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?

Is the idea that it just gives children another way of looking at the issue?

When it comes to minor addition and subtraction don't we essentially just do this by rote anyway? When I need to take 3 from 10 I don't actually do the maths, I just happen to know that it leaves 7. Is that what they are aiming to give the children?

My gut instinct is to agree but am pretty uniformed on this. Better to have a good grasp of quantities in practice (counting real objects etc) before moving on to numbers as an abstract concept IMO.

DS1 had no trouble with number-bonds, but he seems quite good at maths so probably understood addition by the time he learned number-bonds.

It does seem to make some children realise there's more than one way of arriving at the same answer - I've seen preschool children insisting that 6+4 is NOT 10 because that's 5+5...

As the parent of two children in infant school currently learning number bonds I completely agree with you Icebeing. We talk about numbers a lot at home to try and stop what you describe happening, it scares me.

There is no other way of looking at addition...this is a way of training people who can't work out the answer to give the right answer anyway.

TBH I feel the same way about drumming phonics into preschoolers....If you leave learning to read to later then kids get it faster and actually end up being better readers with more enthusiasm for reading.

I don't see it as either/or.

It's totally possible, assuming competent teachers, for pupils to learn both how arithmetic all operations work, and have rapid recall of the basic bonds/tables as the automaticity/fluency makes all mental arithmetic easier.

Oh thank god it isn't just me!

It terrifies me, the way we are trying to teach harder concepts earlier and then in those kids that are just not ready for them we force rules on them instead of giving them space to understand.

I disagree. Number bonds are how you do addition as an adult, surely?

If I'm adding up in my head in a shop then knowing that 7+3=10 is as useful as knowing that 7x3=21. Instant recall of the relationships between numbers (number bonds and number triangles) is the foundation of mental arithmetic.

That said, I agree that a child first needs to have a solid understanding of what addition actually is. Physical props tend to be useful - and Numicon is great to show that eg a 2 and a 5 together occupy exactly the same shape as a 7.

DD's nursery class is introducing number bonds. DD isn't interested. She loves straightforward addition and subtraction though, so we're doing those at home with her.

Likewise reading. School uses phonics, she's a "look and see" reader. We're supporting that at home.

YANBU - I was thinking something similar this week when looking at DS' homework which involved learning number bonds.

I don't want to teach him differently from school and confuse him but I think there has to be understanding behind maths rather than just memorising and regurgitating.

YABVVVU.

How do you expect them to factorize quadratic equations NOT by rote if they don't have an instant grasp of number bonds and factors?

Your and my "heuristic" factorization is based on "just knowing" these number facts, and having them spring to mind shouting loudly when we look at the question.

Number bonds are learnt on top of skills like using a number line, not instead of. Like reading whole words is a skill on top of sounding out.

I mean what do you do when you try to potty train and your kids just doesn't get it?

You wait a while and try again!

You would be crazy to try and do it by rote...plonking your kid on the potty every 10 mins....

Also it would lead to refusal and fear of toilets etc.

I think we are doing the same to kids in English and Maths. Making them hate and fear the subjects by trying to teach them things they aren't developmentally ready for.

and what is happening to times tables?

Ds1 understood number bonds but he is a math nut - he knew his multiplication up to 12s in reception. (a bit obsessed with numbers would be an understatement)

Ds2 has struggled horribly with maths. The school was pushing number bonds to 10 on him, when he couldn't understand the concept of addition, and they weren't trying to teach it to him. They just kept saying he just needs to learn these, that's all, and he'll be fine. No, because he has no idea what 3+7=10 MEANS. As he has memory problems as well, brute memorisation is out anyway. He is being HE'd now, and we're slowly working through how to do addition so that he understands the numbers themselves, because he simply is not going to be able to memorise things that easily.

pausing wtf? It is totally possible to do factorisation by understanding what you are doing. You don't need 'rules' the 'rules' are only there for the people who don't understand to get the answer out anyway. I mean why not just use a computer if you don't know what you are doing?

Number bonds aren't taught as a memory type exercise. They will be taught as interactive activities to show that 7+3=10 so the children are learning how addition works. It shouldn't be about learning by rote and if it's being taught that way, I'd question the teaching!

Alice that is just so crap! Why not leave people till they are ready to learn? Why force everyone at one pace and then kick all those that aren't ready into memorization hell?

I'm 37. I never did learn my 7 or 8 times tables. I have an A level in maths and managed a £12bn budget without issue. On the rare occasion that I need to know some multiple of 7 or 8 it takes just a second or 2 to calculate it.

Understanding "number" is far more important in my view tha learning off rote.

I have to disagree. I think it really helps to hold the numbers constant in their head when doing mental maths. Not all things rote are bad, IMO.

Once you understand the maths, you obviously end up knowing all sorts of things off the top of your head. The things I can quote simply because I use them all the time include, PI to a stupid number of decimal places, the solution to quadratic equations and solutions of the wave and diffusion equations.

Knowing things AFTER you have understood them is totally different to memorizing them IN PLACE of understanding.

I'm really surprised by this. We did number bonds with numicon. YR children were physically picking up a 3 and 7 and fitting them together to make 10. That strikes me as a really good way to start understanding how numbers fit together. Number bonds to 20 we did by adding 10 to one side or the other.

Perhaps our infant school is unusual but I've always been impressed with how they help the children to develop a real feel for numbers rather than just adding up for the sake of it. Ditto with multiplication, they've always been encouraged to understand it with objects rather than learn by rote.

And anyway it can't stay rote learning for long. No one would do number bonds to 50 or 100 by rote, surely?

I had a chat with a Maths Professor who recently dreamt up an incredibly complex 3D diagram of how to tie a chemical reaction into a knot using laser light. He could do that because he understands the functions involved. I very much doubt he would respond either accurately or quickly to a grilling on times tables.

He was totally appalled by the idea of number bonds.

Eh? What are you talking about?

How do you factorize quadratics yourself?

Because I would look at

x^2 + 5x + 6 and immediately think "try 2 and 3". Because I know both my times tables and my number bonds for 5.

If I didn't know my number bonds, I'd have to use a "hack through the rules method".

I think it's very useful for working out say, 86 - 74 in your head. When I was doing this with my son, I would say "Ok, what is 74 to 80" which is a number bond, obviously, and thinking of it in that way helped him a lot.

flomple I am certain that sitting around with lots of small objects and seeing how combining groups makes groups of larger numbers is an excellent way to begin to understand addition and subtraction. My DD has started this game on her own...

I don't see how that becomes number bonds. They are a list of facts to be retained if you can't see the point behind moving the piles around.