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?

Surely nurseries shouldn't be teaching more than counting with physical representation of numbers?

At French maternelle the DC only learn to count to 30 by the end of GS (year 1), 30 being the number of DC in a class so a good physical representation.

Oldandrew's blog about fluency in maths might interest (or annoy) you

"It’s a very simplified, but uncontroversial, model of how we think. We have a limited working memory, where conscious thought takes place, and a potentially unlimited long-term memory. To use working memory effectively, we draw on information that is already in long-term memory. To get things into long term memory we have to overcome the limitations of working memory. Having useful information in long-term memory, and being able to recall it without difficulty, makes thinking easier. In maths it is useful to be able to fluently recall a lot of knowledge, particularly basic number facts, rather than work everything out from first principles. The question at the start about simplifying 49/84 was an example of this, as fluency with the 7 times table makes the question trivial.

In order to build fluency we need to acquire knowledge and to learn to remember it without effort (automaticity).
And if that is our aim then, in maths, the best method is to tell kids what they need to know and set them lots of questions where they practise recalling it."

teachingbattleground.wordpress.com/2014/10/04/fluency-in-mathematics-part-1/

No, the reason for wishing children to learn bonds/tables/halves/doubles/fractions etc (AFTER hands - on work) is so they don't spend a frustratingly long time working out basic number facts when doing more complex work. Having instant recall of facts gives children more confidence (and enthusiasm ) in maths, not less!

OP, I really don't think you have any idea of how primary schools use number bonds in their teaching. (Or SHOULD use them, at any rate). Any teacher that teaches addition and subtraction by using number bonds alone needs to be retrained because they're letting their pupils down. I would be shocked at any teacher using that method on its own because you are right - the children are not gaining an understanding of what is actually happening when they add 2 numbers together.

Teachers first get children to understand very basic addition and subtraction by using physical piles of eg bricks. That is the way that kids get to realise what is actually going on.
It is only when they have that understanding that they will be taught their number bonds, and actually you'd be amazed at how quickly children will naturally start to apply that memory tool (because that's all that number bonds and multiplication tables really are) to do more complex sums more quickly.

You really are overthinking it. Rote learning has a place in maths and it sits alongside pupils' understanding of the concepts behind what they're trying to work out. You can't have one wthout the other, so to say number bonds shouldn't be taught to pupils is wholly wrong.

I'm not sure she has any idea about reading either. You know that children starting school at 6 in other countries are taught phonics and don't just suddenly develop the ability to read don't you?

Ice I think you and I are living in different worlds. As Freckle says,I just don't recognise the regime you are describing.

DH and I have talked about what a shift there has been from our rote learning of methods and tables to my primary school children's experience. These days (or at least pre-Gove) it is/was all about building an underlying understanding of how numbers fit together. Loads of people our age can't do long multiplication or long division because they were taught the method by rote but didn't really get why they were doing it. Whereas the newer methods are much more geared to the child understanding the overall 'shape' of what they are trying to do. Or were, pre-Gove.

Freckle, I don't know how you do what you do, but please keep doing it!

OP, just re-reading your posts, it's a bit of a leap to link ONE method of teaching a part of maths to kids in KS1 to what you view as a lack of understanding of what learning is amongst your undergraduates. As others have pointed out there are GCSEs and A-levels before that, and I think GCSEs are absolutely to blame for that. Well, the way schools teach them, anyway, not the curriculum itself necessarily.

I know the phrase "teaching to the test" gets bandied about so often when it comes to talking about GCSEs but it's so true. There is too much of a gap now between GCSEs and A-levels so that pupils doing A-levels have a massive amount of knowledge to gain in those 2 years. The consequence of that is that they have no time to read around the subject or develop really good study skills. They are so used to being spoon fed for GCSE that they don't develop the skills required for university by the time they get there, as you have found. As I say, blaming the teaching of number bonds to 6 year olds for all those problems is a bit silly really.

"I visited a nursery a few times and they were drilling phonics every time I went in. I mean why do that? If you don't start to teach reading till 6 or 7 kids pick it up so quickly and tend to enjoy reading much more as result."

As has been repeatedly pointed out on this thread, English has an unusually difficult orthography and no matter what age you start, it takes time, time, time to get to the point where you can actually do "useful" reading tasks (like, say, read from a child's science textbook with comprehension and at speed without stumbling over every word).

Yes, we KNOW that many countries start to teach reading later and do OK. Because these countries have much easier orthographies which can be learned in far less time. With Finnish (to give an extreme example) you can go from "zero" to "reading a child's science textbook with comprehension" in a matter of weeks. Of course they can get away with leaving the teaching of reading until age seven.

Another person who doesn't recognise the regime being described by the OP despite me being in an infant school every day.

We do use number bonds but we don't sit and learn them by rote as a class with no understanding or application.

And we do far more hands on maths work than formal maths work- Hence all the photographs in or maths books rather than just lots of written maths facts and answers.

Understanding how numbers work is really important in maths teaching at that age not simply learning facts - but then I don't ever see teachers doing the latter without the understanding and application anyway.

Erm, I am a primary teacher and we don't just teach number bonds and times tables by rote it goes alongside teaching the understanding behind it. It's the same when we teach adding/subtracting 2,3,4 digit numbers - we don't go straight to the column method but do lots of work on place value and what each digit actually means etc.

Kids that do lots of things like Kumon lessons outside of school, where they just do loads of old school column calculation and similar, sometimes have issues with application of maths and word problems etc because they don't understand the idea behind the calculations, and what is actually happening when you 'borrow' from the next Column and so on.

Having said that, the way the curriculum is going, where pretty soon kids will be expected to know number bonds to ten by 12 months old and times tables up to 12x12 by the age of 3, then drumming it in by rote may be the way to go!

As someone who regularly helps teenagers through maths:

I think number bonds are a good thing, as are times tables; they are the building blocks for more complicated things. But I do see again and again that although many teenagers can do the methods without even thinking about them, here is what many of them can't begin to do:

For a real situation, many students simply can't recognise which piece of maths is needed to solve a problem. A typical exam question might describe someone selling drinks at a summer fair, telling their costs and sales, and asking the candidate to work out their profit; all for 5 marks.

Many teenagers sit and stare at it, totally clueless.

It takes me many weeks of explaining that to begin with, they have to piece together the information provided, IN WRITING!!!! (Another problem is students who just won't write anything down, and try to do everything mentally.) I am also forever telling them that the marks are not just for the final answer - marks can be gained by beginning to piece everything together.

OP you talk about if you 'get' addition then you don't need to know number bonds, the problem is in defining what and how to 'get' addition really means when you are dealing with vast numbers of people to whom it doesn't come naturally. You could teach it through counting physical objects or moving along a number line. Someone somewhere has decided that a useful tool in mental arithmetic, rather than counting on in units, is being able to break numbers up into lumps of 10 to speed things up.

My point is that it doesn't matter which way you're taught, eventually you stop needing to use those methods as the number 'facts' are committed to memory. You can tell me that 8 + 6 = 14 straight away without having to find 8 blocks and 6 blocks and then count them up because you've memorised it. Number bonds are just some mathematical facts that it is useful to be able to recall, its pointing out to kids who haven't automatically stored them that these are useful to be able to just know (much like times tables).

Kids spend a huge amount of time in school learning maths through a variety of different methods not just rote learning of facts in order to try and instill an understanding of the underlying principles so that they 'get' it. You can't just jump on number bonds as the root of all evil. What you're talking about in making links and being able to work out solutions to new and unfamiliar problems given known facts takes a great deal of intelligence, maybe you're expecting too much?

But I don't see anyone saying it's an either or situation. The ideal situation is for people to have both sets of skills. Like anything though there will be children that struggle in one set of skills or both.

The flip side of your research Kim is that those 'lower ability' children have been held back by not knowing the basic number facts or processes. If some one had found an effective way of helping those children with those facts and basic skills they might not be 'lower ability'. Contributing to a group in a classroom situation is one thing, but out in the real world those 'low ability' children aren't likely to be doing maths as part of a group. They are going to have to carry out the whole process themselves to get to a correct answer.

It's not just maths.

Try asking your teenager what colour blood is, if they say red then ask them about deoxygenated blood.

Don't be surprised if they don't say red. Even if they have science GCSEs

Agree with OP re:maths teaching. I challenged DCs teacher on why they teach long multiplication using the grid method as it's very clunky and then you still have to teach the traditional method for multiplying bigger numbers. His response was its what we have been told to teach

One senior lady, whose name I forget, says we have got maths teaching totally wrong. She is working on it

Grid method works fine for multiplying bigger numbers.

It transfers perfectly to multiplying algebraic expressions too, which is more than can be said for the traditional method.

It is not just children who think one answer excludes all other possibilities (example given above where 6+4 cannot possibly +10 because that is 5+5).

My staff (aged between 25 and 67) cannot grasp the fact that we all do the same number of hours. They do 12 hour shifts and many, many of them state they do more hours a year than me because I only do 10.5 hours shifts, and loads more than the admin staff who do 8.4 hour shifts. They simply cannot grasp that they do 7 shifts a fortnight, I do 8 shifts a fortnight and the admin staff do 10. On far too many occasions when I have shown them the maths to prove we all work 84 hours a fortnight they tell me either that I am manipulating the maths because I am clever , or that it is a lucky coincidence (rather than something I spent weeks puzzling over a roster where no-one works more than they are paid for!

So I, for one, am very glad that something is being done to show children from a young age that there is more than one way to arrive at the same number.

On the social side, start banging on about how lovely it must be for them to have so many days off, wish you could have 7 days to just laze around. They'll pretty quickly discover that "but we do longer hours, so it's the same".

On the maths side...

I don't agree with your last post op. I "get" addition and multiplication but I still use times tables and number bonds when doing things quickly. I don't agree with phonics at nursery but I know that a very organised, approach with small groups of children starting in reception gets children reading confidently within the year almost without exception. I say they as a teacher who used a less structured approach for several years.

The traditional method is very clunky for multiplying bigger numbers. If the aim is to multiply big numbers quickly and efficiently by hand, then the best method is Napiers - the one with the diagonal lines.