WHY ARE WE TEACHING A KNOWLEDGE-RICH CURRICULUM; HOW IS IT DIFFERENT?
Our Trust maths curriculum is a research-informed knowledge-rich curriculum, which follows the content and aims of the (heavily prescribed) National Curriculum. Its purpose is to provide all students with a rewarding and enjoyable experience of Mathematics that will prepare them to become confident, numerate individuals who are able to deal with all aspects of Mathematics in their chosen career and in their adult life.
Our maths curriculum is presented in strands of concepts that are broken down and sequenced over time. To enable a student to progress in their understanding of a concept they need to recall the previous concepts quickly and accurately. The fundamental idea behind our curriculum is to support pupils to be able to perform simpler tasks so they can then move on to perform more complex tasks. By teaching knowledge first before studying how we can apply that knowledge, our students are more likely to understand and remember new concepts over time.
Our curriculum is continuously evaluated, and we adapt when and where we feel it is needed.
WHY ARE WE TEACHING THIS CONTENT?
Our curriculum is put together so that the interconnected nature of mathematics is prevalent, and topics are not simply taught in a stand-alone manner. Our spiralling curriculum bases future teaching on previously taught building blocks which allows students to deepen their understanding, frequently revisit content and apply their mathematics to a variety of new contexts to ensure mastery of all skills. For example, a possible ‘Angles’ journey:
We also carefully vary the practice questions so that mechanical repetition is avoided, and critical thinking is required.
As part of the disciplinary literacy policy in our school, the correct use of mathematical language and terminology is also taught. We spend a lot of time ensuring students understand command words such as those they may see in exam questions, such as Write Down, Evaluate, Solve, Explain, Prove, Justify, etc. This helps develop confident learners of Maths through the skills of speaking, reading, listening and writing.
We believe that frequent and efficient knowledge retrieval of key facts and procedures will allow students the flexibility to move freely between different contexts. Students will be able to connect new ideas to concepts that have already been understood and hence pull out any misconceptions that could occur.
Each Mathematics lesson is designed to fully challenge students while still being accessible to all through differentiated teacher support. Every lesson is carefully planned by the individual teacher, allowing them to implement their own teaching styles and tailor the content of the lesson to the specific class in front of them.
Fluency, reasoning, and problem-solving skills are developed in every lesson. Maths lessons will feature clear modelling, class discussions, assessment, and independent practice.
WHY ARE WE TEACHING IT IN THIS ORDER?
To learn mathematics effectively, some things have to be learned before others, e.g. place value needs to be understood before working with addition and subtraction, addition needs to be learnt before looking at multiplication (as a model of repeated addition). For some other topics, the order isn’t as crucial, e.g. Shapes and Statistics need to come after Number, but they don’t depend on each other.
Our curriculum is delivered in a chronological order, by starting with the concrete concepts and moving to the more abstract concepts. For example, we know that for pupils to be successful at Pythagoras’ Theorem (end of Year 9) they will need to have a good understanding of Triangles, Squares & Roots and Calculator skills, (KS2 and Yrs 7 & 8 work) so our spiral curriculum has been sequenced to ensure prerequisites skills and knowledge are covered before teaching a new topic. (This can also be addressed in our daily retrieval/starter work). The content covered in KS3 provides pupils with a good base of skills and knowledge to proceed on to studying Mathematics at GCSE.
WHAT DO PUPILS NEED TO REMEMBER AND BE ABLE TO DO IN THIS SUBJECT?
There is a fundamental core of maths knowledge and skills that pupils need to learn. They do this by exploring key aspects of mathematics through the concepts of Number, Algebra, Ratio, Proportion & Rates of Change, Geometry & Measures, Probability and Statistics.
In year 7 Maths we seek to expose students to the importance of mathematics as a universal language which underpins many other areas of the curriculum. We give students the opportunity to become fluent in the basic concepts studied in KS2 while developing their reasoning skills by applying these concepts to new and challenging contexts such as algebraic manipulation and powers.
Year 8 Maths has two key learning priorities flowing through the curriculum which allows for both retrieval and an increase in the depth of knowledge. Students will have the opportunity to revisit content covered in year 7 which will improve student memory and allow for their skills to be built upon and applied to multi-step questions that require the use of numerous mathematical skills. Students will also be introduced to new and exciting mathematical concepts, such as Area/Circumference of Circles and Probability that will develop their critical thinking skills and their ability to answer more complex problem-solving questions.
Like our year 8 Maths curriculum, our year 9 curriculum ensures students continue to revisit knowledge learnt throughout years 7 and 8 so we can further build these concepts to include more challenging reasoning and problem-solving skills. We will also broaden their depth of knowledge and introduce new and challenging content such as Inequalities, Standard Form, Pythagoras' Theorem and Quadratics, that will challenge students as well as develop resilience and confidence before moving into year 10. Year 9 students will cover all the fundamental skills that are required to be successful in KS4 and they will start the development of their exam techniques.
In year 10, students will get the opportunity to really see the interconnected nature of Maths and they will learn to apply the subject knowledge they have already acquired in more complex and sophisticated ways. Students will experience questions that go beyond routine and repetition so they will be required to think about what skills or concepts need to be applied in different contexts. Our aim in year 10 is to help students become more confident and resilient problem solvers by encouraging them to try out different methods to see what works and what doesn’t. We aim for students to start to appreciate the actual process behind reaching an answer. Students will also be formally introduced to GCSE exam style questions and will have the opportunity to develop their exam techniques including common errors and misconceptions, layout and workings, checking answers, mastering using a calculator, command words and how to tackle wordy questions. Higher students will begin to stretch further into more advanced applications of these skills.
In year 11, students will learn the remaining content required to be successful in GCSE Mathematics as well as having the opportunity to fully consolidate their learning throughout key stage 3 and year 10. They will develop their ability to apply their knowledge to a variety of different problems. This will include linking different topics and using underlying core skills over a range of different questions. There will be an emphasis on revision and retrieval of content as well as exam question practice to further develop their exam techniques.
WHAT METHODS DO WE USE TO HELP PUPILS SECURE THIS KNOWLEDGE IN LONG-TERM MEMORY?
We use a range of high-quality teaching activities and approaches to help students secure their maths knowledge. Each topic in Maths contains many sub-topics and skills. As we go up in the year groups, these topics become more in-depth and build on prior knowledge from KS2 and then from KS3 to prepare students for KS4. Therefore, some topics repeat from year to year for consolidation and fluency. When designing our curriculum, it was important to create opportunities for interleaving – building previously learned skills into questions on the current topic being studied.
For example, in Year 8, we felt it was important that Angles should follow Linear Equations because if ‘Angles’ is taught first, it can end up being a repeat of Primary School Angles. However, if ‘Angles’ is taught after Equations then teachers can make the most of opportunities to interweave Equations and Angles. This adds depth and challenge to the topic of Angles, as well as giving students the opportunity to make use of their newly acquired Equation solving skills.
Other methods that are used to help secure knowledge are:
- Robust questioning in class that supports pupils in engaging in daily retrieval practice and modelling of new concepts.
- Repeated and sustained practice using the ‘My Turn, Your Turn’ strategy.
- Increasing retention of knowledge/skills/methods by removal of scaffolded support.
- Use of Knowledge Organisers
- Revision Guides/Knowledge Retriever Booklets (KS4)
- Weekly online MemRi Quizzes
All students regularly review their learning with knowledge recall starters, interleaving lesson and homework tasks and self-assessment of classwork with discussions on misconceptions.
WHAT METHODS DO WE USE TO HELP PUPILS SECURE THIS KNOWLEDGE IN LONG-TERM MEMORY AND APPLY IT IN COMPLEX TASKS?
Staff assess prior knowledge before starting a new topic either using prerequisite tests or other forms of low stake’s quizzes. Retrieval practice is at the start of all lessons to make use of the ‘testing effect’. Topic tests at the end of each topic which are tracked, and intervention (if needed) is put in place.
Students are assessed on the topics covered so far at each whole-school assessment point. These assessments will also include some previous year work. This is for interleaving practice and long- term retention in preparation for GCSE style exams. When assessments are coming up, a detailed revision list is shared (with keywords).
Mathematics underpins other areas of the curriculum, and we aim to teach the mathematical skills needed for pupils to be able to access other subject areas, particularly Science, Geography and Technology. For example, we cover graph work to support Geography and Standard Form to support Science.
To view the Maths Curriculum Overview click here.
More information on the Maths Department can be found on their website here.