This book is designed to help teachers at school and colleges to ask the right questions and provide the right answers. It is based on the teaching and research activities of the Mathematics Education Group at Brunel University. The research studies with some 22,000 learners aged from 10 to 57 years have shown that there are certain basic mathematical tasks which cause common misconceptions: what is learnt today does indeed matter tomorrow. Diagnosis of these misconceptions is, however, subtle; in tasks which look similar, only certain kinds really probe the learner's understanding.
An introductory chapter discusses the need for, and the art of, diagnosis. The central theme of diagnosis allied to prescriptions is then discussed in a set of chapters relating to specific topics. Each of these chapters ends with sets of exercises for teachers to use when testing their students' depth of understanding. It is hoped that these exercises will also act as a stimulus to teachers to develop their own diagnostic skills.
The Need for Diagnosis The Natural Numbers Small Numbers Decimal Fractions Small Numbers Common Fractions Percentage, Ratio and Proportion Shape and Form Similarity The Circle and its Measurement An Introduction to Algebra Statistics On Average Problem Solving Context, Attitude and Anxiety Adults and Numeracy Teaching Maths