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?

I don't think anyone is suggesting doing rote learning INSTEAD of understanding number.

If they are, you have a legitimate complaint to the school.

How can anyone beappalled by the idea of number bonds? How can a child love adding and subtracting but hate number bonds? They are just sums where the answer is 10!

"Farmer Pete he had 10 sheep. All were in the pen.
10 were safe and none had gone. 10 add 0 makes 10.
"Oh dear!", said Pete, "where is my sheep? There's 9 here in the pen."
9 are safe and 1 has gone, 9 add 1 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 8 here in the pen."
8 are safe and 2 have gone, 8 add 2 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 7 here in the pen."
7 are safe and 3 have gone, 7 add 3 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 6 here in the pen."
6 are safe and 4 have gone, 6 add 4 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 5 here in the pen."
5 are safe and 5 have gone, 5 add 5 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 4 here in the pen."
4 are safe and 6 have gone, 4 add 6 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 3 here in the pen."
3 are safe and 7 have gone, 3 add 7 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 2 here in the pen."
2 are safe and 8 have gone, 2 add 8 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's 1 here in the pen."
1 is safe and 9 have gone, 1 add 9 makes 10.
"Oh dear!", said Pete, "where are my sheep? There's none here in the pen."
None are safe and 10 have gone, 0 add 10 makes 10. "

My DD1 has LD and goes to special school. She knows her number bonds to 10 by instant recall because she learned this song.

YABU

Have to say I disagree. I think a good grasp of number bonds helps kids tackle more complex things later on. I think they help children see the "patterns" in number and gives them confidence.

Although I don't even see how it could be taught "instead." As Flomple says, combining groups of physical objects itself leads to understanding of number. It's another important way in.

• or not necessarily even 10, though they often are to start.with

I totally agree with you too icebeing. I kind of have the view now that you have to jump through the hoops at school but real learning happens outside of it x

but i use my number bonds every time i do mental arithmetic i want 10 have 7 i need 3.

And reg. use my times tables. knowing off by rote that 5*6 = 30 is a lot quicker than working out 5+5+5+5+5+5 = 30.

I know this as i don't know my 7 or 8 times tables and it irritates me everytime i have to work it out long hand.

I never realised they were called number bonds until DD started school, but this is how I work out most everyday mathsy things in my head.

It's just a simple memory technique surely?

How do you do any calculations without 'number bonds' or knowing number facts and relationships? Unless I am only going to use counting, I need to use my 'number bonds'. I know 7+3 = 10 so I can work out 27+3 or 870-67 easily.

I agree with a PP that schools are unlikely to be trying to teach number facts without any concrete understanding. If they are, then you've got a point.

I don't think leave it until they are older is the solution. I think using manipulatives more is the answer, grouping grapes and adding them ("you have four and I have six, how many is that? Ok if I give you one of mine how many do we have now?"), counting spots on lego bricks, smarties maths etc, moving onto unifix or cuisinaire rods when that is solid.

We did a lot of lunch and dinner maths with our kids when they were little.

icebeing "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."

This is where we disagree. And I think every one of my children's teachers would disagree with you too. There is a lot of Numicon in our YR and Y1 classrooms...

Being good at arithmetic requires that some simple tasks become automatic - hence things like number bonds and times tables. This certainly isn't useless, as many jobs are made much easier if you are good at mental arithmetic and estimating.

But of course being good at arithmetic and being good at maths are not at all the same thing.

My ds is only a toddler so I know nothing about primary maths but I have a maths degree. I learned with counters and wooden "tens and units" and number lines. I learned to add by counting basically.
Having said that, my mental arithmetic isn't the best but I actuslly think that's cause I'm a visual learner.
I can see how number bonds help mental arithmetic but my instinct is to feel maybe they would be better taught after the "counter" or "number line" methods.

I'm all for rote learning (in addition to actual understanding of maths, of course). DD1 is in Y5, until this year when the syllabus changed she wasn't extected to know her tables by rote. As a result, when doing her maths homework with more complicated multiplications and simple arithmetic, most of the time spent on homework would be spent with her working out each small component of the problem, eg 5x7, which took hours instead of her knowing the simple times tables instantly so she could apply this instant recall knowledge and focus on the actual more complex problem she had been set.

I nearly cried with happiness when I found out that children are being expected to learn tables by rote again.

I see your point though that it would be pointless to teach children tables and number bonds in isolation without any actual understanding of what they mean or how to work them out if necessary. It would be a very lazy and bad teacher, IMO, who didn't place the emphasis on understanding before rote learning. But that rote learning also has a very valuable place in progressing children to the next level.

Number bonds aren't the problem. It's the rigidity of the system that's the problem. Children need to learn methods that suit their learning style but most schools just give them one way to do things and if they don't get it then tough.

I have similar views on phonics (which I teach). Learning to read is a combination of many different skills but so many schools seem to be just concentrating on learning 5 millions different phoneme combinations and all their variations. It is confusing at the best of times and does very little to enhance spelling. Plus you end up with a load of kids who are spelling out every word they read.

I've never heard of number-bonds, but if we are mainly talking about single-digit numbers, I don't think I see a problem. When adding or multiplying multi-digit numbers, we use our memorised knowledge of sum/products of single digit numbers as building blocks.

I can't think what algorithm I would follow to work out how to add 3 to 7, algorithms for addition involve bigger numbers and are based on the assumption that you "just know" the sums of single-digit numbers.

So "number bonds" make sense to me, memorising them is useful in the same way that memorising times tables is.

Sorry, I meant simple algebra, not simple arithmetic. You know, the other maths thing that starts with a!

Children do a lot of adding and subtracting with objects before they record anything so they should have a good understanding of the process before they learn number bonds by rote.

I think you are half right.

Ideally all the children (and adults) really understand maths and can work everything out from first principals, and then also learn/remember the useful facts.

I am totally shocked that you have physics undergraduates who don't like to work things out. Surely that's what physics is all about! To my mind something is going badly wrong at A level / interview if that's what people studying physics think.

But in practice for a lot of people 'knowing the rules' is good enough for many people. So if you 'know' that 20% is 'divide by 5' that works for you in shops.
Or if you 'know' the way to solve a quadratic equation is minus b plus or minus the square root of b squared minus 4 a c all over 2 a you don't necessarily have to know how to prove it.

My DD1 is doing GCSEs this year. She is not a natural mathematician. She struggles with things like simplifying fractions as she doesn't have useful recall of times tables, so she doesn't see e.g. 45/72 and think 'oh both divisible by 9'. If she could do, it would make her life a whole lot easier.

I actually think that primary maths is better than in my day with respect to understanding the basics. e.g. Number lines and grid multiplication make it much easier to understand the concepts.
But there is no getting away from the fact that instantly knowing the answer to 9*7 or recognising that 2 and 8 bond to 10 makes life a lot easier, both for school maths and lots of everyday uses.

On a related note, DD is in reception, and I am a little taken aback at the way she is being taught to read. It seems she is expected to simply memorise words, some quite long, through rote learning. The books she is being given contain many words that wouldn't work with the phonetic approach that was used in my day. (Not sure if phonetic is the right word.) I thought primary schools were supposed to have switched back (at least partially) to phonetic methods.

Hate time tables, for the reasons you describe, but number bonds are't meaningless recitation, they're understanding how numbers work

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.

Have you seen any Numicon pieces? You fit them together, and learn the difference between odd and even. Numicon is why my children spontaneously describe the properties of even numbers plus even numbers.

I came across the grid method for multiplication quite recently, and TBH I think I like it more than the method I was taught.

YABU.

DS is top set maths and his teacher has commented that he's one of the first to pick up new concepts. But his mental arithmetic, and the bits of mental arithmetic that underlie doing maths in general at KS2 and KS3 isn't really quick enough because he hasn't properly internaliised his number bonds (or his tables, to be frank -- at least not to instant recall levels). It takes him a second or two longer than it should to work out 94-76 in his head, for example. And over a lot of calculations all those seconds here and there begin to add up.

Knowing his number bonds won't help him with working out an incredibly complex 3D diagram of how to tie a chemical reaction into a knot using laser light, no. But it'll be useful for accuracy and speed in everyday numeracy.

I disagree. I firmly believe basic numeracy skills were better when children learned consistently by rote. Also - don't countries such as Singapore and China produce far more advanced maths graduates than we do - they have a rote learning system?

I think rote learning helps people to apply basic maths to everyday problems. Most people aren't going to want to become quantum physicists and so have no need to grasp the theory of mathematics - just the practicalities.

I think the lack of rote learning epitomises everything that's wrong with the UK approach to education.