Since the launch of the National Numeracy Strategy and Key Stage 3 Strategy, most teachers use the appropriate Framework for teaching mathematics to plan their work.

When choosing materials for gifted pupils, it is important to be aware of three characteristics of mathematics and the way pupils learn mathematics:

multi-step learning
although school mathematics is frequently taught as a collection of separate one-step skills or routines, genuine mathematical problems are typically multi-step, with would-be-solvers required to identify a number of intermediate stepping stones that allow them to proceed from what is given to what is sought. The relevant techniques have to be identified by the solver, and then marshalled in an appropriate way to achieve a solution. Therefore if a mathematical subject is to be appropriate for gifted pupils, it has to naturally give rise to a rich source of problems which require the integration of separate basic steps to analyse and solve

making connections
the essence of mathematics lies in the links and connections between apparently distinct themes. Therefore pupils should experience mathematics as a subject based on relations, rather than consisting of many unrelated rules, methods and problems. Here the teacher's contribution is crucial, as it is not easy for a pupil to stand back in the middle of tackling a problem, or group of problems, and to look for connections. The realisation that new problems or methods are often more (and sometimes less!) familiar than they seem is a fundamental insight that gifted pupils need to experience regularly

proof
the connections between different parts of elementary mathematics, or between what is given and what is sought in a particular problem, point to a more fundamental principle -- the notion that such connections have a logical basis and so must be established by exact calculation, or proof. At first, such connections may only be vaguely perceived -- perhaps on the basis of a few examples. Pupils are then faced with the question of whether or not something that seems to be true is really true. Such situations should be used to underline the notion of mathematics as 'the science of exact calculation'. An understanding of the need for proof has to be cultivated, and its mastery in simple situations requires practice. Pupils need to understand clearly that in mathematics -- and in particular in school mathematics -- it is exact calculation, or proof, which is the final arbiter of correctness, or truth.

Managing provision in the general guidance

Matching teaching to pupils' needs in the general guidance

Transfer and transition in the general guidance

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