Helping students on their journey towards mastery is exactly what White Rose Maths exists to do. It isn’t always an easy journey, and it’s important to realise that there’s more than one way to get there. Here are some of the issues that fellow teachers often ask us about, together with our thoughts:
How do you know when a student has mastered something?
We think mastery of anything – playing an instrument, speaking a new language, mathematics – takes a very long time. That’s why we talk about the “journey to mastery”, rather than “having mastered”. For example, children start learning to add in early years and keep developing their skills over many years – from single digit numbers, to multi-digit numbers, then decimals, then fractions, then negatives, addition in different units (such as time calculations “35 minutes after 12:45pm”) etc. It would take several years to master addition, arguably one of the most basic concepts in mathematics so what we do is break the journey down into small steps, spending time carefully considering each. Through intelligent practice and building up experience of different contexts, gradually we move towards mastery where studnets are fluent in the unfamiliar and can apply their skills in any new situation.
How do we get through all the curriculum if we’re meant to spend time studying each topic in depth?
We recognise that time is an issue and it’s not easy to cover the full content of the curriculum in the depth we would wish too. Our curricula, both primary and secondary, are designed to give time to think about a topic and develop understanding and also to realise that mastery will not have been achieved by the end of the unit, whatever its length. Our small step approach is designed to ensure that students will come back to topics time and time again, both within the study of the same area of mathematics and in other areas so that they will continue to deepen their understanding through this revisiting and interleaving.
Does teaching for mastery mean we have to teach in mixed attainment classes?
We believe that schools should make their own decisions regarding how to organise their classes, based on their knowledge of their students and their staff. We recognise that both setting and mixed attainment grouping have advantages and disadvantages and good teaching can ensure success in either. It’s important to remember that even in sets, there is always a wide range of prior attainment and students have different needs. To dispel a common myth, teaching for mastery does not mean we do not differentiate, whatever the grouping, but we do aim high for all students. Certainly it may be a concern if a teacher was teaching a mixed attainment class and splitting the class into a higher group, a middle group and a lower group where many students are denied access to particular aspects of the curriculum. Similarly, it would not be appropriate for some students to work only on fluency, others on reasoning and a select few on solving problems. We believe all students should have opportunities to develop reasoning and solve problems as well as develop fluency. Differentiation can be achieved, for example, through varying the degree of support provided, using enabling and extending questions, and providing or asking for alternative representations whatever type of grouping a school chooses to adopt.
Why do you say “mixed attainment” instead of “mixed ability”?
We think that using the language “low ability” can sometimes lead to low expectations and question how “ability” can reliably be measured. We also firmly believe in a “growth mindset” approach and that everyone can get better at mathematics We know from experience that some students can start a year, a key stage or a new school with relatively low prior attainment but over the course of the next term, year etc. rapidly improve and end up as high attainers. It’s their attainment that has changed, not their ability and they had the potential to succeed all along. Because of this, we avoid the use of the word ability all together and talk about attainment – we usually know what students have attained previously and provide all students with the opportunities to improve and succeed.