“Yes, But Why? Teaching for understanding in mathematics” by @solvemymaths

January 20, 2018

Yes, but why? Teaching for understanding in mathematics by Ed Southall

It’s pretty rare for me to use my status as a blogger to ask people for a copy of their book to review. This is because then I’d feel obliged to read it (though feel free to send me your books if you don’t mind the fact it may take me years to get round to reading them). But I made an exception for this book because Ed Southall is the one person I have ever heard talk about teaching for understanding in maths in a useful way, rather than as an excuse for a particular pedagogy.

Everyone wants to teach for understanding, but people assume that the way they conceive of mathematics or individual topics in mathematics is the correct understanding. My degree in Pure Mathematics convinces me that the only people who really understand mathematics are those who have studied Analysis or Algebra at undergraduate level. Those with a background in applied maths or physics might think the use of mathematical models shows true understanding. Engineers might think that application to real life technical problems is the best demonstration that maths is understood. There also seems to be a large cohort of people involved in teaching maths, especially at primary level, who seem to equate understanding with representing mathematical ideas in diagrams or with objects.

This book takes the approach that understanding can be approached by fleshing out the maths we are (probably) already familiar with. There are perhaps a few too many diagrams in there, but there is also a wealth of explanations about terminology, history and context alongside justifications for almost every procedure we might teach up to GCSE and what I can only describe as “fun facts” about familiar bits of mathematics. It also provides frequent warnings against the most common misconceptions that can be caused by teaching something you do not fully grasp. I qualified as a maths teacher in 2001, and as a pure mathematics graduate I am sure I had more “purely” mathematical knowledge than most, but I had not known where the word “surd” comes from or that the division symbol is called an “obelus”. Other elements of the book, like how many steps there are in “BIDMAS”, I recognised as things I had to learn the hard way when I started teaching.

Unlike almost everything I have heard about “teaching for understanding” previously, Southall implies that the best way to teach for understanding is to have as much understanding as possible yourself, and then helps the reader with that. For that reason, the book would be particularly useful for:

  • New or trainee maths teachers lacking confidence with their subject knowledge, looking to identify gaps in their knowledge.
  • New or trainee maths teachers with stronger subject knowledge, who want an understanding of how “school mathematics” differs from the mathematics they already know.

The one weakness of the book is probably the “Teacher Tip” sections, with suggestions for how to teach. None of them particularly appealed to me as good teaching approaches, and I would look elsewhere for advice on teaching methods. But the book remains the only one I could recommend as the first place to go for developing maths subject knowledge. I can’t be the only maths teacher who thinks it’s cool to know the equals sign was invented in Wales.


Yes, But Why? can be found on Amazon here and Ed Southall’s blog can be found here. 



  1. Reblogged this on DT & Engineering Teaching Resources and commented:
    “Yes, But Why? Teaching for understanding in mathematics” by @solvemymaths

  2. ‘Unlike almost everything I have heard about “teaching for understanding” previously, Southall implies that the best way to teach for understanding is to have as much understanding as possible yourself’.

    Which should be a statement of the bleeding obvious, made over and over again in every PGCE course. Why isn’t it?

  3. Reblogged this on The Echo Chamber.

  4. Thanks for the recommendation.

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