Exact and Approximate Arithmetic in an Amazonian Indigene Group

@article{Pica2004ExactAA,
  title={Exact and Approximate Arithmetic in an Amazonian Indigene Group},
  author={Pierre Pica and Cathy Lemer and V{\'e}ronique Izard and Stanislas Dehaene},
  journal={Science},
  year={2004},
  volume={306},
  pages={499 - 503}
}
Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with… 
Language and the Origin of Numerical Concepts
TLDR
The research findings indicate that, whether or not humans have an extensive counting list, they share with nonverbal animals a language-independent representation of number, with limited, scale-invariant precision.
Links Between the Intuitive Sense of Number and Formal Mathematics Ability.
TLDR
Evidence for the relationship between the nonverbal Approximate Number System and culturally invented system of exact numbers is reviewed, describing how group and individual differences in the ANS correlate with and even predict formal math ability.
Cultural Variation in Numeration Systems and Their Mapping Onto the Mental Number Line
The ability to exactly assess large numbers hinges on cultural tools such as counting sequences and thus offers a great opportunity to study how culture interacts with cognition. To obtain a more
Linguistic and cultural variables in the psychology of numeracy
Although anthropologists pride themselves on paying attention to the small details of everyday life, experimental psychologists arguably have an even smaller scale of research – examining variables
Education Enhances the Acuity of the Nonverbal Approximate Number System
TLDR
It is found that education significantly enhances the acuity with which sets of concrete objects are estimated, and it is hypothesized that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction.
Exact Equality and Successor Function: Two Key Concepts on the Path towards Understanding Exact Numbers
TLDR
This work focuses on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS: the fact that all numbers can be generated by a successor function and the fact of equality betweenNumbers can be defined in an exact fashion.
Cross-cultural differences in representations and routines for exact number
TLDR
How cross-linguistic and crosscultural diversity—in Amazonia, Melanesia, and around the world— gives us insight into how systems for representing exact quantities affect speakers’ numerical cognition is described.
Individual differences in non-verbal number acuity correlate with maths achievement
TLDR
There are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual Differences in the present correlate with children’s past scores on standardized maths achievement tests, extending all the way back to kindergarten.
...
...

References

SHOWING 1-10 OF 65 REFERENCES
Numerical Cognition Without Words: Evidence from Amazonia
TLDR
Results of numerical tasks with varying cognitive demands show that numerical cognition is clearly affected by the lack of a counting system in the Pirahã tribe, suggesting an analog estimation process.
Nonverbal Counting in Humans: The Psychophysics of Number Representation
TLDR
The results support the hypothesis that adult humans share with nonverbal animals a system for representing number by magnitudes that have scalar variability (a constant coefficient of variation) and provide a formal model of the underlying nonverbal meaning of the symbols.
Numbers, language, and the human mind
Introduction 1. Numbers and objects 2. What does it mean to be a number? 3. Can words be numbers? 4. The language legacy 5. Children's route to number: from iconic representations to numerical
Core systems of number
Addition and subtraction by human infants
TLDR
5-month-old infants can calculate the results of simple arithmetical operations on small numbers of items, which indicates that infants possess true numerical concepts, and suggests that humans are innately endowed with arathmetical abilities.
Sources of mathematical thinking: behavioral and brain-imaging evidence.
TLDR
A series of behavioral and brain-imaging experiments provides evidence for both sources of linguistic competence and mathematical intuition, and suggests that mathematical intuition may emerge from the interplay of these brain systems.
...
...