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Monday 09 June 2008

Intuitions of number-space in Amazonian indigenous groups

Science. In press
CEA
Can you calculate without having a numeral system? To answer this question, since 2002 a team of CEA, CNRS and Inserm researchers coordinated by the head of the joint Inserm-CEA-run Cognitive Neuroimaging research unit, Stanislas Dehaene, has focused on the Mundurucu people, an Amazonian indigenous people who live in small villages isolated from western-world influence and who possess only a limited numerical lexicon. Drawing on methods developed in cognitive psychology, the team has recently revealed that the Mundurucu people possess an intuitive sense of number-space relations, although their sense of measurement [1] is learning-acquired. These results, which were published in the 30 May issue of Science, determine how mathematical mapping is split between cultural invention and intuition. Most significantly, these results underline the importance of adapting the methods for learning in this field.


These results build on preliminary conclusions obtained in 2004, i.e. that although the Mundurucu possess few – if any – words for expressing number and no counting system, they are nevertheless able to add, subtract, and approximate number. The researchers now reveal that this number sense is conjugated with intuitive spatial organization mapping.
 
A wealth of research led on western-world adults had already demonstrated that simply thinking about a number or performing a mental arithmetic task automatically enrols a spatial bias[2]. This phenomenon stems from the links established between number and spatial representations in the parietal lobe located in the upper part of the brain, which is observable through neuroimaging.
 
These new results underline that these number-space associations pre-exist any learning-based mathematics. Mundurucu people shown (figure 1) a line labelled at left with a representation of the number 1 and at right with a representation of the number 10 (these were actually points in circles) were asked to use a cursor to place the number 2 on the line; they were able to place the number 2 on the number 1 side (the left), while placing a number greater than 5 to the number 10 side (at right).
 
In addition, Mundurucus map numbers in space according to a logarithmic scale. When asked to place the number 5, they placed it close to the 10. Their intuition tells them a 3 or a 4 would be somewhere in middle, between 1 and 10, whereas western-world adults spatially map numbers on a linear scale. These results mean that the measurement sense is learning-acquired.Furthermore, the team had previously observed how western-world children switch from a logarithmic representation to a linear representation of number at between 6 and 10 years of age. This research highlights the pivotal role of education in mathematical development: without it, we have no way of knowing whether there is a constant spacing between numbers 1, 2, 3, 4 and so on.


[1] Intuition of number organization in space
Graphique 1:
Relations nombre-espace chez les Mundurucus
 
 
 
 
* On a logarithmic scale, the position of a number is determined
in a way that numbers sharing the same relationship
(for example 1, 2, 4 and 8) are regularly-spaced.
 
 
   
                                                                                    **A linear scale is a scale where the interval between consecutive                                                                                                 numbers remains constant.
 
 


[1] The measurement sense is the switch from a logarithmic representation of number to a linear representation
[2] Intuition of number organization in space
Article reference:
S. Dehaene, V.Izard, E. Spelke, P. Pica (2008). Log or linear ? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures. Science, in press
CEA Research teams – references:
CEA /Saclay - Institut d’imagerie biomédicale (I²BM) – NeuroSpin
CNRS / Université Paris 8 – UMR « Structure formelle du langage : typologie et acquisition métrique et poétique », Saint-Denis
 
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