Firstly, it is important to pause and think about all classes. Any class of pupils with more than one pupil in it is a mixed ability class. Ability is an index of learning rate – it is about how readily a pupil acquires understanding of a novel idea. It is not fixed and can change from topic to topic. In a mastery approach, we want pupils to progress through learning mathematics together. So, very large differences in learning rate can introduce difficulties in timing this progression. There is no way around this, there is no way of aligning pupils’ learning rates. But there are easy and effective strategies for addressing the issue. For example, different pupils could have different prep or consolidation activities.

It is also true that all classes containing more than one pupil are mixed attainment classes. Attainment is a measure of where a pupil has reached in their learning of a domain. There are no particularly accurate ways of measuring this, so, at best, it’s a pretty broad statement. Working in a mastery approach with pupils of mixed attainment is necessary because all classes are. The issue is when the difference in attainment becomes large.

Nobody would suggest, for example, putting a pupil who cannot yet count in a class with a pupil who is working on second-order differential equations is a good approach. So, there is general agreement that there is some point at which the differences in attainment becomes large enough to warrant pupils following different courses.

The question is, how large? And how large are schools being asked to cope with?

Well, actually, the differences can be really rather large and a mastery approach can still be highly effective. A key ingredient of a mastery approach is diagnosing and fixing any gaps in prerequisite knowledge before pupils begin to learn a new idea. Done well, this can ensure that pupils with quite different prior attainment can work on new ideas at the same time and at pace.

However, some schools are being asked to work with differences that are so large that the effectiveness of the approach is compromised too severely. What to do? Well, perhaps, as many schools have done, use in class groupings. This can work with a mastery approach, but it is extraordinarily complex and creates a huge work burden for teachers.

Fundamentally, a mastery approach is just not compatible with a large attainment gap. I would therefore advise any school wishing to use a mastery approach to avoid mixed attainment classes.