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Yes, but why? Teaching for understanding in mathematics

Yes, but why? Teaching for understanding in mathematics

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February 2017 | 336 pages | SAGE Publications Ltd
Getting the right answers in math is only half the problem. Understanding why what you’re doing works is the part that often stumps students and teachers alike. Does math feels like a collection of random rules and steps that somehow lead you to an answer? Don’t worry, you’re not alone.

Ask yourself: why do we have odd and even numbers? Why do two negative numbers multiply to make a positive? Why do fraction operations work? What is cosine and where does it come from? Yes, but why? answers all of your questions, and sheds light on the hidden connections between everything in mathematics at school. Math makes sense. It always has, but until now maybe no-one ever showed you.

A must-read for those training to teach primary or secondary mathematics via university-based (PGCE, BEd, BA w/QTS) or school-based (School Direct, SCITT, Teach First) routes and current teachers wishing to deepen their mathematical understanding.
Chapter 1: Types of Numbers (Part 1)
Chapter 2: The Four Operations
Chapter 3: Angles and Shapes
Chapter 4: Types of Numbers (Part 2)
Chapter 5: Fractions and Proportionality
Chapter 6: Measurement
Chapter 7: Algebra
Chapter 8: Statistics and Probability
Chapter 9: Functions and Linear Graphs
Chapter 10: The Pythagorean Theorem and Trigonometry

Ed Southall’s new book “Yes, but why? Teaching for Understanding in Mathematics” is the most interesting mathematics education book that I have read in a long time. It is packed full of fascinating nuggets of information, pedagogical advice and suggestions for the classroom. The authors meticulous research is clear throughout, as is his consideration to correct pedagogy. In my opinion, this book should be required reading for all trainee maths teachers, and even the most experienced teachers will, no doubt, learn something.

Dr Tom Bennison
Mathematics Teacher

This is the book that we've all been waiting for! I thoroughly enjoyed reading it and was astonished by how much new stuff I learnt. This book makes mathematical concepts crystal clear. It provides fascinating insights and helpful teaching tips for a comprehensive range of topics. This book has given me a fresh burst of enthusiasm for teaching our wonderful subject! It's a must buy for all new and experienced maths teachers.

Jo Morgan
Maths teacher writer of and SCITT Teacher Trainer

I am currently in my 12th year of teaching maths, and it scares me just how little I really understand about the subject I love.


Why are eleven and twelve not called one-teen and two-teen? Why does a negative times a negative equal a positive? Why can I just flip the second fraction over and change to a multiply when I want to divide? Why does the Venn diagram method produce the highest common factor and lowest common multiple of two numbers? Why is the volume of a pointed shape equal to a third of the volume of the full shape?


I kind of know the answer to these, and I can carry out the skills relatively comfortably myself (unless it is a really nasty fraction, of course), but that is no real help when I am trying to introduce the topic to students and they are asking me why. Now, thanks to Ed’s book, I have the answers and a whole lot more besides.


For this is not just a book packed full of fascinating facts. Scattered through the pages are practical teaching tips that can be used straight away in the classroom.Having read the book, I don’t just have more answers to students’ questions, I also have new ways of introducing and extending topics, and a much more in depth knowledge of a subject I thought I knew pretty well.


Personally, I would make this book compulsory for all trainee teachers, all NQTs, all maths teachers, all Heads of Department, and all Senior Leaders. Basically, everyone. I just wish I had negotiated some kind of commission deal!

Craig Barton
Maths Teacher & TES Maths Adviser, Creator of and

If you teach Maths, this is THE book that you need to read - whatever stage of your career or phase you teach. It goes without saying (but I’ll say it anyway) that 'knowing' the material we are teaching is vitally important but Ed manages to combine essential content knowledge with pedagogical knowledge and he does it with such clarity and passion that this book is exactly the type of “subject knowledge” the profession needs.

Page after page is full of “golden nuggets” and practical advice; “Yes, But Why? Teaching for Understanding in Mathematics” should be required reading for every Maths teacher!

Mel Muldowney
Associate Subject Leader of Mathematics, Winner of TES Maths Team of the Year 2016 and Creator of

For the curious learner inside and in front of every maths teacher asking “Yes but why?”, Ed has compiled an accessible and comprehensive compendium of “well, becauses”. He offers straightforward explanations and diagrams in a thorough breakdown of maths topics from grade 1 to 9. The text is peppered with much-needed derivations of technical vocab, algebraic proofs, and historical origins of maths, not to mention mathematical oddities like the meaning of ‘degenerate polygons’, the ‘obelus’ and ‘sexy prime triplets’! This book has made me a more informed maths teacher and it’s now my go-to repository of mathematical explanations to guide my lesson planning and delivery.

Bruno Reddy
Founding head of maths at King Solomon Academy

The structure of the book is helpful and the visuals are really helpful as are the teachers tips they really support the readers understanding of the process.

Mrs Dawn Burnham
Early Years, Farnborough College of Technology
April 3, 2017

Sample Materials & Chapters

Chapter 1: Types of Numbers (Part 1)

For instructors