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For example, 'visualization' is taught in the following manner.
"2 * 2 * 2 is not the same as 2 * 4 although the 'quantity' is same" I would be taught. The difference is, when one says 2 * 2 * 2 boxes, one is saying 2 rows of 2 boxes each and 2 such layers on top of one another. So, its a cube with 4 boxes in the bottom and 4 boxes on top of them. Total 8 boxes. Where as 2* 4 means 2 rows of 4 boxes side by side. This is, so to say 2 - dimensional and the former is 3 dimensional.
And 2 (squared) is a square with a side of 2 units and 2(cubed) means a cube with 2 units per side.
And then such a discussion would flow into calculating number of books in two stacks, three stacks, 9 stacks, etc. where each stack contained some x amount and also, the answer should be given as ' so many books in the front rows and so many books in the top rows etc. This would generally flow into both geometry and exponents and into number series and into arithmatic and into algebra.
This is one of the ways we were taught to 'visualize' things and go ahead to understand higher and higher concepts based on basic visualization. I remember Amma saying '2' doesnt mean anything. Its like 'a' or 'an' or 'the'. What follows the 'article' (english grammer term) is what it describes. similarly what follows 2 (like 2 apples, 2 balls, etc.) is what 2 means in that problem. And then, since 2 of any object, when added to 5 of any object make 7 of that object. And then I was told that it is expressed by a small 'x' and I would have to write or draw ( i loved to draw so many boxes or apples or hats
) addition and multiplication tables with 'x' added. And this would lead into the above visualization.
Jai Sai Master!!
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