Non‐symbolic halving in an Amazonian indigene group

Abstract

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS.

Fractions We Cannot Ignore: The Nonsymbolic Ratio Congruity Effect

“… Despite published statements by Rochelle Gelman and Stanislas Dehaene suggesting fractions are not compatible with basic human architecture, we note that in other work, they make hypotheses to the contrary suggesting that basic number modules are compatible with rational numbers (McCrink et al., ) or even real numbers (Gallistel & Gelman, ). These points notwithstanding, their published arguments about innate constraints of the system are cited very frequently and continue to exert considerable sway. …”

“…1 On this prevailing view, fractions are a product of human artifice and are therefore not naturally compatible with preexisting cognitive architectures. However, several lines of research have indicated that fractions may not be as artificial as innate constraint theorists have argued (e.g., Jacob, Vallentin, & Nieder, 2012;Matthews & Chesney, 2015;McCrink, Spelke, Dehaene, & Pica, 2013;McCrink & Wynn, 2007).…”

Sounding the depths at the confluence of numerosity and language

“…The Mundurukú have numbers for sets with one (pug/pug ma) and two (xep xep) items, and these are elicited in nearly 100% of cases in which subjects are asked to describe such sets (Pica et al 2004). McCrink et al (2012) demonstrate that, despite the generally anumeric nature of Mundurukú, its speakers are as capable at halving large quantities via approximation as are control French speakers. Such work suggests that the ANS can be implemented to halve quantities regardless of a native speaker's language.…”

Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders

“…Cross-cultural, child development, and brain research all support the idea that halving, the practice of dividing a whole into two parts made precisely equal through comparison, is a widely known and pedagogically accessible mathematical practice [5,42,51]. Yupiaq and Carolinian knowledge holders use repeated halving of pieces of string, strips of paper, or coconut fronds, etc.…”