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?

IceBeing, I have literally just (well, about 40 mins ago) had an A level student ask me "why are you showing us the proof when we only need to learn the answer?" Its like banging your head against a wall. There is far too much emphasis on passing exams in school (which most kids do by rote learning), and far too little on applying the knowledge or actually enjoying your studies. When marking exams there are times when a student demonstrates excellent understanding of the concepts but can't get the marks because they haven't used the specific words / phrases that the mark scheme wants.

Oh, and I think that in your generally point about rote learning YANBU. Dunno much about number bonds though.

OP I've not read the whole thread and don't know how many FS and KS1 maths lessons you've observed.

However the teaching of Maths in the early years is completely based around using visual resources and explaining how you came to your answer. Just getting the correct answer isn't enough unless you can explain to your classmates how you got there.

Children don't start learning numbers bonds until late yr1/ yr2 (depending on the child) when they understand the concept.

Sorry, not rtft, but....
you obviously end up knowing all sorts of things off the top of your head
Well maybe YOU ended up knowing things off the top of your head, but the point of maths teaching these days is to give children lots of different tools to solve problems. When I learned it was column method for all functions. I never got it. I was crap at maths. Now they do number lines and chunking and stuff so if they don't have a column mentality they can still do it a different way.

I do see your point if all your kids are learning is rote, but that's not my experience of a primary school which is not especially strong with maths.

There is however a danger that people who have a facility for maths dismiss the need for children to be taught a variety of methods, so that those whose brains work differently can be good at maths too.

Just because you didn't need any number bonds, please don't assume that nobody else does.

Lougle, how could you, I'm going to be singing that all night now.

The new curriculum does not require rote learning at the expense of all else. All it requires is that children should be able to recall and use number bonds and tables, in combination with understanding of place value and the 4 operations to solve problems. How you get to that point has been left entirely up to the discretion and professional judgement of teachers. It's not very far from the previous curriculum.

OP YABVU. Children are not introduced to number bonds until they have a lot of experience of number and the four operations. This continues alongside learning number bonds and beyond it. In terms of reading. Children in other countries learn to read in a language with a clearer orthography than ours. They learn to read quicker because it takes less time to learn 30 possible ways of writing 26 sounds. With the best will in the world you are not going to get children to learn 180 odd representations of 44 sounds in 12 weeks even at 6. It will still take 2 years, they will just be older when they finish it. Although you are quite welcome to try if you wish.

Children don't start learning numbers bonds until late yr1/ yr2 (depending on the child) when they understand the concept.

Mine was given number bonds in September of yr1. Before ANY work had come home on addition. Number bonds for 10. Expected to be memorised. When I complained and said that he didn't understand the concept, they said "he just needs to learn the number bonds for now - they'll understand what they're for later."

Yup, YABVU.
It's not - and never has been in all the years I've been teaching, and before that when I was at school - 'either all'
Yes, of course you need to understand the hows and whys and the whole concepts of addition / subtraction / multiplication / division but if you can't 'instantly' just 'know' the number bond (or come to the the answer to a multiplication/division) then you are at a serious disadvantage throughout your daily life, not just in lessons at school.

Number bonds in Yr1 came in with the new curriculum. (Who are teachers to argue with the government )

I don't think it's great that your son was given them so early Alice. To my knowledge this isn't the norm, however I can only speak from my own experiences. I also don't think it's the end of the world, as long as the concepts are being taught alongside them.

I half agree and half don't.

Number bonds weren't called that when i was little, but we also had the coloured sticks that could be used to add together. I agree basic addition is more useful than knowing what 2 numbers add to 10 - in Australia, DS1 learnt them as "friends of 10", FFS! Would have helped us parents to know what the fuck they were on about....

But rote learning of times tables I think IS very important. I still know all of mine up to times 12, and all my squares up to 25. I learnt rules about multiplying by 11, by even numbers, by dividing by 4 etc; all of which stand me in good stead now. I was always good at maths, including mental arithmetic (bit slower now I'm old!) and have 2 maths A levels.

I don't think learning the basics by rote precludes understanding the basic principles, unless the basic principles are not then taught!

And this:
"We ask our physics undergrad students "what does learning mean to you"

A depressing number of them respond "collecting information and making sure I can recall it well" "

I think that a large proportion of students feel that way in ANY subject. The motivation to learn has become "what do I need to know to pass the exams?" I discovered this when I was lecturing at degree level, and in the FIRST MODULE the students would listen to/read the information given, and rather than learn it because it was interesting and relevant, would want to know "is this going to be in the exam?" Like that was all that mattered! All information given to them as part of their teaching was to inform their learning towards the goal of becoming knowledgeable in the subject matter, not JUST passing the sodding exams!

OP - my DD is just coming to the end of primary school, my DSS2 is just coming to the end of secondary school - in France. DSS1, who also went to school in France, is at university in the UK in his second year of a very quantitative economics degree (and a star student). We are a very mathematically inclined family and have always paid a lot of attention to maths performance. Our DC are required, in the French system, to do a lot of problem solving.

Number bonds, like times tables, featured heavily in Years 3 and 4! Learning number facts by heart for easy recall is not the problem! The problem is lack of depth and practice solving problems!

Slight derailment, but please don't blame students for only wanting to know what's necessary to pass the exam!

Successive education secretaries have made it clear that schools are to be ranked according to their exam results and teachers' pay is determined by the same. Students are constantly told they need to achieve certain grades in order to be successful in life, and many FE colleges and sixth forms won't take students unless they achieve a certain number of grades at GCSE.

Is it really any wonder that students believe what they have been told of and over again - that passing exams is more important than anything else?

Knowing number bonds by heart in year 1 was in the original NNS in 1999. And in the 2006 Primary Framework. Those weren't statutory but you'd be hard pushed to find many schools that weren't using them.

The only reference in the statutory box under the year 1 objectives mentions 'use and represent number bonds to 20' Which is very different to drill children in number bonds to 10. Admittedly the nonstatutory box does make mention of memorising. In any event there's no statutory requirement to teach the objectives in the year they appear in the new curriculum, only by the end of the key stage in which they appear.

Well yes, Suburban - and this is possibly a root problem in the whole education system, isn't it.

AnnieLobeseder
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.

But as I said in the thread about times tables, some kids are really bad at rote learning. The example you gave my son would calculate 10x7 and halve it, giving 5x7 almost as quickly as the instant recall. Yes, not quite as quick but

1. he has built much better number sense having learned to do that which serves him well in the college calculus classes he is now taking. Number sense is a meeelion more times important for later maths than rote learning some random math facts. Yes rote learning speeds fluency but so does a calculator.

2. it works when you have to do 5x27 which rote learning of tables doesn't.

Schools spend so much time with rote learning maths facts that they have less time to spend teaching much much more important early math concepts like conservation of volume and length, place value really teaching it, many primary aged children are weak on place value and it shows up later. Patterns, kids who are strong in higher level maths are really good at spotting patterns. Being able to see in 3D so important for exponents, geometry etc. Being able to visualise numbers and how they work together so that you know your math facts not because you just learned them by heart but you can visualise them in your head and how they work together. Number lines and negative numbers.

IMO schools are way too concerned with teaching kids tricks and memorising to solve puzzles, all well and good while you can remember the trick, sucks if you forget it. If you learn why the trick works, can derive it from start to finish then you can never forget it.

If you truly understand that y3 x y2 = (y x y x y) x (y x y) and you know your fundamental maths rules (associative and commutative properties for multiplication) then you never need to know by heart the first rule of exponents ym x yn=y(m+n) because you can always figure it out. You will learn it through practise but if you haven't done exponents for several years and have forgotten the rule you can always get it back. Not only that but if you really understand why that first rule works you will also understand why ym x z^n can't be simplified. You can easily spot the kids who only learned the rule, they are the ones that try to shoehorn the two different terms into the rule and struggle to understand why it doesn't work.

*YouTheCat
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.*

I completely and utterly agree. Some kids are not great learning to read that way. One of my sons learned mostly by inference and context. The other one, well I'm not entirely sure how he learned. He was interested in reading at a very early age so we started working with him a little, naming stickers on everything around the house, reading some very simple primer books with him. However I have no idea how he learned to read "All nude, all of the time" and "Gentleman's club" until he asked me what they meant from the back seat of the car one day! I certainly didn't teach him any of those things!

If you focus your energy on one thing too much something else will suffer.

I guess it comes down to this. Do we want our population to be able to do mental arithmetic or do we want to teach our population to do maths. If all we want is a basic level of maths competency then sure, don't bother with the rest, but if we want our STEM workers to be able to compete against the rest of the world then they need to spend these early crucial years doing something other than just chanting numbers.

Most of all, what we need to teach is that Maths can be fun and exciting and a puzzle to crack. That no matter where you are in the world or what you are doing maths is around you and useful. Maths is often taught as this dry crumbly subject that is so boring. There is no real intrinsic motivation to learn more.

I once taught a middle school student (in a LEA where they still had them) who declared that there was no point in learning maths because she was going to be a hairdresser just like her mum, her aunt and her big sister. They had told her that maths was a waste of time. Until she learned differently trying to teach her maths was going to be like pounding a nail in a block of granite. My job at that point became less about square roots and statistics and more about helping her see the relevance of maths to her and how it could be fun. We did a big crystal maze (this was the early 90s) game to practise all our maths skills that term.

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,

Try and get that past the government.

I think that until the central education body (DFE, DFES, DCSF, whatever they want to call it) is taken over by a research based, non-political, not-for-profit organisation, debates such as this are going to endlessly continue.

Schools are subject to the decrees from on high that we 'must' teach this, that or the other - despite what our own professional judgement or experience may be. This would be fine if it came from a place of academic research or experienced education professionals but it doesn't. The Gove legacy is a prime example of this.

The teaching of Maths and English (by and large) is not the problem. It's the curriculum that is imposed upon us, often influenced or written by people who have zero understanding of how children learn. It is accompanied by (often unrealistic) targets of what children should achieve at a certain time.

It's this 'I went to school, I know what should be happening in schools' attitude that gets me.

Number bonds, for many children, speed up calculations. I think they are useful and I would encourage children to know them but it's not the most important thing they learn. I certainly wouldn't teach them to Reception aged children unless they understood other key concepts such as 1-1 correspondence, more/less than etc. However, as Boney said, try and get that past bastard Ofsted the government representatives.

Ah the unit plans. A cock up that only got worse with the blocks in the primary framework. Let's teach 5 million objectives over 3 lessons and it won't matter if you don't get it, because we're going to come back to it 7 more times over the year.

Nothing wrong with teaching lots of strategies for mental calculations, but if you teach more than one at a time and don't embed it with plenty of practice before moving onto the next one you end up with a jack of all trades master of none effect.

Ah the blocks. Sorry, that should read - Aaaarrrgh!!! The blocks!!! They were such shit. In fact the whole Primary Framework was. What. Monumental waste of money.

What a

I was taught in the late 70s and early 80s and at the time it was fashionable to teach the method over the facts. I didn't learn my tables and struggle now, it is soooooo handy to have instant recall of number facts!

It's a huge source of amazement that nobody ever looked at block A1 for year 1 and thought hang on. It was a bit of a stretch to think you could introduce rote counting to 20, counting 20 objects, reading and writing numbers from 0-20, comparing numbers to 20, 1 more and 1 less, ordering numbers, addition as counting on and subtraction as counting back and recording addition and subtraction sentences in 2 weeks. From a starting point where they'd be expected to count 10 objects, recognise numerals to 9 and do very simple addition and subtraction using objects.

We looked at it and refused to do it...

No one in the school I was in at the time thought it was worth the very expensive paper it was written on.

It was sort of a spiral curriculum on acid when everyone else was starting to look at mastery based stuff.