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?

They bloody well do if I've taught them quadratics, Kim!

Memorising stuff gets you through school exams, but you need to actually understand stuff from first principles and be able to create your own methods if you are ever going to use maths at work successfully.

OP - YANBU. I've studied mathematics at graduate (master's) level and never heard of number bonds until this thread. I agree with you - if children have to memorise the most basic additions such as 2 + 8 = 10, there is something very wrong with that education system.

Bonsoir - My DD is about the same age as yours IIRC (in CM1 this year) and she has not done any number bonds at all.

My DD is in CM2. She did them as did the DSSs and the cahiers you can buy for revision/reinforcement of the French NC definitely cover them.

When we all start shopping at markets then it will be worthwhile spending time teaching children number bonds.

"I agree with you - if children have to memorise the most basic additions such as 2 + 8 = 10, there is something very wrong with that education system."

????

So, that "2 + 8 = 10" that you wrote down just there--are you trying to tell us all that you had to count on your fingers to work it out?

I can assure you that your daughter is learning number bonds, by the way. They may not be CALLED number bonds, but she will be learning to add and practicing again and again until she knows them pay.

We didn't call them number bonds either, when I was at school, but the basic concept was the same.

"(I am not advocating discovering quadratics). When I was tutoring, I started on expanding 2 brackets - and drawing out the curve. This helped the pupils see where the different coefficients came from. "

Sure--that sounds like the right kind of approach.

Good teachers (in all subjects) use techniques such as presenting information while eliciting input from students"Has anyone spotted the pattern yet?" "Rightnow, based on what I just showed you, can anyone work out what the next step is?" etc. etc.

No problems.

It's full-fledged "discovery learning" that is the problem. As discussed here, the evidence that this kind of teaching really, really doesn't work is absolutely overwhelming.

apps.fischlerschool.nova.edu/toolbox/instructionalproducts/8001/EDD8001/SUM12/2004-Mayer.pdf

Omg, "discovery learning" - there is a name for! Is that what it's called.

I did discovery learning method for my Nuffield A levels Physics twenty odd years ago and IT WAS RUBBISH! I was robbed of my A grade I tell you, otherwise I would have had a clean sweep of 3 As.

Oh and OP I think YABVU btw. UK education is not perfect but it is a lot better than other countries, especially Asian countries and their teaching methods from what I've seen....and yes, yes, I know Singapore is way up there in the world rankings in maths etc. but I' m not convinced that it is not down to attitude and the tutoring culture rather than superior methods- although in Singapore teaching is at least consistent, in uk it is very variable.

I have seen children in say, year 3, who appeared to be geniuses with their rapid recall in mental maths but by year 5 , they are totally lost because they cannot handle word problems and problem solving.

Genuine question here: if you were starting a curriculum all over again, what would you put in it? So much time is spent learning to do calculations that 100% of those kids will be able to do on their smartphones anyway by the time they are teenagers. Translation/interpretation technology is developing to the point that knowing another language just as a tool may become unimportant. You don't actually need to be able to spell as your computer does that for you. All the facts about everything are in the internet in your pocket. What should school be doing in everyone's opinion? I know that it should be teaching critical thinking, but how should it do that? What else?

Apart from that:

I think memorising and rote learning is quite handy to give a structure for other things. I find it convenient to know my times tables automatically, as I can work things out quickly. I think I use chunking in my head too, and number bonds, though I'd never actually heard of those things before.

It seems to me a bit like learning dates, Kings and Queens of England, capital cities etc. Somehow if you know when/where they are, it gives you something to peg the rest of the information on when you find it out.

What mystifies me at the moment is the weird spelling homework my kids get (not UK). They have to divide the word up into phonemes. I don't really understand it or see the point, assuming they can read the word without difficulty, so they have to do that on their own

Okay, so this idea has turned up several times:
"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."

So why is it that kids in Welsh medium schools who don't begin to learn reading or writing in English until 6 or 7, don't seem to be 3 years behind? What's the difference? And are ages for starting to teach reading coordinated with difficulty of orthography across the globe?

Schools teach number bonds and times tables and they teach children the meaning and mechanics of multiplication and addition.

I can't remember very much time being spent on number bonds when my children were in KS1 - it was something that you were supposed to practice at home because it would be helpful - there was no great stress if they didn't know them automatically by a certain age. I think it is based on the idea that adults are greatly helped by automatically knowing that 6+4=10, 10-4=6 etc. therefore children will also be helped if they can quickly move to the stage where they don't always have to work out 6+4 or 10-4 each time they do the sum.

I think the biggest problem with maths is that for most people it is comparatively hard work in the early stages. My children much prefer English Literature because it involves listening to stories and lots of discussion. They complain that maths lessons make them feel hungry. However, I don't think this is an indication that they are rubbish at maths - they just have to work harder in maths - and that is OK.

My 4 year old is at a Welsh medium school and will not be taught any English until age 7.

However, we speak and read English at home. Also, Welsh is a much more phonetic language than English and so once they've learned how to learn with the easier language they can use those methods to learn English.

(N.B, I don't think English Literature and other humanities are easier than maths - just for many people more accessible in the early stages).

It is the same as you never actually have to learn F=ma...it just turns up in your brain because you use it so often.

People's brains work differently, and for some people, it will take a very long time for the facts to just turn up in their brain and it is useful to memorise them.

Memory is a practical tool. If I were an actor, I suppose I could just rehearse so often that I learnt my lines eventually, but it is more efficient to deliberately sit down and memorise them. I still have to rehearse and understand and interpret my lines, but the act of learning them by rote speeds up the process of reaching a point where I can perform.

Leaving aside curriculums and exams, I think good teachers use a range of methods to teach and adapt them to the child they are teaching.

When it comes down to it the UK still leads the world in high end engineering, which is applied maths. Dyson may have moved his factories to the far east, but the R&D is still in the UK and he now employs more people in the UK than when he manufactured here.

My dh is an engineer and he was involved in making the machines that were sent to the far east to manufacture computer chips.

I was born in the 60s and one of my favourite toys was an abacus. . I used to play for hours making patterns with the beads but they we just number bonds ie 1 on the right 9 on the left, 2 on the right 8 on the left etc I know I use them in mental arithmetic all the time, even though I don't remember being taught number bonds at school ( it was a very long time ago )

Kids can learn polynomial division at A-level without learning long division down the school. I've taught it loads of times.

My ds always claims he can't do long division even though I have shown him how to. He got a high A at A level and a gold at senior UKMT. I gave up worrying about his long division a long time ago

School starting age probably isn't correlated with orthography. But that misses the point being made slightly. The OP was arguing that Finnish children start school later and learn to read in a term, therefore if we left starting school until 7 our children would learn to read in a term. It's a commonly made argument but a complete fallacy.

Finnish only has about 32 phonemes and mostly one way of writing each of those. Once children are taught those 32 letter/sound correspondences they can decode virtually anything put in front of them. Compare that with the one way of writing each of the 44 English sounds that children are taught in the first term of reception. It's a similar body of knowledge and most children will be able to read and spell words with those letter/sound correspondances. But in order to read everything, they are going to need to know the other 140 ways of spelling those sounds too. There is no way you are going to teach that in 12 weeks whether the students are 7 or 70.

It's an interesting debate and I don't know the answer. I think the OP may be right in that for many years children were taught without the concept of number bonds but nobody really left primary school without understanding the basics of addition and subtraction.

I do believe that some measure of memorisation is needed, though. Back in the 1980s I ended up being a school governor at a local primary school and I remember the head and deputy head talking me through the curriculum. I asked about times tables and they said, "Oh, these days we don't teach times tables - the idea is that children need to understand the concept of multiplication and that's more important than rote learning."

I was really shocked but too timid to say anything - but I did wonder why I could see it was daft but they (and presumably other educationalists) couldn't. Because obviously you need to be able both to know tables off by heart AND understand the principle behind them. In fact, I remember when I was a child that after a few years of learning tables I had a moment of illumination when I realised that six times four meant 6 + 6 + 6 + 6, which I hadn't grasped up to that point.

here is another explanation of why the Chinese are very good at maths...

gladwell.com/outliers/rice-paddies-and-math-tests/

I think Welsh medium schools are generally chosen by parents who are committed to supporting English proactively at home, which usually includes reading. (This is probably part of the reason why kids in Welsh medium slightly outperform those in English medium in Wales--the Welsh medium schools tend to have a more middle class intake.)

In recent years, the Welsh education system in general (Welsh medium and English medium) seems to have become a lot more "softly softly" than the English system--a later start to academics, more play-based in the earlier years, and so on. I am just basing this on what I have heard from people who have put kids through both systems.

The educational performance of Welsh children in general is kind of weak and has fallen noticeably behind the rest of the UK, which does not support the notion that delaying the teaching of reading and maths results in a boost to academic abilities later on.

www.bbc.com/news/uk-wales-25196974

Rafa - I don't really have much of an opinion either way, but having heard from various sources that the UK could/should delay school starting age, was curious to hear what the evidence was. I'm still not very clear on your argument - why does it matter if it takes longer than 12 weeks? What comparisons can actually be made between English speaking countries who adopt different approaches, or different approaches tried within the same country? (I guess what I'm asking is - is "more difficult orthography" theoretical at this point, or has it been tested?)

NewStatesman - yes, I think that parents making an early choice about education does tend to skew the Welsh medium intake towards more engaged parents which is always an advantage. But I would point out that doesn't necessarily mean privileged - majority of pupils on free school meals isn't privileged (don't know how this compares, I just know the Welsh mediums in my area when I lived in Wales had majority on free school meals). I don't know if engagement trumps poverty in later outcomes.

Slightlyglitterstained: It's a fair question. There is actually a dearth of real data on the effects of teaching reading at various ages.

The only body of evidence I'm really aware of is that of Dolores Durkin, who did a lot of work on this area decades ago, when there was a lot of debate over the right age to begin reading. Her research found that there was a persistent advantage to starting reading earlier. There hasn't been much actual research since then, as far as I can tell--perhaps because it was accepted that Durkin had basically provided a conclusion about the question already.

I thought this was an interesting article: learnthingsweb.hubpages.com/hub/Dont-Use-Finland-as-a-Case-Against-Early-and-Baby-Reading

I think the concern about "12 weeks" relates to the sheer amount of time that it takes to get from zero to "actually reading real, useful texts in a useful way, with speed and comprehension." Because the trouble is that it takes quite a while to get from the first state to the second state in the case of English, and in the mean time, kids wouldn't be able to do things like read their school books to help them learn history and science and build a strong vocabulary and so on.

Of course children SHOULD understand HOW numbers work and after that they could also learn by heart some basic addition facts (what you call "bonds") which help people add more complicated sums, long division and subtraction. We can't have EITHER understanding OR by rote, why can't we be flexible? Why go from one extreme to the other??! How do you expect children or later mature students to go through a very difficult exam with lots of questions when they have to work out their times tables on the spot? They will have no time for that!