Teaching for Mastery
A mathematical concept or skill has been mastered when, through exploration, clarification, practice and application over time, a person can represent it in multiple ways, has the mathematical language to be able to communicate related ideas, and can think mathematically with the concept so that they can independently apply it to a totally new problem in an unfamiliar situation.
The approach is motivated by a commitment to transforming achievement for all. This means placing a high value on mathematics education, promoting a growth mindset, focusing on every child achieving a high expected standard.
At Chilwell Croft Academy, we follow NCETM (National Centre for Excellence in the teaching of Mathematics) objectives for all year groups which clearly supports ‘Teaching for Mastery’ approach.
In our school, to be consistent with the new curriculum following a mastery approach of catering for different attainment levels within a classroom, we include giving pupils differing amounts of time using concrete resources to help them grasp concepts. To stretch and deepen the learning of the ‘rapid-graspers’, more challenging questions and problems to work on and reason about, are provided in the lesson.
The whole class teaching model—a key feature of teaching for mastery—can sometimes look slower than usual. But, the focus will be on the depth of pupils’ learning hence making a high impact on teaching.
Concrete – Pictorial – Abstract
Concrete – opportunity given to children to use concrete objects and manipulatives to develop an understanding of what they are doing
Pictorial – children should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.
Abstract – with the foundations firmly laid, children should be able to move to an abstract approach using numbers and key concepts with confidence
To ensure children are able to be fluent with a good ‘sense of number’, pupils need a range of experiences where they can talk though strategies, discuss possible answers and justify their outcomes. Children need to know ‘how’ and ‘why’ numbers work the way they do and be able to explain this.
Reasoning is a daily expectation within Maths lessons to allow children regular opportunities to explore numbers, make conjectures, investigate patterns, explain possibilities and represent findings.
We implement a 5 step progression to reasoning which shows the stage within reasoning that children are working at, based on the NRICH ‘hierarchy’ of reasoning skills:
Step 1: Describing-Simply saying what they did, say what they see
Step 2: Explaining-Offering a reason for what they did.
Step 3: Convincing-Convincing themselves or a friend that they have a solution or case.
Step 4: Justifying- say why they are convinced
Step 5: Proving: provide an argument that is mathematically sound, often based on generalisations. Making a watertight case, and proving it using resources if necessary. At a higher level, this leads to developing an algebraic proof.
The hierarchy informs our questioning and expectations.
- Finds the unknown elements in the context of part/part/ whole relationships. This supports the development of algebraic thinking.
- Makes an abstract word problem or equation pictorial (concrete – pictorial – abstract)
- Allows for deeper analysis and understanding of the problem by teaching children to:
Identify all information given and its relationship to other pieces of information
Identify missing information that needs to be found
Understand what mathematical operation to use to find the answer
Chilwell Croft will begin a full implementation of Inspire Maths across the school in September 2017, so we are in our early phase. It is a whole-school primary maths programme that provides everything we need to support an approach to teaching and learning mathematics which is greater in depth and meets the higher expectations of the 2014 National Curriculum.
Inspire Maths is a transformational, whole-school approach, to raising pupils’ achievement in maths. The programme of resources is built upon the internationally acclaimed approach to teaching mathematics in Singapore. Published by Oxford University Press it is based on the leading Singapore Maths series ‘My Pals are Here’.