1 April 2017

Yes, But Why?

I'm sure you've already heard about Ed Southall's new book 'Yes, But Why? Teaching for Understanding in Mathematics'. It was published less than a month ago and is already on its third print run. It has been incredibly well received by both primary and secondary teachers - everyday I see tweets about how useful it is.

I remember a couple of years ago when Ed (@solvemymaths) first had the idea of writing this book. There was no subject knowledge handbook for trainee maths teachers - it was a clear gap in the market. By writing one, Ed has provided something that maths education badly needed - an expertly written reference manual for mathematics teaching.

People assume that a maths degree is sufficient subject knowledge for teaching secondary mathematics, but there's a lot more to it than that. In maths, subject knowledge includes knowing common misconceptions, effective teaching approaches, alternative methods, underlying concepts, links between topics, interesting maths facts and stories, and more... Even the most experienced maths teachers with high levels of subject-specific expertise can develop their knowledge further.

Since reading Ed's book I've noticed a subtle shift in my teaching style. For example I found myself excitedly talking to my Year 11 class about the difference between an ellipse and an oval. They were surprisingly fascinated - one of them was really pleased with himself when he spotted the link to the word ovary. And in a recent lesson on geometric proof, I talked for a while about Euclid - it was the longest period of silence I've had from that class! They genuinely seemed enthralled. A highly knowledgeable teacher is confident and engaging. That's the kind of teacher I want to be.

In this post I've featured a few extracts from 'Yes, But Why? Teaching for Understanding in Mathematics' to give you an idea of why it's worth buying.

Statistical Graphs
Histograms are really unpopular amongst GCSE teachers. I'm a statistician and even I admit that I don't look forward to teaching this topic. Ed explains very clearly why histograms use frequency density instead of frequency - in fact I plan to use his examples next time I teach it.

Ed's book tells me that histograms were developed by English mathematician Karl Pearson in around 1910. This is of personal interest to me because Karl Pearson was the man who founded the world's first university statistics department at University College London in 1911 (the very same department where I did my statistics degree ninety years later).

Given that maths teachers often find statistics difficult to teach (or even, dare I say, not enjoyable...), I think that the statistics chapter of Ed's book will be incredibly useful. In the section on pie charts, Ed shares a good example of a useless pie chart, and encourages teachers to discuss the pros and cons of each type of statistical graph with students.

Teacher Tips
Practical tips feature regularly throughout the book. This tip regarding area is very sensible - asking students to find the area of a parallelogram when only the base and perpendicular height have been provided seems a little silly.
Deriving y = mx + c
I'm guilty of telling students that the equation of a straight line is y = mx + c without telling them why. If they know that gradient is 'change in y ÷ change in x', then it's pretty simple to derive y = mx + c, as shown below.

This is obvious, if you stop and think, yet I've never shared this with my students. I guess the problem is that for teachers, right from day one of their training, there is no time to stop and think.

The book features a list of unusual units of measure, and lots of other wonderfully geeky mathematical trivia. I love this stuff!

'Yes, But Why? Teaching for Understanding in Mathematics' is informative, witty, enjoyable and incredibly useful. It's available to buy now. If you're still undecided, you can preview the first chapter here. Let me know what you think.


  1. I'll read this book once I've finished Boaler's maths mindset. Thanks, @Mr_J_Maths.

  2. I've really enjoyed reading it as well. So much to learn and reflect on. In many cases - like you say - it's not that Ed presents things I don't already know (although there is obviously a lot of that as well!) but rather little nuggets that I should share more with students that I don't.

    As someone who primarily teaches adults, I find teaching the subject as part humanities really serves it well. Mathematics as a subject is one that is the culmination of thousands and thousands of years of great minds. There are so many stories to tell about the origins and why Pythagoras' Theorem was important in those times - about why it wasn't even his theorem. All this stuff enriches the learning experience for the student with the added bonus of not having to remember the theorists name for assessment. They only need to remember what they added to the mathematical world!