IDEAS FOR MASTERY THE MASTERY MODEL


A ‘CAN DO’ APPROACH TO THE ‘CAN’T DO MATHS’ PROBLEM


Every learner can succeed at maths – that’s the starting point of maths mastery. So how can it help bring along students of all abilities? By Laura Shenker


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eaching for mastery is to teach with the highest expectations for all learners, regardless of their background. Mastery emphasises


the importance of deepening students’ understanding of a subject, so it is secure enough to allow them to critically engage with new content areas and apply their prior learning to develop their understanding. Dr Helen Drury, executive director of Mathematics Mastery, defines knowing you’ve mastered something in mathematics “when you can apply it to a totally new problem in an unfamiliar situation”. Mathematics Mastery, a programme that supports more than 170,000 teachers in over 540 schools in the UK, uses the mastery approach throughout its curriculum and its teacher professional development programme. The approach is founded on core


mastery principles: conceptual understanding, mathematical thinking, and language and communication. Each of these is linked to strengthening students’ approach and resilience in the face of mathematical problem-solving.


TOP TIPS FOR MATHS TEACHERS TO ENGENDER MASTERY


1. Build a safe space in your teaching area where your students are encouraged to explore different ways to solve problems.


2. Examine multiple representations (pictures, manipulatives) of different concepts to build a deeper understanding of each domain.


3. Challenge students to justify their approach and reasoning to their answers – ask if the solution to a problem would differ when a variable is changed and why.


4. Ensure students are taught, and continue to use, accurate mathematical language in full sentences to express their reasoning.


5. Use positive language to encourage students to not give up and build resilience to problem-solving.


6 AUTUMN 2019 • InTUITIONMATHS


Conceptual understanding Through using objects and pictures (consider what suits the needs of your students) to represent abstract mathematical concepts and ideas, students can solidify their understanding of different domains. These practical representations of mathematical concepts allow students to experience the concept before simply copying it down, ensuring they understand the maths behind the mathematical expressions they write. Using different methods also allows students to make connections between different areas of mathematics, deepening their understanding. By asking students questions such as


“what’s the same and what’s different?”, with different representations displayed or accessible to them, teachers can facilitate their learners to spot patterns and make connections. Students can continue to build on these patterns and connections as they progress through new content areas.


Mathematical thinking Mathematical thinking is equally important to supporting students to become resilient problem-solvers. Teachers and trainers should encourage students to question in mathematics and apply different techniques to support them to solve mathematical problems. The techniques can vary from asking students to specialise (providing an example), to correcting (asking what needs to be changed), to convincing (asking a student how they are sure about their answer).


This is underpinned by instilling a mindset in students that they can succeed if they make the effort, and supporting them to keep trying.


The mastery model of teaching and learning has had success in Shanghai and other international settings. The approach rejects the idea that some people ‘just can’t do maths’, encouraging learners to believe that they can succeed.


The focus is on all learners working


together on the same lesson content at the same time. This is intended to ensure that all students master concepts before moving to the next part of the curriculum sequence, leaving no individual behind.


Language and communication A crucial strand in developing students’ conceptual understanding and mathematical thinking is for teachers to use language that challenges the students, prompts them to make connections and spot patterns, and provides them the freedom to explore mathematically. To support their development, it is essential that students are taught to use mathematical language accurately and confidently. Teachers should support students to use considered full sentences to describe their approach, judgement and reasoning when solving a mathematical problem. Reflective exercises are a way of


reinforcing the use of accurate mathematical language, as they allow students to consolidate their knowledge across different domains and consider how they have used their prior learning to approach problem solving. Teachers are encouraged to adapt the techniques discussed to their own settings to meet the needs of their students. However, students must be empowered to explore mathematical problems in order to achieve mastery. They must be encouraged to approach


a problem using a variety of techniques, consider multiple representations to solidify their reasoning and feel confident expressing this using accurate language. To empower their students, teachers must create an environment in the classroom where all students feel they can succeed in and enjoy mathematics.


Laura Shenker is director of design and development at Mathematics Mastery, a non-profit organisation looking to improve maths education in the UK by using mastery approaches to learning.


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