What's the big deal about times tables?

Did you even look at the paper? This is definitely approachable - considering it was designed for 11 year olds who have had no exposure to this type of Maths before which shows you know nothing about problem-solvin.g Though I shouldn't be surprised considering you misquoted me and even ignored the proof I did provide. Who cares what Tim Gowers says!? I dread that day in 50 years when I look back at my life and see how the Swedes have dominated all areas of academia and industry and think, damn why did I ever listen to Tim Gowers.. Chlorophile was right.

Well actually, I qualified for and did the JMO so I think I'm qualified to talk about it. The kind of maths in the JMO (and the further MOs) is absolutely nothing to do with rote learning. I've had Golds in all of the Maths challenges and qualified for follow-on rounds five times - which again, definitely does not make me an elite mathematician but I'm not rubbish either - and I have never in my life specifically prepared for them. Neither have I ever done 'rote-learning' for them (or for Maths, in general).

On top of that, I don't know if it's me just being thick, but I don't understand how that article supports what you're saying. If you could enlighten me, that'd be greatly appreciated...

Yes I can see why the article isn't enlightening - the crux of the argument was someone who practised mathematical methods (taught at schools) could logically solve a problem that at first glance might have required a stroke of genius from a prodigious mathematician. In fact most "strokes of genius" are just a result of pattern recognition that arise from hours and hours of practise of what one might call "mundane" mathematics. I could explain it better if you have a working knowledge of chess? Have you seen those JMO questions? You can solve them through rote-learning of prime numbers, TT, properties of triangles etc. For example A2 is basically a triangular number sequence and an inspired Mathematician could ask himself if there was an easier way to compute the nth term of the triangular number sequence which would them lead him onto arithmetic sequences. In fact this was how I first stumbled onto Arithmetic progressions

Pattern recognition and hours of practise is absolutely not the same as rote-learning! If your argument is that hours of practise is required to be a good mathematician then I couldn't agree more. I absolutely wouldn't class that as rote-learning though and it's a completely different thing to learning your times tables. Learning TTs is no different from learning a list of random words - it's just conditioning yourself to give a specific response to a specific trigger. Learning patterns from practise is something a lot deeper and a lot more intuitive and abstract. Practising these maths challenges definitely helps a great deal and knowing the properties of triangles (given, that is just learning - although the proofs are easy - but again learning the properties of triangles is half an hour's worth of work) definitely helps, but the crux is practise and mathematical maturity. The more mathematics you come across, the better at the subject you get.

The government has now apparently "declared war on illiteracy and innumeracy" by declaring the expectation that all 11 year olds (although another article claims it's 9 year olds, not sure which one it actually is) know up to their 12 times table. I honestly do not understand the point of this. Learning times tables is nothing to do with maths, it's just rote-learning. I left primary school bitterly hating maths because practically all we did was times-table recall, which I was terrible at. Up until this day, I have still not learned my times tables yet it doesn't seem to have done me any harm whatsoever.

So why is there this obsession with times tables? It just seems pointless and counterproductive to me.

And like I said in my first post, Practice starts at rote learning. Learning your TT isn't factual recall. You can memorise your TT unto 12x12 but when someone asks you what 12x13 is you might recall 12x12 and then add a further 12. Someone then might ask what 11x13 is and you could recall what 11x12 is and then add a further 11 - soon you'll ask yourself is there an easier way to do this and you'll stumble upon adding 1 and 3 and inserting that sum between the 1 and 3. You'll then ask yourself why that works and these methods will replace factual recall.

That's not great though. You are managing the situation by using a work-around. Your life would have been easier had you mastered your tables at an early age.

My point isn't that learning the times tables is utterly useless, it's that it seems like my entire primary school maths education was devoted to learning the times tables. I hated the subject and went into secondary school bitterly hating it. I was absolutely shocked when I got put into top set in Year 7 because I thought I was terrible at Maths and it was only until my brilliant Year 8 teacher when I realised what a great subject it actually is.

Why though? It'd probably take me a good 30 seconds to work out 64*88 but I'd say I'm perfectly competent mathematically. I honestly do not understand why you think numeracy is so vastly important.

Learning your TT is completely factual recall. What you're talking about is building an understanding on top of some basic information. I know my 2 times table, 5 times table and 10 times table, and I use that to work everything else out. That requires an awful lot less learning and it's a lot simpler than just memorising everything.

No it isn't. If someone asked me what 11x14 was I wouldn't reply 154 because I have memorised what 11x14 was but because I can calculate 11x14 is incredibly fast because I have recognised a pattern and practised it hundreds of times. Despite not being able to recall the value, I would pass the government guidelines. Don't you ever wonder how people can recite the values of 1x1 to 1000x1000?

That would definitely be more accurate, I'm not sure about more useful...

Learning your TT is completely factual recall. What you're talking about is building an understanding on top of some basic information. I know my 2 times table, 5 times table and 10 times table, and I use that to work everything else out. That requires an awful lot less learning and it's a lot simpler than just memorising everything.

That's not great though. You are managing the situation by using a work-around. Your life would have been easier had you mastered your tables at an early age.

Just like to chip in that I find that I also do this and got through all the times table tests by knowing how to multiply numbers by breaking things down into simpler forms e.g. (10 - 3)(6) -> 10x6 - 3x6 instead of 7x6 and it's always served me well, and extends much better into larger numbers where times tables are no help.

Imo the ability to break down an expression logically into simpler forms and calculate it from there is far, far, far more important than rote learning 144 equations off by heart.

It just times tables gives maths a bad name.

If you're calculating 154 then it's not recall and you've therefore not got to that value through rote-learning. Pattern-spotting isn't rote learning. What I was told to do in Primary School was rote-learning. I wasn't taught any quick ways of working out multiplication sums or patters, I was taught to listen to an audio CD that went "One times two is.... two! Two times two is... four!".

I would have started off with memorising 154 and then replacing factual recall with a very fast calculation. Undoubtedly the methods taught at school are inefficient but this should inspire a student to find a faster way of solving the problem.

Well there's no reason why you had to memorise 154 in the first place. I think the 2, 5 and 10 times tables are more than enough for reasonably quick calculations in base-10. Ultra fast mental arithmetic may have been useful 20 years ago but the education system has to stop being stuck in the past.

And most pupils aren't very inspired so probably won't work out a faster way.

They aren't inspired because there is no penalty to not knowing TT.
If you didn't have a calculator, how would you accept b^c * b^d = b^(c+d) instead of b^(c*d)? You wouldn't have sufficient mathematical knowledge to prove it and would rely on computing a couple of examples but if you're reliant on a calculator, how would you compute those examples?

Well there are some pretty simple algebraic proofs for that fact but regardless, what situation is a normal person likely to find themselves these days where they will be required to calculate a "complicated" sum and they don't have access to a calculator?