Some adults lack a sense of the "equal distance of 1" between the whole numbers (the numbers on a number line). Without this concept, addition makes no sense. All math including basic addition is learned by rote as a mechanical process.I have a memory of Dehaene arguing that people have an "innate" number line inside their minds.
It was Dehaene:
I propose that the foundations of arithmetic lie in our ability to mentally represent and manipulate numerosities on a mental “ number line ”, an analogical representation of number ; and that this representation has a long evolutionary history and a specific cerebral substrate. “ Number appears as one of the fundamental dimensions according to which our nervous system parses the external world. Just as we cannot avoid seeing objects in color (an attribute entirely made up by circuits in our occipital cortex, including area V4) and at definite locations in space (a representation reconstructed by occipito-parietal neuronal projection pathways), in the same way numerical quantities are imposed on us effortlessly through the specialized circuits of our inferior parietal lobe. The structure of our brain defines the categories according to which we apprehend the world through mathematics. ” (TNS, p. 245).Makes people who don't seem to possess an internal number line interesting.
Précis of “The number sense”
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I've been relying on number lines to explain things to myself and to C. ever since coming across Dehaene's work.