You're in the supermarket. You have an 8.99€ bottle of wine and a 6.20€ chicken meal in your basket and are working out if you can add the 4.70€ dessert without going over 20€. You do the sum in your head and then walk to the shortest check-out queue. This scenario requires the solution of two maths problems. The first is the sum 8.99+6.20+4.70 euros and the second is the judgement of which line has the fewest people in it. One involves the addition of Arabic numerals and the other the rapid estimation of ratios (you don't count everyone in every line).
We tend to see the first type of calculation as more important than the second. That's why the maths we learn at school begins with learning numbers and arithmetic. Yet research in psychology shows the second type of calculation is, in the fact, the crucial indicator of mathematical ability.
The big new ideia in maths education is that young children should spend time improving their estimations skills before learning how to count with exact numbers. The theory emerged from Johns Hopkins University in the US, which conducted experiments in which children were shown sets of dots. Some dots were blue and some were yellow - each child needed to say whether there more blue or more yellow dots. Children who scored highest at the dot task also performed best at standardised maths tests.
This was surprising. Maths is a system of manipulation abstract symbols that has taken humans thousands of years to develop. On the other hand, estimating ratios involves what academics call our inner "number sense", a deep-rooted ability to compare quantities which is also present in other animal species.
The realisation that the best indicator of success in the abstract world of maths is our inner, animal number sense ran counter to prevailing opinion in mathematical psychology.
Alex Bellos, Mathematician
Further thinking: Educationalists are wondering whether maths teaching needs to be completely reinvented.
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