Jai Sai Master !

Dear Ananth garu

Ofcourse, as usual, I can think of a lose translation but it would be much better to know from you, it's significance rather than it's meaning as it is.

Same here.

Jai Sai Master !

Jai Sai Master!

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!!

Jai Sai Master!

Usually, kids are taught to 'cross multiply' when two fractions are equated to one another.. that is : if a/b = c/d , cross multiply and you would get ac = bd; which is fair enough. Its taught in a kind of rote way. But there is a better way to teach it, a more palatable logical way, where we explain the logic behind the cross multiplication.

Let me illustrate by example.
say (2x-3)/(x-1) = 1.
By cross multiplication, we would get (2x-3) = (x-1). {cross multiplying with 1/1 on the right side}.
This is how it usually is taught. But a better way is to explain to the kid by an example. Ask the kid regarding when the result is 1 in  a division. That is, ask, while explaining that 10/10 is 1.  Explain verbally, for instance, "if there are 10 apples with me, and i have to divide them equally to 10 students, how many will each get?". The answer would be 1 each. Then ask " how many students are there if I have to distribute 20 apples and each should get only 1?" The kid will think and answer "20". If not, suggest it with explanation.
Then explain that when the numerator and denominator are equal, then only will the division will have the result of "1". And so, if (2x-3)/(x-1) is given as 1, it means, (2x-3) must be equal to (x-1).

Explaining maths, algebra and geometry this way, makes it very interesting, challenging and engaging to kids. Hope this gives some food for thought.

Jai Sai Master!!