Philosophy and Vision
The Mathematics Mastery approach has three key principles: deep understanding, mathematical thinking and mathematical language, with problem solving at the heart of our curriculum.
Deep Understanding
We believe that every student is entitled to a deep understanding of mathematics.
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.
Learning is more effective when it is understood.
Whilst students can memorise facts, definitions and procedures without knowing why, such learning is neither efficient nor desirable. A ‘relational’ understanding of mathematics is more powerful, long-lasting and useful than an ‘instrumental’ understanding.
Mathematical Thinking
We want students to think like mathematicians, not just DO the maths.
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.
It is important we support all students in developing their mathematical thinking, in order to improve their facility in learning key mathematical ideas and processes, and as an end in itself.
Mathematical Language
We believe that pupils should be encouraged to use mathematical language throughout their maths learning to deepen their understanding of concepts.
Every Mathematics lesson should provide opportunities for students to communicate and develop mathematical language. Students should revisit mathematical language from previous years and explore the concepts in greater depth. There should be opportunities for students to clarify vocabulary and explore activities that develop an understanding of the different concepts. Students should have the opportunity to practise using vocabulary and apply their knowledge and understanding in different contexts that require other areas of mathematics
Problem Solving
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.
Problem solving is at the heart of the Mathematics Mastery approach. Students must be encouraged to explore, recognise patterns, hypothesise and generalise in their learning. With careful planning, even seemingly straight-forward tasks can be converted into opportunities for students to investigate, seek solutions, make new discoveries and reason about their findings. As such, the majority of the tasks and activities we have developed focus on taking an exploratory, problem-solving approach, promoting open ended questions and points for discussion throughout.
Concrete, Abstract & Pictorial representation:
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.
Approach:
We believe that through hard work and effort everyone can get better at maths.
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.
Curriculum Overview
We believe in a cumulative mastery curriculum, where students use prior knowledge to build on their conceptual understanding of maths concepts throughout the year.
Our curriculum is designed to help students to truly master mathematics, so they can apply their skills in unfamiliar situations whenever needed. Topics from the same content areas have been grouped together to form mastery half terms. More time is spent teaching fundamentals to avoid reteaching in later years.
We believe that every child can learn mathematics, given the appropriate learning experiences within and beyond the classroom. Our curriculum map reflects our high expectations for every child. Every student is entitled to master the key mathematical content for their age, by receiving the support and challenge they specifically need.
By structuring our curriculum so that all students in a year group are learning the same content at the same time, have longer to focus on each topic. Our aim is to create the optimal conditions for students to learn through problem solving and to learn to solve problems.
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.
KS4 Curriculum (Y9-11) – links to GCSE specifications
We follow the Edexcel exam board GCSE specifications:
Year 9 :
Autumn term: Graphs and proportion and Algebra
Spring term: 2D Geometry, equations and Inequalities.
Summer term: Handling data and probability and Geometry (Transformations and Trigonometry)
Year 10:
Autumn term: Number and Application of Algebra.
Spring term: Percentages and Probability and Geometry.
Summer term: Ratio and Proportion, similarity and data handling.
Year 11:
Autumn term: Reasoning and proof and Inequalities.
Spring Term: Algebraic proof and reasoning, geometric proof and Further Graphs.
KS3 Curriculum (Y7-8)
Year 7: New
Autumn Term: Number systems and the axioms, Factors and multiples and order of operations, Positive and negative numbers and Expressions, equations and sequences
Spring term: Angles, classifying 2-D shapes, constructing triangles and quadrilaterals, Coordinates, area of 2-D shapes and Transforming 2-D figures.
Summer term: Primes, factors and multiples, Fractions, Ratio and Percentages.
Year 8:
Autumn Term: Primes and factorising, add and subtract fraction, Positive and negative numbers and Sequences, expressions and equations.
Spring Term: Triangles, quadrilaterals and angles in parallel lines, Length and area: parallelograms and trapezia, Percentage change and Ratio (and SDT)
Summer Term: Rounding, Circumference and area of a circle, 3D shapes and nets, Surface area and volume and Statistics.
Assessment
Year 7, 8 & 9
For each year group we use pre- and post-learning module assessments and termly summative assessments. These should be used to support your continual assessment for learning that is used to scaffold each lesson to suit your students’ needs.
- Half termly pre- and post-assessments.
- End of the year fluency, essentials and depth assessments
Year 10
- Pre-requisite and Post – learning module assessments.
- End of term- GCSE practice papers (One paper each)
- End of the year – Mock exam – (Full set from the Edexcel Exam board)
Year 11
- Weekly exam-Practice papers
- 3 mock exams. (November, February & April)