Writing in the Times Educational Supplement in London (the TES), David Boorman questions plans to introduce a timed test of times tables to English schools.
Boorman’s first concern is that of ‘maths anxiety’. He worries that timing tests in this way will lead to more anxious students. I have no doubt that timed tests can make students anxious – although the evidence is hard to pin down – but I also see it as part of a teacher’s job to allay those fears and present such tests as a normal part of school life.
Boorman can’t see the need for a time limit, asking, “How long did Shakespeare take to write his plays? Does anyone care?”. I think this misses a key point: We want to test whether students have retained times tables as facts in their long term memory rather than checking whether they can work them out using working memory. If we ensure that time is limited then we are more likely to test the former than the latter. This is important because in higher level maths, students are rarely asked to simply work out a single multiplication. Instead, such skills will be embedded in a larger problem. Working memory is severely constrained and so it is important to free it up to focus on the problem in hand. If students memorise times tables then they release working memory capacity to focus on other aspects of the problem.
Boorman’s second point is a concern about a ‘times table check mindset’. He points out that many students might be able to find 5 x 7 but then be unsure of the answer to 7 x 5; something I am quite prepared to accept. But he uses this example to set time tables knowledge in opposition to an understanding of multiplication.
We often see this argument in the rhetoric about early mathematics education. And yet I have seen no convincing evidence to suggest that knowing facts somehow gets in the way of understanding. Yes, knowing times tables facts is not sufficient but I don’t think anyone ever claimed that it was. Ideally, students know their facts and also have a deeper appreciation of multiplication. In the case of the 5 x 7 example, the student would need to be taught about the commutative property of multiplication e.g. by considering a rotating rectangle. Why can’t we teach times tables and also teach commutativity?
Finally, Boorman demonstrates quite a limited view of why we want student to learn times tables. He complains that they are not useful in everyday life:
“I’m often told by friends and colleagues that they can help at the shops. However, I’m sceptical at best. Take six times eight, for example. When and why would one purchase 48 of an item? Of course, it could be six items priced at 8p each, but then what items are priced at 8p?”
Boorman’s colleagues have obviously got the wrong end of the stick. What is it about maths that makes people demand that every individual skill needs to have some mundane, everyday use? We don’t do that with other subjects. Nobody goes into a primary school class, observes a session of clay modelling and exclaims, “But when will students need to be able to do this at the supermarket!?” And nobody stops children from writing stories on the basis that they will never need to write stories in real-life; that only professional authors need to be able to write stories. And yet you hear these arguments about maths all the time.
Times tables are not particularly useful on their own and they are not intended to be. Maths is not a flat subject; it’s hierarchical with basic skills feeding into more complex skills. As we have seen, a facility with times tables frees up working memory to solve other aspects of a problem. For instance, an important skill in senior maths is to be able to factorise quadratic equations and this is much easier to do if you know your times tables. If students don’t know their tables then this limits their access to higher level maths. You can do all the investigations, critical thinking activities and genius hours you like but if students can’t do maths then you are effectively shutting the door on most STEM careers.
Perhaps most worrying of all, David Boorman is a lecturer in primary education and so he has the opportunity to promote these views about times tables to the next generation of primary school teachers.