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Purposeful Maths Calculation Policy

Calculation Policies are a contentious topic, and we know there are many sides to this debate. We have taken the time to write this short blog to introduce our calculation policy for several reasons:

● Explain the background to why we have introduced one

● Explain how we use it

● To receive feedback (both positive and constructive) so we can improve it!


We think a great starting point for this is to read Jo Morgan’s blog on “Autonomy Vs Consistency” which can be found here ( Like all of her work, it gives you something to think about. It goes into great detail and is a fascinating read. What resonated with us is the “Autonomy Spectrum'' she explained, shown below:

I am lucky to lead an experienced department made up of great teachers who are all subject specialists, so our intention is definitely not the red zone. Whilst this may work best in some situations it certainly would not be the best for my department. I believe the sweet spot for my department is somewhere between the third and fifth block from the left. I would like some consistency to help students when they move between teachers (due to split classes, changing sets, or new academic year) without turning my team into robots who would be restricted with zero autonomy.

We have centralised assessments and feedback policies to ensure each student is hitting the same check points and receiving consistent feedback. Our schemes of learning have clear paths to take and what topics should be taught. However, the class teacher can choose which “abstract” method they believe fits the class best.

The four stages: Physical, Pictorial, Semi-Abstract, Abstract

Each “sub unit” in our schemes of learning has these 4 stages mapped out in our calculation policy using a specific example.

We had spent some time looking at the concrete – pictorial – abstract model but found the gap between pictorial and abstract was too wide. Hence, we introduced a “semi-abstract” stage with the aim of making this step more manageable.

Each class starts at the “physical stage” and moves right as they understand the steps. How long a class spends on each stage is up to the class teacher. The aim is for each student to eventually get to the abstract stage so they can solve problems efficiently. However, if students are comfortable at a previous stage and are understanding the work they don’t have to get to the abstract stage. For example, expanding double brackets:

Some students may feel comfortable using the semi abstract method (grid method in this case) but start to make mistakes when moving to the abstract method. Staff don’t have to move students to the abstract stage initially. It is important all students have the same experience though, as when this topic is revisited later in the year (or future years) the child may have a different teacher and we want to be able to go back to familiar methods.

Didn’t you say teachers can choose the methods they teach?

They can, and they do! The “abstract” method is where we would traditionally start teaching and staff can still choose methods that they prefer. The ones in the policy are methods we often use – but are not limited to. The introduction of manipulatives is new to the department and we are doing a lot of work to embed them in our practice. Therefore, the policy is designed to show teachers how best to use them for each topic – as this is where we lack experience. The policy was put together to reduce workload so individual staff members didn’t have to think about how to use the manipulatives. We then centrally plan examples, and spend department time solving problems. It is a working document that the department are trialing this year. At regular intervals we will discuss what is working, what isn’t, and what needs tweaking.

We welcome feedback on it, as we aren’t for one second saying it is perfect! However we think it is a great starting point for discussions!

Thank you for reading,

Phil and Martin

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