Can someone please tell me why division is taught in such a confusing way in year 3?

[Divideandrule]

I have been polite in saying confusing, I really mean bloody stupidly. DD has come home confused as they have to use number lines and do repeated subtraction or something? She was trying to explain it to me and I didn't get it. (This is the child who enjoys and is good at maths, totally gets place value etc, in high group).

So, I showed her the bus-stop method for the same calculations. Eureka moment and a big smile on her face.

Do I have a word with her teacher about this? I get the need for some methods working for some children and different ones working for others. Surely if she understands the way I showed her - incidentally we had remainders with numbers so had to carry - she should go with that?

Anyone?

It is. And I had a wonderfully happy time at primary school doing things I could already do. And it didn't dampen down my work ethic or ability to rise to a challenge, either, just gave me lots of free time to pursue my personal interests instead of having to spend time struggling to understand what I was learning at school.

"But the current Government is of the view that it is better to make all children plod through at the same pace, to ensure the weakest have gained a proper understanding of the subject, which is a bit concerning."

I agree, it is very misguided to think it is OK to make all children plod through at the same pace in order to serve the needs of the weakest children. Bright children are harmed by not needing to apply themselves in the primary year.

@rabbit I understand perfectly well that maths teachers have a responsibility to teach maths to all the children they have in their class. I also understand perfectly well that most primary school teachers do not understand maths at all, and that too often they fall back on these methods for the people who don't understand (which includes them) as a defence against their own lack of facility with maths and that they get confused and defensive when the children who do get it straight away are ready immediately to move on to the sensible way of doing things. They want to drag children down to the 'introduction to maths' level because that is what they feel comfortable with. This is why the kids who are good at maths become disillusioned, especially when they are told off for getting the right answer quickly because they understand when the teacher wants them to do it painfully sloooooooooowy because that is the way they (the teacher) feel comfortable with things progressing.

My DD2's school has just had an OFSTED where this point exactly was made. While a lot of the stuff coming out of the OFSTED was clearly belligerent 'war on teachers' beaurocratic posturing, this point was correct. Too many primary school maths teachers are too hung up on elements of process and are losing sight of outcome.

Because to solve 33 + 9 using a written method is a waste of time. You can simply add 10 and subtract one which is much more efficient. Children use column because they don't think about the question and use their understanding to choose the most efficient method, rather than the one they always use.

However, I will ammend and say yes you can use it to help if you don't know how to add 10 and subtract one, in my hurry out the door I meant to write I have seen children do 3 + 9 using the column method and that does not help at all!

@throckenholt

Some children 'get' mathematical concepts very easily. They have an innate relational understanding of maths. They are the minority. I would say, in my experience, that there are probably 2 or 3 in each class of 30... so at best 10%. For that minority, the current teaching methods might seem like a bit of a plod, but what about the other 90%? As a teacher, I am responsible for the progression of all 30 children. I am a mathematically minded person myself, and so I know that I do push those 2 children in my class to explore further concepts.

If you take my small sample size (of the classes I have taught) and project it onto the population, then look at the number of people who become primary school teachers, the chance of them being within that 10% of 'natural mathematicians' is incredibly low.

@thetasigmamum

You're right- the vast majority of primary school teachers have a very low level of maths themselves. The requirement is a C at GCSE. I, personally, have A Level maths but I am the exception.

1. Primary school teachers have to teach 10 National Curriculum subjects. They cannot possibly be an expert in all 10 subjects.

2. The qualifications for getting into teacher training courses are low. My uni asked for a C and 2 Ds. The reason the requirements are low are, in my opinion:
   a) teaching is not a well paid enough profession to attract people with higher qualifications
   b) teaching is about the ability to explain things to a specific audience. I know some exceptionally bright mathematicians and physicists who would be awful teachers because they wouldn't be able to make it accessible.

I don't have a degree from Cambridge in maths, but I did do Year 2 and Year 6 SATS myself when I was in primary school. I was taught the old, traditional methods and I got a level 3 and a level 5. I wasn't bored of maths, and there was no push (at the time) for teachers to differentiate. We did reams and reams of the same method (I remember being very proud of myself as I'd done 8 pages of column addition when I was in year 2). I understood it at that age, but I wasn't moved on to something more challenging. That idea isn't a new issue.

My boredom with education began when I went to secondary school. I spent the whole of year 7 learning the things I'd already covered in primary. Incidentally, my secondary school is currently in 'special measures', and my primary is 'outstanding'.

Also, schools that follow the national framework (now defunct, but this government has offered no alternative) follow the pattern of revisiting topics every term.

We teach:
Autumn: A1, B1, C1, D1, E1
Spring: A2, B2, C2, D2, E2
Summer: A3, B3, C3, D3, E3.

For example, in year 3 A1 looks at breaking (partitioning) numbers into HTU. A2 looks at using this knowledge to round to the nearest 10 or 100. A3 looks at giving estimates for sums and differences, using knowledge of rounding.

@juniper904

I think, after a long time thinking about this, my conclusion is that we have been crap at teaching maths for a very long time in this country. Which is why so many adults are heard to say I never understood maths (including sadly lots of primary school teachers - even the primary maths specialist who was brought in to explain the new methods ).

We need to totally reassess how we teach the basics. I think it would be much better if we had specialists in primary schools teaching maths, music, science, languages (maybe all of it !). Even if it meant teachers touring a group of local schools.

Maths doesn't need to be taught by people with degree level maths, but it does need to be taught by people with a real feel for how it all works. People who can think on their feet, understand where the confusion is and reword their explanation, come at it from a different angle. Example - we used an abacus to show our kids how numbers work - very good at showing place value. They hadn't got it from number lines, or counting counters (or any of the other methods at school) and were getting totally demoralised and convinced they were bad at maths. As far as I can see abacus is no longer used at primary school.

The important thing is to realise there is never just one way of working something out. If you as the teacher know all the methods you can use them to get that eureka moment with a child. You can only do that (coming at it from a different angle) if you are really sure of it yourself and you know how it all fits together. I think those with that ability for maths are very few and far between in primary schools.

Sadly I have seen this level of total confusion with maths and a belief that maths is too hard for them, right up to degree level - even with people who had somehow got good grades at A level science (don't they do any maths in science any more ?!). The look of amazement when someone finally puts it into words they understand is wonderful to see. And the question they always ask is why didn't someone explain it like that before ! That is so easy!

slightly off topic, apologies, the headline news is the UK is officially bad at maths!

I was coming to post that - on the front page of "i".

thetasigmamum - I agree with you entirely that a lot of primary school teachers are very poor at maths themselves. That is one reason why the old fashioned methods taught straight away didn't work for many children: because the teachers couldn't do those methods properly themselves and didn't understand them, so couldn't correct their own mistakes, let alone the children's. My mother clearly remembers in her useless private school having the whole class attempting to correct the harassed teacher's mistakes and also clearly remembers that nobody in that (all girls') private school took O-level maths as a result. At least if primary teachers who are not very good at maths understand the modern methods (and thereby improve their own understanding of maths), they are one step further on than the teachers who used to "teach" methods they could neither understand nor carry out correctly themselves. And what's more, they can then explain the maths to the majority of children who likewise would otherwise leave primary school unable to understand what they were doing in maths. There is nothing whatsoever wrong with the philosophy that children and their teachers should understand what they are doing when they do it. Combine that with a good learned knowledge of things like times tables and you really should have a good foundation for learning in secondary school - provided the maths teachers there know what they are doing.

My dss didn't need to be taught phonics to learn to read - they were reading fluently to themselves long before they started school. My dss didn't need to be taught chunking to be able to understand division. There is an awful lot that they are "learning" in primary school that they don't need to be taught and an awful lot they are not being taught that they would benefit from. Ds1, for example, finds it unusually difficult to work out how to put a belt on. He was also unusually slow at wiping his bottom effectively. It does make me wonder whether anybody really has a clear idea what they want children to be able to do by the time they leave primary school and what a fair assumption is when it comes to deciding what a child should and shouldn't be able to make sense of and achieve by himself and what it is fair to expect a parent to be able to teach their child at home if they do not have the requisite innate abilities. School has never been tailor made to suit every child's needs and abilities.

Coming back to this discussion..

On a personal basis, I'm a primary school teacher with a pretty good understanding of maths (As at A level and A Level Further Maths back in the Dark Ages when A* didn't exist). I didn't go on to study it at university - went on to do science for first degree and PhD at Cambridge, but obviously there was a mathematical componand to e.g. my first year Physics course. Interestingly, I'm also from a mixed 'New' Maths and traditional maths background - moved primary schools a lot, some were doing the old Alpha and Beta books and more traditional methods, others were heavily into New Maths. A little bit like the discussions here about having several different methods, I feel I actually benefitted from being exposed to both philosophies of Maths teaching, because I was being given 'understanding from the ground up' in some schools and 'black box' methods in others.

I don't, personally, have any problem with teaching the variety of modern methods, perhaps because I can see clearly where each is going, and understand how each piuece 'builds towards' eventual understanding and mastery. I feel - and again this is a personal view -that by providing different models of images, and different 'ladder rungs' to step up to the final methods, the new methods help more children to succeed, and give even those who could have 'learned the rules' of a traditional method straightforwardsly a deeper understanding of what they are doing when they use it.

What I think is important - and perhaps is more difficult to provide for teachers who have a less secure personal grasp of the subject - is differentiation to make certain that the most able mathematicians get open-ended problems to get their teeth into while others work to gain a true understanding of basics like place value. Most modern teachers are very good at differentiating - I think this is a way in which the teaching I do, and that my own DCs receive, is hugely better than that I got a generation ago. However, in the same way that I am better at differentiating in Maths than I am in e.g. dance (Mrs Two Left Feet), there may be trachers who find that area more of a challenge in Maths.

@teacher differentiation is key. As is being prepared to accept that exposure to a variety of methods is the best way to help children become secure with 'playing around' with figures. I haven't got a problem with modern maths - like you, I had exposure to many different ways of teaching the various concepts at primary school, not because we moved around but because the teachers were, I think, prepared to give lots of different things a go. My problem is with the soullless minions of orthodoxy who will not accept that a child understands perfectly what they are doing and why it has given them the right answer if their big book of how to teach maths declares that at age x a child cannot possibly understand method A but must be forced to use method B even if it is a dumbed down method that doesn't have scalability in approach to the child's learning at ages y and beyond and which doesn't even have philosophical integrity. To defend forcing those who can use more sophisticated methods happily to use chunking, as one example (but there are others) on any grounds other than 'we are being forced to do this by DfES) is either intellectually dishonest or indicative of a person who shouldn't be teaching maths.

Yes, I can see your point, thetasigmamum. I just find it hard getting my head around the idea that someone who is good with numbers would find chunking confusing, rather than limited and basic. Surely all it takes is one lesson to be able to show you understand chunking perfectly well, and then a good teacher will move you straight on to something more interesting and useful, anyway? Or is there some kind of requirement that a whole term be spent on it?

My personal approach to children who are particularly able at Maths (I have a couple in my class at the moment) is to introduce an approach such as 'chunking' as 'a tool for your toolbox that you may find useful'.

I often ask them as part of the first lesson on such an area 'explain to me how you work out this kind of problem' - it gives me an insight into whether their 'current mental image' is of repeated subtraction, or of sharing, or of approximating and refining, or of linking to known multiplication facts and then creating an inverse, or whatever.

Then in Lesson 1, I'd introduce the method we're learning - if those able children show that they can use an 'expanded' method securely (usually with a 'yes Mrs TW2K, I will do this if you ask me to but frankly I do it all in my head anyway' roll of the eyes) and for a variety of (quickly ascending in difficulty) problems, then I will quickly move on to showing them how they can 'contract' it into the 'standard written method'.

Then they get work of ascending difficulty, or expansion into problem solving, or whatever challenge is most appropriate. Often I find them using 'mixed methods' - mental for some problems, expanded methods for others, contracted methods for still others.

I have children in my class working at levels in Maths typical of anything from P levels (can count objects securely but can not reliably add 1 more mentally) to 4b - there really isn't such a thing as a 'big book of how to teach maths' just a 'guidebook to the next steps on the road strarting from where the child is at present'. It would be as absurd to stop those children with utterly secure knowledge of place value and 'expanded' methods of division from moving forward to 'contracted' methods as it would be to make the child learning to add 1 learn the 'bus stop' method 'by rote'.