Yupno Number System and Counting

Wassmann, Jürg; Dasen, Pierre R.

doi:10.1177/0022022194251005

Cited by 59 publications

(42 citation statements)

References 5 publications

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“…Numbers 11 to 20 were counted on the feet, numbers 21 to 33 on other body parts. However, while counting from 1 to 10 was very consistent in Wassman and Dasen's (1994) study, there was a wide variability in the order of the body parts used for counting by different men especially beyond 20. This study shows that counting is a culturally acquired technique.…”

Section: The Influence Of Language On Numerical Cognitionmentioning

confidence: 60%

The Cultural Number Line: A Review of Cultural and Linguistic Influences on the Development of Number Processing

Göbel

Shaki

Fischer

2011

Journal of Cross-Cultural Psychology

190

129

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Approximate processing of numerosities is a universal and preverbal skill, while exact number processing above 4 involves the use of culturally acquired number words and symbols. The authors first review core concepts of numerical cognition, including number representation in the brain and the influential view that numbers are associated with space along a "mental number line." Then, they discuss how cultural influences, such as reading direction, finger counting, and the transparency of the number word system, can influence the representation and processing of numbers. Spatial mapping of numbers emerges as a universal cognitive strategy. The authors trace the impact of cultural factors on the development of number skills and conclude that a cross-cultural perspective can reveal important constraints on numerical cognition."The standard horizontal number line is clearly a product of culture, as it depends on culture-specific conventions of a written numeral system. But it also depends on three innate faculties: our number sense, our sense of the space around us, and the visual imagery system. The representations of our number sense are mapped onto a horizontal line (or arranged in a row) to form an integrated system of numerical representations in the imagery system; when activated, the resulting image is integrated into the representation of egocentric space. So here we have an example of a basic resource of human intelligence that is the product of an interaction between cultural and innate endowments."Numbers are ubiquitous-among other things, they specify times, locations, and wealth; in industrialized countries people process numbers to plan their day, find their way, and calculate their pay, and in more remote places people often use numerosity to keep track of livestock, children, and food. Rarely do we stop to think what an amazing achievement these numerical skills constitute. Only a few hundred years ago a large percentage of the world's population was virtually innumerate and only a minority could deal with exact numbers and perform arithmetic tasks (Ifrah, 1998). Everyday numeracy is an impressive cultural achievement that has shaped how we think about numbers and numerosities in many ways. We learn number processing, and in particular arithmetic and higher mathematical skills, through formal instruction. Differences in numerical experiences between cultures provide us with an opportunity to understand the relationship between culture, cognitive development, education, and human cognition more generally and the influence of cultural factors on the mental representation of numbers in particular. The present article describes this multifaceted relationship.

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Section: The Influence Of Language On Numerical Cognitionmentioning

confidence: 60%

The Cultural Number Line: A Review of Cultural and Linguistic Influences on the Development of Number Processing

Göbel

Shaki

Fischer

2011

Journal of Cross-Cultural Psychology

190

129

View full text Add to dashboard Cite

show abstract

“…These tools may vary on several dimensions: with regard to the contexts of applicability (18,27,49), with regard to their modality (i.e., whether implemented as number words, notational systems, or body-based expressions), or with regard to their properties, such as extent, base size, or regularity (6). Taking this variability into account will allow us to investigate how properties of these tools interact with the cognitive representation and processing of numerical information and how they may contribute to advancing numeracy.…”

Section: Resultsmentioning

confidence: 99%

Mangarevan invention of binary steps for easier calculation

Bender

Beller

2013

Proc. Natl. Acad. Sci. U.S.A.

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When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition.mathematical cognition | binary numeration systems | cognitive tools | cultural representations | mental arithmetic

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“…At the market, for example, objects are placed in piles of a value of 10 toea; if one is interested in the product, one simply picks up a heap and leaves a coin of 10 toea, which obviates the need for calculations. Wassmann and Dasen (1994) probed Yupno knowledge of arithmetic, amongst others by asking subtractions in the form of bride price problems, e.g., 17 -9 became ''you need 17 pigs to pay a bride price, and you have already given 9 pigs to your prospective father-in-law. How many pigs do you still need?''…”

Section: The Importance Of Innate Numerical Skills For Mathematical Pmentioning

confidence: 99%

The Innateness Hypothesis and Mathematical Concepts

Cruz

Smedt

2009

Topoi

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In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist hypothesis? Second, granting that infants have some elementary mathematical skills, does this mean that such skills play an important role in the development of mathematical knowledge?Keywords Innate knowledge Á Nativism Á Mathematical knowledge Á Developmental psychology Á Arithmetic Nativism and Mathematical KnowledgeUntil the late eighteenth century, mathematical knowledge was a paradigmatic example of innate knowledge. It often served a dual purpose, providing both a persuasive reason why innate knowledge exists, and furnishing us with an explanation of how humans can have knowledge of mathematical objects. Due to the increasing importance of foundational issues and the explicit rejection of psychologism (i.e., the view that mathematics lies within the purview of psychology) by Frege and others, nativism has lost its importance in recent philosophy of mathematics. By contrast, contemporary developmental psychologists (e.g., Spelke and Kinzler 2007;Carey 2004;Feigenson et al. 2004) propose that innate ideas are a naturalistic source of mathematical knowledge. They have uncovered evidence for early-developed mathematical skills in infants and young children, such as the ability to estimate and discriminate numerosities (Jordan and Brannon 2006), the capacity to detect ordinal relationships between numerosities (Brannon 2002), and the ability to reason about spatial relationships in a Euclidean framework (see De Cruz 2009, for a review).This article examines the relevance of nativism for the philosophy of mathematics. After providing a brief overview of historical claims for innate mathematical knowledge, we focus on arithmetic as an example of innate mathematical knowledge in current developmental psychology. We examine in detail the claim that infants are capable of predicting the outcomes of simple addition and subtraction events, and look at recent objections to it. Then, we examine to what extent this innate knowledge is important for mathematical practice. Focusing on number theory and arithmetic, we find that there are three possible ways to explore the relationship between innate ideas and mathematical practice.

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Yupno Number System and Counting

Cited by 59 publications

References 5 publications

The Cultural Number Line: A Review of Cultural and Linguistic Influences on the Development of Number Processing

The Cultural Number Line: A Review of Cultural and Linguistic Influences on the Development of Number Processing

Mangarevan invention of binary steps for easier calculation

The Innateness Hypothesis and Mathematical Concepts

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