Continued from Part 1.
The most likely reason that the importance of fluency in times tables has been downplayed is due to ideology. While plenty of primary teachers discover the benefits of fluency in times tables while teaching (particularly if they have to prepare students for SATs), the majority of blogs I read by primary teachers, and 100% of those I read by trainees, have the bizarre idea that maths is divided into discrete categories: “facts”, “methods” and “conceptual understanding” and that it is the last of these that is most important. Unfortunately, the “conceptual understanding” category tends to be code for “relevance”, “group work”, “games” and learning multiple strategies for arriving at answers rather than actually learning the best methods to fluency. In times tables this means that students are taught the most trivial aspects of times tables (that multiplication is equivalent to repeated addition, that multiplication is commutative, and division being the inverse of multiplication) without learning off by heart that 3 lots of 7 is 21. Worse, people talk as if facts and methods are in opposition to understanding; as if learning the times tables will somehow undermine, rather than illustrate, those trivial aspects of times tables.
A further objection to times tables testing is the idea that it will cause “stress” or “anxiety” for students to have to recall basic facts under time constraints. Of course, recalling times tables in an unlimited amount of time is actually pointless, as it would undermine recall completely if students were given enough time to calculate answers. It would be like handing out dictionaries in a spelling test. I think the low expectations here need to be challenged directly. Answering questions on something you know fluently is one of the least stressful tests there is. That’s one of the main advantages of fluency. Can you imagine an art teacher arguing that students shouldn’t have to know what yellow is because the effort of remembering might cause stress? Or a PE teacher saying that students cannot be expected to know any of the rules of football while under the pressure of playing a game? Remembering the basics is not stressful unless you don’t know them well. To be tested on times tables 2 years after the curriculum says you should know them fluently is not stressful unless your teachers have failed you and it is that type of failure that is being challenged by the introduction of the tests.
And finally, one objection that’s come up is the idea that tables beyond 10 are pointless. To be honest, the 11s are not terribly useful, but they are so easy to learn that the opportunity cost of learning them is insignificant. As for the 12s, I have seen it argued that this is some hold-over from pounds shillings and pence that is no longer relevant. If you think that, kick yourself now; you have just accepted uncritically one of the most ludicrous claims on the internet. The 12 times table is one of the most useful. There are 12 months in a year. There are 12 inches in a foot. The number of degrees in a half or full rotation is a multiple of 12, as is the number of seconds in a minute, minutes in an hour and hours in a day. The fact that 12 is a multiple of 1,2,3,4,6 and 12 has made 12 and its multiples extremely useful for dividing up units of measurement for thousands of years. It’s also why we often refer to “dozens” when grouping objects or indicating magnitude. And that’s without the advantage knowledge of the 12 times tables gives in the many mathematical questions that will make use of the number 12 precisely because it has so many factors. If we weren’t biased by the number of fingers on our hands, we would probably have a number system built around the number 12. Seriously, how could any numerate person have missed the importance of 12s?
I’ll leave it there. If we want students to be good at maths, then it should not be too much for them to learn a few dozen basic number facts fluently after more than half a dozen years of education.