Aims and purposes

The teaching of maths enables students to:

· develop fluency in the key underpinning aspects of mathematics;

· approach progressively complex problems over time through varied and frequent practice;

· broaden their conceptual understanding and the ability to recall and apply knowledge swiftly and with accuracy;

· reason mathematically by following a line of enquiry;

· make and test conjectures about relationships and identify and describe generalisations;

· assimilate a range of mental calculation skills and use these confidently in different settings;

· develop flexible approaches to problem solving and look for ways to overcome difficulties;

· make decisions about which operations and problem-solving strategies to use;

· adopt an organised and methodical approach to their work;

· build valuable critical-thinking and problem-solving skills that will help them to successfully navigate the real world.

Content of maths

The study of mathematics is about gaining confidence in exploring, manipulating and describing the patterns ever-present in the world around us. The curriculum is split across three strands – number, shape and space, and using and applying statistics – although the majority of topics draw upon more than one of those strands.

Knowledge and understanding

Students should:

· gain confidence in identifying the mathematical skills required to approach problems;

· develop flexible approaches to problem solving and look for ways to overcome difficulties;

· use an increasingly varied and robust combination of skills to solve problems, including breaking them down into a series of simpler steps;

· exhibit curiosity, both asking questions and seeking solutions;

· recognise and appreciate the relevance of maths to real-life situations and become confident and competent in applying their skills in such situations.

Processes and skills

Students should:

· move fluently between representations of mathematical ideas;

· make rich connections across those ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems;

· understand and question the implications and limitations of their answers, including checking for sense;

· apply their mathematical knowledge to science and other subjects.

Language and communication

Students should:

· use the correct language, symbols and terminology associated with the relevant mathematical topic;

· grasp mathematical language, using it to talk about their methods and explain their reasoning when solving problems;

· communicate their mathematical thinking in spoken, pictorial and written form;

· develop an argument, justification or proof using mathematical language.

Values and attitudes

Students should:

· work with others, listening to their ideas and treating these with respect;

· derive satisfaction from the ability to solve problems;

· appreciate that making and addressing mistakes and misconceptions is a fundamental aspect of successful learning in maths;

· recognise that supporting evidence, such as data, strengthens persuasive arguments;

· understand that numeracy is fundamental to the achievement of aspirations beyond education.

Building on students’ earlier experiences

These experiences are likely to have included:

· investigating maths through practical activity, exploration and discussion;

· using mental and written calculation skills in different settings;

· applying simple mathematical ideas to solve practical problems;

· recognising and talking about patterns and relationships;

· discussing the importance of maths beyond the classroom.

Features of progression

To ensure students make progress in maths:

Students will be supported to:

· consolidate their numerical and mathematical capability from their individual starting point and extend their understanding of the number system and place;

· select and use appropriate calculation strategies to solve increasingly complex problems;

· move freely between different numerical, algebraic, graphical and diagrammatic representations;

· use language and properties precisely to analyse numbers, shapes, algebra and probability and statistics;

· make and test conjectures about patterns and relationships, looking for proofs or counter-examples;

· begin to reason deductively in geometry, number and algebra, including using geometrical constructions;

· develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems;

· develop their use of formal mathematical knowledge to interpret and solve problems;

· begin to model situations mathematically and express the results using a range of formal mathematical representations;

· select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Teaching will:

· ensure that students achieve secure foundations by using discussion to probe and remedy misconceptions;

· build upon those foundations with considered progression of challenge;

· facilitate consolidation of understanding through additional practice and support;

· provide the opportunity to deepen understanding through the challenge of rich and sophisticated problems;

· assist students in making their mathematical thinking increasingly clear to themselves as well as to others;

· offer a range of interesting and engaging enrichment opportunities to illustrate the interconnectedness of maths to the real-world.