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?

That's lovely.

On the other hand, you didn't work out the matrix method for yourself. Or invent matrices, or discover how to multiply them yourself.

You were taught what matrices are, and then taught a method. It's germane because dealing with vector quantities was one of the examples you raised above.

Teaching methods is a huge mistake exactly because it stops children from finding their own way.

Newton saw further than others because he stood on the shoulders of giants. But let's make our kids work out everything from scratch, right?

Your assertion that it is wrong to teach number bonds because you just memorised them naturally is rather arrogantly assuming that everyone is as bright as you. Some kids need a helping hand.

Playing around and discovering what you can is marvellous, fantastic way in, good reinforcement of known stuff.

But getting back to the grid-multiplication method (and apologies for flogging this to death), if you leave it entirely to students to discover for themselves, you're creating a situation where at the end of the lesson the stronger students are doing an easier method they've found for themselves. Jolly good.

And the weaker students are slogging on with harder methods or being unable to do anything at all. And becoming convinced that they can't do maths because the hard method is, well, hard, and even their simple arithmetic errors start feeling like a failure in understanding.

And all the time there was a trivial method you could have shown them (after the playing around) which would not merely have allowed them to get the question out, but would have reinforced the principles for them.

I have to agree with this last point by Pausing - I did have a problem with the physics aspects of applied maths at A level, because I had not done physics. My teacher was an old school aged professor, who used to tell us all sorts of different and clever ways to do things, instead of the basic simple one (or "cow-like" way, as he called it). As a result of this, I spent the first half of the first year being unable to do the simplest thing, to take moments about a point. As soon as someone explained (and it was embarrassingly simple), no doubt using the "cow-like" way, I was sorted - but he'd failed to pick up on my failure for half a year!!

Bad teacher.

Number bonds are just a way of showing children how numbers work.

I taught international students maths for a while. We had students from mainland china who were taught very traditional rote methods for mathematics and students from Hong Kong who did the IB and were taught using, what is in comparison, a more investigative western approach.

The students from mainland china had near perfect recall of many mathematical facts and could calculate far more quickly in their heads than the Hong Kong students who were using calculators. This meant they had automatic access to the basic 'building blocks' of mathematics and could concentrate on investigating and understanding the harder concepts rather than worrying first about what 12^2 was before they could evaluate a definite integral.

You can't investigate everything each time you do some maths, it takes to long. Some things you have to learn, you will have been shown the principles behind it and played about a bit when you learned it (at primary school), after that it is useful to just know.

Most importantly not everyone automatically remembers things like the OP- that's where encouraging students to learn by rote comes in. There needs to be (and this is where the debate lies) a balance between investigative work and rote learning.

Just get out the monopoly board ( we use Star Wars monopoly). We have just spent the whole morning playing this with 3 grandchildren. They know about buying, renting, mortgaging, budgeting, gambling, adding, subtracting, being entrepreneurs, winning and losing. One of the 7 year olds wiped us out today, she had gambled most of her cash on property and it paid off with astronomical rents bankrupting the rest of us.

No, they were particularly poor when you gave them an open ended question. Again, I wouldn't advocate a strictly rote learning approach, as I said, there needs to be a balance between that an investigations, but there is a place for committing mathematical facts to memory.

As for multiplication & division, I would start out very concrete, splitting objects into groups. Connect that to written notation & build up from there. Use practice and tricks to learn all your basic tables, ask worded questions at the same time etc etc. Formally teach written column and grid methods, yes teach long division - you need it for algebraic division at A-level. I don't find it a problem to teach two or three methods to get to a solution just don't try & teach them all at the same time. They all lead to a deeper understanding of the way numbers fit together.

Children are learning this from age 5 or 6 all the way to 16/17 thats enough time to be exposed to and investigate all sorts of ways of playing with numbers.

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

I gad s friend who taught in China for a couple of years - she really struggled with the cultural differences at first; they expected to be told, and really didn't like open questions, and obviously this meant it was very difficult to get a discussion going on anything.

Having to learn times tables by rote destroyed any interest I could have ever had in maths. Our (rather horrible) teacher used to shout out "8x6!" etc and point - you had apprx 3 seconds to stand and shout the answer or you had to stand for the rest of the lesson and get extra homework. She also seemed to really enjoy holding me in over lunch/morning/afternoon breaks to sit me on the floor in front of the times tables poster in silence I quickly got the idea I "couldn't do maths" which I hadn't had a problem with until then. Later in the year she tore up my maths book, in front of the whole class and threw it in the bin (can't remember now what for). I clearly had a terrible teacher, in hindsight, but I never recovered from that as far as maths was concerned. It took a couple of months for her to completely put me of maths for life. As far as I could tell there was no need to do tables by rote that year and not the next or even the one after. I could work them out given time (more than 3 seconds) but learning by rote at that age simply didn't work for me.

*off

I had a friend.

Autocorrect never kicks in when you actually want it...

Your Singapore example is interesting Kim. Children would be expected to draw the diagram to model the question you asked but not to solve it. By the time they are given that sort of question they have already been taught the formal column method of multiplication. So they would draw the appropriate diagram, write out 24x6 horizontally underneath, use their knowledge of multiplication tables and the formal algorithm to calculate it, the write the answer as a complete sentence.

Mental calculation of TU x U doesn't happen until after they have learnt the formal algorithm.

My children learn using the number bonds to aid their understanding of number in that they learn 8-2 then use 10 objects to reinforce 8-2 makes 10

haven't read the whole thing , but how do you do mental addition and subtraction without using number bonds to add to the next 10?
If I were adding say 47 and 54
I would think 90+10+1 (ie number bond from 7 to 10 is 3 , giving me one over)
What other methods are there not using number bonds?

You can't work out change without number bonds-they are not going to understand anything if they haven't got the basics of how numbers work in the decimal system.

The visualising and modelling is important. But I don't think the bar models are ever used to understand number. They're more a pre-algebraic method to understand what calculation you need in a word problem.

Breaking down 24 into 20+4 is more likely to be done with diennes or place value disks and a place value chart for teaching the written calculation or a part/part/whole diagram for mental calculation.

You need them for fast mental arithmetic.