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?

Methods are ok - but that does often prevent thinking. I have seen children who struggle with things like quadratics because the problem is presented differently and they can't use their methods they rely on.

I once had the misfortune of observing a student teacher spending a week with a class trying to get them to figure out how to factorise quadratics by themselves. It was a car crash, and by the end not only could they not factorise quadratics, but they hated quadratics. I suppose some skilled intervention could have nudged them along but it took a week for a minority to get the hang of what I could have taught most of the class in a lesson (this was a B grade class). I could have then presented the unfamiliar context and teased the understanding out of them.

I'm really not a fan of discovery learning. Not when you have a curriculum to get through and end points that all children need to meet.

Iceberg you have learned number bonds whether consciously of subconsciously- why does it matter?

I think the comments about working out change illustrate perfectly why the current focus on arithmetic belongs in the 1930s.

I think part of the problem is that the OP's experience is mostly with undergraduates who are towards the right end of the maths bell curve. Probably because they are the ones who picked up maths facts just through a bit of practice.

Give her a week with bottom group year 5 trying to solve perimeter problems while still adding single digit numbers using their fingers and she might see why numbers bonds need to be learnt?

Of course you need to work out your change.

Cash registers do it for you. If you're on a till all you have to do is count the coins/notes to make up the amount shown.

There is shopping without cash registers! Even today. You also need to know how much to expect so that you are not short changed- perfectly possible with the people operating the cash register. You also, as I did yesterday, need to add up special offers and which is the best way to do it. All using number bonds.

Kids who can't deal with the basics of money are just asking to be scammed.

I do a lot of shopping on markets- no cash registers- the stall holder adds it up in his/her head and therefore so do I- and check the change.

Never mind the change. When you've got £4.80 in your purse and nothing in the bank it's quite useful to quickly total stuff up to see whether you can afford that loaf of bread as well. You could use your phone but it's a bit less obvious.

Number bonds aren't NEW.

I was taught them in primary school 40 years ago. We didn't call them "Number bonds" - we called them "The story of 10" (or whatever), but they were still number bonds. I recently found one of my Primary 1 maths books with 10+0, 9+1, etc all written in there...

I think there has to be an understanding of method and the concept.

Ideally, yes. But fannying around 'discovering' the concept (which is usually so guided as to be basically telling them the concept but in a more drawn out manner) usually leads to kids who aren't confident with either.

I am old fashioned enough to think that if you look after the pennies the pounds look after themselves. If you are going to take the notion that you don't need to bother you can just rely on machines then you are very trusting. I wouldn't just estimate- but if I did then you need number bonds for that too.

Of course they aren't new! A new name- that is all.

If you understand the number system you can automatically understand number bonds. If you can't understand number bonds then you don't understand the number system.

So nobody saying that there isn't enough time to let kids discover methods for themselves what with all the stuff they need to cram in, are you happy with that situation?

Coz my opinion would be that even one thing understood is better than ten things crammed in with no understanding.

erm everybody, not nobody...

I mean who cares if you have robotically adopted a method for long division if you don't actually understand what division is for?

If you are struggling with maths sufficiently that your main concern is being able to handle money then surely it is even more important that you spend more time properly understanding addition, subtraction, multiplication and division and even less time learning arcane methods for doing long division by hand?

No point in moving on until they understand place value and number bonds.

I think the maths curriculum is overcrowded to the point where kids get taught a method, then move onto the next one, then the next one, with very little time for extended practice, application in different contexts and problem solving. However, when teaching a method, I will try to show where it comes from.

Even if I had more time, I still wouldn't try to force kids to discover how to solve quadratics (or circle theorems or whatever stuff incredibly clever people managed to work out for us hundreds of years ago) themselves. I think that's simply wasting time. I'd get them to apply their methods more widely.