Differentiation in Teaching for Mastery

One of the biggest misconceptions that I have come across about Teaching for Mastery is that it doesn't involve any differentiation. In some minds, there is a dichotomy between 'Whole class, mixed ability teaching' and 'Differentiated group work'.

How did this arise?

There was definitely a time when differentiation was seen as the answer to all our problems. I used to split my mixed age class into six groups, three from each year, who were all given subtly different tasks, all carefully matched to my perception of their 'ability', which was determined by which table they sat at.
This focus was also political. David Milliband, schools standards minister in the mid-2000s, led the drive toward 'personalised' learning. The dream was that every lesson would eventually be differentiated for every child, using a mixture of Assessment for Learning and the wonders of technology.

And now?

The political climate has certainly changed, and the National Curriculum 2014 is an example - the expectation that children work through the curriculum at broadly the same rate, regardless of their individual needs is explicit in Mathematics , and implicit in many parts of the English and Science curricula.

So no more differentiation?

As anyone who has tried it will know, you can't just give everyone in the class the same task and hope it works. It takes a lot more than that. Differentiation still needs to happen, but with a different aim.
Differentiation becomes about supporting the children who need the support so that they can achieve the same as their peers.

How can we do that?

Once you think about differentiation in this way, it may change practice. 

• Who supports children - peers, the teacher or an additional adult? It needs to be prompt and effective.
• Who gets supported? Do children have a choice of independence and support? Is it flexible?
• How do children ask for support?

How to differentiate?

Lesson planning

The best strategy for supporting most learners is lesson design. A lesson that has a clear focus, and which builds on existing secure knowledge will usually be more successful than a leap into the unknown. Breaking down the structure of a lesson into a series of small, achievable steps that scaffold the development of concepts allows children who take longer to grasp to keep up.

Representations

Clear and consistent use of representations also keeps the focus on shared understanding. Some children are quick to grasp a superficial aspect of a task that enables them to appear successful.

A confident child can sleep through a lesson on adding fractions, because they have noticed you just need to add the numerators to get the right answer. They may succeed in the lesson, but won't have a model that can be extended to different denominators or multiplications.

Strategies for differentiation

This is an endless list, but it may help you to think about the practicalities.

• Some teachers like to give task choices to allow all children to access challenge. The difficulty may be that the child is not equipped to make the choice. Some children will flounder because they like 'to look clever', whilst others stay in the safety zone of something that they can comfortably do.
• Start a unit or block by reviewing the 'known' learning to check for gaps or misconceptions. Don't reteach the previous year, but set a task that involves prior learning.
• Push on number facts early and often so they don't hold children back when they need them.
• Use an additional adult to look for difficulties in grasping concepts or to identify misconceptions. It helps to do this when there is a lot of partner talk or representation going on, so that the adult can listen in. It also means the adult has to 'float'.
• If there are gaps that are not going to be addressed during teaching, provide opportunities for pre-teaching or planned interventions. The focus should ideally be on 'keeping up' rather than 'catching up'.
• Have a planned strategy for supporting these children. This may mean breaking down the task further or modelling it. Try to avoid taking children out of lessons.

Is anybody listening?

Next time you are at a metropolitan dinner party / down the pub, try this conversational gambit:

"Arthur, what do you think about what Sheila just said?"

Chances are Arthur will say something interesting in response to Sheila, whether they agree or not.

Now try the same question in a Maths lesson. No hands up - just 'cold call' a child.

"Sam, what do you think about what Alice just said?"

Half the time I tried this, I got the answer "I don't know, I wasn't listening."

I began to realise that the children in my classes were very good at 'listening', as long as that meant looking at the teacher; they were not accustomed to listening to each other, still less to responding to each other.

If the children in a class don't see that they learn things together, and don't value hearing other answers, they miss out on a lot of valuable experience.

I have tried strategies such as bringing children to the front of class and making them the teacher, but that isn't practical for every response. So I've starting a two fold approach.

First of all I praise good listening. When a child responds to another child, even if it is just to reiterate what the first child contributed, I recognise and praise them for listening well. I try to cold call children who are modelling good listening to contribute and make this expectation explicit. If a child doesn't have anything to say, I ask the previous child to repeat what they said.

Secondly, I've started to use the ABC model for responding to each other. after a co tribute on, I cold call another child and other them the choice of:
A Agree with the first child (and say why)
B Build on the first contribution,  but develop it.
C Challenge the first contribution.

I saw this strategy outlined in 'Making Every Primary Lesson Count' by Jo Payne and Mel Scott

Two visions of Mastery

My main confusion about the NCETM 'Teaching for Mastery' programme was the name. Not the word 'teaching' - that's fairly self-explanatory. The 'for' is also understandable, in the same way that the 'Department for Education' uses the preposition to demonstrate that it isn't actually against education (not all of it, anyway). No, it's the word 'Mastery' that causes the dilemma.

If you look on the Education Endowment Foundation page for Mathematics, Mastery is at the top of the list. Look:

 

However, the definition of Masterylearning provided includes:

Students must demonstrate a high level of success on tests, typically at about the 80% level, before progressing to new content. Mastery learning can be contrasted with other approaches which require pupils to move through the curriculum at a pre-determined pace. Teachers seek to avoid unnecessary repetition by regularly assessing knowledge and skills. Those who do not reach the required level are provided with additional tuition, peer support, small group discussions, or homework so that they can reach the expected level.

Is this the only vision of what Mastery is?

Vision 1: Mastery is personalised learning

There is one vision of Mastery in which students work at their own pace through material, repeating it as necessary until they are sufficiently confident to move on. This approach works particularly well with a narrow curriculum, e.g. one focused entirely on numbers and calculations.
A student is ready to move on when they attain a particular score on a (timed) test. Then they move onto the next unit, and repeat until they have also 'mastered' that one. It could be seen as differentiation taken to the point of a personalised curriculum. Some teachers belief that through artificial intelligence and computer technology it may be possible to achieve this.
This approach may promote confidence in procedures and accuracy in test situations over a deeper understanding of the material. It can be very successful in developing fluency and confidence, but it may not meet the demands of the National Curriculum, in particular regarding conceptual fluency, mathematical reasoning, problem-solving and keeping the class together.
This version of Mastery has been made popular by the Kumon Maths Programme and Sal Khan's Mastery System.

Vision 2: Mastery is whole class

 The second vision of Mastery is one in which all students progress together at the same rate. In this version, the focus is on deeper understanding of the material to 'take up the slack' between differing ability students. It relies on the teacher to assess the whole class regularly and control the pace of learning so that no-one gets too far ahead or behind. When students do start to struggle, they need more and extra support to keep up. This approach focuses on differentation by support and very clear teaching and modelling to keep children working together.
This version of Mastery is heavily influenced by practice in education systems such as Shanghai and Singapore, where very carefully structured and represented material is sequenced to keep children together. Versions of this approach have been promoted by the Ark Schools Mathematics Mastery programme and the NCETM Teaching for Mastery . The NCETM defines Mastery as

At any one point in a pupil’s journey through school, achieving mastery is taken to mean acquiring a solid enough understanding of the maths that’s been taught to enable him/her move on to more advanced material

What is the difference?

In a personalised curriculum, children may progress at different paces. Some children may take a long time to master some ideas. Some children may make accelerated progress as result of grasping (or appearing to grasp) ideas more rapidly. This can be attractive to some parents.
In an Asian-style 'whole class' curriculum, children progress together. Some children may need more Maths teaching to keep up. All children develop understanding at a slower, but deeper pace. This approach should diminish the apparent gaps in attainment between groups of children. This can be attractive to schools (and governments).

What is not Mastery?

If these two visions seem like polar opposites it's worth considering what they have in common. Both contrast to a view of education in which, to quote the EEF report above, "pupils.. move through the curriculum at a pre-determined pace". This approach, which was commonly found in schools following the National Numeracy Strategy and the schemes and textbooks based upon it, focused on coverage of the curriculum rather than Mastery of it.
The NNS focused on whole class teaching, with differentiated tasks to allow different groups of children to achieve different outcomes. The sequence of lessons continued regardless of the competence of the children, but employed a 'spiral curriculum' model where each topic was revisited every term. Children who struggled with a concept were expected to improve next time they reached it. As a consequence the gaps between the majority of children who mastered the material and the minority who didn't grew over time, resulting in more differentiation, resulting in widing gaps between children who could and could not do Maths..

What is Mastery?

Whichever model you subscribe to, there are some key ideas behind any vision of Mastery.

1. Mastery is for everyone. It is based on a belief that all children will achieve.
2. Assessment is important. Teachers need objective evidence of what children have achieved and can do.
3. Teachers need to move at the pace of the child, and not 'cover' the curriculum. I would argue teachers should not even consider 'delivering' the material for their year group, but instead focus on the current understanding of their children.
4. Teachers need to start where the child is, and progress through a series of clearly defined points, checking for understanding as they go.
5. Mastery needs to be seen as a whole school journey, not as the progress from the start to the end of a particular year group.