Simplicity is the key to teaching times tables

Editor’s note: This is an updated version of a blog post published on October 21, 2021

As teachers, we probably would never ask one another “Why on earth do my pupils not learn how to use a semicolon at home?” It would be a ridiculous question considering it’s learning that needs to be facilitated carefully in a classroom, not taught at home by parents. Yet I suspect many of us have heard colleagues complain that some of their pupils don’t learn their times tables at home.

It should clearly be OUR responsibility to teach times tables, and the upcoming test in year 4 is a reminder we have to do it well. If we put aside any arguments about the existence of that test to begin with, most teachers would agree that having times table facts at hand is vital to lessen the cognitive calculation load in order to “move on to more interesting maths” (Jenny Field 2020).

More interesting maths

What do we mean by “more interesting maths”? Matt Parker uses the metaphor of football. He suggests that if maths is a game of football, the drills are the calculation facts. While everyone just wants to play the actual game — the interesting part — you can’t be any good at it if you don’t put the time into the drills. Unfortunately, the drills are inherently less interesting. As teachers, we have to find ways of alleviating the drudgery of the “drills”.

If we don’t, pupils who don’t memorise maths facts will, as Jo Boaler points out, ‘…come to believe that they can never be successful with math and turn away from the subject.’

This is too important not to get right. Just think of the many primary curriculum areas that demand times table knowledge: ratio, fractions, area, perimeter, angle calculation, algebra and percentage just to name a few. A cursory look at the 2018 SAT tests shows 77 of 110 marks available required knowledge of multiplication facts.

Maths is simple

During a recent online lecture I watched, Dr. Ban Har Yeap spoke about the underlying simplicity of mathematics, illustrating his point by showing there are only three forms of a + b = c.

• Change: an amount can be increased or decreased;
• Part-part-whole: an amount can be made of different components;
• Comparison: different amounts can be compared to each other.

The same can be said for multiplicative reasoning. At its heart, there are three laws (not to be confused with natures) that children need to understand:

• Distributive: a x (b+c) = (a x b) + (a x c)
• Associative: (a x b) x c = a x (b x c)
• Commutative: a x b = b x a

Any strategies that aim to build competency in times table calculations must help reveal these laws to the learner. Memorisation of given facts is not enough. Much has been written about the problematic nature of rote learning. I would add that if you were to ask a child with full times table facts but little knowledge of the three laws to explain how to calculate 18 x 24 by knowing 391 ÷ 23 = 17, you might well be disappointed with their confused response.

A three-step model for times table automaticity

Back to simplicity. I like to think of times table automaticity as a three-step model:

1. Learn the nature of multiplication and create some facts;
2. Develop strategies to derive new facts from those you have already created;
3. Practise deriving new facts until you have reached automaticity.

Step 1 starts early. Field names four prerequisites for times table learning that fit here:

• unitizing;
• understanding equal and unequal groups;
• combining equal groups;
• understanding the early relationship between repeated addition and the multiplication sign.

The lessons devoted to the introduction of new tables in Maths — No Problem! help with step 2, so step 3 is certainly where we need to augment the Maths — No Problem! curriculum.

Tips for a times table practice routine

In my own teaching practice across years 4-6, I devote a weekly 10-minute period to work on automaticity. During that session, I have three activities operating concurrently: array games for those working on the 3 and 4 times tables; bar models for those practising 6, 7, 8 and 9; and a beat-your-personal-best challenge to complete a 10 x 10 grid for those working on advanced automaticity. The point of personal best times is to create a positive wish for speed, as an alternative to a time limit that may instead cause anxiety, i.e beep, your time is up, you have failed!

Setting up the routine takes time and care: visuals like arrays and bar models need checking, writing-grid techniques need to be discussed and a “Beat-the-Clock” classroom display for recording personal bests needs to be created. As Plato once said, ‘Simple can be harder than complex.’

Very soon though, that 10-minute weekly slot becomes a purposeful, easy-to-administer and fun routine.

I have at times worried that I am missing some variation, but I was reassured to read Field openly discussing this in her research into times table automaticity run across five local authorities: “Choice of representation is not about quantity but about quality and progression.”

Which brings us neatly back to simplicity.

You can find the resources I use, alongside a video guide for children and parents, listed as year 4: times tables.

References:

• Field, J. (2020) Teaching learning and understanding times tables, a case study from the perspective of schools participating in a national CPD Programme. www.ncetm.org.uk/features/whole-school-approach-to-learning-times-tables/
• Parker, M. (2014) Things to make and do in the 4th Dimension. Penguin.
• Boaler, J. (2015) Fluency without Fear: Research evidence of the Best Ways to Learn Maths Facts. Youcubed at Stanford University. https://www.youcubed.org/evidence/fluency-without-fear/