Peter Wilder reviews an A-level text which emphasises revision and consolidation. This new maths course is designed for the revised A-level syllabuses which will be examined from 1996 onwards. Pure Mathematics covers all the new A-level core, including "The Mathematics of Uncertainty", and claims to include all the pure maths topics that are required for the major syllabuses, whether modular or not.
This book may be a popular choice for schools and colleges looking for a traditional text. The starting point for the course is level 7 of the national curriculum, and the early chapters revise and extend topics from GCSE. There are clear worked examples and plenty of practice exercises.
Each chapter concludes with a longer exercise. These are often more open and investigative, and many of them encourage students to explore various applications of the maths. I enjoyed working some of these, but I felt some were much too highly structured and failed to encourage students to explore the ideas for themselves.
Consolidation sections are provided at regular intervals, and these offer further practice exercises, as well as mixed revision exercises and more past examination questions.
At the end of the book is a collection of three mock examinations. A-level texts usually include a selection of past examination questions from various boards for each chapter. It is clearly difficult to do this for the new topics introduced into the A-level core, since few syllabuses have examined them before at this level; as a result some of the chapters are thin on examination questions.
New technology can significantly affect A-level maths teaching, and any new text needs to acknowledge this. Availability of graphical calculators with powerful programming facilities is increasing, and many schools now also have a selection of computer software. This book includes three sections of computer investigations, written for spreadsheets. The decision particularly to encourage the use of spreadsheets in the course is justified by their widespread use outside education, and the general applicability to many different tasks both within and outside mathematics.
Topics investigated on the spreadsheet range from the method of differences applied to single arithmetic and polynomial sequences in the first section, to methods of numerical integration to find areas under the normal distribution curve, and iterative algorithms for generating pseudo-random numbers in the third section. It was good to find such topics addressed in a traditional text like this one. This approach of including separate sections of optional computer investigations may encourage teachers who have not yet explored the possible benefits of using computers in A-level maths to try out some of the ideas.
It is disappointing that the only references to calculators are to scientific calculators. The potential for using graphical calculators has not been mentioned, even though many A-level maths students already own these machines, and many more can be expected to do so in the next few years.
I would like to see a text such as this providing suggestions to teachers, and to those students who possess graph-plotting technology about how they can use the technology to gain insight into ideas such as function, differentiation or probability.
Peter Wilder is senior lecturer in mathematics education at De Montford University, Bedford.