By using thinking skills, pupils who are gifted in mathematics can focus on 'knowing how', as well as 'knowing what' (learning how to learn). Mathematics is not just a collection of skills -- it teaches pupils to think, to reason, to solve problems and to think in creative ways.

The sections of the programmes of study that relate to 'using and applying mathematics' outline relevant knowledge, skills and understanding, and provide opportunities for the development of the following thinking skills:

enquiry skills
the ability to ask relevant questions, to pose and define mathematical problems or enquiries, and to plan how to solve them. Gifted pupils can represent problems in algebraic, geometric or graphical form, and can select and organise what to do

reasoning skills
the ability to recognise patterns and generalise, and to give reasons for results and conclusions. Gifted pupils should be expected to analyse their results, looking for cause and effect, patterns and relationships. Activities in mathematics provide opportunities for them to draw inferences from data, to make deductions (stating constraints), and to present concise, reasoned arguments

information-processing skills
the ability to locate and collect relevant data from a variety of suitable sources and to sort, classify and sequence the information. Gifted pupils should be expected to decide what methods and analyses are needed and to process and represent the data, using ICT as appropriate

creative-thinking skills
the ability to apply their mathematical skills to new and unfamiliar situations, to extend ideas, and to solve problems by considering new and flexible ways of doing things. Gifted pupils should be expected to explore connections in their mathematical work, to use their imagination by asking questions such as 'What if?' and 'Why?', and to conjecture and hypothesise. They should explore, identify and use pattern and symmetry in mathematical contexts, and should select and combine known facts and problem-solving strategies in creative ways to solve problems

evaluation skills
the ability to evaluate information and to judge the value of their own and others' work or ideas. Gifted pupils should be expected to review progress as they work in mathematics and to use checking procedures to monitor the accuracy and appropriateness of their solutions and conclusions when solving mathematical problems. They should test and evaluate their hypotheses, and examine critically, improve, then justify their methods and their choices of presentation of their mathematics.

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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