Why Mastery?
You might be forgiven for assuming that primary schools in England are not very good at teaching maths. There was a time when that might have been true (probably just before I became a teacher). But our position in international comparisons has been rising steadily for 20 years.It's probably no coincidence that the vast majority of the increase takes place between 1999 and 2007, the years of the National Numeracy Strategies. In fact, our 2015 score places us firmly in the second highest performing group of countries, along with Russia, Ireland, Norway and Belgium.
That's a great place to be; but the gap between England and the next highest performing group of countries is a statistically massive 27 points. The highest performing group of countries are all East Asian - Singapore, Japan, Korea, etc.
What can we learn from East Asian countries?
It would be ridiculous to throw out all the improvements we have made in the last 20 years and try to import the 'Shanghai approach' or the 'Singapore approach' wholesale. But there may be things that we can learn from these countries:
1. Whole class teaching
Whole class teaching doesn't have to mean passive learning. It can incorporate pair work, group work and investigations, but the expectation is that the class will be learning the same thing at the same time. The National Curriculum(2014) has the expectation that the 'majority of pupils will move through the programmes of study at broadly the same pace', and it's very hard to achieve this if pupils have different learning objectives.
This style of teaching that goes back and forth between teacher led and group led is often called 'Ping Pong'. It's a world away from the 'input - independent - plenary' triad of the Numeracy Strategy.
2. Mixed-Ability classrooms
My hackles tend to rise at the word 'ability', because, while we all certainly have different abilities at different things, these are not fixed. Our abilities change, as we grow and learn. I was a 'low ability' artist at school. I'm an acceptable sketcher now. It just took me longer. I accept that children will grasp things at different rates, and good teaching takes account of this. I don't accept that the child's prior attainment dictates their future capabilities.
In many high-performing countries, such as China, children are not put into sets, streams or groups for Maths in primary schools. This doesn't mean we should not differentiate, but we should base this on what the children can and can't do now, not on prior attainment data that labels them 'higher' or 'lower'.
3. Small Steps
If the whole class are moving together, they all have to succeed. It's no good half the class achieving the learning intention, and the other half picking it up at some later point. So the learning has to be broken down into small steps, that everyone can understand, and sequenced carefully, so that learning builds on firm foundations. Shanghai teachers have a massive advantage here, in that they tend to teach maths across year groups, and so are more aware of the sequence of steps.
4. Challenge and depth
Learning isn't a passive process, at least according to constructivist models. Mastery lessons often start with a real-life scenario or a problem for children to explore and represent, leading into discussion and the examination of strategies to solve it. They link into prior experiences.
The use of variation also creates challenge throughout the lesson along with the expectation that children can explain a process rather than just get to an answer. It's common to include a challenge question to make children think deeper - but this is for the whole class, not just the 'higher attaining'.
The use of variation also creates challenge throughout the lesson along with the expectation that children can explain a process rather than just get to an answer. It's common to include a challenge question to make children think deeper - but this is for the whole class, not just the 'higher attaining'.
4. Representation and Structure
English schools are aware of the value of 'Concrete-Pictorial-Abstract' and the constructivist work of Jerome Bruner. Singapore schools embed this firmly in their exploration of mathematical concepts. Shanghai schools are less wedded to concrete resources, but they use lots of structured representations of number, such as tens frames. The use of a structured representation makes it clear what the
5. Variation
This seems to be quite unique to countries like China, where children are taught from very early on to search for patterns and to see connections. When planning a lesson, teachers use variation to make concepts clearer, such as showing different representations or making subtle changes to a process. When setting tasks, there is often a patterns or a link between the examples that draws out the structure of the mathematics.
6. Sentence Stems
There has been a lot of work done in the last ten years on 'Success Criteria' in English classrooms, largely based on the work of Shirley Clarke. A sentence stem is a model for children to follow, that focuses on the key aspect of the lesson. This allows for chorusing and repetition: 'I say, you say, we all say', as well as a 'hook' to refer back to in subsequent lessons.
7. Textbooks
You can't help noticing that many of these countries use a single textbook, usually produced by a central agency. Whilst this is may be helpful, it doesn't teach the children - there is no substitute for a well-designed lesson and teacher subject (and pedagogical) knowledge. The DfE's attempt to produce a choice of textbooks that embody the above principles has been an shambles so far, but hopefully things will improve as publishers catch up.
So what is a Mastery Curriculum?
A mastery curriculum is one designed for the children to move through at the same pace. It is carefully designed so each step lays the framework for the next and each concept is developed in enough detail that it becomes embedded. It provides enough challenge for the children who see the concept readily, and enough time for those who need it to become proficient.
I'm not saying for a moment that I think our current Mathematics National Curriculum comes anyway near this. Concepts are introduced too early (multiplication and division), some objectives are far too complex and some are repeated or missed out entirely in some year groups. A few make no sense.
What it is and what it isn't.
A key idea when illustrating maths concepts to children is to show a non-example as well as examples (standard and non-standard). So:
Teaching for Mastery is:
- A set of principles.
- All children in the class (with very few exceptions) working together.
- High expectations for all children.
- Small steps that everyone can succeed in.
- Engaging and fun.
Teaching for Mastery is not:
- Passive learning.
- A published scheme of work.
- A scheme of work produced by a Maths Hub.
- A one-size-fits-all pedagogy.
- Something Ofsted are looking for.
- Something Ofsted are against.
- The end of differentiation.
- Turning the tables to face the front.
- Using a Powerpoint in lessons.
- Using a certain set of physical resources.
- Holding back high-attaining pupils.
- Something that we can start doing tomorrow.
