Mathematics 5-11: a Handbook of Suggestions

This HMSO resource from her Majesty’s Inspectors was one of a series intended to stimulate discussion and debate within the teaching profession. Published in 1979 following a two year survey, it was seen that mathematics was given a high profile by teachers but Inspectors felt disappointment that, despite this and the efforts of students and staff, results in a test administered for the purpose of the survey did not produce better results.

At the time of the survey the educational system did not seek to achieve a consistently developing programme of work for students by central direction. This report set out to identify those parts of the subject which, in HMI's view, should be taught to every child, and gives some guidance on approaches which teachers have shown to be effective.

Planning the mathematics programme - the challenge is to encourage children to develop their mathematical education along a broad front of experience while ensuring systematic progression and continuity.

Communication: language and logic - having to express an experience or an idea in everyday language helps even young children to become more clearly aware of it and clarifies what it is that they did not understand.

Number - an experimental and practical approach should be made to number and ideas should arise from investigations carried out by the student.

Measurement - in the early years it is important that children should be introduced to a wide variety of environmental objects and material of many different types, from which measuring can arise. Later, when measuring with standard units, students should be encouraged to offer estimates before any measurement is carried out.

Pictorial and graphical representation - the action of recording mathematical information in pictorial form is often the first introduction to graphical work and graphs should be developed out of what students are learning, rather than taught as an isolated topic.

Shape - the study of shape can promote a rich mathematical language and the vocabulary will become refined as the mathematical experiences become enriched. Classifying and discriminating are essential elements in a good mathematics programme.

The report concluded that while it is desirable that all children should reach a satisfactory level of mathematical competence by the time they are aged 11, those who find the work difficult lapse into bewilderment if essential stages are rushed. On the other hand, time is too precious to be spent on the unnecessary repetition of work already grasped, especially if further practice can readily be undertaken while acquiring a new skill or idea. The pacing of the work calls for careful professional judgment based on a knowledge of both children and the subject.