The CAM Maths Curriculum is designed in a way which ensures nearly all students are able to progress onto the next section of the scheme of work each year. Students start at a point which challenges them but which takes into account their starting point. For example, the C scheme starts at a level which follows directly from the stage the most able students achieve by the end of year 6, meaning year 7s completing the C scheme don’t spend time on things they can already do. At the other extreme, we recognise that some students are working at a level far below the expected level for year 6 students. Such students study the α scheme which supports these students with their number work but also starts to introduce new ideas in an accessible way, such as algebra.
Students generally progress through one scheme of work per year; the scheme of work is designed so that work always builds on the work done in the previous year. In this sense, it is a spiral curriculum. This means that with each scheme students gain new knowledge on the topics previously studied, meet more advanced applications of existing knowledge and become more expert and proficient by gaining additional practical experience with topics. For example, the focus of the algebra strand during term 1 is algebraic manipulation. On the B scheme this focuses on collecting like terms and the language of algebra. On the C scheme this develops to include expanding single brackets. On the D scheme, the expanding brackets work continues with the introduction of more complicated expressions involving brackets. On the E scheme, students meet expanding double brackets for the first time. In addition, there are also “spirals” within a year. For example, algebra work in the first term is generally on algebraic manipulation, whilst work in the second term tends to be on the equations which can be solved using the manipulation skills learnt in the first term. This allows the work in the previous term to be reinforced. New learning is explicitly linked to previous learning: a path is plotted through the entire scheme of work meaning things don’t need to be “undone” before the next step can be learnt. For example, from the B scheme, students are expected to solve equations using the idea of balancing equations rather than undoing operations as this can be built upon to solve more complicated equations in subsequent schemes of work. It also allows for time between first teaching of topics and more advanced later topics.
The scheme of work is based primarily on the principle that students should not only be able to do the objectives on the scheme of work but crucially that they should understand why we do what we do, and why it works. For example, a fairly common method for teaching the division of fractions is “stick, switch, flip” which allows for an entirely procedural understanding of the process of dividing fractions. Our scheme of work allows students to see that multiplying by the reciprocal is equivalent, by analogy with the fact that, for example, halving is the same thing as dividing by two. This means that students’ understanding is built on stable foundations and also facilitates far transfer, meaning students are able to apply what they have learnt to novel scenarios.
Beyond what is specified in the scheme of work, there is an expectation that teachers incorporate opportunities for mathematical behaviour into their lessons. This could be through:
The scheme of work is designed to map a clear and coherent path through the mathematics which students require in order to be successful in GCSE mathematics and Level 2 Certificate in Further Mathematics examinations, whilst also laying foundations for the further study of mathematics. It covers all elements of the National Curriculum, and the AQA GCSE and Level 2 Certificate specifications. Some of the early schemes of work cover elements of the primary national curriculum, for students who are below expected standard for year 6 students in year 7. In addition, there are a small number of topics which are not part of the GCSE specifications but which help to give students a coherent experience of mathematics, for example the inclusion of sampling methods in the E scheme.
It is recognised that not all students will complete all schemes of work. Where students do not have sufficient understanding of the prerequisite topics, it may be that it is not appropriate to teach the following topic. For example, some students will not meet trigonometry at all. Fundamentally, the scheme of work is designed so that students study a level of mathematics which is appropriate for them and will allow them to progress.