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Explaining and Exploring Mathematics

Teaching 11- to 18-year-olds for understanding and enjoyment

By: Christian Puritz

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Paperback | 27 January 2017 | Edition Number 1

At a Glance

Paperback
228 Pages

Dimensions(cm)
24.61 x 17.4 x 1.22

Paperback

$112.75

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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.

Industry 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.

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