Learning Times Tables – Rote Learning Understanding Or Do You Need Both

Recently in UK Nick Herbet, the schools minister, said pupils should learn their tables by rote at primary school.

A few days later it was reported

teaching children maths by making them learn times tables by rote could worsen exam results because they risk failing to properly understand the subject, according to an Oxford University study.

So whose right?  In my view

  • they are both right
  • they are both wrong
  • they are both being silly
  • and by far the most important they both miss the following
      1. interest and motivation are vital for learning
      2. it is better to learn a method to calculate answers to times tables questions than to just memorise facts
      3. with practice at multiplication the answers get memorised automatically

Let’s deal with the first three points. They are both being silly as nobody is saying either

  1. Pupils must learn entirely by memorisation without understanding
  2. Pupils must only learn by developing understanding without any element or practice or repetition

If anything the two ‘different’ positions are actually two different aspects of learning,
so the whole debate is a pointless waste of time.

Instead of bickering and point scoring why not focus on the important things about learning.

Firstly to learn, train or practice anything you need a reason, something which will fill you with a desire to keep working and learning. What keeps athletes and musicians (or doctors, lawyers and scientists) training and practicing for hours every day, for years and years.

They must have some sort of goal which they are aiming for.

If you can inspire children (or anyone) to want to learn, your job is pretty much done.

There are many goals such as such as.

  • To be good at science, maths or engineering
  • To be a great scientist and make new discoveries
  • To understand how the world works
  • To teach others
  • To invent something great like the iPad
  • To help build a rocket to journey to the stars
  • Become the world’s greatest investor like Warren Buffett
  • Become a finance whizz on Wall Street or City of London

The second important fact about learning tables is it is essential to learn a method for working out answers if you can’t remember them. And if you have a method for working out the answer it’s a good thing to check any answer that pops into your head to see if it is actually right.

The next time someone tells you rote learning is bad ask them,

How did you learn

  • your name
  • the letters of the alphabet
  • the names of the numbers from 1 to 10, from 1 to 100
  • the names of colours
  • the names of days of the week
  • the name of months in the year
  • you stop at a red light
  • 2 + 2 = 4
  • how did you learn to count from 1 to 100, this is just the one times table.
    The other tables step forwards (from zero) in steps of 2 to 12
    (or 2 to 10 if you think 12 is too challenging)

And by the way that’s a method for working out an answer in the times tables,
just step forward from 0.

So for 4 × 5 we take 4 steps forward from 0 in steps of size 5

0, 5, 10, 15, 20

But as 4 × 5 = 5 × 4 we could take 5 steps forward from 0 in steps of size 4

0, 4, 8, 12, 16, 20

Which way do you think is easier?

Why not choose the easiest way.

We learn by building associations, which sometimes just come from saying things, or hearing things over and over again. So although learning by rote is used as a term of abuse by some people it is actually part of how we learn.

A very important point is you don’t just learn by memorising (say as lines in a play or a poem) you also learn by answering questions.

Each time you answer 6 × 6 = 36, (or hear someone else answer it) you cement that knowledge a little bit more in your mind.

But what happens if the answer doesn’t come?

Well there’s not much point in waiting more than a few seconds as you can usually work the answers in less than 30 seconds just by stepping through.

And the best thing about this is it helps learn both

  1. both 6 × 6 = 36
  2. and how to work out 6 × 6 = 36 by stepping through numbers 6 at a time

There are certain tricks or short cuts which I explain in Starting Arithmetic
but stepping through always works.

Why bother to learn tables if we can learn a method so we can always work out the answers?

You may remember first learning to drive there seemed so many different things to do all at the same time, the number of tasks seemed overwhelming. With practice changing gear, accelerating, steering, braking, signaling becomes automatic freeing your mind to concentrate on watching the road.

Your mind can only cope with so much at any one time.
When trying to solve more advanced problems if tables have been learned so answers are automatic this frees up the brain to focus on bigger picture.

Regular practice means answers get memorised and so we can answer quickly.
Without regular use, what has been learned fades away.

Use need not only happen at school. Why not encourage your children to enjoy a hobby which involves some maths and tables.

  • cooking
  • carpentry
  • navigation
  • electronics
  • astronomy

Most of what is called maths (or math) at primary school is actually arithmetic.
Although science and engineering may involve more complicated maths
if you are going to work out any definite answer at some point you have to
put numbers in, in which case you are back to arithmetic.

There are some complications

    • there are usually some formula and algebra
    • it is necessary to work with units such as kilograms, meters, seconds
    • many of the calculations involve very large or very small numbers. To make things easier numbers are written using powers of ten, so called scientific notation.

But after all this is just plain arithmetic.

April 2012 was unusually wet in England.
In this post  Times tables what can yo do once you’ve learned them I show you can use arithmetic to estimate the amount of water that fell on England in April 2012 and compare this with the amount of water pumped into water pipes in a year for all UK.

It seems nearly 3 times more water fell on just England in just April 2012 than is used by whole UK in a year!

Now why are our water bills so high?

In the pdf version of this post I show how you can use arithmetic, with a little help from Newton, to calculate how long the moon takes to go once around the earth (27.4 days).

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One Response to Learning Times Tables – Rote Learning Understanding Or Do You Need Both

  1. Paul Muston says:

    I agreed with the Wikipedia entry for role learning that it “is widely used in the mastery of foundational knowledge.” I see many examples of this even in higher education – for example the anatomy taught in medical school. You need this foundational knowledge to successfully reason around a topic.
    Interestingly Nolan Bushell (founder of Atari) has started a company dedicated to speedy rote learning called Brainrush.

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