to think that number bonds epitomise everything that is wrong with the UK approach to education?

[IceBeing]

For the uninitiated, number bonds are groups of numbers that form additions. Eg. The number bonds for 10 are 1-9, 2-8 3-7 etc.

If you understand what addition / subtraction are, then clearly you don't need number bonds. They are a means to get kids to give the right answers by rote to questions they presumably don't understand yet.

This leads on smoothly to learning times tables by rote as a substitute for having any idea what multiplication is, learning the grid method for multiplying multi-digit numbers...learning by rote to rearrange algebraic expressions.....learning to factorize quadratic equations by rote...learning to manipulate vectors by rote...

Then at the end of this I have physics undergraduates telling me they don't like exams where you have to work things out, they prefer questions where you just repeat the right facts.

But it all starts with number bonds.

AIBU to think it matters a hell of a lot more that kids understand how numbers work, what addition and multiplication mean, than that they can give a nice clear confident, and above all, quick answer to a list of approved questions?

AIBU to think the best thing you can do for a kid that doesn't 'get' addition yet, is wait until they are bit older and try again, and that the very worst thing you can do is replace understanding with a rule set to learn?

The new curriculum says that primary kids will have to do long division. A pointless waste of time.

That said, long division is simply short division but where you don't know the times table off by heart and have to use subtraction to calculate the remainders to carry over. It looks confusing though.

My year at primary school wasn't taught timetables by rote, we were supposed to know them naturally.

Guess what, even now, I have to think about my times tables - the numbers don't leap to my mind.

Contrast with squares up to 20 which we were drilled in at secondary (before we were allowed to leave the class) and most of those still leap into my head 20 years later!

I have other blank spots (completing the bloody square for quadratics - the method just slips from my brain), but I think there are levels, like in physical things - first you learn by rote, then, if you have the ability you learn the how and then finally you learn the why. Like driving a car - first you learn the things that you have to do, so you do them automatically and naturally, then you grow in understanding about what's going on under the bonnet, and then maybe how to fix it. Not everyone has the inclination or talent to get all the way up the tree of learning it, not everyone has to.

Ha Noble - I am that person!

I don't know my tables, and so I do long division even as an adult!

I feel ridiculous now (but it was a method that worked, and I understood, so I didn't mess with it no matter how slow it was....) - my mum is much better at the mental arithmetic shortcuts than me, but I never drilled enough at it.

Kim, that would take me six weeks to do, and I'd need a calculator.

Can't be doing with that either.

To use your e.g. - 1420/12 - 12 goes into 14 once remainder 2; goes into 22 once remainder 10. Goes into 100 8 times remainder 4. Answer = 118 r 4, or 118.33333333333333 etc.

Saves messing around with different maths functions. (I haven't explained it well for anyone who doesn't understand how it works, it's easier to draw.)

Kim, you keep answering your own question from 08:20:59! (Ie Why does it help to learn the number facts associated with a concept?)

Necessary but of course not sufficient.

Well yes indeed.

But if you don't know the facts then you can't use them. So there has to be a place for learning the facts.

Some years ago I shared a house with a woman who worked in a shop. She thought getting a better grasp of mental arithmetic would help her at work, and knowing I was very good at it, she asked me to help. I'm not the world's best teacher, but I tried my best. We practised sums, I explained how to juggle the numbers round, but even though I kept dialling the explanations down to a simpler level, she just couldn't get it. I've since learned what number bonds are, and it's clear to me now that my old housemate's problem was that she didn't understand number bonds (and hadn't memorised them as we weren't made to back then).

So on the strength of that, OP, I'd say you're being unreasonable in this specific instance, because number bonds matter, but not being unreasonable in the more general sense that understanding is preferable to memorizing.

ahh the old "but if you don't know any fact then your can't do anything" chestnut.

We have this discussion all the time at work...particularly with reference to exam papers. Which of the equations is it reasonable to assume the students can recall and which do you have to put in the paper as a hint.

I often point out that once it goes beyond F=ma, V=IR, pV=nRT, the vast majority of equations would have at least one of the professional physicists round the room checking the details on wikipedia.

Or in other words the number of facts a professional physicist has loaded in their head at any one time is a tiny fraction of those they have at some point had to memorize for an exam.

I think open book exams would be an excellent start in dealing with this issue.

Oh agreed (we agree on a lot), it's an endless debate how much of what one should squeeze into a time-limited curriculum.

But I'm happy to put "number bonds to 10" in the uncontroversial pile.

Good grief, I have just worked out what the 'grid' method actually is! It had never occurred to me that one would dignify something that obvious with an actual name and protocol.

I don't think I was ever taught it - it is just kinda obvious as multiplication is distributive over addition....

Anyone else think we should be teaching group theory first?

Sorry, that was to Kim.

I learnt number bonds ax a child and still think they are one of the most useful things I have ever been taught.

I am 42 by the way.

I guess I feel like if you can do addition, and you do a bit of practise then you automatically pick up number bonds for 10. They are obviously hard wired into my brain, even though I have never made any conscious effort to learn them or think about them.

It is the same as you never actually have to learn F=ma...it just turns up in your brain because you use it so often.

Actually deliberately sitting down to memorize either number bonds or times tables (or Newtons laws) just seems....wrong.

It is the same as you never actually have to learn F=ma...it just turns up in your brain because you use it so often.
I actually have no idea what that means. What am I failing to frequently do?

Ninja Force = mass x acceleration.

It's a physics thing - if you haven't done any since school then even that will have evaporated!

Nearly 50 here :
No number bonds but a lot of sticking bricks together and a balance with weighted numbers. I loved all that but haven't seen that sort of maths work in my kids' schools. They jumped to written abstract sums too early I felt.

I have a crap memory by the way....

My DM basically remembered every fact she had ever heard. Bloody nightmare to play at trivial pursuit!

My sister's memory is almost as good as my DM but I am stuck with a terrible memory...possibly why I have been forced into understanding primarily as a means of not having to memorize so much.

I actually had to rote learn the colours of all the transition metal solutions for A-level chemistry and it really really hurt!

So you were slagging it off above, and didn't know what it is?

Yes, once laid out it's completely obvious. That's the point. It derives from first principals, and reinforces those first principals: particularly handy when newly introduced complications (eg algebraic expressions) might bemuse students from the righteous path they were happily treading?

So why not just demonstrate it, rather than say the words "multiplication is distributive over addition" and expect each student to invent their own wheel?

Oh I wouldn't tell them that - I would let them figure it out entirely themselves!

I did a fab class at GCSE level in which we played about with quadratic curves, for a couple of hours. At the end of it we had come up with the completing the square method of solving quadratic equations. A million times better than just being shown it!

All the insight and understanding COMES from finding your own method. Being supplied a method deprives students of that truly valuable learning experience!

In fact pausing you have put the proverbial finger on it!

Teaching methods is a huge mistake exactly because it stops children from finding their own way.

I didn't ever tell DD how to add stuff...no 'start at one number and count up to the next', nothing!

She has apparently developed a method - and it must work because she gets the right answers...but I don't know what it is as she does it silently. It is relatively slow...so it isn't recall based...but other than that I don't know.

It's a physics thing - if you haven't done any since school then even that will have evaporated!
That explains it. I never got near physics in school.
We all have different strengths, and maths and science are decidedly not among mine. I still count on my fingers when doing 'mental' arithmetic, I could probably use all the memorization tricks I can get my hands on.