Planning for Reasoning

I’ve known for a while that we need to improve our reasoning and problem solving teaching at my school. Analysis of the SATs papers showed that whilst number skills were really high, skills in ‘using and applying’ (as reasoning and problem solving were called) were less developed. Referring back to the post on why it was good that levels were dropped, it could be said that some children were moving on from primary with level 4 in maths overall, level 4 in number, but only level 3 in using and applying. This use of levels to mask a specific weakness in what a child can do is another reasdon they are bad.

The not-brilliant Ofsted in June, only shed a brighter light on what I already knew – we needed to change our teaching so that children learned to reason more.

This is a hard thing to do, particularly for older children when this expectation hasn’t been there all the way through school. There is a legacy of doing maths in a certain way, which leaves gaps in knowledge and resistance when a new way comes along.

However, 2 key documents from the NCETM have really helped us out. Firstly the Planning for reasoning documents, which have ideas for how to get children reasoning for every objective in the national curriculum. Secondly the Maths Hubs materials for mastery (and mastery with a greater depth) have the expectation that children are reasoning writ large through them.

These documents have been brilliant in supporting me and the teachers to have a greater expectations of what children can do. It would be even better if someone could produce some text books with these expectations equally prevalent…

Medium Term plans in Primary Mathematics

How does your school organise their mathematics curriculum? There are broadly two ways of doing this. You could, in a three term year, divide the content equally between each term and teach a third in the Autumn term, a third in the Spring term and the final third in the Summer term. Or you could teach each domain of maths in more depth, sequentially going through them during the year and not revisiting them.

Here are three different models that all have their strengths and weaknesses.

1. The Scattergun Coverage Model by Hamilton Trust.

I’m not entirely sure how this model was planned, except that it seems to have covered all the objectives throughout the year.

Hamilton Trust cover objectives in a seeming scattergun approach
Hamilton Trust cover objectives in a seeming scattergun approach

This little extract informs teachers in which weeks they will be visiting different objectives. In my school, with the amount of work required to adopt the new curriculum, we thought this would do us fine, but actually what happened (as I’ve written) was that teachers did not take ownership of their planning and instead merely delivered the lessons they found in the order they were given. The outcome was that, whilst individual lessons were often good, the units (a week or fortnight of lessons) were often aimless with no sense of the children being on a learning journey. Maths only happened in the maths lesson and was very much isolated from the rest of the curriculum.

Much of this was my fault. As the maths leader I hadn’t taken responsibility for the planning that teachers had adopted. I’m sure many schools can make the Hamilton Trust plans work for them, but for us it had led to failure and so we needed a change.

2. The year-long blocked approach by White Rose Maths Hub

It’s too late to adopt this now, but you could plan to take it on for September.

The Overview for the medium term plans created by the White Rose Maths Hub
The Overview for the medium term plans created by the White Rose Maths Hub

As you’ll see from the picture, all the number and calculation objectives are taught by the end of Week 9 Spring term, and in much longer blocks than we have used in the past, enabling children to learn concepts with a much greater depth. I think this model will work brilliantly, and I’m currently discussing with the staff whether to adopt it for the next academic year. This maths hub have created tests for their medium term plans so you can assess how well the children are getting on. You can sign up for their free resources here.

3. The Term-by-Term approach (by me)

This approach was recommended to me by a headteacher who was part of the first peer review we had after our not-brilliant Ofsted. She said that I should base my plans on the 1999 schemes of work. So I went back to them and found them still hosted on a website in Dudley. Then I used a document that I only have a paper copy of called the ‘Steps Up’. I believe this was created by a group of Birmingham mathematics SLEs and provides some useful guidance as to what are the steps up to achieving the age-related expectations in each year group.

The model I went for was for the teachers to visit each domain during a term. They would cover all the content by the end of the Spring term (half in the Autumn term, the other half in the Spring term) and then use the Summer term to consolidate the age-related expectations.

My medium term plans are here:

Medium Term Plans

You’ll see that they are not quite finished yet. I haven’t written the Summer Term, nor have I completed the mental maths part of the plans – what you see in the mental maths part are still the old expectations from 1999.

Finally, I made some tests for the plans. These tests are half termly and I used Testbase to make them – a paid for service that hosts all the test questions asked of children in the England’s testing system for the past 20 years. You can find the tests here in their own folder.

You may consider it quite an effort to write a whole load of medium term plans. But it’s given me a much better insight into the new curriculum and a much greater sense of ownership over what we are teaching at my school. The problem with using other people’s plans, is that you end up believing the lie that you shouldn’t have to reinvent the wheel, when actually the process of reinvention is healthy all by itself.

Three ways to Improve Planning in Primary Mathematics

Since June (and the bad Ofsted and bad SATs results) I have been working on improving planning in maths and it’s really worked. Here’s how.

1. Impose a planning format

If you know anything about union and indeed Ofsted guidance you’ll know that is the *wrong* thing to do. But it’s exactly what I did at my school. I imposed a planning format that everyone had to use.

But planning is for the teacher, not the senior leader, I hear many cry.

No. I disagree.

Planning is for the child.

For too long we had written plans that support what the teacher might say in front of the children, how they might model or an activity or what learning resources they should prepare before the lesson. What we had not done is really think about what the child needs to do during a sequence of lessons to achieve the goals set out in the unit of work.

So in fact, while it was an official planning proforma that I imposed, it was actually the principle behind it that was important. And the principle was this: start the unit plan by writing the final lesson’s learning objective. Then work backwards through the learning objectives that build up to the final one to create a learning journey for the children. It’s a bit like that picture I shared 2 days ago. Then, for each day, plan what children who were likely to exceed the set learning objective might accomplish, and do the same for children who would struggle each lesson.

When this was done, each lesson would have 3 learning objectives around a similar aim, and each lesson would also built towards the next lesson.

What was great was that the teachers who got this, swiftly diverged from the planning proforma I had set up. They got the principle, so who cares if the format looks different? So much for the planning format imposition! What I found is that the teachers who needed most support where those who thought they were doing it right by merely filling in the boxes of the planning proforma without really thinking about the principle. And for these the proforma was a great starting point for explaining the principle in greater depth, thereby developing their mathematics subject knowledge.

2. Supply some medium term plans

There’s a lot to think about in mathematics, especially when you’re a non-specialist dealing with a brand new curriculum that you’ve had little or no training for. While I’m a big fan of ‘ownership’, as I wrote about yesterday, there is a limit to how much new stuff any teacher can take on in one year.

So I gave everyone medium term plans. I had some help. Various folk from different parts of the country have made maths plans and overviews and the like, so I used a few different documents to create medium term plans for mathematics for Years 1-6. I’m going to save the post for the ideal mathematics medium term plan model for another day (probably tomorrow), but suffice it to say that the medium term plans I’ve written have been a useful framework for teachers creating their unit plans mentioned above.

3. Link the medium term plans with assessment

The big problem we have at the moment in Primary is assessment. Nobody is quite sure what the age-related expected standard will look like. To make that more confusing, if a child is ‘age-related’ by the end of the academic year in mathematics, what sort of maths should they be able to do by December? or Easter?.

I looked around for some tests, and found none that suited what I wanted, so I made my own. Well that’s not quite true. I am making my own. So far I’ve made tests for Autumn 1, Autumn 2 and Spring 1. Each of these tests is linked with the medium term plan that should have been taught during that half term.

Of course, I don’t actually agree with testing a curriculum that is not best-fit. I’ve already written about the problems of the previous level-based assessment system being best-fit and how it disadvantages children. And of course any test is a best-fit measure. It seems ludicrous to me to create an ‘expected standard’ curriculum and then use a ‘best-fit’ tool (like a test) to measure how well each child has done, but that, again, is another post, for another time.

The point is that by analysing the tests, each teacher has been able to find out which bits of that unit the child did less well on and use that knowledge to follow up and plan further interventions during the next half term.

In conclusion

I’m biased obviously, but I think mathematics is in a much stronger place at my school than it was six months ago. We’ve had more conversations around mathematics knowledge in the last few months than in the previous five years, and I can really see teachers taking ownership of their maths teaching, rather than relying on third party solutions and merely delivering lessons.

In my next post I’m going to attempt to compare some different models for mathematics medium term planning that I’ve seen.

The Importance of Planning: Ownership or Delivery

How do you approach your planning?

For me, if I know a subject well, like maths or science, then I look at the objectives the children need to learn in the year and lessons start coming to me – lessons that I’ve taught before, or new ones inspired by things I’ve heard about or read about. Then I thread those lessons together into a journey and have a unit of work to teach the children.

When things work like this, I have ownership over the planning. It’s mine. I know what I’m doing and feel secure.

For subjects I know less well, I often rely on others planning. Maybe it’s paid-for – I often use Hamilton Trust or Rising Stars schemes. Sometimes, it might be a colleague’s plans.

For these lessons, I feel like I’m delivering somebody else’s property. The plans aren’t mine. I don’t own them and I feel less prepared to make spontaneous changes that might benefit the children.

It’s inevitable that some planning is like this second model, especially in the Primary sector where you can’t be good at everything, especially when you’re starting out. What I’ve learnt this year, since my school’s not-brilliant-Ofsted is the the importance of moving from the ‘delivery’ model to the ‘ownership’ model.

CPD should be around giving teachers the subject knowledge so they can ‘own’ all their lessons, and that’s how we’ve tried to gear things at my school, particularly in maths which has been one of the main areas of development.

Tomorrow I’ll write more about how we’ve changed things in maths to encourage ownership over delivery.

Aimless Planning

A picture of how to plan
Here’s what planning should look like (in green) and what it shouldn’t look like (in red)

Planning is such an essential part of what teachers do, that it’s hard to believe that we sometimes get it wrong. But we do and we had. I had.

At my school, after a poor inspection outcome and our worst SATs results for 10 years, first came the hand-wringing, then the soul-searching and finally the cold, hard analysis of what we needed to do to fix the mistakes. Quite simply it was planning. Not teaching. Not behaviour. Not assessment. Planning.

The picture above shows what we had been doing and what we needed to do. The red blobs are the lessons. Each individually was a good lesson – it moved the children on during the lesson, there was good modelling, children made progress and did good work. However there had been no journey from one lesson to the next. There were just lots of individually good lessons that seemed to build on children’s starting points, but actually didn’t have an overall aim.

The green lessons are what we are doing now. Starting with an overall aim for the end of the unit (which typically are one or two weeks long), we build backwards to plan the lessons that are needed for the children to reach that aim. And we keep planning backwards until we find the children’s starting point. It’s been a much more healthy and vibrant process and, though it’s early days, it seems to be really working.

If you’ve read some of my previous #lentblog posts, you may well consider it inevitable that schools end up doing that ‘red blob’ aimless planning. There is such a pressure to perform within a lesson, for children to make progress within that singular lesson, that it’s easy to lose sight of the big picture of where you are trying to get the children to. And also there are so many supposedly useful schemes and resources out there for lesson preparation that it’s easy to forget that one of the most important tools a teacher has is their own subject knowledge, and not the ability to use somebody else’s downloadable content.

For the rest of this week, my focus in #lentblog is going to be on planning, some of the resources I’ve created and the lessons I’ve learned from trying to improve planning.

Let’s all go to the ICT suite and make posters

Sometimes you’ve got to give credit where it is due. And today’s credit goes to Rising Stars, Miles Berry, Terry Freedman and a load of other ICT specialists. It goes to the Switched On ICT Scheme of Work.

Gone are the days when ICT consisted of going to the ICT suite and making posters. No longer is ‘Knowledge and Understanding of How to Use Publisher’ the pinnacle of ICT excellence. ‘Embedding ICT’ consists no more of allowing pupils to research during lessons, nor playing a game on the interactive whiteboard.

No. Now we have Switched On ICT.

Now I have children in my school who are blogging, creating wikis, making games, drawing, writing and using maps. And I have teachers who are more confident at using these tools to enhance their English and maths teaching.

Blogging, to take one example, is great because it gives children an audience to write for, which is motivational for them, but more importantly demands a precision of language that might be otherwise ignored in ICT. Children can’t spell or punctuate badly in a public space like a blog, so they have to edit and refine their work, improving their writing habits while they do so.

I introduced Switched on ICT to my staff about a year ago and this academic year we have used it in all our topic planning. Well, let me qualify that – we have embedded Switched on ICT units within existing topics as either ‘cart’ or ‘horse’. Here’s the metaphor – when Switched on ICT is the cart it follows the topic as an add-on – it might be vaguely related with the subject matter of the topic – but not wanting to create spurious or tenuous links, it might exist on its own – like a mini-week of ICT within the sweep of the larger topic. Whereas when Switched on ICT is the horse, it leads the rest of the topic – pulling it along with it.

An example of the cart in action is this. Last term Year 4 did ‘We are musicians’ learning various compositional knowledge using ICT. It had a link with the topic, but the teacher taught it as a week on its own. One week in which the children were taught music and ICT – a bit like a cart being pulled along by the ‘horse’ of the main topic.

An example of the horse is again from Year 4. This term they are doing “We are co-authors”. It works really well with their Rainforest topic because they can have a Wiki as the overall outcome of their whole topic, working as co-authors to make it – I think they’ll probably finish up with a kind of A-Z of rainforests. In this example the Switched on ICT unit leads the whole topic.

Not only is Switched on ICT an inspiring way to enliven topics, but it is also really easy to plan and teach from. I’ve had teachers without much confidence in ICT tell me that all they had to do was open up the book, read through the sequence of lessons and begin teaching – which is much preferable to shutting the book and finding excuses for not teaching it – something that I’ve known happen to some other bought-in schemes.

So let’s not go to the ICT suite and make posters. Let’s teach from Switched on ICT instead.

Unconference my planning

Watch on Posterous

The danger of following a spiral curriculum (a la Bruner) is that if you always follow the same path, you hit the same bits of learning at the same point on the spiral. Sometimes that means hitting difficult concepts at the end of a term when everyone is tired.


At GTA UK this year I came across the idea of an ‘unconference’ for the first time. This is where you turn up without a specific agenda, but generate it on the day by the people who are there. Google Docs are an ideal tool for this as many people can collaborate in the same online space at the same time. I decided to do an unconference with my Year 6 maths group to generate the plans for the term. I had no pre-conceived idea of how this might work out except for this:


1. We would start with a wallwisher to discuss ‘What is Maths


2. We would use a Google spreadsheet to think about:
  • what we are good at;
  • what we are not so good at;
  • what we would like to learn this year.
As might be predicted, ‘division‘ came up as the concept that most children would like to learn.


So the next day, the first lesson was on division


  • Social Slider