Choosing a maths textbook has never been an exact science. Before the national curriculum, piles of under-used books in the stockroom testified to one person’s whim or another’s failed choice. Exam specifications and textbooks could be, and often were, chosen independently of each other. As long as the books offered reasonable coverage, factors such as the structure and design of the course, the author’s philosophy and treatment of particular topics were likely to be more decisive.

Pressure to gain A* to C grades at GCSE and government control of content and structure have changed all that. Nowadays, schools are more likely to select a specification, then choose the textbook to match. There is a widespread assumption that the closest match will be found in textbooks that have been written by the examiners, but this doesn’t necessarily mean that the exam-badged title is the best one for your school.

How do you set about making your choice? There are four key issues to think about:

1 Support How far does it support the pupil and teacher? In particular, does it reflect significant changes in the syllabus, such as the return of proof, the teaching of coursework and data handling, the place of Using and Applying Mathematics (UAM) and the use and non-use of the calculator?

2 Design Will pupils find the book attractive? If not, there are problems from the start. Think about the use of colour in text and illustrations, the use of photographs as opposed to Clipart pictures, page layout and quality of the paper. If the book looks and feels cheap, pupils will value it far less.

3 Structure How does the internal structure (for example end-of-chapter summaries, self-tests, highlighted sections) support pupils working on their own?

4 Content I used two topics to look at the presentation of the mathematics: Pythagoras and the circle theorems. Pythagoras, because it has the capacity to enthral and entertain at all levels. It also entails a great deal of geometry, practical work, and work with number patterns, not to mention all the tried and tested applications.

Before proof was reinstated on the syllabus, the circle theorems were often presented as a series of facts; even obvious links between them were ignored. The return of proof allows for the development of this section of the syllabus as a fully connected, logically developed piece of mathematics.

... and ‘extras’

Look to see what supplementary materials are available through a publisher’s website, or homework texts, related to chapters and exercises.

Tom Roper is lecturer in mathematics education at the University of Leeds Centre for Studies in Science and Mathematics Education

TEXTBOOKS SURVEY

TITLE: Collins Collins Mathematics for GCSE Higher, Intermediate, Foundation AQA, specifications A and B www.CollinsEducation.com Price: pound;13.99 Tel: 0870 0100 4412

SUPPORT: Introduction explains UAM, calculators, proof, coursework and data handling in the text. Non-calculator questions are clearly marked; all other questions can be done using a calculator. Two worked coursework examples are given and coursework tasks are suggested at the end of each chapter.

DESIGN: Excellent page design; simple and uncluttered. Diagrams are clear, but there are no photographs and the sparse artwork is cartoon or Clipart in black and white. Good quality paper.

STRUCTURE: Chapters start with pre-requisites and end with exam questions from a variety of boards and summary of what the pupil should have learned, with a helpful guide to self-grading. Intermediate text only offers periodic revision papers.

CONTENT: Higher level assumes Pythagoras covered and concentrates on applications and links to trigonometry. Introduction at intermediate level is through numbers rather than areas. Stimulating coursework activities create opportunities for work on number patterns and suggest that the theorem may be true for more than just squares on the sides of right-angled triangles, conveying the many possibilities in the theorem. Circle theorems at higher level are presented as facts; pupils are encouraged to use them and proofs are built into the exercises as structured questions identified as proofs. The logical structure of this part of the course is therefore lost. At the intermediate level, the pupils are challenged to prove them, a challenge too far.

VERDICT: Best of the series on offer, backed up by separate homework textbooks and a website. Teacher support especially noteworthy.

TITLE: Heinemann Edexcel GCSE Mathematics Higher, Intermediate and Foundation Price: pound;14.50 Tel: 01865 888080

SUPPORT:There are separate chapters on UAM, data handling, and calculators and computers. No special effort is made to deal with proof. There is no icon to indicate which exercises or questions are non-calculator. This is at odds with the promise on the cover that the text provides new non-calculator work.

DESIGN: Full-colour artwork with photos and text highlighted in colour. Diagrams are clear, although some pages in the intermediate and higher books are off-puttingly crowded, but the foundation volume is attractive. Paper quality is poor.

STRUCTURE:Key points are summarised at chapter ends. The chapters on UAM and data handling provide guidance on course work. There are two practice exam papers, one calculator-based, and one non-calculator. Every chapter includes worked exam questions. Highlighted marginal text draws attention to special points.

CONTENT: Introduction to Pythagoras through a statement and illustration that uses areas. At intermediate level, the emphasis is on area. Little attempt to develop work in number patterns and the wealth of opportunities offered by this theorem is overlooked. At the higher level, circle theorems are developed by proving each one in turn, followed by examples. (Page 528 has been poorly proof-read and leads to an incorrect proof.) The right angle in a semi-circle property is proved separately, rather than as a consequence of the angle at the centre, which destroys some of the logical development of the topic. The Intermediate level makes a praiseworthy effort to prove these results.

VERDICT: A good buy, but little perhaps to distinguish it from the pack.

TITLE: Oxford Intermediate GCSE for AQA (Content identical to Oxford Edexcel except for source of exam questions) Price: pound;13.50 Tel: 01536 741068

SUPPORT:UAM and data handling are catered for in the coursework section and appropriate chapters or sections. No special effort is made to deal with proof, which is incorporated when necessary. Some exercises are marked as non-calculator, but there are others that merit this description, but don’t receive it.

DESIGN: Full-colour artwork, with limited use of photos. Text is colour-coded, diagrams are clear and the paper quality is good. Some pages have a cluttered look with margins full of boxed texts emphasising or explaining points in the main text.

STRUCTURE:Chapters start with pre-requisites and end with summary. Coursework section has worked projects, and generous selection of exam questions, two practice papers (calculator; non-calculator), and revision exercises. Four ‘skills breaks’, where work is tested by exercises and problems on a theme. A glossary is included.

CONTENT: Pythagoras is not covered in the higher text except as a necessary pre-requisite to 2-D and 3-D trigonometry, where it is called a rule not a theorem. In the intermediate text, it is again a pre-requisite and termed a rule, but the emphasis is on area. The approach is rather dry with no exploration of the wealth of possibilities that this theorem offers. The circle theorems are developed logically and the interdependencies made clear. However, at the intermediate level they are simply stated and, sadly, no attempt is made to connect them.

VERDICT: A good buy but again little to distinguish it from the pack.

TITLE: Hodder amp; Stoughton GCSE Mathematics A for OCR Foundation, Intermediate and Higher Price: pound;14.99 Tel: 01235 827720

SUPPORT: UAM and coursework are covered in the introduction, while some chapters are more activity-based than others. Proof and data handling are included when appropriate. Some exercises are described as non-calculator, but without the instant recognition of an icon. Separate teacher’s resource books are provided.

DESIGN: Limited use of photographs, artwork is mainly Clipart or cartoons and colour is restricted to alternate pages, which makes the mono pages look very dull. Good quality paper.

STRUCTURE: Each chapter starts with the pre-requisites and ends with a summary of the key points and a revision exercise. The text is peppered with examiner’s tips.

CONTENT: Introduction to Pythagoras at intermediate and higher levels is based on areas of squares. Adopts a task approach, but there is little number pattern work and approaches at different levels are identical. Higher level needs more challenging content to reveal the possibilities in the theorem. Angle properties of a circle are developed through drawing and measuring early in the higher book and proved later. Angle in semi-circle is proved in the early chapter. I’m not keen on this separation of the application and the proofs. Good attempt at intermediate level to lead pupils through a proof of the angle in a semicircle, having introduced the theorem through drawing and measuring. Connections between other theorems are overlooked.

VERDICT: A good buy but again little to distinguish it from the pack.

TITLE: Hodder amp; Stoughton GCSEMathematics C: Graduated Assessment Stages 5 amp; 6 and 7 amp; 8 Graduated Assessment for OCR Price: pound;9.99 Tel: 01235 827720

SUPPORT:The introduction spells out the essentials of the coursework element and provides an example task in structured and unstructured form. Some intriguing activity exercises are provided to develop coursework skills. Non-calculator exercises are clearly marked. Teacher resource books accompany each volume, providing answers, suggestions and photocopiables.

DESIGN: Diagrams are clear, but there is limited use of artwork. Photographs are small but clear and attention-grabbing. Pages are alternately mono and coloured. Good quality paper.

STRUCTURE:Each chapter starts with pre-requisites and concludes with a list of key ideas. There are regular revision exercises and exam tips. The teacher resource books provide module tests.

CONTENT: Pythagoras is introduced through areas of squares and there is considerable practical activity. However, the theorem is reduced to one about lengths of sides of the triangle rather than areas of squares on the sides. The circle theorems are not developed, but theorems about tangents and circles are. While the pre-requisites for the chapter list congruency, no clear formal proofs of the theorems are provided. The teacher’s resource book indicates this is beyond the syllabus, but suggests the teacher might discuss the proofs with the class. More help is needed here. Many younger teachers will not have seen the proofs of these theorems.

VERDICT: A good buy. Intersting resources demonstrated in the teacher’s resource books. Series offers very good suport.

TITLE: Letts GCSE Maths Intermediate classbook All exam boards at Intermediate level only Price: pound;12.99 Tel: 020 8740 2266

SUPPORT:The text is aimed squarely at self-study learners who are unsupported or in FE colleges. There is little support for teachers of the kind offered in other texts.

DESIGN: Spot colour only, with limited use of photos. Artwork mainly cartoon or Clipart. Pages cluttered and dull and the diagrams look cramped. Won’t appeal to intermediate level students who need a clear focus and more visual stimulation.

STRUCTURE:Key questions for understanding highlighted, with answers at back. ICT opportunities flagged. Five review chapters and a large bank of exam-style questions. Instructions for non-calculator exercises, less distinctive than icon. Glossary. Advice on how to build up a Key Skills Portfolio at level 2. Would make excellent addition to more standard texts.

CONTENT: Pythagoras is introduced via areas, with suggestions for practical work, and some historical background helps to enliven the approach. At intermediate level, this is a very user-friendly approach for students studying on their own. Unlike intermediate books in other series, circle theorems are not covered.

VERDICT: Separate homework text. Aimed largely at students working alone, but as good as if not better than most in this market.

TITLE: Nelson Thornes Key Maths GCSERevised Higher, Intermediate I amp; II, Foundation. All exam boards www.nelsonthornes.com Price: pound;11.92 Tel: 01242 267100

SUPPORT: There are two intermediate texts. Each chapter begins with a preview and is structured around core and extension material, which allows for some differentiation. Each chapter concludes with a test yourself exercise. Proof and data handling are covered within appropriate chapters, but there is no help with coursework. Non-calculator exercises are clearly marked with an icon.

DESIGN: Good use of photographs, Clipart and cartoon-style artwork, and colour to highlight text. The page has a clear and uncluttered look to it and the paper quality is good.

STRUCTURE:Test yourself exercises conclude each chapter, but there are no exam questions or past papers.

CONTENT: Pythagoras introduced through areas, an approach emphasised at intermediate level; number pattern work is developed in extension material at higher level. Circle theorems introduced through drawing and measurement. The logical sequence of the theorems is disrupted at both levels by dealing with the cyclic quadrilateral before the theorems on subtended angles. Proofs of the subtended angle theorems are asked for in the extension exercise, but are not given even in higher text. Proofs should be a standard part of the course, linking theorems together as a coherent piece of maths. To imply that because you draw and measure some angles and observe a relationship then the relationship must be true is not acceptable at higher level.

VERDICT: This is a popular series, but I felt the new format did not serve the maths as well as it should have done.

TITLE: Longman GCSEHigher Mathematics I All exam boards at Higher level only Price: pound;12.50 Tel: 0800 579 579

SUPPORT:The course is divided into five units within each of the two texts. Each unit contains work on one of the five major divisions of the syllabus. Non-calculator exercises are clearly marked with an icon. The second text also covers material beyond GCSE in preparation for A-level and contains summaries of book 1 and further examination practice exercises. A section discusses how to tackle investigations.

DESIGN: Spot colour only. Limited use of photos. Most of the artwork is clip art and cartoons. Diagrams are clear and paper quality is average.

STRUCTURE:Each chapter starts with the pre-requisites and key points are summarised at regular intervals. Each unit concludes with a summary, numeracy practice, an investigation, and two examination practice papers, one calculator, the other non-calculator, based on the material covered.

CONTENT: Pythagoras is assumed to have been covered before the start of the course and is revised. The circle theorems are illustrated and then proved formally using activities involving the calculation of angles.

VERDICT: Aimed squarely at higher level, this text does well the job it sets out to do. Website with ICT support material.

TITLE: John Murray Maths Now! GCSE Higher I and Intermediate I (Identical content packaged for CCEA) Price: pound;10.99 Tel: 020 7493 4361

SUPPORT: Calculator and non-calculator exercises are marked with icons, and a further icon indicates when a graphics calculator should be used. The history of mathematics is a distinctive feature. Certain exercises are marked as Ma1 and provide investigative work; others offer excellent opportunities for computer work. Teacher’s guides offer four photocopiable revision and consolidation sections.

DESIGN: Limited use of photographs and artwork. Colour is used throughout and the paper is good quality.

STRUCTURE: Each chapter concludes with a summary of key points, revision and extension exercises. The teacher’s resource book includes supplementary questions, some of which will stretch the more able.

CONTENT: The intermediate text doesn’t refer to Pythagoras and the higher text assumes it has been covered. When quoted, the theorem is described as being about lengths of sides rather than areas of squares on the sides. The treatment is rather dull and doesn’t reflect the full possibilities of the theorem. Of the circle theorems, only the angle in a semicircle is developed and proved for use with Pythagoras. It is odd that tangents from a point to a circle are claimed to be equal through the use of symmetry rather than proved to be so through congruency.

VERDICT: History of maths is used very well, but elsewhere was less satisfying. A good buy; it will not disappoint, but is run-of-mill.