I disagree strongly with Ms Boaler’s stance, reported in TES last week, on children learning their times tables.
Knowing your times tables supports mathematical learning and understanding, and my experience is that young children find learning them fun. They enjoy chanting their times tables and learning the relationships between them (such as the six times table being twice the three times table and why that is). Knowing the times tables fluently helps them to develop their learning in maths because they can take that knowledge for granted, which frees up cognitive space for them to learn new mathematical ideas and apply maths to solve problems.
I’ve been in a primary school classroom recently where some of the previously lower-attaining children are making great conceptual progression. They understand the problems to be solved, they have strategies for tackling them. However, there is still one thing getting in the way: they don’t know their times tables and this is seriously inhibiting their progress, preventing them from using maths to solve problems.
I have also experienced primary classrooms where all children do know their times tables. The confidence this gives them in tackling other areas of mathematics and in solving mathematical problems empowers them and enables them to really enjoy maths.
Learning some material so that it can be recalled automatically (in other words, memorising) assists, rather than detracts from, the process of developing conceptual understanding in maths. Educational research shows that memorising supports understanding and understanding supports learning. In Shanghai – which, according to international tests, tops the league tables in school-level maths education – primary school children are encouraged to memorise their times tables. (They’re also encouraged, in parallel, to think deeply about the links between, say, the three and the nine times table.) This means that Shanghai secondary schools can take number fluency for granted, enabling their children to make far more progress than is typical in jurisdictions such as the UK, where secondary school children are generally far less fluent with numbers.
Learning mathematics involves knowledge of three main types: factual, procedural and conceptual, and research evidence suggests all three should be developed in parallel. Neglecting the factual inhibits the development of procedural and conceptual knowledge and damages mathematical learning.
Many of our teenagers and adults suffer from maths anxiety because they found maths so hard at secondary school and have never become confident with it. My experience of working with adults who did poorly in maths at school suggests that they find working with numbers and other aspects of maths needlessly difficult because they lack the automatic recall of basic number facts. Their opportunities are restricted because they fear working with numbers. If only they had learned their times tables at primary school!
It is not the learning of times tables that is causing anxiety but rather it is lack of times table knowledge that is causing the anxiety. It should be an educational entitlement that all children are helped to learn their times tables.
Ms Boaler’s argument might have some value in schools where children are forced to memorise their times tables and encouraged to develop no other strategies with which to tackle mathematical problems. But we know of no such schools in England. Nor have we seen any in our travels to Shanghai.
The journey of mathematical learning involves the acquisition of several complementary skills.
It would, of course, be wrong to tell children that all they need to do is memorise some facts. It would be equally wrong to tell them that they can get by without having done so.
Charlie Stripp is director of the National Centre for Excellence in the Teaching of Mathematics (NCETM)