In this three part series, I’d like to discuss about what Mastery means in teaching and learning Maths, what active learning means, and if and how the two interplay with each other.
What is Mastery?
The essential idea behind mastery is that all children need a deep understanding of the mathematics they are learning. It is not just being able to memorise key facts and procedures and answer test questions accurately and quickly. It involves knowing ‘why’ as well as knowing ‘that’ and knowing ‘how’. It means being able to use one’s knowledge appropriately, flexibly and creatively and to apply it in new and unfamiliar situations.
Broadly, the mastery approach includes, but not limited to, the following:
Intelligent Practice: The arrangement of tasks and exercises to draw pupils’ attention to patterns, structure and mathematical relationships.
Variation Theory: What is same and what is different in a given set of tasks
Multiple representations: Pictorial, concrete and abstract representations of mathematical concepts
There is also an explicit focus on covering one topic in great depth and moving on to a new topic only when the child’s understanding is secure in the previous topic. The whole class ends up doing the same activity at the same time, with the pupils who need to be challenged given questions of greater depth on the same topic, rather than being given a different topic.
From a pupil’s point of view, a pupil really understands a mathematical concept, idea or technique if he or she can:
- describe it in his or her own words
- represent it in a variety of ways (e.g. using concrete materials, pictures and symbols – the CPA approach)
- explain it to someone else
- make up his or her own examples (and non-examples) of it
- see connections between it and other facts or ideas
- recognise it in new situations and contexts
- make use of it in various ways, including in new situations
Developing mastery with greater depth is characterised by pupils’ ability to:
- solve problems of greater complexity (i.e. where the approach is not immediately obvious), demonstrating creativity and imagination
- independently explore and investigate mathematical contexts and structures, communicate results clearly and systematically explain and generalise the mathematics.
In the next post, I will discuss about what Active learning means. Meanwhile, I’m curious to know, what is mastery, from your perspective?
- Teaching for Mastery: Questions, tasks and activities to support assessment, Mike Askew, Sarah Bishop, Clare Christie, Sarah Eaton, Pete Gri n and Debbie Morgan, https://www.ncetm.org.uk/public/files/23305581/Mastery_Assessment_Y3_Low_Res.pdf, 14/10/2015
- Intelligent Practice, http://www.mathshubs.org.uk/bespoke/april-2015/intelligent-practice/, 14/10/2015