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Explaining and Exploring Mathematics Christian Puritz (Formerly Royal Grammar School, UK)

Explaining and Exploring Mathematics von Christian Puritz (Formerly Royal Grammar School, UK)

Explaining and Exploring Mathematics Christian Puritz (Formerly Royal Grammar School, UK)

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Explaining and Exploring Mathematics Zusammenfassung

Explaining and Exploring Mathematics: Teaching 11- to 18-year-olds for understanding and enjoyment Christian Puritz (Formerly Royal Grammar School, UK)

Explaining and Exploring Mathematics is designed to help you teach key mathematical concepts in a fun and engaging way by developing the confidence that is vital for teachers. This practical guide focuses on improving students' mathematical understanding, rather than just training them for exams. Covering many aspects of the secondary mathematics curriculum for ages 11-18, it explains how to build on students' current knowledge to help them make sense of new concepts and avoid common misconceptions.

Focusing on two main principles to improve students' understanding: spotting patterns and extending them to something new, and relating the topic being taught to something that the pupils already understand, this book helps you to explore mathematics with your class and establish a successful teacher-student relationship.

Structured into a series of lessons, Explaining and Exploring Mathematics is packed full of practical advice and examples of the best way to answer frequently asked questions such as:

  • Do two minuses really make a plus?

  • Why doesn't 3a + 4b equal 7ab?

  • How do you get the area of a circle?

  • Why do the angles of a triangle add up to 180 Degrees?

  • How can you integrate 1/x and calculate the value of e?

This book will be essential reading for all trainee and practising teachers who want to make mathematics relevant and engaging for their students.

Explaining and Exploring Mathematics Bewertungen

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.

Über Christian Puritz (Formerly Royal Grammar School, UK)

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.

Inhaltsverzeichnis

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

Zusätzliche Informationen

GOR008633879
9781138680210
1138680214
Explaining and Exploring Mathematics: Teaching 11- to 18-year-olds for understanding and enjoyment Christian Puritz (Formerly Royal Grammar School, UK)
Christian Puritz (Formerly Royal Grammar School, UK)
Gebraucht - Sehr Gut
Broschiert
Taylor & Francis Ltd
2017-01-27
218
N/A
Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Dies ist ein gebrauchtes Buch. Es wurde schon einmal gelesen und weist von der früheren Nutzung Gebrauchsspuren auf. Wir gehen davon aus, dass es im Großen und Ganzen in einem sehr guten Zustand ist. Sollten Sie jedoch nicht vollständig zufrieden sein, setzen Sie sich bitte mit uns in Verbindung.