This story is an adaptation of From the President, HCF, Newsletter of the Australian Association of Mathematics Teachers (AAMT) Inc., Number 5, October 2000. It relates the personal experience of Vince Geiger, AAMT President. I recently had the pleasure of listening to Sue Willis speak at an ACER conference on numeracy research. During her presentation Sue emphasised the importance of children learning mathematics in a deep and connected way. Sue's address struck a resonant chord with me because of an experience I'd had with my own daughter, Violet, a few days earlier. Violet is in Year 3 and she, like many children her age, is working on the addition and subtraction of numbers. A difficulty arose when doing homework one night - this is when I was called in. Violet was stuck on the following problem:
Now she had no problem with finding differences like 16 - 3, the problem only arose when 'the second lot of ones is bigger than the first lot of ones'. When she had first brought the problem to me she was attempting to solve it by a 'carrying' method which of course is not of great assistance in this situation. It was a reminder to me, all too close to home, of the problems associated with children learning algorithms in a way that does not address their connection with appropriate contexts. Over the following four days, Violet and I worked on this and similar problems. We talked about the significance of place value and about different ways of doing problems of this type. It was, at times, a frustrating experience for both of us as each time we made progress with one problem we seemed to go back to almost the beginning with the next. On the morning of the fourth day, however, Violet simply said over breakfast, 'I know how to solve that problem'. She then proceeded to tell me that instead of worrying too much about the 'ones' you could simply take the 9 from the 10 (in the tens column) leaving you 1 to add to the 6.Violet was particularly pleased with this effort and by way of celebration proceeded to show me how her method could be used to solve a range of problems of this type. It seemed she had made the sort of connection Sue was to speak about some days later.
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