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.