Friday 10 October 2014

Post 2: The importance of being visual and verbal

When my son was quite young, about 3-4 years old, there was a lot of scribbling and drawing. There still is. The main story in this post is that: we never know when and how they are doing and learning very important stuff in all that scribbling. It may not be all scribbles to them even if that is what it appears as to us. 

So, here is the story. He had learnt to count up to 10 and 20 quite quite quite early. And by simply talking about things, I think that he somehow latently and implicitly knew two very important things in learning to count things: 

  1. Numbers and their symbols are not the same thing: The symbol is representational. Meaning every language writes the symbol differently, but the particular number in question, the concept of 1 thing, 2 things, etc. persists. (So, for example, we have three languages in the house, but another post on that). 
  2. Numbers are used to count things: so, the larger the number of things, somehow the bigger or more complex the representation of that number, and smaller the thing, simpler the representation. 

So, imagine my surprise, when at 3 or 4 years of age, I found him "drawing" the following (this picture is a much-later version, and hence much clearer and the handwriting much nicer, the original versions were on a little blackboard and chalk, when he pretended he was "teaching" mum): 


The thing is, he is 6 now, and he can work easily with tens, hundreds, and thousands. He does not yet formally know place value beyond that (in the sense that I have not yet worked with him beyond that or introduced anything formally, but you never know how they surprise you!), but in this drawing play, I learnt something very important: almost always, pattern based, partial understanding precedes formal and deeper understanding, for children as well as adults. And we should encourage this play. 

I also think he had captured the idea that numbers can grow as big as you want them to, and so his question on the previous post, came after a lot of this kind of play, both on paper and verbally. For example, he would say random and wrong numbers, as follows: 

Me: How many rotis is mumma going to make today? (Rotis are Indian bread that we make fresh everyday, so dough making time is the Indian version of kids doing play-doh in the kitchen). 

He: 5 hundreds and 4 thousands, and 95 hundred. (followed by giggles). 

Me: Ha, funny funny, but seriously, how many should mumma make? How many do you eat? 

He: 1. 

Me: How many does mumma eat? 

He: 2. 

Me: How many for papa? 

He: 4. 

Me: How many should I make then? 

He: hmm, 7. 

So, when this kind of conversation happened, I never said, you are wrong, that is not a right number.  I never think, it is too early either. I let him babble away, and to my surprise, several days later, he would start saying the correct stuff. Statistical pattern recognition, statistical human learning, pattern based learning. Something to totally encourage. 


4 comments:

  1. Bingo! I have had the exact same observations with Aadyaa. She would surprise me with intuitive addition and subtraction at an early age and I sense we complicate things for them by formalising the process! Very nice post...Sending the link out to Appu who has a star kid doing advance mathematics since an early age...she might have stuff to share as well!

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    1. Hey, so nice - so what year is Aadya in now? Considering they are a couple of months apart, it will be so interesting to compare notes on that. How old is Appu's son? You must send me her email...

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  2. Wonderful experience. Very interesting and effective way of learning with understanding. Such a play way method gives the child a strong foundation and base for technical studies. Well done, keep it up.

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