Developing Reasoning Through Algebra and Geometry (2004)

This booklet, developed for mathematics departments by the National Strategies, is based on materials developed by six working groups as part of QCA’s algebra and geometry project.

The project focused on the place of algebra and geometry in developing concepts and skills in reasoning. The booklet brings out key themes from this work that are central to the intentions of the 1998 Mathematics National Curriculum. These are illustrated by reference to ideas developed by the working groups and approaches they have taken in classrooms.

The two central themes of the project were (i) to clarify the role that algebra and geometry have in developing mathematical reasoning, explanation and proof, and (ii) to propose teaching strategies that may be used to give these skills a higher profile in these areas of the curriculum.

Reasoning is an important strand within mathematics and it is also important as a wider ‘thinking skill’ that can be developed through learning mathematics. Each section of the mathematics programmes of study begins with a subsection in which the skills of reasoning are specified alongside those of problem solving and communicating. In this context reasoning includes:
■ recognising patterns and opportunities to generalise
■ explaining why an answer must be correct
■ constructing chains of deductions
■ understanding the difference between a practical demonstration and a proof
■ appreciating assumptions and constraints and knowing how varying these would affect the results.