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To begin, let me introduce some young able mathematicians whom I met in Australia while observing trainee primary teachers on their teaching practice school placements. The setting is the eucalyptus forests of the Great Dividing Range, some 800 miles north of Sydney, where small, isolated communities eke out a living within the economically declining rural industries of forestry and beef cattle. In a Central School (Years K to 10), I was observing a Kindergarten (Reception) class on digit recognition where the children were colouring in large copies of 1 to 9. William, aged 4, was clearly bored. Seating myself beside him on the floor, I whispered in his ear: "What's the biggest number you know?" "Oh" he said, "one hundred thousand." "Well" I replied (thinking that his understanding of 'biggest' might be 'longest number name' rather than 'largest sized number'), "do you know a mill ion?" "Of course" he shot back. "OK then" I continued (wondering if he was just parroting some recent conversation with his parents) "write a million down on the back of your paper." Without hesitation William wrote down 1,000,000. So we went on to talk about billions, trillions, zillions and so on - that all-important lesson where you confirm your suspicion that powers of 10 can increase indefinitely. It's just that most people aren't ready for that lesson until they are much older than four years. |
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