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?

Romann I think that is a very interesting question indeed. The internet etc. has seriously moved the goal posts on learning from one in which having a lot of data in your head was a sign of education to having a lot of concepts, and techniques for finding and interpreting data from the internet is a sign of education.

Any maths technique that you need pen and paper to execute is essentially useless. There may be some value in doing things in your head - certainly for getting order of magnitude answers / estimates.

With the increasing sophistication of things like Wolfram Alpha, you don't need to be able to do algebra or integrate etc. either.

Education is certainly now more about knowing which tools exist, and when they might be useful than it is about actually being able to use any of them.

"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"

There are many more states between zero and the fluency that you describe above. However, to get from zero to reading with comprehension, 12 weeks is not an unrealistic timeframe.

For comparison, children start 1st year of school here in France on September of the year they turn 6. By the time December holidays come, they are reading in French. Not terribly fast, but they read and understand real, useful texts. Speed comes with practice, naturally.

Bonsoir - I asked DD if they ever memorized number bonds (1-9, 2-8 etc) and her reply was that they did one fiche in class last year where they filled in blanks for 1 + _ = 10 etc but otherwise no, they were not asked to memorize such relationships between numbers 1-9.

Romann - in response to your question: I would include in any curriculum all the things you wonder whether it is necessary to include, given current technology.

One of things that DC need to learn is how to think logically, which is not the same as critical thinking (I think that critical thinking is not possible without logical thinking - surely you can only think critically if you can construct two or more logical arguments first?). Arithmetic and algebra, statistics and probability are all used by all of us, every day, to think logically about the world.

Automated correct spelling helps us read, understand and write more quickly. We need to automate the easy stuff in order to use our brains for the harder stuff...

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

Haven't read the whole thread yet but I just HAD to respond to this. My DD started number bonds in reception. We were explicitly asked to help them at home with this (I didn't).

Hmm. In response to IceBeing's suggestion that the internet has changed what you need to learn, I would say yeeeees, but... I don't think I agree with your conclusions. Not completely anyway.

If we want to be able to create the next Wolfram Alpha, then we certainly do need to be able to do algebra and integrate. If you want to write a macro in Excel (as one of the commonest forms of programming done by non-professional programmers), or even just figure out which one to cut & paste in from the internet, you will need algebra.

Having fast, good, search engines helps to reduce the amount of syntax that programmers need to memorise, but it doesn't eliminate the need for drill - lots and lots and lots of practice.

I see drill and rote memorisation as fundamentally different things (though drill can be a good way to remember things, I think).

"Automated correct spelling helps us read, understand and write more quickly. We need to automate the easy stuff in order to use our brains for the harder stuff..."

That's exactly it. Just ask a good piano or ballet teacher. They drill kids in positions and steps and scales and arpeggios and make them practice lots and lots. Not because they are trying to DESTROY THE KIDS' CREATIVITY!!! but because when you "automate" basic skills, it frees up the thinking bit of your brain for the harderand more creativework.

I can't understand how anyone who has spent any time with their fellow human beings can argue for a 'correct' or 'best' way to teach any subject. Great teachers adapt to the needs of the learner.

I don't teach children but I have trained horses. One of my 'watchphrases' is: 'If he can't learn the way I teach, can I teach the way he learns?'. It saves much fustration and undue harshness.

If I can accept that equines will all respond differently & adapt my approach accordingly, I think it is reasonable to assume teachers do the same. All horses need to reach the same end point on the basics, although some may go on to excel in certain areas, the same as people, so I do not think my analogy is too far fetched.

'If he can't learn the way I teach, can I teach the way he learns?'.

Ideally, yes, we all would like to do this for each individual student. Sadly larger class sizes make that very difficult to do enough of.

Which is why I think so many students are taught so many strategies. Pressed for time and with larger classes, teachers show every one every method and ask them to choose the one they prefer...

Any maths technique that you need pen and paper to execute is essentially useless.

This is so depressing. I want to teach maths, which is entirely different to training a monkey to bash things into wolfram alpha. You want to de-skill people?

Maths is about getting students to think logically and spot patterns and formulate arguments. It's not a data entry sort of subject.

TBH, I dOn't think it is remotely necessary to understand multiplication before you learn ydour tables. At school (what is now Reception) we recited the alphabet every day and the times tables every day.

Most of us could see what multiplication was by the end of Y1 and knew all tables by rote. This was not a bad thing. When we started algebra (in Y3, or maybe it was Y2) we could recognise a number's factors quickly and easily which was jolly helpful.

DD - now 15 - did not learn tables by rote, and told me recently that she didn't really know them until y7 or 8. How is that helpful. Believe me, she's not dim. She's in top group for every subject including maths, but she has struggled hugely with it. I know her confidence would be so much greater if she'd learned her tables by rote very early on.

Slightly, it doesn't matter if it takes more than 12 weeks. The evidence for starting later is quite weak, I think, but one of the arguments that is always brought out in the debate is that Finnish children start school later and learn to read in the first term. The argument being that they learn to read quicker because they start later therefore we should start later. They learn to read quicker because Finnish is easier to learn to read. Well that and the fact lots of children start school there already able to read.

I'd have no problem starting here at 6 if that's what eventually happens, but it would mean accepting that children wouldn't really be properly reading until 8 or 9. Probably all it would do is create a huge gap between those children who start school having been taught to read at 4 or 5 by their parents and those that start unable to read.

Hrmph, just realised some of this thread was so flabbergasting it ate my spelling.

epitomE

So much for late night posting.

(Yes, I know it's nerdy to care. But I do.)

I think it's to start teaching them that there are lots of patterns and rhythms in numbers, setting the stage to make things easier in the more complex maths that comes a while after basic arithmetic. The number bond thing is the kind of shortcut a lot of (more mathematically minded?) kids notice on their own, so it's just sharing that shortcut through the whole class.

Yes, but Kim, that's not the full lesson, is it? I teach secondary where kids are set more strictly than primary and still I would expect flummox from a few when introducing or extending any concept.

So 22 + ? = 30 you would get some kid who got it to fill in the rest of the class Then 32 + ?. Then 42+?. Then ask the flummoxed kids if they could see a pattern them coax out number bonds from them then try 33+? and see light dawning a few more times. Then set a bunch of questions to practice then move to 22 + ? = 40. If the kids know the original number bonds then at some point there will be a click between the two. I wouldn't say that learning the original number bonds was useless if their use in other contexts needed to be made explicit.

I'm pretty sure both the NNS and the Primary strategy were big on applying number bonds you know to work out other calculations e.g. 2+1= 3, so 20+10=30, 0.2+0.1=0.3, 72+1=73 etc It was in both the ks1 and ks2 curriculum.

I also would have thought that number bonds are usually taught as part of a range of methods, not the only method - so a lesson on 2 figure addition might discuss counting on and number bonds to ten as alternative methods of solving a problem, and there are manipulatives available to demonstrate both methods.

Rafa - yes, the link NewStatesman shared earlier had something like only 27% of Finnish children who weren't reading at all when starting school formally. Though tbh Finland has so many other differences...

Interesting point about a later start to teaching reading potentially creating a big gap between those whose parents teach them earlier and those who don't get that.

But you see children who struggle to apply number bonds to other situations.

I imagine that's not unique to maths though. I imagine there are kids who get maths who would get the other situations whether taught or not, kids who get it once it's taught, kids who need more practice than others and then kids who really struggle.

Have you ever taught isometric drawing? It's a funny topic. Some kids can just see how to do it straight away then draw fantastic 3d diagrams. Some kids need a bit of a demo but then they're away, some can carefully copy a diagram, and some spend the whole lesson trying really hard and still struggling to draw a cuboid. It's a mental blind spot for 3D visualisation, and their struggle doesn't mean that I taught isometric drawing badly, or that the other kids weren't helped by my teaching. I think number sense can be like that too.

Surely there is one way to make sense of 56 = 7 x 8?

m.youtube.com/watch?v=4NO-h9PFum4