Maths is a journey and long-term goal, achieved through exploration, discussion, incremental practice, and challenges through problem solving and application problems. At each stage of learning, students should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.
There are 3 levels of learning:
· Rote learning: surface, temporary, often lost
· Deep learning: it sticks, can be recalled and used
· Deepest learning: can be transferred and applied in different contexts
The deep and deepest levels are what we are aiming for by teaching maths using the Mastery approach.
At KS3 we currently have 2 Schemes of Learning…
Year 7 are following the new White Rose Maths 5 year Scheme of Work. The scheme of work has been designed so that any student following the main content, regardless of prior attainment, will cover all of the grade 5 GCSE content by the end of year 11. The higher content, up to Grade 9, is built in to the scheme of work to stretch all learners.
The White Rose Maths Scheme of Work has been designed with Teaching for Mastery in mind. Each half term is split in to smaller blocks that ensure students spend enough time getting a deep understanding of the work. In addition to this, the scheme uses interleaving topics as a key element. For example, Year 7 starts with algebraic thinking, which is then continually used throughout the year to reinforce and extend their knowledge further.
Year 8 are following the second year of the Edexcel 5 year Scheme of Work: Delta 2 and Theta 2 and Pi 2. Students will cover all units that are required as prior knowledge before moving on to the GCSE course in Years 9, 10 and 11. The KS3 section of the Edexcel 5 year Scheme of Work has been designed with Teaching for Mastery in mind. Each unit includes work that focusses on developing: Fluency, Mathematical Reasoning, Problem Solving, Modelling, Interleaving topics and STEM questions. All of these ensure that students spend enough time getting a deep understanding of the work.
At KS4 we are following Edexcel’s GCSE Scheme of Work starting in year 9. Students are expected to put into practice the skills and facts they learned at Key Stage 3 to develop and consolidate their abilities to discuss, interpret, describe and solve problems and present reasoned arguments using mathematics. They will continue to learn topics and skills in: Number, Algebra, Ratio, proportion and rates of change, Geometry and measures, Probability and Statistics. Within these areas there is a greater emphasis on independent and collaborative learning. Students will continue to develop their skills in multi-step and increasingly complex problem-solving questions. The aim is to enable students to meet the rigours of the new Mathematics Specification, equipping them to succeed in using Maths in other subjects such as Science, Geography, PE, Technology, as well as in their home, and later, their college, university and work lives.
All Schemes of work will be reviewed at the end of each year.
Multiple representations for all! - Concrete, pictorial, abstract
Objects, pictures, words, numbers and symbols are everywhere. The mastery approach incorporates all of these to help students explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so pupils truly understand what they’ve learnt.
All pupils, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. Pupils are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols.
Concrete – students have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.
Pictorial – students then build on this concrete approach by using pictorial representations, which can then be used to reason and solve problems.
Abstract – With the foundations firmly laid, students can move to an abstract approach using numbers and key concepts with confidence.
Our approach to teaching and learning supports our curriculum by ensuring that lessons build on prior learning and provide sufficient opportunity for: exploration, discussions, questioning and reasoning, model answers, incremental independent practice and challenging work in context. We have developed this approach using Barak Rosenshine’s Principles of Instruction (2012) and our own experience of what works in the classroom to develop our ‘Common Lesson Format’:
Reflection Task: Begin a lesson with a short review of prior learning from previous topics of work.
Exploration and Discussion: Students are presented with a problem that allows them to discover, through high level framed questioning, the new material themselves.
Model Answers: Students discuss the new material in the form of a model answer where they work together to complete a model solution to a question on the new material.
Incremental Independent Practice: Students complete questions on the new material including small incremental steps to stretch all learners and force students to think about what they are learning and why they are learning it.
Challenge Questions: Students are provided with a challenge question that combines their current learning with prior learning to interleave topics and give the students the opportunity to form links between different mathematical topics.
Live feedback: Throughout all of the above, the class teacher is continuously providing live feedback for students in the form of: regular AFL, high level framed questions and live marking of the work. This not only checks for the students understanding but also highlights and addresses any misconceptions.
As we use a Teaching for Mastery approach our students study topics in greater depth, with the expectation that we don’t move on to the next topic until all pupils have a secure understanding of the current topic. This provides pupils with the time and space to gain this secure understanding. In our lessons you will typically see all pupils grappling with the same challenging content, with teachers providing additional support for pupils who need it. Rather than moving on to new content, the higher attainers are expected to progress on to the Challenge question and produce work of greater depth.
Our Students will be able to:
· Recall of facts and procedures from our working and long term memory
· The flexibility and fluidity to move between different contexts and representations of mathematics – interleaving topics.
· The ability to recognise relationships and make connections in mathematics
A mathematical concept or skill has been mastered when a student can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations.