How do we know when a child has really understood a new mathematics concept? Is it when they can show a whole page of ticks? Or when they can answer related word problems? Or is it when they get the question right in a test?
As an SLE for primary mathematics, I have the luxury of regularly visiting schools in my local area to support in the development of standards in mathematics. The staff are enthusiastic and hardworking, as are the majority of the pupils, but too many times in schools, teachers will consider that the pupils can ‘do’ fractions or angles (or whatever is being taught) and are frequently proud to tell you that pupils are now working on the next year group’s content. What the children have not had is the opportunity to apply their learning and gain a full understanding. Time to introduce the Mastery Approach!
The key idea of mastery is that pupils gain a deep understanding of the mathematical concept being taught, so that they can apply it to new situations and contexts. If you consider the statement, “I can do multiplication”, what would you want pupils to be able to do? Fluency in mental and written calculations is your basic level of skills, but this is just the tip of the iceberg. You would want to see that learners can represent multiplication in different ways – using concrete, pictorial and then moving to symbolic representations. You would want pupils to be able to make connections to repeated addition, use arrays, link to division and use accurate vocabulary to explain and reason about their work. Real-life word problems to provide context and purpose for learning are essential, but similarly is the application to puzzles, problems and investigations to promote deeper mathematical thinking.
But all this application results in moving more slowly through concepts and will take time to develop thoroughly, slowing progress in an already overloaded curriculum. Yes, a thorough exploration of concepts in detail will take longer however, more time spent in depth means that pupils gain a better understanding, which means that on return to a concept, the children need far less repetition before moving on. In addition, continuous links made to other areas of mathematics will revisit these much more frequently and connect ideas rather than fragment mathematics topics.
Another feature of the mastery approach is the importance of high expectations - that all pupils are capable of achieving high standards and that the majority of learners will progress at the same pace. Initially this often results in mutterings of disagreement when you introduce this to teachers. However, with carefully considered planning, this is very achievable. Differentiation is provided through the support of the less able, with fluency taught through essential practice and consolidation tasks, teaching conceptual understanding through multiple representations and dealing with misconceptions immediately. Those pupils who have achieved fluency can move on to the application of skills in different contexts. More able learners are challenged through higher order questioning and rich tasks that develop problem solving and reasoning skills. No one moves onto a higher year groups objectives, everyone is working on the same concept, and it is possible to provide whole class lessons but with different levels of support and challenge.
Within a short period of time, the introduction of the mastery approach has had significant impact for both learners and teachers in my school. Pupils are much more secure in their understanding of mathematical concepts, talking about their work with increased confidence, using accurate vocabulary and pictorial representations to aid explanations. The less able have particularly benefitted, by demonstrating much greater progress. Higher ability children are being challenged in a wider variety of ways, are more deeply focussed and show greater levels of resilience through stimulating tasks. Teachers are finding the whole class approach more manageable and the lack of groups in the class ensure that pupils are given greater opportunity to access a level of work that they may not have been able to before.
So is the mastery approach just another initiative for teachers to contend with? Definitely not. Whatever further changes in curriculum content we may have in the future, the mastery approach is high quality pedagogy, aimed to help every child succeed in mathematics.