I am about to waffle quite profusely about mathematics but I need to get it down on ‘paper’ so that it might make more sense in my head.
I currently teach the lower ability of two year 6 maths sets. The children range from level 2A – 4C and all of the children are underachieving, and have been since at least year 4 according to their data. Obviously somewhere along the way something hasn’t worked with these children and I’m now having the pressure piled on to do something with these children in the next 8 teaching weeks that hasn’t happened for the past few years: get them back on target.
In many ways it has made me re-evaluate my teaching, and many times come to the conclusion that I must be a rubbish teacher for these children not to have made the progress they should have, and although I know I am not totally responsible for all their previous years of misunderstanding, obviously I haven’t managed to put enough of their misunderstanding right.
In my quest to be not so rubbish I have done quite a bit of question asking, reading, watching and discussing with fellow teachers about how we teach maths and the ways that children learn it.
The very first thing that happened was that I put out an innocent request for ideas on how to teach my class to convert units of measure eg converting grams to kilgrams and vice versa, as I was using the framework site to plan my next unit and this is part of what comes up. I’ve tried several (fruitless) times to teach this to my class and was dismayed to see that it had come up again, hence my call for help. The help which came was not expected but did lead to more of a realisation than I could have imagined. I got told, quite bluntly: why on earth was I trying to teach a level 5 skill to children who were at level 3? The answer: because the framework told me to and I hadn’t actually thought about whether it was really appropriate. I must admit I’ve never really liked the new framework; it’s far to jumpy which leads to a lack of consolidation and this was just what I needed to abandon it: no more planning from the framework for me! From now on I intend to use APP at the appropriate level for my class as a basis for my planning and see if this helps.
The next thing to happen was I almost came to blows with my HT about our calculation policy; we are supposed to be developing one as a cluster of schools so that all the children that feed into the same secondary school go up being taught the same methods. This seems fairly sensible to me. The policy we were presented with is basically this one here, from the Leicestershire local authority, and although most of it seems fairly logical, it’s the division methods in particular that strike me as being awful and I said so. I would love to really find a division method that makes sense. I have tried teaching my class chunking on six occasions so far, going right back to basics, using number lines to demonstrate what’s happening etc and still they don’t get it. I think there are too many stages. I taught them the short division method with much more success (only 2 out of 24 unsuccessful) but was shot down in flames for admitting I used it, even though I know several other members of staff use it too. Whilst looking for new division methods (of which I haven’t been successful yet) I came across a document from the NNS comparing methods used in 1999 to 2003, which stated that children that used the partitioning method for division (advised by the Leics LA document above) faired least well overall compared to chunking and short division. This article also has some interesting thoughts on why children find division so difficult:
In thinking a bit more deeply about maths teaching though, we place so much emphasis on how the method works but the children still don’t know when or why to use it; surely a focus on what each method is for would be more helpful than knowing the ins and outs of the method itself, as after all is the method not only a tool to solve the problem and if we don’t know the problem we are trying to solve we can’t then choose an appropriate tool to solve it?
While I was over on the Leicestershire site I also had a look at the progression of skills into the KS3 policies being suggested and was flabbergasted when I saw that they are expecting subtraction with decimals to be done using completely inefficient methods such as jumping on number lines. After looking at these documents I actually spoke to some real secondary school maths teachers (my boyfriend is one) about whether they thought these were suitable methods and which methods they currently taught. The answers were for multiplication: Napier’s bones, and for division: the short method (sometimes known as the bus stop method).
Next, I read Understanding the Score, a document produced by Ofsted and brought to my attention by the writer of this blog, who is doing the MaST (Maths Specialist) course. I found the article very interesting, if not a little heavy going, particularly the bits of best practice and I’ve yoinked some of the ideas where I know that I teach the same things. It has made me consider the way I approach teaching maths by a) thinking about what I want the children to learn, and b) thinking about how the children are likely to learn that best. It also includes a list of ‘good’ maths lesson features for primary and secondary which is a useful check list and I shall be using it to try to improve my teaching.
Finally, last night I watched Dispatches: Kids Don’t Count, the first in a two-part documentary about the state of maths education in England. It was interesting to watch and didn’t include too much teacher-bashing but did show some of the problems faced by teachers today. It included some useful ideas from the Maths Makes Sense scheme, although I’m not overly convinced of the use of cups to teach ‘real life’ maths. I’m not sure how it works when you move beyond smallish numbers to, say, 35 x 27 – are you really going to move that many groups of cups from the resources table to the maths table? Do you really have enough cups? Or are the cups no longer needed at this stage? It also did a lot of SATs bashing in the way the revision for the tests was being handled in that school but it is not like that everywhere. Anyway, the programme made me think about how I can present my maths lessons in a more visual way so that children can ‘see’ the abstract concepts in action. The second part is on next week so it shall be interesting to see what that has to offer.
So where am I at now?
- Plan the next steps that are appropriate to the children using APP as my guide, not just because it tells me to in the framework.
- Make sure that my learning objectives and tasks match each other closely for all groups of children.
- Make sure children are secure in the basics from previous years and plug the gaps before trying to move them on.
- Models and visuals are important to teach maths concepts all the way through primary school, not just in the earlier years. I am going to try and do more of this in my teaching (but not necessarily using cups).
- Make sure children are secure in the vocabulary of maths and understand when and why they need to perform an operation, not just how.
- Try to find a method of division that works and does not require ridiculous amounts of steps and places where error can be introduced.