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?

Napiers! Is that what it is called? God, I think I hate that one the most

They all happily bung numbers in, start doing something to the numbers then suddenly, there is a bottom lip tremble... and they give in!

I suspect that because it is as you say, noble. It is a really useful, powerful tool that those students who get use to very good effect. Of course I don't teach the students who use it to good effect...

I have no idea where the 'scare' come into maths. My sister is a primary teacher and she swears it isn't her... but somewhere along the line a sizable chunk of students get lost and are not noticed. We ask every September and again in November when they have calmed down and trust us a bit more. The stock answer in September is that they are just too stupid to learn maths or their teacher was just crap.

Ask again in November, when I have spent hours asking them to apply their faulty maths to real life situations, and they have better answers. They were in Foundation, did well in a test and were moved to Higher... but someone forgot to fill in the gaps, so a confident student became dispirited and failed to achieve a C. They had a very angry teacher... older, close to retirement, and obviously equally dispirited with the tut hey are being forced to teach. My favourite - which I had to check up on as it terrified me - oh, the HTs daughter taught us cos no one else could. Was true, local Academy....

I don't blame any teacher for this. I doubt anyone could teach the less able/confident student what is required these days. Not because the teacher is incompetent but because the goals, the curriculum is not fit for purpose... well, that is if you consider the purpose should be to nurture and support all kids to achieve what they can achieve. Rather than insisting everyone attain above average achievement!

I cannot put into words how much I hate the current insistence on GCSEs for each and every student. It is poisonous and vile and has little or nothing to add to many students lives.

I disagree. I'm teaching 7 year olds number bonds to ten at the moment. I've had a fair few lightbulb "eureka" moments when they realise if they can number bond to 10, they can use that knowledge and apply it to number bonds to 20, 30, 40, etc. The reason most adults just "know" that 6+4 is 10 is because they learned the number bond as a child.

Also, xtables have to be learned by rote or they will NOT be remembered. I've got kids who "think" they know their x tables but what they've actually learned is the end total. For example if I ask them if they know their 3 times table they'll happily recite 3, 6, 9, 12... but if I say "what's 3 x 4?" they can't answer me.

I think lack of practice, a move towards using open ended problems to teach concepts rather than to extend thinking and a firm belief that you are good at maths or not good at maths probably explains most of it, nomama.

Gok's point about structured teaching of phonics is probably relevant to maths too. There was a definite move towards lots of fun games and WOW activities to make maths fun because if you didn't children would disengage and not learn anything. What this means is that they get less practice because worksheets and textbooks are bad. So those children that need more practice to secure a concept end up not really grasping it. Then they get moved on to other topics and the problem repeats. Unlike with reading, which is considered important, society tells them that some people aren't good at maths and they are those people. Which becomes a self fulfilling prophecy.

Personally I think that primary school maths is taught far better than it was in my day. And there are actually less 'rules' Eg - now teachers aren't allowed to tell pupils that to x by 10 you add a nought on the end of the number.

I have always done maths using rules, needed to learn x tables by rote. Some people don't need to but then they are what I'd call natural mathematicians and I am not.

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.

More likely, OP, is that you work at a uni where they want you to take on more students and you're having to take on those who are less able.

There is too much of a gap now between GCSEs and A-levels so that pupils doing A-levels have a massive amount of knowledge to gain in those 2 years. The consequence of that is that they have no time to read around the subject or develop really good study skills

This was being said of GCE O-levels and A-levels when I did them back in the 1970s. The transition between examination levels GCSE -> A-level -> degree has never been properly managed in this country (l.e. England & Wales). The Scots may have a better system.

I'm in Germany, ds is almost 8, and we have had some very interesting discussions with the teachers about how and what they should be learning.

The last parents' evening we went to (it's a whole-class thing where they tell you what your kids are learning and what you should be doing at home to support this - great fun, lasts at least 3 hours and by the end of it I have about 10 A4 pages of notes and want to cry), the maths teacher was explaining that we need to practice something which sounds a bit like number bonds with our dcs, it's a sort of bonding up to ten and then seeing what else you need in order to get to the right answer.

Anyway, she gave an example, saying "We all know that that's how you work it out - you do ABC, then XYZ and you end up with the answer, right?".
I thought WTAF?, put my hand up and said "No, actually, that is not at all how I would work out the sum, and expecting all the children to think in that (very convoluted) way is ridiculous".
They love me at school

I think showing different ways of getting the answer or working with numbers is a good thing, but not everyone thinks the same way, not every "system" makes sense to everyone.

That's why only teaching number bonds / phonics / sight reading etc can never be a good thing.

now teachers aren't allowed to tell pupils that to x by 10 you add a nought on the end of the number.

Why not? Surely learning that there are patterns in maths is absolutely fundamental - it's basically all about patterns.

Someone upthread said if you want to do quick calculations, you should just use a computer - which is all very well, but you still need enough understanding to know what to input into the computer; it can only speed things up if you understand what needs doing in the first place.

Because, ebearhug then you get kids saying that 5.5 * 10 = 5.50

I was just thinking about it, and I think I learnt about it around the same time I was learning about HTU, so it all fitted in. And lots of people struggle with where decimal points go. I have never made that error in the workplace, oh no...

Thank you for this thread, IceBeing. I agree with everything you have said. The only quibble I have is with use of the word maths to describe arithmetic.

The entire focus is wrong. The focus is on getting the right answer, whereas maths is about applying concepts and being able to sense whether that answer might be appropriate. The reason we focus on reasonably straightforward operations (basic operations - addition, subtraction, mutiplication, division, long multiplication, long division, fractions, decimals, percentages and simple word problems along the lines of 'a train leaves Glasgow traveling at 38 mph...'), learning tables off by heart and getting answers reliably right is that this is all that was needed by students who were going to find work in factories or farms or shops and never advance into algebra. Because we have not sat down and given any thought to what children really need in a world where most will advance into algebra, we have retained the same old fashioned approach. Other countries have sat don and done the necessary thinking however.

The scare factor comes in when students understand it is all about getting the right answer and think there is one answer that is right and all the rest of the answers are wrong. Children do not like to be wrong. Girls in particular do not like to think they have fallen from grace with the teacher, which is what many feel when they get a page back with a lot of Xs. There is also a fear of advancement because of the association of larger numbers with greater degree of difficulty. This impression is heightened by the fact that children usually start tables on the lowest numbers and progress to the (random) cutoff of 12, the highest/biggest number. By contrast, learning to read offers rewards of entertainment and fun, and the more complex material you are able to grasp the greater the reward.

Best to eliminate the numbers altogether and focus on teaching via algebraic thinking right from the start. The Russian educationalist Vygotsky developed a theory that students need to be given 'tools for thinking', as opposed to tricks to use to get the answers right. Davydov elaborated on Vygotsky's theory and applied it to maths. The result is a maths approach that starts with the general concept and moves to the particular (calculating). In the west we expect students to learn the particular and then learn to apply the concept. We teach lower order procedures just because that is what has always been done, and expect students to build up to higher-order thinking when actually there is no obvious transition from 'set of lower-order arithmetical skills' to 'conceptual-mathematical thinking'.

All the Russian families I know have taken one look at what is taught in elementary school 'maths' and have recoiled in horror. Three families I know have done it in various neo-Vygotskyan ways at home and the result is children who have mastered calculus in their early teens and have no fear.

A contextual overview of Vygotsky and the significance of his ideas.

webpages.charter.net/schmolze1/vygotsky/renshaw.html An exposition of the neo-Vygotskyan Davydov's approach (somewhat unfair I feel in its criticism). See esp 'the Teaching Experiment of Davydov' for an idea of how it works and the theory behind it.

Superimposing the Vygotskyan theory on existing curriculum, a half-way house.

A very interesting blogpost in the US context, (which is directly comparable to the UK context in many respects).

Pressone, how about taking two bottles of water with a known volume (each half a litre for instance) and pouring them into containers of different shapes -- one tall and narrow and one more like a bucket, just to show that although quantities don't have the same appearance they are still equal?

There was a definite move towards lots of fun games and WOW activities to make maths fun because if you didn't children would disengage and not learn anything.

Trying to make any kind of learning fun is a terribly misguided idea. We only think it is necessary in maths other because we suffer from the misconception that maths is hard, too abstract, too removed from natural experience, and there is no joy in understanding it.

math thank you so much for those links - will have a good read!

Mostly I think it happened in maths and phonics, because the content is perceived as dull and boring. Unfortunately once you start to get into whole class games unless they are very well planned you can end up with a lot of wasted time while children are just waiting their turn.

We fail to appreciate that children get great pleasure from understanding, or from discerning the inherent order.

We throw in cartoon characters and other gimmicks to make it 'accessible' and fail to realise that children are attracted to beauty and order and do not need the bells and whistles in order to be motivated to explore it all.

Having read all the posts since my last one, I would like to ask if people actually know what the work 'epitomise' means?

Of course number bonds aren't the whole problem. They epitomise the problem.

Is that any clearer?

The UK approach is try and explain, give up, replace understanding with a method to get quick accurate answers without understanding. Wash and repeat.

Starting kids in formal education earlier won't close the gaps in achievement, because kids will always be able to take on board different ideas at different rates. All you do by starting the drilling earlier is to turn kids off learning - and you have to drill because you now start so earlier, almost none of the children can actually understand what is going on.

Sorry i havent read the whole thread but i think i agree with what is being said.
I am also outraged at my son's math homework being an online game (with a stressful music you cant turn off). I have to re-do all the learning with a pen and paper after he completes his games (he is in Y1). I know that he is just trying to get the correct answer in the game, without thinking. Whereas with a pen and paper it is a different story!!!

math totally agree! I tried to get DD interested in letters by making up a game etc. But she wasn't any more interested than before. When she decided to learn about letters, she just wanted to get on with it - no frills required.

Then, as always, she switched off it again. Every thing seems to come in little bursts. She is learning addition and reading exactly how she learned to walk - intervals of intense practise with large gaps in between.

I think she is testing her developmental level and taking a break when necessary. It seems so natural to learn that way - I can't imagine forcing her to practise something she isn't currently into.

pharoah nice attempt at a slur on my uni. Sadly you are incorrect. We take on exclusively students with A* AA or higher.

In fact many of our students have 3 or more A* but they still view learning as a fact compiling exercise and dislike the elements of the course designed to make them think.

I take your point that this is just an example but I don't really agree with you. Surely most of us actually use number bonds ourselves with subtraction, we just don't really think about it consciously? I don't think knowing number bonds, or times tables or any rote learnt facts prevents children understanding the concepts.

I agree with Pharoah that maths seems to be taught better in primary schools these days. The grid method for multiplication seems at showing value much better than long multiplication ever did, for example.

People used to know how to use slide rules....

not so much now.

Why exactly do we need to be able to multiple 3 digit numbers together using a grid? Surely this is what smart phones/calculators are for?

Seems almost a perfect example of a technique you can learn to produce something that there is absolutely no actual need for you to do.

Just another arbitrary bunch of rules....coz that's what maths is right?

It just seems to me a good way of helping to understand the maths, rather than taking away the need for understanding. But I'm not a maths specialist and I'm sure you're right that a good few students are rather shy of hard work - I've seen this in my (non maths) field too.

Oh it isn't work shyness. I have seen students attempt to learn every single question and answer they have been exposed to in a year, along with every single past paper question and solutions. This is A LOT of work. Far more than just trying to get the underlying principles and hence not need to memorize anything much! The students who do this either don't seem to accept that understanding is something to strive for, or believe they are incapable of it, or, most commonly, have always used this strategy in the past successfully.

The last one is the biggest tragedy...and the one that I believe is the direct result of over testing, over drilling etc.

Blimey! That would be a lot of work. But perhaps there were always some with this approach? Is it necessarily a recent phenomenon?