Natalie Angier in the New York Times today reports (login required) on the key roles intuition and estimation have in mathematical ability. Our thousands of years’ progress in the sciences might well owe a large debt to a skill we share with the humble rat.
[Quick estimation test - How many cats?]
As Angier says:
Whenever we choose a shorter grocery line over a longer one, or a bustling restaurant over an unpopular one, we rally our approximate number system, an ancient and intuitive sense that we are born with and that we share with many other animals.
These are automatic skills which often fail us, not least when we are suckered into ‘special offers’ or ‘buy now pay later’ sofa financing arrangements. When they fail, we might resort to more abstract, formal calculation – those maths skills we associate with terrifying hours in tests at school of carrying digits, partitioning numbers, finding the highest common denominator, and so forth.
“Math-making seems the opposite of automatic”, Angier notes, but innate estimation and taught arithmetic may be more closely related than we’d thought. New research is finding that ”how readily people rally their approximate number sense is linked over time to success in even the most advanced and abstruse mathematics courses… [suggesting] that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.”
We wouldn’t argue with this one bit. Whilst some might decry teaching estimation skills as tantamount to training children to be sloppy and less rigorous, it is clear after a little thought that even the finest minds rely on estimation. I’ll bet my left hand everyone from Feynman to Fermat now and then found themseleves pursing their lips and staring up at the ceiling whilst they conjured a rough answer to a problem, before sitting down to work it through with pencil and paper (or quill and parchment).
In fact, general reckoning and estimation skills abound in the UK Primary National Strategy for maths and are well represented in Maths-Whizz. From fun games for five-year olds involving estimating numbers of goats in a barn, to complex estimation procedures in Key Stage three mental maths, a number of our exercises ask children to use their guts before their frontal lobes, figuratively speaking…
Angier concludes that “behind every great leap of our computational mind lies the pitter-patter of rats’ feet, the little squeak of rodent kind.” It is reassuring to know we might owe our finest mathematical minds to skills laid deep in our evolutionary history. But if you want to give your innate estimation skills a go, try this little estimation test on the New York Times website.
Alternatively, you can look out for our Mental Calculation Strategies and Pencil and Paper methods topics in Maths-Whizz!
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UPDATE (18/09/08):
In a post yesterday, Jason Kottke linked to a great post by Abbas Raza (3QuarksDaily) on using educated guesses to make surprisingly accurate estimates of seeming incalculable quantities. Abbas must have a finely-developed approximate number sense, and equally finely-developed formal maths skills…
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[...] with the rat’s newfound ability to make snap estimates I’m beginning to feel a little inadequate in the face of all this natural-world numeracy. [...]