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?

Now you want to just use a calculator and get an answer?! I thought you wanted to understand the concepts...

Do you honestly use maths every day in a university context and are not able to see that the grid method of multiplication is the epitomy (your favourite word) of grappling with concepts rather than just "getting an answer"?

Do
375 x 42

Now do
(y3 + 14y2 - 17y - 5) x (4y^2 - 30y)

Can you see how the grid method works for both? When you learn it in primary school with just numbers, you are learning how multiplication works, and connecting each step back to something you can visualise ("2 lots of 70"). And can then transfer that seamlessly to much more complicated situations like algebra. The method is completely transparent: you can see what you're doing and why at every stage, and see that multiplying algebraic expressions is the same operation as multiplying numbers.

The entire point of using a method which feels unnecessarily clunky for smaller numbers, is that you are grappling with the concepts of multiplication, not just those small numbers.

But for you this is just pointless and you might as well use a calculator?

The concepts are algebra and beyond.

It should not be taking children 3 or 4 years to understand the concepts of more and less and what the operations of multiplication and division involve.

You are looking at the operations themselves and getting the answer right as the be all and end all of mathematics, Pausing.
Which is better, a cake made by using a mixer or a cake made using a wooden spoon and elbow grease?
Hint: that is a trick question.

mathanxiety, do you actually know any maths? I mean, to do?

Not to just say, "OMG aren't complex numbers just so cool" or "Set theory, man, aleph-null just blows my mind," but to do a maths degree?

Because if a person can't actually work the concepts, then they don't understand them. So while failing to "get the right answer" in arithmetic can just be a sign of careless mistakes, if you're not getting the "right answer" in your Galois Theory paper, then you didn't understand it. That's the point about maths. It is real, it's beautiful, and it's also the same and true no matter who's doing it or which method they're using.

I did write a lot more about the ways notation, manipulation and understanding interact. But I've concluded it's not worth saying. A bit like trying to explain to someone who doesn't drive why this car is pleasanter to drive than that one - when they've read the spec so they Know Better.

Why yes I do know maths, as a matter of fact. I tend not to blast people on MN out of the water with examples from textbooks though.

How much grappling do you expect people to have to do to understand multiplication?

Vygotsky was writing in the 1920s and most of his ideas about how the brain works are known now to be fundamentally wrong.

High performing maths countries ALL place an enormous amount of emphasis on fluency and automaticity. Once students have learned how a concept works, it is very important to memorize the maths facts associated with the concept (number bonds, tables, algorithms etc)

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,
You're badly underestimating the intelligence of small children. The average four year old is capable of learning and understanding not only addition, but subtraction, multiplication and division. The only thing they need to memorize is how to count.
If one of your students doesn't 'get' a concept that you're trying to teach, do you wait until they're a bit older and try again? As a teaching method, it makes absolutely no sense.

I wish I was a bit better at times tables, myself. Automatically knowing 8*4 (for example) would be so much easier that counting 8+8+(8+8) in my head.

Placemarking till I have a chance to read the threa properly.

I have an appointmentnthisnweek with DD Y1 teacher about maths, number bonds,doubling and halving. From DDs answers to questions I give her i think she can remember more than she understands and I am worried sheis missing out on actually learning the basics.

So "1+9 is just fine" as she's learnt the song, but ask her 9+1 imediatly after and she cant answer

Take a look at the links I posted, TheNewStatesman.

Interesting debate!

DS1 is dyslexic and struggles with rote learning. Learning his times tables has taken us YEARS (same as spellings). He was "bad" at maths, but now in y7 he is "good" as whilst he finds rote learning hard, he understands maths and can always figure the answers out. He seems almost suspicious of blurting out answers and strongly prefers to "just work things out".
So for him 24x12 or 12x13 is no harder than 12x12, or 6x6.

Number bonds did nothing for him.

Sorry for random chunks of text! Weirdo phone.

I would love to know how many children who "know" their tables to 12 x 12 can then work out "13 x12" or "24 x 12".

We gave our Y7s a test before Christmas chopped from a SATs paper that was like this. Had a section of an unfamiliar times table then asked for the next answer. The vast majority, even in my bottom set, got it right.

NimpyWWindowmash

I'm dyslexic and possibly aspie, I have to do that. I know 12 x 12 = 144, but I have to work it out if I'm going to use it.

kim - ouch

I generally agree with you OP, in the sense that I am also a lecturer (not long moved to the UK system), and my new undergraduates seem intellectually terrified of 'learning' rather than 'getting the right answers' - I had to spend the last semester trying to get them to loosen up enough to conduct actual investigative/evaluative work. This is not at all my experience of teaching at undergraduate level in other European countries, and my discussions with colleagues suggest it is very common here, so I am coming to the conclusion that it is an educational 'inheritance' issue.

However I am also pretty much functionally innumerate and would benefit greatly from any system of number-wrangling which allows me to 'get the right answer' without having to think about how maths works or 'understand' it - I cannot do basic things like long division, numbers just don't make any sense to me.

How do we find a balance between 'deep understanding' of the topic, and 'just getting enough practical experience of it to get through so we can focus on the things that we actually are interested in'? That's a bit facetious of me, but I suspect if encouraged to focus on 'understanding methods' I would still be, at 40, trying to learn how to do long division.

Cuntcourt - if it's any consolation I managed to get 2 maths O levels and 2 maths A levels without being able to do long division! I still can't do it. It was one of those things that made fuck all sense to me, too longwinded, so never got the hang of it.

Thanks Thumbwitch! I have just hurt my brain thinking about all the things I can't do in maths. I don't understand 95% of the posts above, sadly, and if I lost a finger I think I would be in big big trouble.

Maybe it's a bad example so, it was the only 'maths term' I could think of. But what I'm saying is, are the methods being used now maybe better for people like me, who will never ever understand anything about maths, and can only hope to pass by rote?

OR am I actually (as a clever person with a doctorate and all the rest) suffering from having been taught badly, and just in denial, and actually 'everyone can understand maths'? Because I don't instinctively feel like I can understand anything to do with maths (although I could cope with things like geometry, venn diagrams, anything I could 'translate' out of maths for myself).