Now the hard work starts.

I am now approaching the half way point of the second year of the Primary Maths Specialist teacher course. My Professional Learning Log has been looked at and signed off by the LA consultant. All that I have to do now is to write my assignment!

No worries there then.

A mere 5000 words detailing my school based research that I have or am currently carrying out. It doesn’t sound too difficult but I am approaching a state of near panic.

One of the problems is that my ideas are all too woolly. I’ve had months to sort this out but still don’t really feel that I have a specific question to investigate. It’s all a bit vague. I want to look at whether increasing the use of practical resources at KS2 can help children feel more involved in maths lessons. In my school maths consistently remains one of the least popular subjects, especially in upper KS2. I was hoping that more opportunities to use concrete apparatus might make this apparent dislike less.

It sounds quite specific but the more I look into it, the more I realise that it is actually a huge area.

A big problem is also that although staff seemed keen on the idea, they haven’t actually done much in practice so that I don’t really have an awful lot to research.

The lead tutor from my university is coming to talk it through with me in just over a week so I’ve got that long to really try and get to grips with it. If I don’t, then I don’t think that I will get the most out of her visit.

One of the other course tutors has recently finished her masters and recommended a book ‘How to do Your Research Project’ by Gary Thomas. This arrived yesterday and certainly seems as though it might have some useful ideas and strategies.

Step for this weekend is to try and get my rationale sorted out. I want to really pin down what I am going to do and why. I know that I need to cut out the waffle and be a lot more succinct. Then I need to see what opportunities there may be in school over the next week to look at what is actually happening in at least a couple of lessons.

Nothing like leaving things until the last minute. I always used to tell my son off for doing that. Now I know who he gets it from!

Fascinating Fractions

Fractions is never an easy subject to teach. I remember it was always the one topic that I dreaded teaching when I was in year 3. No matter how I tried to deliver it, some of the children remained confused.

This mornings lesson really needed to go well as we were being visited by one of the numeracy consultants from the LA as part of my MaST course. It wasn’t encouraging when two of my boys announced that ‘I don’t get fractions!’ When I pursued that, they both felt that fractions were hard and that they generally didn’t understand lessons involving them.

We were looking at comparing fractions eg which is bigger 2/3 or 4/5. I was quite surprised by how many children had no idea of where to place a selection of fractions on a 0-1 number line. We spent quite a long time discussing where each one would go and using the fractions ITP to help.

Then I introduced them to the idea of an array and asked how a 3 x 5 grid could help them decide which fraction was bigger. They quickly spotted how it could be used and felt that it was clearer and easier than a number line.

Then I really pushed them and asked which was the larger out of 4/5 or 7/9. They each had a piece of paper and had to fold it into fifths one way and ninths the other way to create a folded grid of 45 squares. This was an incredibly difficult task. How often do we ask children to fold anything other than halves or quarters I wonder? Not being able to start by folding in half made it a real challenge for most of them.

What was really interesting was the level and perseverance. Not one child wanted to give up, they were all determined to fold their paper accurately. They shared their ideas about how they could find fifths and ninths and tried different ways to see which worked best. The two boys who said that they didn’t get fractions produced a very accurately folded sheet and could quite easily see which fraction was the largest. And could tell me that the difference between them was 1/45.

I need another lesson to develop that and actually do more work on folding the paper into different fractions which I think was a really useful activity. It gave the children a real feel for how big a certain fraction was compared to another.

The consultant was impressed with the amount of discussion being done and the level of language being used. I felt that every child had developed their knowledge of fractions and maybe most importantly, they enjoyed doing it.

Thoughts on reading

For our university session this week, we were asked to read an article by Paul Ernest ‘ The impact of beliefs on the teaching of mathematics’. This explores how a teacher’s beliefs about the way maths should be taught impacts on their teaching and therefore on children’s learning.

Ernest makes the distinction of 3 different beliefs or philosophies about maths;
1 – The instrumental view that maths is an accumulation of knowledge, a set of unrelated rules and facts
2 – Maths is a static but unified body of knowledge that just needs to be learned
3- Maths is a process of discovery and learning. It is not static but continually being created and revised.

He sees these as a hierarchy with instrumental teaching leading to passive learning as the lowest and the problem solving approach as the highest.

I would argue against teachers necessarily following any one of these philosophies. I think that in my own practice I use all three approaches at different times. When learning any new skill or concept I may well start with the instrumental approach hopefully drawing on what the children already know. I would then move onto putting this into context with other skills, making the links with existing knowledge explicit. Finally I would set problems that would give the children a chance to explore, apply and extend those skills. The different teaching approaches could be appropriate at different times and in different contexts.

Ernest identifies 3 patterns in the use of materials depending on which philosophy you follow;
1 – the strict following of a book or scheme
2- modifying the scheme with addtional problems and activities
3- the teacher or school constructing the maths curriculum.

Certainly in my own we don’t have any scheme that we follow. We use the framework simply as a framework which is adapted as necessary and is constantly evolving as lessons are evaluated and changed.

I don’t know of any primary school that does follow a scheme strictlybut neither do I know of anywhere that has created their own maths curriculum from scratch. Any school that did that would still be bound by the requirements of the National Curriculum. I think that most schools do take a middle road approach to the use of materials. We use pages of text books where the practice of a certain skill is appropriate and create problems or real life contexts where we can.

I do agree with his point about social context and it is one that I have made before in this blog. The system of assessment and the requirements of the curriculum do have an effect on teaching and this is probably especially true in years 5 and 6. It doesn’t really matter what your belief system is when you are expected to get all of your children to jump through level 4 hoops on a certain day in May.

The article was written in 1988 and I feel is perhaps less relevant now than it was then. In my experience (admittedly not wide) primary school teachers make a huge effort to make maths real for children and do not follow an instrumental approach rigidly. Problem solving is an increasingly important element of the maths curriculum at all ages.

It will be interesting to see what other people in my group feel about this tomorrow.

Holiday Tasks

Well, I signed up to postaweek but have obviously failed 😦

This is my first post for over a week and the last one was just a slide show rather than anything deep and meaningful. Not that I am claiming that this blog is ever deep and meaningful, it’s mainly just me thinking aloud.

However as it is holiday time, I will have more time to try and get things back on track. So my first task is to try and work out what I actually need to do in the next two weeks.

Firstly there are the obvious things like catch up on sleep and tidy the house. However I do need to get my MaST work sorted. The new module started in February and we have had 4 meetings but my independent work has so far amounted to Zero!

Well, that’ s not strictly true. I have submitted a proposal for my assignment. At some point it will be returned and I will actually have to do some work on it. However I need to look at what I can be doing out of the classroom.

I need to look at my Professional Learning Log first of all. They are being looked at in June and I really need to have some work in it by then! I never actually got round to filling in the sheet for the end of Module 1 so that might be worth doing. I also need to go over my notes from the 4 meetings that we have had so far and see what I need to do in the classroom.

I need to read more. I need to research my assignment and find things that I can quote or that might help me as I carry out my research. I also need to read more around the subject generally. I haven’t really read anything since I read ‘What’s the point of school?’ in January. I have bought the latest edition of  Issues in teaching Numeracy which is actually a collection of articles and therefore maybe easier to digest than a whole book.

I also really need to get myself organised. I have a student next term which creates possibilities and difficulties. It means that I will have time to talk to children and actually carry out my research. However it does restrict the amount of time that I have to teach and so carry out things that I want to do.

I have also got to do the necessary planning for next term and spend at least half a day in school sorting out my classroom.

And it would be nice to actually spend some time just being on holiday!

Classroom Research

I’m not sure if that is the right title or not. It might be more appropriate to call it lack of classroom research.

I’m trying to work out what I need to do to be more successful with my MaST work this year. The crucial thing seems to be that I need to be more analytical of my classroom practice and that of other people. A comment on my last assignment was that I needed to analyse in greater depth my observations of children. And as this year’s assignment is a whole school project, I assume that means that I will also need to analyse other people’s observations? It all seems horribly woolly at the moment.

I’m not sure how to approach this or where I’m falling down. Partly I think it is that I don’t always know what questions to actually ask the children when I am talking to them but it’s more that I don’t know where to go once I have their responses.

What does their response tell me about their learning? I’m not always sure that it tells me anything other than they understand (or not) at that particular point.

What are the ways forward for this problem?

Reading may be a possibility. To tryand identify how researchers have analysed children’s responses in the books that I already possess. Or maybe look at general publications on carrying out classroom research. I’m sure that I have a link to one already.

We are already nearly a month into this year’s course and I haven’t actually written up any classroom observations because nothing has really seemed to be significant. I think that I need to start recording things whether they seem to be significant or not, just to give me something to work on.

I’m beginning to feel out of my depth. Hopefully I can work my way through.