Why arithmetic for children

Did you note that I made a "silly" mistake in my last post ? In trying to work out an answer to my question "What is three times four ?", I started with the number three, and then went on to add three to the last result three more times so that I had four threes in all. But look, my "times" should have been three and I should have started with four ! Of course, we know the end result would be the same, thanks to the "commutative law of multiplication" - or better, the "associative law of addition". But how do the numbers know these laws ? Or, for that matter how do I know them ?

Well, why should children know this and do these activities ? Because they will "need" them later ? Or because they will help them in their daily lives ? Do these activities enter in their lives at all ? Children of age three, or even younger, might enjoy the "raising or folding fingers and making some sounds" activity in itself or because of the approval of adoring parents. ( Incidentally, is playing such games  AT HOME common all over the world, over all strata of society ? ) What situations we can find in the social lives of children which "invite " numbers and arithmetic ? PLEASE stop reading on and think over this. I will give you my answers in my next post !

How do I know ?

Let me ask you a very simple question - I hope you won't take it amiss.

 What is three times four ?

I would answer : twelve. ( I suppose so would you. Also, I am assuming that you have figured out that my question is about "NUMBERS", and not about some words of the English language : "three", "times", "four" . Compare with the question  "What is a noun ? ".)

But how do I know the answer ?

Well, I remember it. But how did I know it the first time in my life ? Perhaps I was told that it is so.

But could I figure it out NOW ? ( Could you ? ) Recalling the multiplication table will not do.

May be I can figure it out thus : I start out with "three" and add "three" to it. I get "six".  (  How ? ) Then I add "three" to "six" and get "nine". And finally, I add "three" to "nine" and get "twelve". Whew, what a relief ! But look, how did I know when to stop adding "three" to a result obtained on the way ?  Well, at the back of my mind, I was counting the "times" : start with "one", then "two", next "three", next "four", and stop.

But how did I know "three" added to "three" gives "six" ?  I guess I have to figure that out afresh.

Let us imagine a three year old child trying to figure it out ( that could be me or you - when we were three year olds. ) What is the "background knowledge" and "context" ?  I must "know" the words "three", "and", "six", and the context. What could be the CONTEXT ?  Perhaps, some fingers of the hand raised or folded down. Perhaps, some pebbles ( in the good old days ) or chocolates spread out on the table, or perhaps, some tally marks "|" "|", "|", or some little circles, or blobs , on a piece of paper. And then doing something very strange : looking at or pointing to a pebble, chocolate, finger, tally mark, and so on, or picking up a pebble or a chocolate, and saying ( aloud at first, and then perhaps to myself !) "ONE". And then . . . . .

Was this all easy ? Why did I ( agree to ) do it ? Was it because I was  promised that if I did it, I would get a chocolate ? It wasn't easy, and it isn't easy for today's three-year olds.

In the beginning

Teaching and Learning with UNDERSTANDING :

When a newborn arrives in our family, we almost instinctively start TALKING to it.  Why do we do it  ? ( We humans are talking animals - homo loquens ! ) At first, we may just babble and not say any  words of our language. Eventually, the baby responds to our talk by making its own sounds, and finally learns to say OUR words, i.e., learns to imitate our words. Perhaps, the most common word successfully imitated - in the English language - is MAMA. Why does the baby do this ? Does it "understand" what the word means, or even that the word has a "meaning" ? Our talking is usually accompanied by some actions ; for example, we may touch the baby, we may smile at it , we may hold it up close, and so on. Most importantly, perhaps, it is Mama herself who talks. She may give feedback by smiling back at the baby after its successful imitation. By the time the baby has completed three years of its journey in OUR world, including our LANGUAGE, perhaps sooner, perhaps later, our language has become a part of its world and its language. It has learnt to use our common language correctly - most of thhe time, at least.  The child is now ready to go to school !

Now imagine that YOU were the child.  What words - and actions - did you learn? And how ? That is to say, what THEY were doing to you when you were learning and what you were doing ?