Musings: A Compendium of Mathematical Methods by Jo Morgan

The book

Morgan, J. A Compendium of Mathematical Methods. 2019. John Catt Educational.

My reading viewpoint

I was lucky to receive a review copy of this from Jo. As a self-confessed maths geek I was keen to read and learn from this book. As always, I approach with a primary maths focus.


Jo’s book does exactly what it says on the tin: shares a huge selection of methods and strategies for a range of mathematical concepts and operations. Beginning with the essential four operations, links and connections are made across methods and more complex mathematical ideas. The methods range from those commonly taught across primary and secondary phases to methods found in other countries and other centuries. Excerpts from old textbooks adds to the intrigue.

Each chapter follows the same format, which made reading and grappling with the ideas more straightforward. After a useful vocabulary check, each method is exemplified using the same two examples throughout the chapter. Jo methodically works through each method, allowing for readers with less competence (like me with surds!) to develop their understanding and follow the process. Each method comes with a ‘Jo says’ box sharing her thoughts. As Jo herself states, these are not explicit preferences or criticisms but they do offer a real insight, for example by highlighting where a method would not work, is not intuitive or particularly efficient. The use of the same calculations and different strategies is brilliant as it allows for the reader to make connections between methods and across concepts.

As noted above, connections are made between different methods used in different chapters. For me personally this was a huge help, particularly when reading and thinking about concepts that are beyond my area of expertise such as dividing polynomials. The Compendium covers secondary mathematics however a number of chapters are incredibly interesting and useful for primary practitioners.

Overall, I found this book fascinating. I never knew there were so many methods and strategies and have learned a few myself (see below) as well as deepening my understanding of those I was aware of. Jo is clear and concise throughout, and I loved the ‘try it yourself’ options at the end of each chapter which allowed me to have a go with some of the methods I liked. While I read The Compendium cover to cover, it would be a great go-to ahead of teaching a particular concept and could easily be read by chapter.

My key takeaways

1. Exploring methods deepens subject knowledge. OK, this may be an obvious starting point. But for me, this was particularly the case for multiplication (see below). Through exploring and trying out a range of methods for different concepts, I have a more secure understanding of the way an operation works. This would be a great post-SATs exploration for Year 6. It also expanded my understanding. For example, I am aware of the constant difference model for subtraction, but I never thought to apply it to negative numbers i.e. 3 – (-4). My note simply says “This is AWESOME!”

2. Lattice method for multiplication is something I would teach. I have seen the Lattice method before, but have never fully understood it until now. Not only does Morgan provide two clear examples, she also explores why it works. It now may be my new favourite method.

3. I have learned new methods. I could include examples here, but I know without full explanation and exemplification they will be meaningless. Go buy the book and learn some for yourself!

I think you should buy this book if…

  • You have a procedural understanding of many concepts and want to deepen your understanding.
  • Like me, you love reading about different approaches and strategies.
  • You teach maths in UKS2 or secondary.



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