Planning across the key stage in mathematics

The revision of the key stage 4 programme of study provides an opportunity to review and refresh your sequences of work. When reviewing planning across the key stage, developing new sequences of work or revising existing ones, you should consider the following.

Where are the opportunities to develop students’ experience of the key concepts?

The key concepts that underpin the study of mathematics should be taught through the key processes, using the range and content statements to provide the contexts and the curriculum opportunities to provide depth and range of experience and challenge. In planning, the focus needs to be on developing a coherent body of knowledge, skills and understanding that reflect the nature of mathematics rather than focusing on the development of individual technical skills.

Continuity and progression should inform planning, to ensure that learning opportunities build on previous experiences and offer new challenges. Curriculum opportunities need to offer all learners the entitlement to develop understanding rather than focusing on coverage of content. This involves considering how the key concepts will be integrated into teaching and learning across the key stage. For example 'How will you give your students the opportunity to be creative?' This requires them to adopt a questioning approach towards mathematical activity. 'Why does it work?' 'What happens if…?' Students need to be able to combine understanding, experiences, imagination and reasoning to develop new mathematics for themselves and apply mathematics to problems in familiar and unfamiliar contexts.

How can planning ensure that students make progress in the key processes?

The aspects of content and process are tightly bound, but it is the process skills that are at the heart of the revised programme of study, with the range and content being the context within which the processes can develop. Topics within the range and content can be revisited, building on what the students already know and providing fresh challenges to motivate, stimulate and further develop their understanding.

In key stage 4 students take increasing responsibility for their own learning and develop their confidence and competence in a broader range of mathematics. They need to understand the role of proof in mathematics and be able to develop their own proofs for important results such as Pythagoras’ or circle theorems.

Key processes need to be seen and taught holistically, but this does not preclude taking opportunities to focus on one or more of the key processes at any one time. Although there is a sense of progression from representing to analysing to interpreting and evaluating, this is not the reality of most mathematical experiences that involve problem solving. When problem solving, we not only tend to cycle around the processes several times, but also move backwards and forwards between these stages as ideas mature, modify and change. This idea is reflected in the diagram below.

How can you provide opportunities for students to engage with real audiences?

Schools are encouraged to provide curriculum opportunities that offer students experience of mathematics outside as well as inside the school environment. Inside school, departments should consider whether the application of mathematics in other subject areas is utilised in terms of its contribution to a student’s whole experience of mathematics. Outside school, links can be made with local higher education institutions and businesses, as well as regional and national projects such as the Science, Technology, Engineering and Mathematics Network (STEMNET) and the Millennium Mathematics Project (MMP).

Students can draw on work experience and other work-related learning to provide rich and relevant contexts within which they can develop their knowledge and understanding of mathematics. As students become more aware of how society and the world of work operates, they can use their mathematics in a broader range of contexts, including making healthy lifestyle choices, managing personal finance responsibly and respecting and celebrating diversity.

Schools should be able to draw on the expertise and support offered by the Secondary National Strategy (SNS), professional associations and organisations such as the National Centre for Excellence in the Teaching of Mathematics (NCETM).