Why You Should Welcome Times Tables Tests: Part 2
January 30, 2016Continued 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.
Scenes From The Battleground 
What I don’t get is if we are so into understanding and not facts, how come the children don’t understand anything ?
It’s low expectations, trendy teaching, and the same idiot mentality “I can look it up on Google, I don’t need to know things”.
Precisely because ‘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’.
As you rightly point out, Andrew, the key to this is automaticity. The studies of Feltovich, Prietula and Anders Ericsson have shown the character of cognitive behaviour can change, even within a few hours of practice. With enough practice, one can learn how to do several tasks at the same time. ‘Research on the effects of practice has found that the character of cognitive operations changes after even a couple of hours of practice on a typical laboratory task. Operations [such as learning times tables and sound-spelling correspondences] that are initially slow, serial, and demand conscious attention become fast, less deliberate, and can run in parallel with other processes (such as the ones you mention in Post 1). With enough practice, one can learn how to do several tasks at the same time. Behavioral studies of skill acquisition have demonstrated that automaticity is central to the development of expertise, and practice is the means to automaticity. Reducing the demands of cognitive operations release (e.g. attentional) resources for other (often higher) functions (e.g. planning, self monitoring)’. K. Anders Ericsson, Neil Charness, Paul J. Feltovich and Robert R Hoffman, (eds), (2006), ‘Studies of Expertise from Psychological Perspectives’ P.53
Amazing how often elaborate and expensive scientific studies are needed to confirm what anyone with half an ounce of common sense has known all their lives.
[…] in British schools « What education bloggers have said about times tables tests Why You Should Welcome Times Tables Tests: Part 2 […]
I agree with you that there is nothing to fear and much to gain from real fluency. It seems obvious to me that really knowing your tables is key to success in maths.
As a primary school teacher it would be easy to be offended by your comments. In fact you did make me swear out loud. However I cannot deny that children in my class failed to gain fluency in their tables.
Although I taught, and tested, tables weekly, some children in my classes did not gain fluency. A source of much self-reflection on my teaching. I have tried to understand what is happening, or rather what is not happening. Perhaps it was my own, imperfect, interpretation of the NNS and then the Numeracy Framework. I do know that all the primary teachers I know, agree on the importance of tables fluency. Now we just need to work out how to impart this to the children.
I do not see a problem with learning or testing times tables. All comments on cognitive thinking are very true and transferable to very many different subjects. The issue I have with the topic of time tables test is the amount of focus it receives that consumes energy that could be spent discussing areas of eduction that bear so much more significance to the quality of the learning process, e.g. should schools aim to master the topics or just burn calendar days progressing through the curriculum, should children have individually tailored instruction with frequent, high quality feedback or how to creatively use the modern technologies to release time of teaching staff… The time tables is a very simplistic tool that looses a lot of its value once one progresses beyond trivia.
Reblogged this on The Echo Chamber.
16 times tables would be very useful for computer science!
Very prescient !
The lack of Maths graduates employed as Maths Subject Leaders in primary schools is a big part of the problem with times tables teaching (and primary maths in general). I have met colleagues with Drama, History, Film Studies and Music degrees, many of whom were great teachers but were utterly crap when employed as Maths Subject Leaders. But its not their fault, I myself was once bullied and cajoled into being a Maths leader in a primary school – for which my MA in English proved to be of no use at all. I was utterly crap at it too. But don’t fret – former LA maths advisors and SIPS working as consultants (old style progressives – and also not Maths graduates!) can come into school for £1000 a day to show everyone how its done.
Maybe you should do a twitter survey to get a picture of how many primary schools actually have Maths graduates working as Maths Subject Leaders.
Or better still Andrew, set yourself up as a Maths consult for primary schools (please).