Number Of Words Research Articles

Enculturation and the historical origins of number words and concepts

In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical.

The Relationship Between Confidence and Conformity in a Non-routine Counting Task With Young Children: Dedicated to the Memory of Purificación Rodríguez.

Counting is a complex cognitive process that is paramount to arithmetical development at school. The improvement of counting skills of children depends on their understanding of the logical and conventional rules involved. While the logical rules are mandatory and related to one-to-one correspondence, stable order, and cardinal principles, conventional rules are optional and associated with social customs. This study contributes to unravel the conceptual understanding of counting rules of children. It explores, with a developmental approach, the performance of children on non-routine counting detection tasks, their confidence in their answers (metacognitive monitoring skills), and their ability to change a wrong answer by deferring to the opinion of a unanimous majority who justified or did not justify their claims. Hundred and forty nine children aged from 5 to 8 years were randomized to one of the experimental conditions of the testimony of teachers: with (n = 74) or without justification (n = 75). Participants judged the correctness of different types of counting procedures presented by a computerized detection task, such as (a) pseudoerrors that are correct counts where conventional rules are violated (e.g., first counting six footballs, followed by other six basketballs that were interspersed along the row), and (b) compensation errors that are incorrect counts where logical rules were broken twice (e.g., skipping the third element of the row and then labeling the sixth element with two number words, 5 and 6). Afterwards, children rated their confidence in their detection answer with a 5-point scale. Subsequently, they listened to the testimony of the teachers and showed either conformity or non-conformity. The participants considered both compensation errors and pseudoerrors as incorrect counts in the detection task. The analysis of the confidence of children in their responses suggested that they were not sensitive to their incorrect performance. Finally, children tended to conform more often after hearing a justification of the testimony than after hearing only the testimonies of the teachers. It can be concluded that the age range of the evaluated children failed to recognize the optional nature of conventional counting rules and were unaware of their misconceptions. Nevertheless, the reasoned justifications of the testimony, offered by a unanimous majority, promoted considerable improvement in the tendency of the children to revise those misconceptions.

Tapping into the interplay of lexical and number knowledge using fast mapping: A longitudinal eye-tracking study with two-year-olds

Language skills and mathematical competencies are argued to influence each other during development. While a relation between the development of vocabulary size and mathematical skills is already documented in the literature, this study further examines how children’s ability to map a novel word to an unknown object as well as their ability to retain this word from memory may be related to their knowledge of number words. Twenty-five children were tested longitudinally (at 30 and at 36 months of age) using an eye-tracking-based fast mapping task, the Give-a-Number task, and standardized measures of vocabulary. The results reveal that children’s ability to create and retain a mental representation of a novel word was related to number knowledge at 30 months, but not at 36 months while vocabulary size correlated with number knowledge only at 36 months. These results show that even specific mapping processes are initially related to the acquisition of number words and they speak for a parallelism between the development of lexical and number-concept knowledge despite their semantic and syntactic differences.

Priming reveals similarities and differences between three purported cases of implicature: Some, number and free choice disjunctions

• Implicature consists in a series of sub-computations, but these can be computed online or stored. • Evidence from priming suggests the quantifier some and number words involve a shared computation. • The most likely candidate for this shared computation is the negation of alternatives. • Alternatives for number are lexically stored, but the alternatives for some are computed online. • Free Choice disjunctions do not show evidence for a shared computation with either some or number . Across a wide variety of semantically ambiguous sentences, implicature has been proposed as a single mechanism which can derive one reading from another in a systematic way. While a single formal mechanism for computing implicatures across disparate cases has an appealing parsimony, differences in behavioral and processing signatures between cases have created a debate about whether the same computation really is so widely shared. Building on previous work by Bott and Chemla (2016), three experiments use structural priming to test for shared computations across three purported cases of implicature: the quantifier some , number words, and Free Choice disjunctions. While we find evidence of a shared computation between the enriched readings of some and number words, we find no evidence that Free Choice readings involve any shared computation with either some or number. Along with evidence of a shared mechanism between some and number implicatures, we also find substantial differences between these two cases. We propose a way to reconcile these findings, as well as seemingly contradictory prior evidence, by understanding implicature as a sequence of separable sub-computations. This implies a spectrum of possibilities for which sub-computations might be shared or distinct between cases, instead of a single implicature mechanism that can only be either present or absent.

Linguistic Complexity: Relationships Between Phoneme Inventory Size, Syllable Complexity, Word and Clause Length, and Population Size

Starting from a view on language as a complex, hierarchically organized system composed of many parts that have many interactions, this paper investigates statistical relationships between the linguistic variables “phoneme inventory size,” “syllable size,” “length of words,” “length of clauses,” and the nonlinguistic variable “population size.” By analyzing parallel textual material of 61 languages (18 language families) we found strong positive correlations between phoneme inventory size, mean number of phonemes per syllable, and mean number of monosyllables. We observed significant negative correlations between phoneme inventory size and the mean length of words and the mean length of clauses, measured as number of syllables. We then correlated the linguistic complexity data with estimated speaker population sizes and could reveal that languages with more speakers tend to have more phonemes per syllable, shorter words in number of syllables, a higher number of monosyllabic words, and a higher number of words per clause. Moreover, we reproduce the results of former studies that found a positive correlation between population size and phoneme inventory size for our language sample. The findings are discussed in light of previous research and within the framework of Systemic Typology. We propose that syllable complexity is a key factor in the correlations identified in this study, and that Zipf's law of Abbreviation explains the associations between “word length,” “syllable complexity,” “phoneme inventory size,” and the extralinguistic variable “population size.”

De la protraction en maya?

Abstract Overcounting is a neologism which was proposed in the late XXth century to define « the operation that designates a number by its orientation towards a boundary ». With a few examples taken from Asiatic languages, Mayan numerations from Central America are generally given as representative of this uncommon type of linguistic operation to build words for numbers. However, our analysis of the operative pattern in this kind of Mayan numeration (which has cohabited for many centuries with a more simply additive type of number construction) as well as the analysis of the data from pre-hispanic times and the colonial period brought us to question this definition, at least for Mayan languages. Our study indeed shows that the so-called “overcounting” system in Mayan numerations, if it was definitely present there a long time before the Europeans, was strongly associated to an aspect of the comput that sets to work an “encapsulation” of the vigesimal scores and where a number is actually not designated for its orientation towards the higher boundary but where the aim is to process in a non-linear way following an “encapsulation of the numerical knots” and looking for a retrograde anteriority.

The history of number words in the world's languages—what have we learnt so far?

For over 100 years, researchers from various disciplines have been enthralled and occupied by the study of number words. This article discusses implications for the study of deep history and human evolution that arise from this body of work. Phylogenetic modelling shows that low-limit number words are preserved across thousands of years, a pattern consistently observed in several language families. Cross-linguistic frequencies of use and experimental studies also point to widespread homogeneity in the use of number words. Yet linguistic typology and field documentation reports caution against positing a privileged linguistic category for number words, showing a wealth of variation in how number words are encoded across the world. In contrast with low-limit numbers, the higher numbers are characterized by a rapid and morphologically consistent pattern of expansion, and behave like grammatical phrasal units, following language-internal rules. Taken together, the evidence suggests that numbers are at the cross-roads of language history. For languages that do have productive and consistent number systems, numerals one to five are among the most reliable available linguistic fossils of deep history, defying change yet still bearing the marks of the past, while higher numbers emerge as innovative tools looking to the future, derived using language-internal patterns and created to meet the needs of modern speakers. This article is part of the theme issue 'Reconstructing prehistoric languages'.

Facilitating young children’s numeracy talk in play: The role of parent prompts

Previous research has demonstrated the contribution of parents’ number language to children’s own engagement with numbers and later mathematical achievement. Although there is evidence that both the quantity and complexity of parent number talk contribute to children’s math learning, it is unclear whether different forms of parents’ number talk—statements versus prompts—offer unique contributions to how children engage in math. We examined parent number talk among 50 dyads of parents and 2- to 4-year-olds during pretend play, coding parents’ provisions of informative number statements and prompts inviting children to engage in number talk. The total amount (tokens) and diversity (types) of children’s number words were analyzed separately. Parents’ number utterances, particularly prompts about number, were infrequent. Both parents’ number statements and their prompts were uniquely related to children’s number word tokens. Only prompts were associated with children’s number word types. Follow-up analyses indicated that prompts were associated with lengthier parent–child conversations about number than parent statements and that children used larger number words when responding to parent prompts than when they themselves initiated number talk. These findings highlight the importance of parents’ prompts for enhancing the quality of parent–child math exchanges by providing opportunities for children to advance their current use of numerical language. Consequently, parents’ use of number-related prompts may play an important role in children’s early math engagement.

The processing of prices across numerical formats

We evaluated whether the format in which prices are presented determines the processing of their magnitude. A price comparison task was used in which two-digit prices with Arabic digits, written number words and auditory number words were presented in the euro currency. Prices were number-monetary category (NMC) compatible (49 euros - 36 cents) when the number and monetary category of one price were larger than those of the other (49 > 36, euros > cents); or NMC incompatible (49 cents - 36 euros) when the number of one price was larger but the monetary category smaller than those of the other (49 > 36, cents < euros). In addition, there were unit-decade (UD) compatible prices when the decade and unit of one price were larger than those of the other (49 euros - 36 cents, 4 > 3, 9 > 6); and UD incompatible prices when the decade of one price was larger but the unit smaller than those of the other (46 euros - 39 cents, 4 > 3, 6 < 9). The results showed NMC compatibility effects in all numerical formats. However, the UD compatibility effect was not found in any numerical format. The results are discussed within the hybrid model of multisymbolic magnitude processing.

Starting small: exploring the origins of successor function knowledge.

Although most U. S. children can accurately count sets by 4years of age, many fail to understand the structural analogy between counting and number - that adding 1 to a set corresponds to counting up 1 word in the count list. While children are theorized to establish this Structure Mapping coincident with learning how counting is used to generate sets, they initially have an item-based understanding of this relationship, and can infer that, e.g, adding 1 to "five" is "six", while failing to infer that, e.g., adding 1 to "twenty-five" is "twenty-six" despite being able to recite these numbers when counting aloud. The item-specific nature of children's successes in reasoning about the relationship between changes in cardinality and the count list raises the possibility that such a Structure Mapping emerges later in development, and that this ability does not initially depend on learning to count. We test this hypothesis in two experiments and find evidence that children can perform item-based addition operations before they become competent counters. Even after children learn to count, we find that their ability to perform addition operations remains item-based and restricted to very small numbers, rather than drawing on generalized knowledge of how the count list represents number. We discuss how these early item-based associations between number words and sets might play a role in constructing a generalized Structure Mapping between counting and quantity.

Symbolic Magnitude Understanding Predicts Preschoolers’ Later Addition Skills

ABSTRACT Young children’s symbolic magnitude understanding, or knowledge of how written numerals and number words can be ordered and compared, is thought to play an important role in their mathematical development. There is consistent evidence that symbolic magnitude skills predict mathematical achievement in later childhood and adulthood. Yet less is known about symbolic magnitude understanding before the start of formal schooling, a time when children are rapidly developing knowledge of small whole numbers. In this study, preschoolers (N = 140, Mean age = 4 years, 5 months) were assessed using measures of numerical skills (cardinality, symbolic magnitude, addition) and executive functioning (working memory, inhibitory control, attention shifting) in the winter and spring of the school year. Symbolic magnitude predicted later addition skills, fully mediating the relation between children’s cardinality and addition skills. Moreover, children’s domain-general executive functioning skills and domain-specific numeracy skills explained a similar amount of variability in children’s later addition skills. Results highlight the role of symbolic magnitude in the development of children’s understanding of mathematics.

Neurodevelopmental differences in child and adult number processing: An fMRI-based validation of the triple code model

The triple code model of numerical cognition (TCM) details the neurocognitive mechanisms associated with perceiving and manipulating numerical information in exact symbolic (Arabic digits and number words) and approximate nonsymbolic numerical magnitude (e.g., dot arrays) representation codes. The current study provides a first empirical fMRI-based investigation into neurodevelopmental differences in 30 healthy children’s and 44 healthy adults’ recruitment of neural correlates associated with the Arabic digit, number word, and nonsymbolic magnitude codes. Differences between the two groups were found in cingulate regions commonly associated with domain-general aspects of cognitive control, as opposed to neural correlates of number processing per se. A primary developmental difference was identified in verbal number discrimination, where only adults recruited left-lateralized perisylvian language areas in accordance with the TCM. We therefore call for a revision of the verbal code and a formulation of separate child and adult-specific neurocognitive mechanisms associated with the discrimination of number words. Although further research is necessary, results indicate that numerical discrimination abilities in middle-school-aged children operate close to adult-level maturity. Neurodevelopmental differences may be more apparent in younger children, or on the level of functional network dynamics as opposed to a shift in recruited neural substrates.

The Advantages of Pleco and Google Translate Applications in Assisting Mandarin Language Learning

As technology develops, dictionaries have changed from paper to electronic. Electronic dictionaries can be an alternative medium for language learning because they combine sound, visuals and text that make learning foreign languages easier. One example of using an electronic dictionary is in reading subjects. Users can learn about how to pronounce a vocabulary and sound tones correctly by utilizing the audio feature in an electronic dictionary. Vocabulary recall through mobile device applications is far more effective than through other media. The electronic dictionary application that is widely used by Chinese Literature students in learning Mandarin is the Pleco and Google Translate application. Therefore, the authors are interested in making comparisons of the similarities and differences between the two applications for the recommendation of Mandarin learning aids. This study uses a comparison method by comparing the functions of the two e-dictionaries. From the results of the comparison, both applications have keyboard features, handwriting features, voice record features and scanning features for translating words. The difference is in the radical features, stroke, number words and sentences sample

Mapping between number notations in kindergarten and the role of home numeracy

Two recent studies investigated how children learn to map between digits, number words, and dots (Hurst, Anderson, & Cordes, 2017; Jiménez Lira, Carver, Douglas, & LeFevre, 2017). In the current study we aimed to replicate these previous findings by examining a much larger sample (N = 195 kindergarteners, aged 2 years 6 months to 5 years 2 months) and taking into account home numeracy activities, that is, daily parent-child interactions with numerical content. In line with previous studies, the results showed that children first learn to map number words onto dots, and number words onto digits, and only afterwards – to map digits onto dots. Furthermore, number words ↔ digits mapping was a better mediator of the relation between digits ↔ dots and the dots ↔ number words mapping tasks, than the dots ↔ number words, suggesting that children rely on their symbolic number knowledge to learn the relation between digits and dots. Finally, both basic and advanced home numeracy activities were positively related to children’s mappings skills. Furthermore, we observed that with increasing the children’s age a shift from basic to advanced activities was present. These results emphasize the importance of tailoring the home numeracy activities according to children’s age.

Word Order Predicts Cross-Linguistic Differences in the Production of Redundant Color and Number Modifiers.

When asked to identify objects having unique shapes and colors among other objects, English speakers often produce redundant color modifiers ("the red circle") while Spanish speakers produce them less often ("el circulo (rojo)"). This cross-linguistic difference has been attributed to a difference in word order between the two languages, under the incremental efficiency hypothesis (Rubio-Fernández, Mollica, & Jara-Ettinger, 2020). However, previous studies leave open the possibility that broad language differences between English and Spanish may explain this cross-linguistic difference such that English speakers may generally produce more modifiers than Spanish speakers, including redundant ones, irrespective of word order. Here, we test the incremental efficiency hypothesis in a language production task crossing language (English, Spanish) with modifier type (color, number). Critically, number words occur on the same side of the noun in both English and Spanish. If broad language differences are responsible for the higher rate of color word production in English compared to Spanish, then the same effect should hold for number words. In contrast, the incremental efficiency hypothesis predicts an interaction between language and modifier type, due to different ordering for color words but identical ordering for number words. Our pre-registered analyses offer strong support for the incremental efficiency hypothesis, demonstrating how seemingly small differences in language can cause us to describe the world in surprisingly different ways.

Innovative procedure for soppiness investigation spending writing and facemask gratitude

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Sequential Number Word Formation in the Tungag-Nalik Languages (New Ireland)

Sequential Number Word Formation in the Tungag-Nalik Languages (New Ireland)

СИСТЕМНО-БАЗИСНОЕ ОПРЕДЕЛЕНИЕ ПРОФЕССИОНАЛЬНОЙ ПОЗИЦИИ СТУДЕНТОВ ВЕДОМСТВЕННОГО ВУЗА

The article is devoted to the system-based analysis of the definition and measurement of the professional position of the individual cadet of a departmental university. A basis is a set of elements that is characterized by completeness, orderliness, and measurability. The «set of elements» has the following «substrate characteristics» such as «relation», «mapping» and «transformation», which define the first level of «immersion» in the concept of «basis». In turn, at thesecond level of «immersion» in the concept of «basis», corresponding to three factors («completeness», «orderliness», «measurability»), there are corresponding triple characteristics that determine the third level of «immersion»: 1) «full» is «factorness», «multiply connected» and «integrity»; 2) «the order» is «symmetry», «dichotomy» and «adenomasness»; 3) «measurable» is a «measure», «projection» and «rating». At all three levels of «integration» into the concept of «basis» there is a single generalized dichotomy «external – internal», which in our article is projected on a separate personal dichotomy «social-individual». «Multi-connectivity» means the existence of many dichotomous factors for which there is no single dichotomy, i.e. there is no «node» with a single factor dichotomy (reminiscent of Kettell's factor strategy, consisting of 16 different factor dichotomies in his typology of personality qualities, where there is no single dichotomy). «Unconnectedness» means the existence of a set of factors for which there is a single dichotomy, i.e. there is a «node» with a single factor dichotomy. In the «dimension», the following triples are obtained: 1) measure the representation (image, word, number), 2) projection of data conversion (image to word, image number words number). The last conversion (words to numbers) will be used in this article, and it is, by the way, more common in measurement diagnostic practice. 3) the assessment of the level of measurement of information (low, medium, high) will be used in this article and, by the way, it is also more common in measuring diagnostic practice. In our article, «completeness» is defined by a factorial multi-connected integral set of types. «Orderliness» is defined by a symmetric-dichotomous unconnected factorial verbal structure of a set of types (a single dichotomous multi-factorial verbal structure of types or «verbal basis»). The «measurability»of types is associated with a single dichotomous verbal-numerical evaluation metric scale or with a «numerical basis». «Measurability» makes it possible to create dichotomous basic multifactorial methods based on a dichotomous symmetric verbal-numerical scale evaluation of types.

Do children derive exact meanings pragmatically? Evidence from a dual morphology language

Number words allow us to describe exact quantities like sixty-three and (exactly) one. How do we derive exact interpretations? By some views, these words are lexically exact, and are therefore unlike other grammatical forms in language. Other theories, however, argue that numbers are not special and that their exact interpretation arises from pragmatic enrichment, rather than lexically. For example, the word one may gain its exact interpretation because the presence of the immediate successor two licenses the pragmatic inference that one implies “one, and not two”. To investigate the possible role of pragmatic enrichment in the development of exact representations, we looked outside the test case of number to grammatical morphological markers of quantity. In particular, we asked whether children can derive an exact interpretation of singular noun phrases (e.g., “a button”) when their language features an immediate “successor” that encodes sets of two. To do this, we used a series of tasks to compare English-speaking children who have only singular and plural morphology to Slovenian-speaking children who have singular and plural forms, but also dual morphology, that is used when describing sets of two. Replicating previous work, we found that English-speaking preschoolers failed to enrich their interpretation of the singular and did not treat it as exact. New to the present study, we found that 4- and 5-year-old Slovenian-speakers who comprehended the dual treated the singular form as exact, while younger Slovenian children who were still learning the dual did not, providing evidence that young children may derive exact meanings pragmatically.

Can you trust your number sense: Distinct processing of numbers and quantities in elementary school children

Theories of number development have traditionally argued that the acquisition and discrimination of symbolic numbers (i.e., number words and digits) are grounded in and are continuously supported by the Approximate Number System (ANS)—an evolutionarily ancient system for number. In the current study, we challenge this claim by investigating whether the ANS continues to support the symbolic number processing throughout development. To this end, we tested 87 first- (Age M = 6.54 years, SD = 0.58), third- (Age M = 8.55 years, SD = 0.60) and fifth-graders (Age M = 10.63 years, SD = 0.67) on four audio-visual comparison tasks (1) Number words–Digits, (2) Tones–Dots, (3) Number words–Dots, (4) Tones–Digits, while varying the Number Range (Small and Large), and the Numerical Ratio (Easy, Medium, and Hard). Results showed that larger and faster developmental growth in the performance was observed in the Number Words–Digits task, while the tasks containing at least one non-symbolic quantity showed smaller and slower developmental change. In addition, the Ratio effect (i.e., the signature of ANS being addressed) was present in the Tones–Dots, Tones–Digits, and Number Words–Dots tasks, but was absent in the Number Words–Digits task. These findings suggest that it is unlikely that the ANS continuously underlines the acquisition and the discrimination of the symbolic numbers. Rather, our results indicate that non-symbolic quantities and symbolic numbers follow qualitatively distinct developmental paths, and argue that the latter ones are processed in a semantic network which starts to emerge from an early age.