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.

How big is a million?

 

I wasn’t sure exactly what I wanted my pupils to learn from this lesson. Maybe nothing more than a feeling of awe at creating something as big as a million. I certainly didn’t expect it to take off the way it did!

I began by giving each table a set of Dienes apparatus. I then read the story ‘How big is a million?’ At each point of the story I stopped and directed them to the relevant apparatus so that they could see how the numbers were growing.

When I finished the story, I asked them to discuss how the numbers grew. I was looking for discussion about how they became ten times bigger each time. Then I asked them if they could use the apparatus on the tables to work out how big a million cubes would be.

Discussing how big a million cubes might be.

 One or two groups needed a bit of direction but most of them were able to see the link between the way the numbers grew and were able to work out that it would be a cube that was 1m square. There was lots of enthusiasm and discussion involving picking up the apparatus to make the point. I was really pleased by how involved they all were.

My TA had scoured the school for metre sticks and I then got the children to help me build the cube net. There was a definite gasp when it was finished. Space for a million cubes!

Our finished One million cube net.

 The children then wanted to know how many cm cubes would fit into our classroom. I asked how we could work it out and some of them worked out that we needed to measure the length, width and height and that would give us the volume of cubes.

Quick work with yet another metre stick and a calculator gave us a total of 106 million cubes. Another Wow moment.

It was then time for assembly. A group of my boys got told off for talking before the assembly started when they should have been quiet. I didn’t have the heart to be cross though as they were estimating the measurements and trying to work out how many million cubes would fit into the hall. I have been promised that they will do it on Monday!

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.

Where now for support?

And so TeachersTV breathed its last on Friday. I don’t know know whether anyone noticed amid all the royal wedding celebrations but it is no longer with us. It was a fantastic resource that I have gained a lot from, both in terms of specific lessons and in general good practice. It cost too much to support and so we have lost it.

Local authorities too are being pared to the bone. Our LA used to fund development meetings for groups of schools on a termly basis for both maths and literacy. These were a fantastic source of ideas as well as a chance to catch up with colleagues and find out about what was happening elsewhere. As a coordinator I found the support of the maths consultants invaluable.

Due to the cuts the maths department at the LA  has been drastically reduced. Our brilliant lead consultant now only works part time and isn’t really working directly with schools anymore so her expertise is lost to the majority of teachers. Development groups seem to have died a death too.

This is by no means a political post. If the money isn’t there, then we can’t spend it (I’m married to an accountant and he feels very strongly about this!). However the question remains. Where do schools go to for support now?

Schools that are deemed to be struggling will still receive support I’m sure but what about the rest of us. Even outstanding schools can’t afford to stand still. It is very easy to become complacent and start to coast but how is that going to be prevented in the future?

Teachers TV and local authority support will be missed by a lot of teachers who gained inspiration and help from them. If you are reading this, then you are almost certainly someone who has a network such as twitter where inspiration and help can be found on a daily basis. However the vast majority of teachers do not access these resources. When I mention twitter or teachmeet, I am greeted with horrified looks and I’m sure that my school is not unique in this.

I know that the official line is that schools will support each other but I’m not sure how this will work in practice. Do schools have to ask each other for help? How many would do that? And it isn’t necessarily help that is needed, just a chance to receive some new input to stimulate thought about teaching. The sort of thing that you used to get on really good courses or inset when they used to happen.

I am very lucky in that I have benefited from some fantastic LA staff and courses. I also access support via twitter and PTRC. I do my bit to try and spread the word but feel very sorry for newish teachers who will not receive the help that I have had and maybe don’t know where to go to access it now.

Quite a gloomy post I feel but I am quite apprehensive about the future of education at the moment.

Making maths more interesting part 2

i was sent into a state of near panic when I received the email that TeachersTV would not be available after 29th April. I have never really bothered downloading the videos, just watched them as I needed. However being given a final cut off date spurred me on to actually find and download the ones that I needed.

I was absolutely amazed by the sheer amount of stuff that is on the site. I have used the outstanding lessons to help my teaching and the murder mystery video was the subject of my previous post on this subject but there is so much more.

I kept getting sidetracked by the suggestions of “you might also be interested in……..” One of these suggestions was a set of four videos on teaching algebra and good starting points. As algebra is going to feature heavily in this year’s MaST course I felt that it would be a good idea to investigate. The series consists of two lesson starters involving pattern and formulas as well as the handshake lesson. I have downloaded them and will now think about where I can incorporate them into my planning for next term to try and liven up my teaching a bit.

I was also inspired by a colleague on my MaST network who has done lots of work on using picture books in maths lessons. She bought a selection along to our last network meeting and I instantly fell for them. I have been on to Amazon and bought How big is a million (Usborne picture books) which will fit into our space topic next term (well sort of) and Anna’s mysterious multiplying jar. I will use these with my children and see how they go down.

It isn’t that I think my lessons are boring but that I want to try and make it as accessible as possible for all of my children. They all love watching videos and looking at picture books so this may capture the interest of some children who don’t think that Maths is for them.

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!

Mathematical Art

So what do you do when you arrive in your classroom 15 minutes before the start of afternoon school, after being out all morning , to discover that your PE lesson has been cancelled, it’s raining so you can’t go outside and you have absolutely nothing planned?

Panic obviously! Not helped by the fact that it was indoor play and the children kept wanting to come and talk to me and show me pictures of their new guinea pigs etc. And I hadn’t had any lunch!

Escher tesselations obviously. No preparation necessary apart from a supply of paper and some card. This was partly an activity that I have done several times before but modified/improved after our last session at NTU.

I by putting on this youtube video
http://www.youtube.com/watch?v=njp6yexWbfw and just let them watch it while I cut card into small rectangle pieces. Then we watched it again together because I love the soundtrack.  This time they looked more closely at how the tesselations were created and tried to see if they could spot the base shape. They had done some tesselations previously of complex shapes such as Christmas trees etc last term so the idea wasn’t new to them.

The lesson was interrupted by the head teacher who wanted to dicuss Bittersweet Symphony as it is one of his all time favourite tracks so we watched all again. They loved looking at all the different images and kept finding new things to talk about.

Then I displayed the lesson notes from Primary Resources
http://www.primaryresources.co.uk/art/docs/Making_Escher_Patterns.doc

This gives the children a very basic idea of how to create an interesting tesselation from a basic rectangle. I demonstrated one to show them how easy it could be and then let them get on with it.

35 year 5 children who varied from being statemented to very able, all dived in and worked without any fuss. The biggest problem in the whole session was only having one roll of sellotape between everybody.

Their tesselations were varied, some were very complex and created really interesting patterns. Others were very simple but just looked really effective. Everychild completed a tesselation pattern of their own shape. Then they had the fun of turning them into fish, monsters or whatever. None of the patterns is finished but we will display them on the class blog when they are done. Their first question was “Can we put them on the blog”.  They love the fact that their work has a wider audience now.

I will pursue this by looking at how shapes tesselate in more detail and link with work on angles. I also want to see what other shapes they could use to create other patterns. Lots of investigative work to come.

I have lots to reflect about MaST at the moment and also things that I have read recently. I will catch up on posting when life gets a little less hectic and I’m not doing the Lambeth Walk everynight.

Making maths more interesting

I feel that I need to liven up some of my maths lessons. I have a very boy heavy group and some of them find it hard to maintain concentration. The murder mystery was great with all of them totally involved and on task for the whole lesson so it might be worth while looking at other video clips that could be used to stimulate maths lesssons. I know that there are starters on Teachers TV but I wonder what else would work? Any suggestions gratefully received.

One of my aims for this year is to get everybody making more use of our fantastic school grounds for maths. I’ve already done some measuring and will do some work on area and perimeter next term. I want to use the parachute as well to do some number bonds work. Physically moving should hopefully really get them thinking about the properties of numbers.

We’re doing ratio later on this week so I have been a bought a pack of mini smarties as an incentive. Last year this lesson worked really well (it’s based on a resource from primary resources) but of course there is no guarantee that it will work as well this time.

I have another HEI session tonight at NTU so it’s going to be a long day 😦