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How can you implement a mastery approach in primary maths?

Monday, 20 June 2016
There are a lot of schools trying to adopt a mastery approach in the teaching of mathematics. This is a positive move, but does not always involve a complete change of your pedagogy. Here is an outline of the main elements of a mastery approach and how these can be incorporated into your planning.
The term ‘mastery’ has been used in terms of the approach but also for assessment and even the curriculum. I see it mainly in terms of an approach and feel that there are certainly elements of this that are having a positive impact on our primary maths teaching. Ultimately, a successful mastery approach can be achieved through thorough step by step planning and a sound pedagogical subject knowledge of mathematics – both key elements of great teaching.

There are two assumptions with encouraging schools to adopt a mastery approach, firstly, that teachers are not already checking that children have mastered a skill, concept or procedure before moving on, and secondly, that the mastery approach is a completely new idea from Shanghai/Singapore rather than a new emphasis within an existing pedagogy. Have a look at your own teaching first, evaluate what works well and pinpoint areas that could be improved. Then see if any of the following strategies would help with this. 

So how can you implement these main elements of a mastery approach into your teaching?

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Most teachers will be eager to support any measure that improves teaching and learning for their children and will want to consider best practice in primary mathematics teaching. It is valuable to look at current, old and new ideas and focus on aspects that can be used successfully on our classrooms to improve standards. 

An outline of the mastery approach:

•  class working together on the same topic
We have had a strong emphasis on every child making progress in every lesson and this was achieved through differentiation, by having different groups working at different levels and sometimes individual children working at their own level. Perhaps this had too much focus and it was sometimes difficult for teachers to manage in practice.
Now the emphasis will be on keeping the class together until specific concepts or skills are mastered and then moving them on together. This doesn’t mean that all children will be doing exactly the same content, which will invariably leave some behind and not challenge those that are ready to move on. It involves effective use of models and images to support understanding and represent the mathematics and carefully planned problems and challenges.

•   speedy teacher intervention to prevent gaps
If some children have not met the expected outcomes or have gaps in their understanding, many schools are giving them short, immediate extra time on maths later in the day. Obviously implementing this is dependent on the staffing in your school. If a child hasn’t grasped a skill, concept or procedure it is not because the child is not able, but that the teacher, as yet, has not shown them the most appropriate representation of that idea. It is not going over the same content from the lesson, but using alternative approaches. Whether you have the time to either plan for these extra sessions or give 1-1 support later in the day will be an issue in achieving this. If it is left to TAs then they need to have resources available to use which would probably be generated by teachers.

•   challenge provided by going deeper not accelerating
For those children that have mastered the skill, concept or procedure then they should not continue to the next stage, but should be presented with higher order thinking tasks, ideally related to the maths focus. This is where a bank of problem solving activities and investigations is important so that they can be planned and prepared for. (Broadbent Maths users can find activities linked to each unit from the Class Planning pages for each year group).
•  teaching is focused, rigorous and thorough

This is where a teacher’s knowledge of mathematical structures and small steps of progression within a maths topic is essential. (For Broadbent Maths users Small Steps of Progression for 19 different maths strands).
The idea is to focus on one small step at a time in a lesson, with an emphasis on the mathematical structures involved. Following this ‘clarifying’ part of the lesson there should be some practice, including the use of variation so children can begin to see patterns and rules.
•  more time on teaching topics - depth and practice
‘More time’ is subjective and has been interpreted in different ways. If you consider the pace of the numeracy framework where sometimes a topic was only allocated 2-3 days, then 1 week on a topic would be ‘more time’. In my experience, 2 weeks is a good length of time to give depth on a specific area of focus.
So how long is a long time? Basically, until a child has mastered the concept, skill or procedure being taught.
•  carefully crafted lesson design - scaffolding
The actual structure of the lesson or sequence of lessons needs considering. An explore-clarify-practice-extend-review model over several lessons works well, giving opportunities to provide further clarification through whole class teaching followed by specific practice. The aim is to move children towards independence, so careful scaffolding of support is in place, with the responsibility slowly shifting over to the children for their learning.
•  engaging pupils in reasoning

Children should be given every opportunity to solve problems to apply the skills, concepts and procedures they are learning, and also to allow them to reason and think mathematically. Nothing new in this and it is not particularly linked to the new ideas from SE Asia who largely took their approach from the Cockcroft Report from 1982. However, reasoning and problem solving is not always easy for a teacher to make central to the approach in a class, particularly if the focus is on learning skills or procedures. It involves careful questioning and the types of activities that give opportunities for exploration and play. Time needs to be allowed within a lesson sequence for children to reason and think about their maths and explain their reasoning, verbally or in written form.

Related articles

Teaching mastery - will you use the NCETM assessment materials?
These are available free to schools. 

Do we need textbooks to teach primary maths? And if so which ones?

In Shanghai and Singapore there is good use of textbooks

Are blocks of longer units the way forward when plannign maths?

Mastery involves spending longer on a topic - but is this instead of a spiral curriclulm?

Teaching maths to include variation to help understanding

Teaching maths to include conceptual variation
Both procedural and conceptual variation are used well within teaching maths in South East Asia.

Mastery in maths - using a twenty-frame to represent addition

A mastery approach to maths includes the careful use of appropriate models and images. 
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