Abstract
BackgroundThe generic concept of number line, which maps numbers to unidimensional space, is a fundamental concept in mathematics, but its cognitive origins are uncertain. Two defining criteria of the number line are that (i) there is a mapping of each individual number (or numerosity) under consideration onto a specific location on the line, and (ii) that the mapping defines a unidimensional space representing numbers with a metric — a distance function. It has been proposed that the number line is based on a spontaneous universal human intuition, rooted directly in brain evolution, that maps number magnitude to linear space with a metric. To date, no culture lacking this intuition has been documented.Methodology/Principal FindingsBy means of a number line task, we investigated the universality proposal with the Yupno of Papua New Guinea. Unschooled adults did exhibit a number-to-space mapping (criterion i) but, strikingly, despite having precise cardinal number concepts, they located numbers only on the endpoints, thus failing to use the extent of the line. The produced mapping was bi-categorical and metric-free, in violation of criterion ii. In contrast, Yupnos with scholastic experience used the extent of the segment according to known standards, but they did so not as evenly as western controls, exhibiting a bias towards the endpoints.Conclusions/SignificanceResults suggest that cardinal number concepts can exist independently from number line representations. They also suggest that the number line mapping, although ubiquitous in the modern world, is not universally spontaneous, but rather seems to be learned through — and continually reinforced by — specific cultural practices.
Highlights
Mathematics is a fundamentally abstract human conceptual system
Our results show that adults from the isolated and largely unschooled Yupno community in the remote mountains of Papua New Guinea, despite having precise cardinal number concepts, do not spontaneously exhibit number line intuitions when presented with an external line
Unlike schooled Yupnos, unschooled participants had serious difficulties understanding the fundamental endpoint anchoring required by the number line task
Summary
Mathematics is a fundamentally abstract human conceptual system. The degree to which mathematics is grounded in universal, biologically endowed intuitions, is still an open question [1,2,3,4,5]. Number estimation research has shown that number lines are highly intuitive, and one of the key methodologies in the field makes explicit use of an external number line [19,20] This number line task, where participants are asked to locate numbers on a line marked with a beginning number (usually 0 or 1) on the left endpoint and a larger number (often 100 or 1000) on the right endpoint, has been reported to be readily understood even by kindergarteners [19,20] and unschooled people from indigenous cultures [6], and has been assumed to provide straightforward behavioral evidence of number line intuitions. No culture lacking this intuition has been documented
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