Thursday, 24 November 2016

Use it or Lose it !

This is not a column about sexual health.

I’m talking about the basic math facts — times tables and all that stuff that should be stored in our long term memory:

Will we really forget those facts if we don’t use them? 

Our brains are flexible. Neuroscientists use the word "plastic". They tell us that the brain's circuits can be repurposed, new ones can grow, and that frequent use strengthens neural connections. My guess is that YES, our memory of these basic facts will fade if we don't use them.

But I have a follow-up question.

Do you know that  1 / 1.04 = .96154? 

I do know that! And it's a fact that I don't use.

Here's the story.

Fifty years ago I worked for a large Canadian insurance company. I was a clerk in the mathematics section of the Policy Change department. My job was to compute how much to charge or refund when clients changed their insurance policies.

Among the many options available was the possibility of paying premiums in advance. The company liked it when clients did this, and to encourage them the company offered a discount.

We used an interest rate of 4%.  So, if the premium was, say, $150.00, and the payment was being made a year in advance, the client would pay $144.23, which is what you get from the following computation:

$150.00 / 1.04.

To the nearest five decimal places, 1/1.04 = 0.96154, so we could also calculate the discounted premium this way:

$150.00  ×  .96154.

Actually, 1/1.04 is slightly smaller than 0.96154, but for all practical purposes the two methods are identical. Yet, despite their equivalence, our boss made us use the second one. Instead of dividing by 1.04 we had to multiply by 0.96154. It was not because our boss had some weird mathematical fetish: an official company policy memo explicitly stated that when computing prepayments of premiums, we had to use the factors from the supplied interest tables. Policy trumps mathematics.

After a short time on the job, the "fact" that 1/1.04 equalled .96154 had established permanent residence in my mind and it still remains there even though I haven't used it for over half a century.

* * * * *

This sort of thing is not unusual.

  • My parents-in-law, veterans of WWII, could recall their military ID numbers for their entire lives, even though they seldom used them.
  • My wife and her mother used to play a game when she was a child. They recited the alphabet backwards as rapidly as they could. It's a skill that my wife has not used for over 60 years. Yet yesterday she showed me that she can still reel off the alphabet backwards without hesitation. 

So my intuition that facts fade from memory when they are not used may be wrong. Some of us retain basic facts and practiced skills even if we don't use them for an extremely long time.

* * * * *

On the other hand - 

Sometimes when people say "Use it or lose it" they really mean

Use it and you won't lose it!

Well, we all know that statement is false.

How else to account for my spotty recall of simple multiplication facts? I've used those basic multiplication facts quite a lot since leaving that insurance company, and I'm still not "fluent" with them. I can fire off the squares of the natural numbers up to 12 × 12, but ask me what 12 × 7  or 12 × 11 is and I have to perform a mental computation. And 13 × 13 is 169, but what is 13 × 9?

Some people can recall basic math facts quickly and without conscious effort — they automatically know them without thinking. Like the way I know that 1/1.04 is .96154.

Others will never completely achieve this type of fluency. When someone says "Twelve times seven" it may not provoke the involuntary "Eight-four". Instead, the reaction may be "seventy plus fourteen" having broken 12 × 7 into 10×7 plus 2×7.

To be truthful, I am fluent with most of the basic multiplication facts. But, I really do still have trouble with a few parts of the 6, 7, 8 and 12 times tables. And, as I prepared this post, I actually did have to retrieve 12×7 by that quick mental computation. However, once done, I could instantaneously recall the answer for the rest of the post, and I know that the automaticity will remain for several days, maybe even a couple of weeks. But it’s as impermanent as those facts acquired by cramming for an exam: very soon it will fade from my memory.

My advice 

If my children were young, this is what I would tell them today:

Practice your times tables. Memorize as much as you can. It is worth the effort. Maybe you will never be able to keep all of them in your head. But if you can keep a few there, and if you learn how to be flexible with numbers, you will find ways to derive the more difficult ones very quickly — almost as fast as if you had actually memorized them — and it won’t stop you from learning more mathematics.

As for getting every single one of those basic facts into genuine long term memory in a way that they can be instantly and automatically recalled: forget it — for me, and maybe for quite a few others:

It's • Not • Gonna • Happen


Just as I was finishing this post, I came across an article (linked below) by Maria Konnikova in The New Yorker magazine. It's about the tenuous relationship between practice and achievement across a variety of fields (including mathematics). It's really worthwhile reading. 

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