A new look at old numbers, and what it reveals about numeration

Sounding the depths at the confluence of numerosity and language

Linguistics Vanguard ◽

10.1515/lingvan-2014-1002 ◽

2015 ◽

Vol 1 (1) ◽

Cited By ~ 1

Author(s):

Caleb Everett

Keyword(s):

Recent Work ◽

Numerical Cognition ◽

Number Words ◽

Number Systems ◽

The Relationship

AbstractResearchers in a variety of disciplines are currently exploring how number words and other culturally variant symbols for quantities enable and enhance numerical cognition. In this article I survey the ways in which fieldwork among Amazonian languages is helping to elucidate the relationship between numerical cognition and language. I highlight several noteworthy findings in recent work on this topic, address their implications, and also consider the potential of future fieldwork on languages with typologically remarkable number systems.

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Units-first or tens-first: Does language matter when processing visually presented two-digit numbers?

Quarterly Journal of Experimental Psychology ◽

10.1177/1747021819892165 ◽

2019 ◽

Vol 73 (5) ◽

pp. 726-738

Author(s):

Alexandre Poncin ◽

Amandine Van Rinsveld ◽

Christine Schiltz

Keyword(s):

Numerical Cognition ◽

Fourth Graders ◽

Number Word ◽

Older Children ◽

Mental Calculation ◽

Magnitude Comparison ◽

Simultaneous Condition ◽

Number Words ◽

French Speaking ◽

German Speaking

The linguistic structure of number words can influence performance in basic numerical tasks such as mental calculation, magnitude comparison, and transcoding. Especially the presence of ten-unit inversion in number words seems to affect number processing. Thus, at the beginning of formal math education, young children speaking inverted languages tend to make relatively more errors in transcoding. However, it remains unknown whether and how inversion affects transcoding in older children and adults. Here we addressed this question by assessing two-digit number transcoding in adults and fourth graders speaking French and German, that is, using non-inverted and inverted number words, respectively. We developed a novel transcoding paradigm during which participants listened to two-digit numbers and identified the heard number among four Arabic numbers. Critically, the order of appearance of units and tens in Arabic numbers was manipulated mimicking the “units-first” and “tens-first” order of German and French. In a third “simultaneous” condition, tens and units appeared at the same time in an ecological manner. Although language did not affect overall transcoding speed in adults, we observed that German-speaking fourth graders were globally slower than their French-speaking peers, including in the “simultaneous” condition. Moreover, French-speaking children were faster in transcoding when the order of digit appearance was congruent with their number-word system (i.e., “tens-first” condition) while German-speaking children appeared to be similarly fast in the “units-first” and “tens-first” conditions. These findings indicate that inverted languages still impose a cognitive cost on number transcoding in fourth graders, which seems to disappear by adulthood. They underline the importance of language in numerical cognition and suggest that language should be taken into account during mathematics education.

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Awareness of Preservice Mathematics Teachers about Prehistoric and Ancient Number Systems

Malikussaleh Journal of Mathematics Learning (MJML) ◽

10.29103/mjml.v3i2.2904 ◽

2020 ◽

Vol 3 (2) ◽

pp. 57

Author(s):

Nazan Mersin ◽

Mehmet Akif Karabörk ◽

Soner Durmuş

Keyword(s):

System Analysis ◽

Descriptive Analysis ◽

History Of Mathematics ◽

Number System ◽

Ancient Greek ◽

Black Sea Region ◽

Ancient Egyptian ◽

Number Systems ◽

Counting Methods ◽

History Of

This study seeks to analyse the awareness of the pre-service teachers on the counting methods, systems and tools used in the prehistoric method and the Ancient period and to examine the distribution of this awareness by gender. A total of 42 sophomore-level students studying at a university in the Western Black Sea region, Turkey, participated in this exploratory case study. The data were obtained through a form consisting of 6 questions, one of which is open-ended, after the 14-week course of history of mathematics. The data collection tool included questions on the counting methods used in the pre-historic period and the Ancient Egyptian, Ancient Roman, Babylonian, Ancient Greek and Mayan number systems. The data were analysed through descriptive analysis and content analysis. The findings indicated that the pre-service teachers most reported the methods of tallying, tying a knot, token, circular disc. Also, the question on the Ancient Egyptian number system was answered correctly by all pre-service teachers, the lowest performance was observed in the question on the Mayan number system. Analysis of the answers by gender revealed that the male pre-service teachers were more likely to give false answers compared to the female pre-service teachers.

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Constructing a Concept of Number

10.31235/osf.io/5ytd3 ◽

2021 ◽

Author(s):

Karenleigh A. Overmann

Keyword(s):

Numerical Cognition ◽

Explanatory Power ◽

Two Dimensional ◽

Multiple Forms ◽

Distributed Objects ◽

Content Structure ◽

Contemporary Research ◽

Number Systems ◽

And Behaviors

Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like linearity that may persist in the form of knowledge and behaviors, ultimately yielding numerical concepts that are irreducible to and functionally independent of any particular form. Material devices used to represent and manipulate numbers also interact with language in ways that reinforce or contrast different aspects of numerical cognition. Not only does this interaction potentially explain some of the unique aspects of numerical language, it suggests that the two are complementary but ultimately distinct means of accessing numerical intuitions and insights. The potential inclusion of materiality in contemporary research in numerical cognition is advocated, both for its explanatory power, as well as its influence on psychological, behavioral, and linguistic aspects of numerical cognition.

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

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2020.0206 ◽

2021 ◽

Vol 376 (1824) ◽

Cited By ~ 1

Author(s):

Andreea S. Calude

Keyword(s):

Human Evolution ◽

Experimental Studies ◽

Consistent Pattern ◽

Theme Issue ◽

Number Words ◽

The Past ◽

Language History ◽

Number Systems ◽

The World ◽

History Of

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’.

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Constructing a concept of number

Journal of Numerical Cognition ◽

10.5964/jnc.v4i2.161 ◽

2018 ◽

Vol 4 (2) ◽

pp. 464-493 ◽

Cited By ~ 5

Author(s):

Karenleigh A. Overmann

Keyword(s):

Numerical Cognition ◽

Explanatory Power ◽

Two Dimensional ◽

Multiple Forms ◽

Distributed Objects ◽

Content Structure ◽

Contemporary Research ◽

Number Systems ◽

And Behaviors

Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like linearity that may persist in the form of knowledge and behaviors, ultimately yielding numerical concepts that are irreducible to and functionally independent of any particular form. Material devices used to represent and manipulate numbers also interact with language in ways that reinforce or contrast different aspects of numerical cognition. Not only does this interaction potentially explain some of the unique aspects of numerical language, it suggests that the two are complementary but ultimately distinct means of accessing numerical intuitions and insights. The potential inclusion of materiality in contemporary research in numerical cognition is advocated, both for its explanatory power, as well as its influence on psychological, behavioral, and linguistic aspects of numerical cognition.

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Counting and the ontogenetic origins of exact equality

10.31234/osf.io/mtzd7 ◽

2021 ◽

Author(s):

Rose M. Schneider ◽

Erik Brockbank ◽

Roman Feiman ◽

David Barner

Keyword(s):

Matching Task ◽

Important Data ◽

Number Concepts ◽

Counting System ◽

Number Words ◽

Exact Number ◽

Number Systems ◽

Us Children ◽

Exact Equality ◽

Symbolic Number

Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a “set-matching” task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children’s ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number.

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Estimation as analogy-making: Evidence that preschoolers’ analogical reasoning ability predicts their numerical estimation

10.31234/osf.io/pdszc ◽

2020 ◽

Author(s):

Joseph Alvarez ◽

Monica Abdul-Chani ◽

Paul Michael Deutchman ◽

Kayla Dibiasie ◽

Julia Iannucci ◽

...

Keyword(s):

Cognitive Skills ◽

Analogical Reasoning ◽

Number System ◽

Reasoning Ability ◽

Approximate Number System ◽

Numerical Estimation ◽

Structure Mapping ◽

Number Words ◽

Number Systems ◽

Linguistic Representations

All humans and many animals can represent approximate quantities of perceptual objects nonlinguistically by using the Approximate Number System (Dehaene, 1997/2011). Early in life, children in numerate societies also learn to describe this system using number words. How do linguistic representations of number become related to nonlinguistic representations of number? We hypothesize that the analogical process of structure mapping (Gentner, 1983) helps children to form mappings between the linguistic and nonlinguistic number systems on the basis of structural similarities between the two systems. To test this, we tested and analyzed 47 four-and-five year olds’ performance on estimation and analogy tasks. We found that analogical reasoning ability uniquely predicted several components of estimation performance, even when controlling for other domain-general cognitive skills. This provides strong evidence that analogical processes are uniquely related to the development of early estimation.

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