Should Toddlers Memorise Their Times Tables?
"Yes! They should."
But Bijan, most toddlers can't even count, let alone add. How do you expect them to learn their multiplication tables?
I didn't say that they should understand what multiplication is, I said that they shuold memorise their times tables.
But, shouldn't they understand it before they memorise it?
In my book, "Why and How Toddlers Should Memorise Their Times Tables", I have recounted an annecdote about a 15-year old pupil of mine who knew her times tables perfectly, but did not understand the concept of number.
But, Bijan, how can that be?
Can toddlers recite "Hickory, Dickory, Dock?"
Yes, so?
So, do they need to know what "Hickory", "Dickory" and "Dock" mean before they memorise it?
No, but's just a nursary rhyme. There's a lot to learn in the times tables.
That reminds me of the old addage, "How do you eat an elephant? A bite at a time"
Precisely, by the time they get to the last bite, the elephant would have become rancid and the toddler will be a grandparent.
But what if I told you that the entire times tables that a child will need to memorise can be reduced to a mere 36 items and that these can be incorporated into games, so that the childwon't even realise the important mathematical arsenal that is being put at their disposal.
Arsenal, what arsenal? There's a calculator everywhichway you turn nowadays, so who needs the times tables?
I agree with you. We don't need the times tables to be able to multiply nowadays, not anymore.
Well, at laest we agree on one thing. So, why are making all this fuss about kids having to learn theri times tables?
Imagine you're going to China and I said to you, "You don't need to learn Mandarin (or Cantonese), I have here a very special parrot that will interpret everything you or anyone else says for you." Would you say that this is a better alternative to learning Chinese?
Absolutely. It would take me months or even years to learn to speak another language.
But it only takes young children a couple of weeks before they can converse comfortably in another language, especially if they are cut off from their first language.
So, what's your point, Bijan?
OK, imagine that armed with the magic parrot, you land in China.
Yeah?
Now, you go into a bar and you meet someone that you would like to strike a conversation with.
Sounds like fun.
Now, you'd want to find out as much as you can about this person wouldn't you?
Sure.
OK, you start by asking, "What is your name?" and then you have to wait for the parrot to translate this for you. Then s/he says, "Well, my real name is Mayling, but to Westerners, I introduce myself as Mary." You then wait for the parrot to translate that for you.
So far so good.
Really? You'll soon be losing the thread of the converation though. For example, what if in the next part of the conversation you ask her to tell you about her family and she speaks for one whole minute. You then have to wait for a minute for the parrot to tranlate that for you, by which time your interlocutor has lost interest in you or what she was saying (even though she might well still be fascinated by the parrot).
Yeah, could be.
Now, imagine that when you were a child, you could have had the opportunity of learning Chinese, but your parents didn't think it was important, so they did not take advantage of that opportunity. Remember that at that age, it is no strain to learn a language, it comes naturally. Would you have any regrets about that?
Well yes, I would.
Well, it's the same with the times tables. The calculator is like the parrot and as soon as you hit high school, when you are not dealing with number patterns anymore, but algebra, then the calculator will slow you down so much that by the time you have calculated the 'answer', you will have lost the thread of the underlying principle that the teacher was hoping you would grasp. And the tragedy (yes, I said tragedy) is that you would have grasped it if you hadn't been preoccupied with fiddling with your calculator or trying to search your memory for the right number combinations. And just like learning Chinese as a child, learning the times tables as early as possible would elliminate the 'friction' that a calculator will cause and will 'lubricate' your mental cogs to help you to understand more advanced (and more fun) mathematics, better and faster.
Now, that sounds intriguing.
Good! So, are you going to buy my book now?
But Bijan, we have been through so much together; aren't you going to give me a copy for free?
You are right, we have been through a lot together and I know that, as a good friend, you really want to encourage me to continue my good work in this direction, so I will charge you double.
What?
OK, look, you being such a good friend and all, I will give you a 50% discount, so I'll only ask you for the regular price of the book, how's that?
It sounds a lot better than it did before.
That gives me an idea.
What?
May be I will write a book about cognitive biases next.
I thought you said you were going to continue with the series on mathematics education.
One of the effects that mathematical thinking has on people is that it brings them closer to a holistic perspective where they see the interconnectedness of everything a lot more clearly.
And your point is?
My point is that, even in a book about how and why toddlers should learn their times tables, I have made serveral references to the effect of cognitive biases on children's disillusionment with mathematics. So you see, even if I write an entire book on cognitive biases, it will still be relevant to the pursuit of my dream.
Relevant, but tangential.
Touche.
More about the book
In the book, "Why and How Toddlers Should Memorise Their Times Tables" I have explained the importance of memorising the times tables and its effect on children's confidence and enjoyment of mathemtics. I am serious. A seemingly simple thing, like memorising your times tables early, can make or break your confidence in, and enoyment of, mathematics.
But, that's not all. How you (or your child) learn the times tables is just as important.
With the (patent-pending) method that I have suggested in the book, chidren will know their times tables even without knowing how to count.
If you are a teacher saying to yourself, "but children need to be able to understand what they are doing", in the book, I have addressed that objection too; so let's stop misinterpreting Piaget.