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DEVELOPING AN UNDERSTANDING : The other day I was showing the children's book '203 Cats' to my 7-year-old niece. She had recently learnt how to write large numerals in her school. She, very confidently, looked at the title and read 'Twenty-three Cats'. I asked her to look at the title again and read it to me. She again read 203 as twenty-three.
Then I wrote 2 13 on a piece of paper, and asked her to read this. She read it correctly as two hundred and thirteen. So why couldn't she read 203 properly?
Where did the problem lie ? Could it be that she had never thought about the importance of the position of a digit in a numeral? Or could it be a problem related to her understanding of zero ?
To answer these questions, at least partially, maybe we should go back a bit in time, and see how my niece's teacher had taught her to read and write numerals.
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f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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