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Why You Should Welcome Times Tables Tests: Part 1

January 30, 2016

I promised I’d write about this last weekend, and then ran out of time, so apologies for the delay.

I support the introduction of times tables tests at the end of Key Stage 2. The main reason is that I am a secondary maths teacher and I see so many students arrive at secondary school not knowing their times tables. The complacency of those who say “primary schools already do this” amazes me. There are some primary schools that are good at this, but to be honest, since the end of the original NNS I can’t think of any year 7 class (other than when covering at a top grammar school) I’ve had that turned up to secondary fluent in their times tables. And this includes top sets and classes at independent schools. Very often the only students who know their times tables were educated overseas, taught by their parents or had private tuition (particularly Kumon maths). Worse though, is how often students think they know their times tables properly but don’t. It’s common for me to ask a class who knows their times tables and get 50% of hands up, then to ask “What’s 7 times 8?” to a student with their hand up, only for them to start counting on their fingers. Often students arrive at secondary not only not knowing their times tables, but convinced that as they could work through a table by repeated addition, then they have mastered the skill. Often they know virtually nothing of the 12 times table. Some students are not even fluent in their 2 or 3 times table after 7 years of daily maths lessons.

The reason the lack of fluency makes a difference is something that should be obvious to anyone who has followed the debates about cognitive psychology and education in recent years. Our working memories are limited. The way we cope with more complicated calculations is to fluently recall helpful information from long term memory. We also learn better if we do not overload our working memories by thinking about too much at once. In practice, this means it is much easier to grasp the idea of simplifying fractions, and remember it in the future, if every time you think about simplifying fractions you do not have to think hard about times tables calculations at the same time. It takes a second to simplify 49/84 if you realise at a glance that both numbers are in the 7 times table, and know exactly how many times 7 goes into both numbers without thinking about it and the idea of simplification is easily remembered if you didn’t get distracted by the need to work out times tables. Every maths teacher has experienced the student who thinks all simplifying of fractions should involve division by 2, because those are the only questions on simplifying they have ever mastered. Also common is the student who loses track of what they are doing part way through simplifying a fraction, and writes down the common factor in the simplified fraction rather than dividing by it. These are failures that occur because of a lack of times tables knowledge. And all fraction calculations tend to involve similar considerations of times tables. As do the methods for dividing and multiplying larger numbers, negative numbers or decimals. Multiplication and division are also fundamental for accessing proportional reasoning and much of algebra. Even topics in geometry (eg. angles in regular polygon) and statistics (eg. pie charts), are often easier if you can divide fluently. If you don’t get how fundamental times tables are to learning maths, I am prepared to argue that you don’t understand how to learn maths. Maths is cumulative and fluency at one level leads to understanding (and more fluency) at the next.

Continued in part 2.

 

18 comments

  1. How to cancel 15/25 …..do the same to the top as bottom..so it’s… 7.5 over ….um….
    I won’t say which yr groups have this type of conversation., but maths teachers will be able to guess


  2. I can clearly remember the journey to school every day, where my parents tested me on my times tables – I hated it. But it did make things a lot easier when I got to secondary school, so I’ll be doing the same.


    • Indeed. My father made me a grid (up to 13×13) and I got a reward (Revell’s 1/32 Stuka kit) when I was fluent and 100% accurate. Took me three days. Thank god he did, too. The “bright idea” when I was at school was not teaching proper handwriting. I still can’t do joined up handwriting.


  3. i agree with you on virtually every point. One question though, why bother with 12 times tables? As we operate (Ireland) with a decimal system do you feel 12 times tables are any more important that 15 times tables or 16 times table? Just a small point, but I am interested why people still teach 12 times table and no higher.


    • That will be in part 2. See if you can guess.


    • May I venture that although 12 has a lot of tradition to it eg feet and inches etc, stepping outside the confines of 10 is a good thing anyway. I test my own children on things like 9×13, 4×15, 6×14, 3×18 etc
      Most of these type I use long term memory. My son would probably be thinking 9×10 plus 9×3 and therefore be using a bit of working memory.
      Anyway knowing the twelve times table saves this kind of splitting up.
      And practically we should stop at some point but I personally am not against children learning the 13 times table if they want


    • I often wish I knew my 14s when I watch American TV shows and they give people’s weights in pounds.


      • Well, as 14s are 7s with alternate ones missed, I imagine you do. The important ones above ten are the prime tables: 11, 13, 17 etc.


  4. I showed this to my eldest daughter, who has an average of 97% UMS over 6 A level Maths and Further Maths A level units, and she told me she was only ever taught her times tables up to 10… and still doesn’t know her 11 or 12 times tables!


    • To be honest, because of the advantages for working memory, the need is probably inversely related to mathematical ability. But that “closing the gap” aspect is important. Students shouldn’t have to be natural mathematicians to go into a discipline wiyh significant mathematical content at university. That said, I believe even the most able will gain some marginal advantage from times tables knowledge.


    • I bet she knows her 11s
      Has she not spotted the pattern yet!
      Even when you get to 121 and 132 surely those are familiar numbers (more familiar than 122 and 131)


  5. I have no problem with the idea that pupils should know their multiplication facts, but it would make so much more sense if the test were given at the end of year 4 or 5. That’s when they should know them at the latest. By the time they sit it at the end of year 6 it’s too late. Overall there is a worrying inconsistency in English education. You/we/they (I’m a bloody foreigner) abandoned text books and left teachers to their own devices. Teachers in primary schools are the product of the system and therefore, themselves, did not all have a very good education in some subjects. Maths is one of them. Far too much is expected of the primary maths curriculum and until now, it has been very much geared towards intelligence rather than knowledge and skill. I’m sure as a secondary teacher, you’d prefer the pupils to come to you entirely confident in their arithmetic skills – more complex applications and problem solving can come with experience.


    • A great blog post, but you don’t need to follow recent debates in cognitive psychology to appreciate the difference that fluency (or lack of) makes, you just need to stand in a classroom during a primary maths lesson. Furthermore, actually showing primary children that maths is cumulative can be a revelation to them.
      The original NNS was pretty good at embedding fluency and had maths-as-cumulative in its planning structure, problems seem to have started with the introduction of the Primary Framework . The Primary Framework’s PNS had an explicitly tick-box structure which instigated a ‘cover’ way of thinking about maths planning and teaching; ie ‘have you covered this?’ ‘ we’ve covered that’, and ‘they should know this because we covered it last term’! The PNS was crap and its effects have become self-evident, however things are going to get worse. Bereft of even the dubious support once provided by the PNS, primary schools are resorting to buying whole school maths schemes and most of them are very very bad indeed.
      We need a new NNS ( or perhaps just a modified version of the original ), and you, Andrew Old, need to be involved in designing it. So stop blogging and start lobbying.


      • Just to clarify, I didn’t say “debates in cognitive psychology” I said “debates about cognitive psychology and education”, i.e. the arguments about the basis by which we understand learning. We still have teachers (and people controlling teachers) who will judge lessons positively on the basis of lack of teacher input, levels of activity and discussion, use of open-ended questions, peer and self-assessment, differentiation and everything other than whether the children are getting better at maths than when they started. In these cases, it is necessary to actually return to the evidence on how learning actually works.


  6. I teach French. Only two days ago I began teaching the time to year 7s. I always have to check they can tell the time in English first. Once again we hit a problem with understanding what minutes past or to there are when the big hand points to the number 1,2, 4, 5 etc. This is a second set – they all have level 4. They brightly count in 5s to show me they know their 5 times table but when I ask what 4 x 5 is they look puzzled. We are talking about the 5 times table at age 11 or 12!!


  7. […] Teaching in British schools « Why You Should Welcome Times Tables Tests: Part 1 […]


  8. Reblogged this on The Echo Chamber.


  9. Absolutely agree. Another thing kids don’t learn are their addition and subtraction facts. This is also important, but counting on fingers serves as a work-around so that it isn’t quite so noticeable–apparently. It’s very noticeable to me, and severely impedes students’ working memory when solving problems.

    I was working at a middle school assisting math teachers. In one class, for special ed kids, it was obvious that many did not know their addition and subtraction facts. The teacher agreed with me that it was a problem for some of the students. I recommended giving them drills and warmups as part of a daily routine. She said “Good idea” and never did it.



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