Times tables – Does rote learning REALLY improve pupils’ maths skills?
In some senses, we can see that repetitive learning of times tables 'works', says Craig Parkinson – but with so much more information and research now at our disposal, we need to ask ourselves whether the old ways really are the best…
The National Curriculum talks about ‘mathematical fluency’ (not to be confused with ‘speed’), with KS2 times tables tests pencilled in for the 2017/18 academic year.
This focus shows the increased importance of pupils acquiring number facts – but teaching mathematical fluency is often wrongly associated with learning by repetition.
Chanting a times table grid can put students off the subject for good, and doing poorly in times tables tests has wrongly led to many students believing that they can’t be successful in maths.
Having mathematical fluency and knowing your tables is undeniably an important skill. Singapore maths teaches that it’s better to have the methods to solve one problem five ways rather than five problems one way, but that can all go to pot if you miscalculate the final answer.
At Maths — No Problem!, we believe that learning multiplication facts can be achieved without resorting to parroting/chanting and rote learning.
The lessons of the 70s
Those who attended primary school in the 1970s will remember how times tables were learned then – stood behind our chairs, chanting them over and over again at the end of the school day.
I remember the feeling of doing it as if it were only last year, never mind nearly 40 years ago.
Why was it so memorable? Looking back, it had two chief parts.
Firstly, it was a unique activity. No other learning was done that way.
Secondly, it felt slightly uncomfortable. The volume of the five times table was much higher than parts of the eight or six times tables.
I remember the awkwardness of the sevens.
So why would we want to return to such a practice?
The Maths — No Problem! series draws on the work of Arthur J Baroody, and the three stages of learning multiplication facts: counting, figuring out and then remembering.
This is reinforced by the findings of Jerome Bruner, where students learn by moving from concrete examples to pictorial representations, then finally abstraction.
In Baroody’s work (Mastery of the Basic Number Combination: Internalisation of Relationship or Facts?) we see agreement with Richard Skemp’s ideas regarding relational understanding.
As teachers, we can control the inputs of learning but the processing is innate to the pupil. If we teach in a way that’s aligned with how they process information, the desired outcome of fluency can be more readily attained.
We have come a long way – pedagogically and societally – from the 1920s when Edward Thorndike promoted repetitive drill as a key component of a learning theory.
The Maths – No Problem! series builds ideas and concepts before students take part in drill and practise with variability, not repetition.
There are now many more strategies available to students when it comes to learning their times tables. The work of Mary Folsom (1975) and John Trivett (1980) shows how to achieve efficiency regarding the learning of times tables.
The commutative nature of multiplication means that learning all your tables is both unnecessary and inefficient. We know that retrieval time for number facts, such as 6 x 2 = 12, is variable and dependent on how the student is exposed to this fact.
Compare learning ‘2 lots of 6’ to ‘6 lots of 2’ – If you’re interested in how they differ, see Brian Butterworth, et al (1999) ‘Multiplication Facts: Passive Storage or Dynamic Reorganization?‘.
The limitations of rote learning
It is wrong to blindly apply methods from the past at a time when we know so much more about how we learn best.
Repetitive learning of times tables ‘works’, but is it the most effective way? What does research tell us about methods that are more effective? And why?
We know that there are no silver bullets regarding learning (likewise with exercising or dieting) – but it doesn’t stop us looking!
We know that learning times tables takes time. Children benefit from receiving repeated opportunities to count, then figure out before remembering. To jump straight to ‘remembering’ causes pupils to experience the known difficulties of being prematurely exposed to abstract concepts.
We also deprive our students of the joy and challenge of learning; we cause learning to be done to them rather than being owned by them. They enter a didactic contract – they wait for the teacher to tell them what to know, and then they focus on remembering it.
The Maths — No Problem! approach gives students the chance to move through a learning process that goes from counting (in ones, twos, etc) to figuring out answers for themselves by making connections (skip counting, pattern spotting, etc) to finally remembering and potentially creating their own shortcut.
When we, as teachers, tell children they can do the nine times tables by using their fingers, we prevent students from discovering this for themselves. We also stop them from transferring their knowledge to create connections in multiple ways (3 x 9, for example, is the sum of 3 x 5 and 3 x 4).
The rote that we should have is repetitive teaching of number facts, whereby we, as teachers, regularly narrate the students’ discoveries.
In teaching the idea that four groups of six are 24, for instance, we should first begin with concrete, tangible examples and then move to pictorial representations.
When we talk to our students about their learning, we show that we value their thoughts, ideas and discoveries. In return, they invest more of their resources in their own learning. This isn’t something that rote learning of times tables can achieve.
Craig Parkinson previously worked as a physics and maths teacher, and is currently a freelance educational trainer, consultant and coach, specialising in Visible Learning, SOLO taxonomy maths mastery and philosophy.
For more information about Maths – No Problem!, visit mathsnoproblem.co.uk or follow @MathsNoProblem on Twitter.
