ashurst conjecture on lower bounds of a probability distribution associated to a word on a finite nilpotent group. We obtain an extension of a result of [R. D. Camina, A. Iñiguez and A. Thillaisundaram, Word problems for finite nilpotent groups, Arch. Math. (Basel) 115 (2020), 6, 599–609] by providing improved bounds for the case of finite nilpotent groups of class 2 for words in an arbitrary number of variables, and also settle the conjecture in some cases. We achieve this by obtaining words that are identically distributed on a group to a given word. In doing so, we also obtain an improvement of a result of [A. Iñiguez and J. Sangroniz, Words and characters in finite 𝑝-groups, J. Algebra 485 (2017), 230–246] using elementary techniques.

The reciprocity of spatial-numerical associations of vocal response codes depends on stimulus mode.

Individuals make faster left responses to small/er numbers and faster right responses to large/r numbers than vice versa. This "spatial-numerical association of response codes" (SNARC) effect represents evidence for an overlap between the cognitive representations of number and space. Theories of the SNARC effect differ in whether they predict bidirectional S-R associations between number and space or not. We investigated the reciprocity of S-R priming effects between number and location in three experiments with vocal responses. In Experiments 1 and 2, participants completed a number-location task, with digits as stimuli and location words as responses, and a location-number task, with physical locations as stimuli and number words as responses. In addition, we varied the S-R mapping in each task. Results revealed a strong SNARC effect in the number-location task, but no reciprocal SNARC effect in the location-number task. In Experiment 3, we replaced physical location stimuli with location words and digit stimuli with number words. Results revealed a regular and a reciprocal SNARC effect of similar size. Reciprocal SNARC effects thus seem to emerge with verbal location stimuli and vocal responses, but not with physical location stimuli and vocal responses. The S-R associations underlying the SNARC effect with vocal responses thus appear bidirectional and symmetrical for some combinations of stimulus and response sets, but not for others. This has implications for theoretical accounts of the SNARC effect which need to explain how stimulus mode affects the emergence of reciprocal but not regular SNARC effects.

The obscured structure of the number in preschool education (pre-symbolic stage). Prime part

The article highlights certain aspects of the obscured structure of the number, which occur irregularly in the teaching of numeracy in Preschool Education. Its absence, as an effect, leads to the child's misunderstanding of the concept of number. In the presymbolic stage, the number is taught through the word. Structural particularities are found in the semantics and phonetics of the number word and are substantial in the processes of speech and listening. The objectives are to make known the obscured structure of the number and its elements and to analyze the nature of the name of the number. It is justified that the basis of the word "ONE" are the first sound manifestations of the infant. It states that there is the same and equal relationship between the acquisition of knowledge of language and speech with the acquisition of knowledge of number through the development of tonal auditory balance. Methodology: the theoretical analysis of the structural parts (semantics and phonosemantics) of the number and the identification of reciprocal correlation between the constructions of the knowledge of spoken numeral word in Preschool Education through the implemented technology. Contribution: the development of the method for learning the concept of number.