Maths Insight: Copymaster Resource Book, CD and Teachers' GuideReview by: Jennie GoldingMathematics in School, Vol. 34, No. 4 (Sep., 2005), p. 34Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30216617 .

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REVIEWS REVIEWS REVIEWS REVIEWS Number Without a Worksheet The Early Childhood Mathematics Group ATM Publications 2004 ISBN 1 898611 29 7 36 pages, paperback Price to non-members 012.00 Personal members price 08.40

For a new teacher to Reception or a more experienced Reception teacher looking for practical activities to promote mathematical thinking, this booklet may be worth a look. It contains twelve activities built around the Reception key objectives for number. Each includes clearly outlined learning intentions, ideas for extension and simplification, key questions, variations of the task (including adaptations for outdoors!) and recording suggestions. The booklet is primarily designed to support the transition between Reception and Year 1 by guiding teachers away from worksheets towards hands-on learning and whilst it is unlikely to be of direct use to Year 1 teachers past the first term, it certainly provides food for thought.

Emma Chapman

Calculator Graphing Barrie Gilpin and Alan Graham A+B Books 2004 ISBN 0 9541020 4 5 128 A4 pages 011.95 www.AplusB.co.uk

This A4-sized book contains a wealth of calculator exercises that are bound to appeal to all those with an interest in the use of graphics calculators to enhance teaching and learning. The exercises are written specifically for the TI-83 plus but can be easily adapted to other models. I used a TI- 89 when working through the book. The contents cover Cartesian, polar, parametric and sequence graphs in a way that shows how mathematics can model motion and the fascinating and beautiful patterns in nature. There is an interesting section on projectiles and pendulums that presents these areas of A2 mechanics in an appealing way for able KS4 pupils. The section on polar explorations includes work on spirals and links these to patterns on shells. There is an 'exploratory feel' to the exercises and the reader is drawn into a 'what happens if' mode of working that leads to both discovery of new mathematics and mastery of the calculator. This book is literally packed with material designed to make pupils think and explore. Another interesting section deals with thinking, braking and stopping distances and introduces the use of tables and lists to enter data along with the linear and quadratic regression facilities on the calculator. I used sections from the book with pupils in years 9 to 12. ! found the units on sequence graphing particularly useful. There is an introductory section entitled 'Is it Magic?' where pupils are invited to think of any number, divide by 5, then add 3. The same operations in the same order are then repeated on the subsequent

34

output. This simple feedback loop provides a very nice way to introduce term-to-term relations and allows important concepts such as convergence to be introduced fairly early on in the secondary curriculum. There is also much to be gained from comparing the way recursive sequences are entered into the calculator with the suffix notation used in textbooks. And here too is further opportunity to reinforce important vocabulary - (recursive, iterate, converge, diverge). My favourite chapter in the book was 'Steps into Chaos', focusing on how the logistic equation, un

=

kun_1 (1-un_), is used to model

population growth. This provided an enjoyable extracurricular topic for able Y10 pupils who used the calculator to explore convergence and oscillation by varying the value of k in the logistic equation. As k went beyond the value of 3 the chaotic behaviour of the sequence was evident from the graph plotted in 'Time mode'. The section contains excellent material for use in the numerical methods section of A2 Pure Maths, with opportunity to use the calculator's 'sequence-web' mode and its zoom facility very effectively. Staircase and cobweb diagrams homing in on a point of intersection can be compared with the convergence of un to a limiting value. I enjoyed using the book. Although the mathematics is high-powered, humour and cartoons are ever present to add appeal for younger readers. There is plenty of material for use both within and beyond the curriculum at all key stages. If your ICT suite is overbooked and you want to use technology to explore important areas of mathematics further, then this book, an OHP view panel and a set of graphical calculators could provide a very effective alternative.

Keith Noble

Maths Insight: Copymaster Resource Book, CD and Teachers' Guide NFER Nelson 2003 ISBNs 1 85838 521 0, 1 85838 523 7, 1 85838 524 5, 1 85838 525 3 (approximately 120 pages each) for each of ages 9 and 13.

Maths Insight 9 and Maths Insight 13 are sets of paper and computer-based teaching materials that have been written to develop mathematical thinking in students from the top 10% of the ability range of pupils aged 9 and 13, respectively, and are published under the World Class Arena umbrella. The resources encourage students to use and apply the mathematics they have already learned, developing a depth of under- standing and application beyond that usually expected by the national curriculum for these age groups. Students may be asked to combine elements of knowledge from different areas of mathematics, sustain reasoning through a sequence of steps, or apply knowledge in a tricky or unfamiliar situation. Students are required to describe how they came to their conclusions, thus broadening reasoning skills.

Using the CD provided in the teachers'

guide, teachers can select up to five problems (of forty or fifty in a book) that students can attempt as individuals or in groups. Students using the CD can try the question on screen and print out, or e-mail, their answers for marking or discussion. The teachers' guide provides suggestions for how to use and extend the questions to support teachers in developing their best mathematicians, including key points that highlight the particular difficulties that the question presents, useful starting points from which to introduce the question, and further information about each.

As with the original world-class test questions and practice materials, these are excellent resources, and well pitched for the intended target group to use independently, individually or in groups. But why stop at that? The five 'Starter' questions in each book are closed although requiring creative understanding; other questions vary from limited scale, although easily extendable, to really quite substantial investigations. All of these questions are accessible to less obviously able students if scaffolded appropriately, and many would make superb starting points for whole-class investigation or discussion, developing precisely those transferable mathematical thinking skills so marginalized in many classrooms. They are easy to use, particularly in digital form, support notes for teachers are superb, and secondary mathematics departments would do well to have both sets not on their bookshelves but in use in their classrooms.

To those who feel that they cannot justify the time for such quality provision, I would argue that we cannot afford not to provide it: the evidence is that students with these sorts of experiences are more confident and motivated mathematical thinkers (and medium-term, formal summative assess- ments will reflect that).

Jennie Golding

Teaching Maths using ICT Adrian Oldknow and Ron Taylor Continuum 2004

ISBN 0 82647 059 9 Softback

019.99

This book is a very welcome and timely addition for any mathematics teachers' personal library as well as that of the department. It is an updated and revised version of a similar title, first published in 2000. The change of emphasis from Teaching Maths with ICT to Teaching Maths using ICT is encompassed with this revision.

A clear and concise introduction helps the reader put into context the teaching of mathematics using ICT - both locally and nationally, as well as highlighting the aims that the authors are pursuing. A glance at the chapter headings gives an insight into the emphasis pursued by them en route to achieving these desirable targets:

Mathematics in School, September 2005 The MA web site www.m-a.org.uk

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