Many schools in England are now adopting a Mastery approach to teaching various areas of the curriculum, including mathematics.
However, interpretations of what this means vary. The National Centre of Excellence in Teaching Mathematics [NCETM] has a whole area devoted to exploring and explaining what this approach might involve: please see https://www.ncetm.org.uk/resources/47230
Below we have summarised some of the key points and ideas about this approach:
Concrete, Pictorial and Abstract
The value of using concrete materials and practical resources to support and extend learners’ understanding is fundamental to mathematics pedagogy. However, there can be a need to ensure that learners see the abstract mathematical statements alongside their practical experiences in order to reinforce the link. It can be useful to say, ‘This is how a mathematician might record this’. The use of pictorial images can reinforce the links. The Emile suite of games provides a seamless link between the pictures and the abstract concepts. Engaging with Emile’s adventures offers memorable experiences that children can draw upon and visualise when thinking about their mathematics.
Varied and intelligent practice
Many of the ideas behind a Mastery curriculum originated with the Cockcroft report (1982). These have been developed and used successfully in other countries, including Shanghai and Singapore. Teaching materials from these countries often stress the value of variety and practice – different to mere rote learning, in which concepts and ideas are applied in a range of meaningful settings.
Talk in the classroom
The value of rehearsal, sometimes chanting of key facts can aid memorisation, as we know from all the work that teachers have always done on the multiplication tables. Alongside such rehearsal and group chanting, there is an important place to talk in the mathematics classroom. It is from opportunities to talk with other pupils and their teachers that children begin to develop their mathematical reasoning and learn how to explain and justify their ideas. Think about how you organise your classroom to facilitate this.
Teachers in Shanghai and Singapore focus on one key idea in each session and spend time on ensuring that the children all understand this, rather than moving more rapidly through a range of ideas- pace in learning is what matters to them.
Careful assessment enables teachers to identify and address any misconceptions rapidly- teachers offer formative feedback whilst children are working, rather than marking piles of books later in the day. Homework is also set to ensure that the children’s understanding is secure.
Of course, there are significant cultural differences between England and these countries but this does not mean that we cannot learn from them, nor that they can learn from us!