## Should we return to learning times tables by rote?

What really is the best way for children to learn their times tables in primary school?

Michael Gove has some pretty controversial views on how he wants to change the curriculum for primary school students, in particular his plans to teach times tables with a focus on memorising rather than understanding has caught our attention. But how is this positive progress when learning by rote is merely a task on memory, and many say its repetitive nature is boring for students?

Learning times tables is important, but students should understand and have the ability to work them out logically rather than to simply memorise from a sheet. When learning by rote students are missing out on the understanding and ability to manipulate numbers; many don’t realise that in order to find 6×8, they can begin at 6×2, double it to get to 6×4, and then double it once again to find 6×8. If students were taught this way, they would have a much better grounding and understanding of maths and numbers on which they can then develop and build.

Learning by rote was common practice in the seventies and a general view from adults that were taught by rote in primary school is that the very memory of chanting their times tables over and over again makes them shudder, yet often admit that they can still remember them today. However others had extra help to develop understand the basic principles of maths, which were missed in Primary School, so they knew enough to pass their GCSE’s clearly suggesting a more effective approach is needed in the classroom.

Today we understand the importance of getting students to think independently and to have students solve problems themselves, because learning and gaining a greater understanding is far more beneficial in the long run than having numbers that mean little to them, repeated non stop. With what we now know, why would we want to go backwards in the way we educate our children? Engagement and enjoyment of maths doesn’t come from memorising a sheet of facts, but by interacting and helping children to see how their skills are relevant to everyday situations. Developing opportunities for them to apply their knowledge to different problems, places them in a great position for learning more complex problems as they move to secondary school. Employers report that even young people with Grade C and above at GCSE maths, are unable to apply their skills in everyday situation, this is a direct consequence of memorizing without understanding.

It could be there is confusion from the teachers who don’t know the best way in which they can engage their students; they themselves may have learnt their timetables by rote. Maybe Primary teachers need to spend their ‘INSET’ training days actually looking at the way they deliver maths and look at different and possibly more effective methods of doing so. Learning from memory may result in children “knowing” their times tables, but do they demonstrate understanding in order to extend their learning to other situations? Therefore this is merely a short-term achievement, and a lack of understanding will in fact hinder them in the years to come when they move onto learning more difficult problems. Importance really needs to be placed on learning and understanding rather than reciting from memory because repeating times tables over and over doesn’t mean anything to the majority students and can result in disengagement at an early stage!

Back to the blog### 4 responses to “Should we return to learning times tables by rote?”

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I’ve got to agree with the absolute majority that disagree with this post. Learning times tables by rote is foundational to all maths understanding.

The main criticism that it is ‘memorizing without understanding’ completely misunderstands the impact of lack of times table knowledge in future years. Without a firm foundation students are incapable of developing maths knowledge. As I tutor I have seen a significant fall in ability but, more worryingly, a reduction in the appetite to discover new things.

I’d much rather give students the ‘understanding’ after the ‘memorizing’ than try to do both.

I think some form of rote learning for the times table is necessary. I teach High School math and one major problem I’ve found is my students rely too heavily on their calculator and are unable to make approximations. The latter is very important, imo, as it lets you know whether you’ve made a mistake in your calculations. e.g. 37*58. I know 4*6 = 24, so 40*60 = 2400 and 3 *60 = 180. thus 37*58 ~ 2200. If I use my calculator and get an answer way off this then I know I’ve entered the data wrong.

Having learned my TT by rote, the above is automatic for me. This ‘freed’ up my brain for learning new mathematical information and applications when I was at school, making the whole process of HS math a lot easier. Certainly a lot easier than what I see in my students today. They are overwhelmed by the amount of new math information they’re expected to retain while still struggling with the basics such as TT.

That all said, one can’t just teach TT solely by rote. There needs to be context and explanation so the student understands. For eg. when we lived in HK we tried sending our 7 year old daughter to a local primary school to give her the opportunity to learn Chinese. The local school system is still heavily into rote in everything, esp math. After a couple of months she was able to recite her times tables in Chinese right up to her 12 times. Great, except if asked what it was she was chanting, she didn’t have a clue! It wasn’t because she didn’t know the English of what she was chanting: she just had no idea what the rote learned chant actually meant. It hadn’t been taught to her (or the rest of her class).

After a few months of this experiment, we gave up and enrolled her into an International school. She was miserable at the local school as there was no learning but by rote in every subject.

Multiplication is repeated addition…I understand this! I can say 2×4 =8 and then double the ans to 16 and this is 2×8…I understand this! I understand a lot of stuff but when asked for 7×8 thank goodness I do not have to go through all the processes I understand to get the answer 56. Why? Because wonderful teachers and my parents had the foresight to see that I would need to know the answer without even thinking…and made me learn my tables by rote!

Whilst it is true to say that I am not keen on rote learning, I accept completely that it works very well for some (learners & teachers alike), I also agree that being able to access certain facts quickly is a huge advantage, however, I wouldn’t suggest technology as a substitute for knowledge.

I don’t believe that the only alternative to times tables is a calculator, in fact the opposite is true. Having efficient and effective ways to calculate times tables means that when presented with multiplication of double digits, children don’t need to be provided with another method to remember but can extend what they already know.

My major concern is that young people believe there is too much to remember and become disengaged unnecessarily. By removing the pressure associated with remembering facts and focussing on application, learners are more willing and able to develop their skills.

Having a toolbox full of tools is useless unless you understand which one to use in a variety of different situations. I have never heard an employer complain that a school leaver doesn’t know 7 x 8 but they often comment on young people’s inability to calculate simple percentages and problem solve. “Knowing” times tables is not an indicator of mathematical ability, merely memory – I would argue that calculating (mentally, not with a calculator) demonstrates greater potential. Speed might be compromised but usually not significantly enough to have a detrimental effect on the problem solving.

Let’s focus on the outcome rather than the process, what works for one child doesn’t work for another (by outcome I mean functionally numerate school leavers). Let’s allow teachers the flexibility to determine the best route for their students rather than have Government dictate that rote learning is the preferred option.