Humans were not born to do maths. Those, like me, who don’t dream in numbers, think this is stating the obvious, but it’s worth remembering, even so.
The human brain that lets us add, subtract, read, write, walk and chew gum (sometimes at the same time!) evolved from a brain that had different demands imposed upon it, most of which revolved around staying alive long enough to have offspring. So how have we co-opted brain regions specialised for navigating ancient woodland and savannah into helping us file our tax returns?
As reported in the National Geographic this month, one way is this:
Structures in the human brain once devoted only to visualizing spaces are now also involved in performing simple mental math…
According to the research, it seems the eyes do have it when it comes to reading our inner mathematical thoughts. Researchers have tracked eye-movements and identified the region of the brain that lit up when participants looked left, and the region associated with gazing rightwards.
They then used activity in these brain regions to show that participants tend to process numbers of different sizes as locations in space, an effect snappily titled ’spatialnumerical association of response codes’, or SNARC. The researchers predict that adders (not those adders) will mentally move their eyes rightward, whilst subtracters move them leftward.
If the predictions hold true, this would reinforce the idea that we think of numbers in spatial ways and that the wonderful flexibility of the brain enables us to handle abstract problems of number and language using older, more concrete mental skills (like figuring out where you are).
Of course, we are often taught maths using spatial concepts – number lines, manipulatives and so forth – and researchers acknowledge that this could be an artefact of the way arithmetic is taught to younger children, as hops along a number line. Adding (or counting on) is a rightward hop, and subtraction (or counting back) a leftward hop. Your eyes might naturally tend in one direction or another, depending on the operation.
Still, the fact that we teach with numbers on lines, or as floors in a building etc, might just be reflections of that innate tendency to ’see’ numbers in space. It would be interesting to test the authors’ predictions with novice mathematicians and expert ones. If memory serves, university mathematicians start to process numbers as they do language, just as expert musicians make a similar transition. Because simple 2D visualisations aren’t sufficient for thinking about Mandelbrot sets, or Riemannian Geometry the experts may show less of the whole eye-moving effect when thinking about maths.
The bottom line, as it always is, is that Maths-Whizz knows all this. We teach early adding and subtracting with leftward and rightward jumps, and lead students into abstract pencil and paper arithmetic at year 3 by encouraging them to visualise those jumps in blocks according to the numbers’ place value. e.g. 125 + 43 starts at 125, and then jumps 40 to the right, and another smaller jump of 3 more.