Overview

Full Product Details

Author:   Christian Puritz (Formerly Royal Grammar School, UK)
Publisher:   Taylor & Francis Ltd
Imprint:   Routledge
Weight:   0.453kg
ISBN:  

9781138680197

ISBN 10:   1138680192
Pages:   226
Publication Date:   27 January 2017
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Introduction Part I: 11-14 years old 1. Decimals and multiplication by 10 etc. 2. Multiplying and dividing by decimals 3. Adding fractions 4. Multiplying and dividing by fractions; and by 0? 5. Using patterns with negative numbers 6. Use hundreds and thousands, not apples and bananas! 7. Angles and polygons 8. Special quadrilaterals 9. Basic areas 10. Circles and pi 11. Starting trigonometry 12. Square of a sum and sum of squares 13. The difference of two squares 14. Another look at (a-b)(a+b) 15. Number museum: how many factors? Part II: 14-16 years old 1. The difference of two squares revisited 2. The m,d method: an alternative approach to quadratics 3. Negative and fractional indices 4. A way to calculate pi 5. Pyramids and cones 6. Volume and area of a sphere 7. Straight line graphs 8. Percentage changes 9. Combining small percentage changes 10. Trigonometry with general triangles 11. Irrational numbers 12. Minimising via reflection 13. Maximum area for given perimeter 14. Farey sequences 15. Touching circles & Farey sequences again Part III: 16-18 years old 1. Remainder theorem… 2. Adding arithmetic series 3. D why? by dx; or What is differentiation for? 4. Integration without calculus 5. Integration using calculus 6. Summing series: using differencing instead of induction 7. Geometric series, perfect numbers and repaying a loan 8. Binomial expansion and counting 9. How to make your own logarithms 10. The mysterious integral of 1/x 11. Differentiating exponential functions 12. Why do the trig ratios have those names? 13. Compound angle formulae 14. Differentiating trig ratios 15. Fermat centre of a triangle

Reviews

Colin Foster, University of Nottingham There is certainly a pressing need for something that would assist school teachers in presenting mathematics in more discursive and mathematically rigorous ways, and that seems to be very much the focus of this proposal. However, none of these is similar in style to the proposed book. The conversation format is a unique feature, and the focus on mathematics and quality of explanation, depth of thinking is particularly pronounced. I could imagine the book appealing to teachers who use the materials (and books) provided by the UK Mathematics Trust, but they don't have anything like this. Many teachers would benefit considerably from the advice given (implicitly) here about how to introduce and build ideas and tackle misconceptions. John Woolmer, Winchester College, UK I like the proposed material which judging by the sample chapters will be well presented, at times unusual, and always stimulating and clear. Juan Perez, Former Teacher, UK This proposal aims to cover a genuine gap in the market of books for (primarily) Maths teachers offering a rationale and an explanation for many of the facts given to students. The proposed book brings together some beautiful mathematics, making strong connections between the foundations of the subject and the facts that are distilled and eventually presented to students. Maths teachers will find many of the ideas developed in this book of great value as connectors between topics, laying the foundations and the rationale of much of what they present to pupils. In summary, I am very happy to recommend the publication of this book.

Author Information

Christian Puritz studied maths at Wadham College, the University of Oxford and completed his PhD at Glasgow University, UK. Following on from his studies, he taught mathematics at the Royal Grammar School, High Wycombe, UK for more than thirty years. He currently offers home tuition for children of all abilities.

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