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.