“Pupils enjoy mathematics and demonstrate a high level of confidence when tackling new concepts. Pupils know how to improve in mathematics, because teachers check pupils’ understanding carefully and quickly address any misconceptions during lessons. Teachers provide pupils with lots of opportunities to explain their reasoning and to apply their mathematical skills in problem-solving activities. Pupils are confident to apply their mathematical skills consistently well across the curriculum”
The Mathematics Mastery approach has three key principles: deep understanding, mathematical thinking and mathematical language, with problem solving at the heart of our curriculum.
We believe students should:
- Make connections between previous learning and their current thinking,
- Deepen understanding through the application of a concept,
- Research and seek information.
We believe that students should:
- Explore, wonder, question and conjecture,
- Compare, classify, sort,
- Experiment, play with possibilities, vary aspects and see what happens,
- Make theories and predictions and act purposefully to see what happens, and generalise.
We believe that pupils should be encouraged to use mathematical language throughout their maths learning to deepen their understanding of concepts.
Problem solving is at the heart of mathematics. We believe that problem-solving is both how and why we learn mathematics, and that it should be integrated throughout every lesson to develop students’ depth of understanding of the subject. Students must be encouraged to explore, recognise patterns, hypothesise and generalise in their learning. Straight-forward tasks can be converted into opportunities for students to investigate, seek solutions, make new discoveries and reason about their findings.
We use a concrete-pictorial-abstract approach in lessons, so students can deepen their understanding of mathematical concepts through a variety of representations.
- Concrete – the doing – At the concrete level, tangible objects are used to approach and solve problems. Almost anything students can touch and manipulate to help approach and solve a problem is used at the concrete level. This is a ‘hands on’ component using real objects and it is the foundation for conceptual understanding.
- Pictorial – the seeing – At the pictorial level, diagrams and other visual representations (e.g. bar models, number lines, diagrams, charts and graphs) are used to approach and solve problems. These can often be pictorial representations of the concrete manipulatives, in which case it is important for the teacher to explain this connection.
- Abstract – the symbolic – At the abstract level, symbolic representations are used to approach and solve problems. These representations can include numbers or letters. It is important for teachers to explain how symbols can provide a shorter often more and efficient way to represent mathematical relationships and operations.
- Fixed mindset – this is someone who believes ability and intelligence are things that you are born with. They believe natural talent alone creates success and one doesn’t need to put much effort into achieving things they are naturally good at. People with a fixed mindset tend to give up easily with tasks, as they get upset by mistakes, and are afraid of challenges and failure.
- Growth mindset– this is someone who believes intelligence and ability can be developed over time through effort, dedication and hard work. They tend to persevere with tasks and enjoy challenges due to the belief that effort needs to be expended to learn. People with a growth mindset believe they can be successful if they apply effort and hard work, and are more likely to continue working hard despite setbacks.
So how does this relate to maths? In the UK, our attitude towards maths is very much in a fixed mindset. We often hear people say they are ‘rubbish at maths’, but if children hear this, it could encourage them to believe that maths isn’t important.
At Mathematics Mastery, we promote a growth mindset belief – that all children can achieve regardless of their background. To encourage children to develop a growth mindset around maths, the way in which we speak to pupils is very important.
Mastery objectives are cumulative.
5 year plan
Our curriculum is designed to help students to truly master mathematics, so they can apply their skills in unfamiliar situations whenever needed. We don’t believe in unnecessary repetition in Key Stages 3 and 4 and our plan covers the whole secondary period. Students should continually use prior knowledge alongside new learning in as many future lessons as possible as well as in other areas of the curriculum and beyond. This continual recapping supports a deep conceptual understanding of how those concepts interact with others in mathematics.