Maths

Purpose of study

Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology, and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

Aims

Our curriculum aims to ensure that all students:

• Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that students develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
• Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Our curriculum builds on the KS2 National Curriculum Programme of Study for Mathematics, and our Scheme of Learning references prior learning in every unit. In our lessons we revisit topics that students have met at primary school, and ensure that knowledge is secure before we develop it further. For example, we have addition and subtraction problems as our first unit in year 1 and year 2 of our 7/8 curriculum, so that we can assess students’ prior knowledge and the methods that they use. We use that analysis to build and extend understanding to more complex problems than they would meet in the primary curriculum. On entry to Settlebeck School, all students are assessed using Progress Test Maths, with the outcomes used to inform the curriculum.

Students build their knowledge and skills within 6 areas of mathematics:

• The structure of the number system
• Operating on number
• Multiplicative reasoning
• Sequences and graphs
• Statistics and probability
• Geometry

Learning in maths is hierarchical, so to learn mathematics effectively, some concepts need to be learnt before others e.g., students need to know and understand place value before they can master addition and subtraction. Addition and subtraction need to be learnt before learning about multiplication as a model of repeated addition. In other areas of mathematics, learning is not hierarchical e.g., although students must learn about shapes and statistics after securing their knowledge and understanding of number, they are not dependent on each other.

There are three types of knowledge within maths that students must master to be successful:

• Declarative knowledge – facts, formulae, concepts, principles, and rules
• Procedural knowledge – methods, algorithms, and procedures e.g., long division, the stepped approach to solving quadratic equations.
• Conditional knowledge – reasoning, problem solving. Students learn to match problem types with strategies.

As students progress from novice to expert, they increase their fluency of mathematics and start to build connections within their body of mathematical knowledge. They also widen and deepen this body of knowledge and increase their levels of mathematical thinking, accessing increasingly complex problems. Students can effectively solve problems when they have learned to deploy facts and methods with speed and accuracy.

For example, when learning to solve equations – students learn algebraic notation at Key Stage 3. They build on Key Stage 2 work with ‘missing numbers’, and start to use symbols for unknown quantities. They progress to solve line equations by the end of KS3, combining them with their knowledge of brackets and inequalities. They then extend their understanding to forming equations and solving them, becoming increasingly competent before learning about simultaneous equations. As students progress towards the end of KS4, they can apply their knowledge and skills when tackling complex problems and learning about algebraic reasoning.

Our curriculum enables students to systematically acquire core mathematical facts, concepts, methods, and strategies to be able to experience success when problem-solving and to become proficient mathematicians. The curriculum provides them with opportunities to develop what are assumed to be generic skills for problem-solving, such as analysis and evaluation. It carefully sequences content, instruction, and rehearsal so students learn new and consistent patterns of useful information. This forms a basis for further concepts, rules, and principles to be introduced and learned as students progress through the curriculum. Throughout the curriculum concepts are revisited through interwoven topics

When designing our curriculum, we have considered the needs of all our students. To ensure that students with SEND have the opportunity to develop the same knowledge and skills as their peers, we adopt a range of strategies within the classroom such as in class support from a teaching assistant, smaller group teaching and tactile resources. Progression through the curriculum is adapted to ensure that students can develop the knowledge and skills they need to be able to learn more abstract areas of mathematics.

On entry to the school and termly throughout KS3 we assess using Progress Test Maths, retrieval activities, questioning, end of topic tests and within each lesson. At KS4, learning is assessed through retrieval activities, questioning, end of topic tests and within each lesson. Verbal feedback is a feature of all lessons and allows any gaps in knowledge, skills and understanding to be address quickly. We use all the information gleaned through assessment to inform and, where necessary, adapt the curriculum. Regular assessment also enables us to implement a programme of additional support when learning has faltered.

The Maths offering ensures that students are given the opportunities to excel and prepares all students for their next steps. Some students complete Entry Level or Functional Skills qualifications if these are more appropriate than GCSE, and appropriate candidates study a FSMQ in Additional Maths to prepare them for A Level study.

We have a developing programme of extra-curricular opportunities, including entering Maths Challenges and Maths Feasts, Masterclasses with Lancaster University, joint STEM trips with other departments and Maths Inspiration, all of which broaden the experiences that our students have.