Notably, last month we saw Jo Boaler, professor of maths education at Stanford University, and Charlie Stripp, director of the National Centre for Excellence in the Teaching of Mathematics (NCETM), supposedly at loggerheads on this very subject.
Jo Boaler argued the UK Government position that every child must memorise their times tables up to 12 x 12 by age nine is ‘absolutely disastrous’. In contrast, Charlie Stripp stated knowing the times tables supports mathematical learning and understanding.
Here at Mathematics Mastery, we believe children who have a strong grasp of their times tables are more confident when learning new mathematical concepts and, importantly, enjoy the subject more. But note here I’ve said ‘strong grasp’ and not simply ‘memorised’.
Times tables are taught in early years through songs and chants, along with counting and grouping cubes. We then move on to using images and written multiplication. These techniques enhance understanding and fluency, by enabling the students to make links and spot patterns (such as the relationship between the two and four times table).
We agree with Charlie, and know from experience, that when a child doesn’t know their times tables, it can obstruct progress – as they can’t draw on this knowledge to solve other maths problems. We have taught lower-attaining students who understand more difficult mathematical concepts, yet struggle to develop or practise their new learning because of insecure number skills – with lack of times table knowledge as a root issue.
However, we also agree with Jo that being able to memorise things quickly – like the times table – is not the same thing as being good at maths.
Jo’s key issue seems not to be with times tables themselves (at no point does she say she’s against the concept of times tables, or that having times table knowledge is itself negative or useless). Rather it is the emphasis on memorisation, speed and testing (in other words the human influence on times tables) that she is strongly against. In Jo’s words: “It is not terrible to remember maths facts; what is terrible is sending kids away to memorise them and giving them tests on them which will set up this maths anxiety.”
We agree with Jo that times tables should not necessarily be tested. Instead we think teachers should focus on times tables as part of lesson transitions, ‘do now’ activities and ‘number talks’. This way, the ‘factual’ learning (which Charlie emphasises as being hugely important) is still taking place – but in a non-threatening environment.
In our programme, we align the factual learning with the conceptual, so students can deepen their understanding of the relationships between numbers. For example, children explore ‘commutativity’ in order to recognise why 3 x 5 and 5 x 3 give the same result. So if a child understands the concept of commutativity, AND they have the factual knowledge from their times tables that 3 x 5 = 15, they do not then need to have ‘memorised’ 5 x 3 = 15 as a piece of separate, standalone knowledge.
Instead, they will have the understanding needed to a) link the two calculations together and b) grasp why they give the same result. The knowledge that the answer is 15 in both cases will come from a strong conceptual understanding rather than simply memory – which is the mastery approach through and through.
Charlie believes that learning some mathematical material so it can be recalled automatically (in other words, memorising) “assists, rather than detracts from, the process of developing conceptual understanding in maths”. He mentions that “educational research shows memorising supports understanding, and understanding supports learning”.
This last point is a crucial one. Memorisation with no understanding can only get you so far. There will be a point where the knowledge can’t be fully applied because it isn’t fully grasped.
Jo says she has never memorised her times tables and that it has never held her back, even though she works with maths every day.
We’d like to interpret this as a statement of encouragement for all the children (and indeed adults) who’ve struggled to remember their times tables. We do not believe she is suggesting that, for those who HAVE grasped or memorised them quickly, it is inherently a bad thing.
The mastery approach emphasises that getting facts to ‘stick’ in one’s memory is easier if the facts are developed over time and practiced regularly but not ‘drilled’. The links and parallels between facts should be highlighted and played with, and the multiple representations of facts must be demonstrated and discussed.
Are times tables the be-all and end-all of mathematics? No. Are times tables an extremely useful mathematical tool for future learning? Yes.
Moral of the story? In reality, when it comes to times tables Jo and Charlie probably agree on a lot more than they disagree on. It’s the issue of testing the times tables and memorisation as a marker of success that is the real sticking point.Back to news list Next article