The book

** Pershan, M.*** Teaching Math With Worked Examples.*** **2021. **John Catt Educational**

My reading viewpoint

My current role allows me to explore different ways in which mathematics can be taught to primary school children. Therefore, when I saw this book on Twitter, I felt it important to have a look and see what I thought. Teaching with examples is something that appears in a number of books including Craig Barton‘s. Of course I, like all teachers use examples in my teaching all of the time. This book focuses attention on using these effectively to teach new mathematical concepts.

I also have to thank the NCETM for being kind enough to interview me for their podcast, thus prompting this review!

Summary

Teaching Math with Examples does exactly what it says on the tin. The author is an experienced (American, hence the name) maths teacher who makes use of worked examples in his daily teaching. He has researched this approach extensively and recognises that teachers often do not have time to fully engage with educational research. In this book, he shares both an accessible introduction to the research and ideas around worked examples and also practical advice from his own classroom.

So what exactly is an example? As I said, most teachers will use examples constantly in maths lessons, so why do we need a book to learn about it? Well, Pershan argues that examples should be worked – that is, include the solution. While it is a little more nuanced than that, he argues that ‘if we value achieving mathematical understanding, we can see the studying of a solution for what it is: a core mathematical act.’ (p.12) So the book largely focuses on teaching using these worked, completed examples – sometimes correct, sometimes not, sometimes complete, sometimes not – and how using these can make us more effective.

This isn’t a new idea and I have read numerous books extolling the virtues of a worked example. However, what I really like about Teaching Math with Examples is the depth of understanding I have gained from this approach. Other books lack the detail and research. I also like a book that provides a resource and this is no exception – check out SERP’s Math by Example!

Teaching Math with Examples is easy to read and easy to see where it can be applied in the classroom. I like the layout with summaries ending each chapter, heaps of research distilled into easy-to-read bursts and a great final chapter which basically does my key takeaways for me! The only small drawback is since it is an American text, sometimes some of the explanation wasn’t clear to me, for example looking at equations. I am sure a more experienced mathematician would have no trouble, though, and it didn’t really detract from what I took out of the book.

My key takeaways

**Just how much are my pupils thinking when I work through an example with them, and what can I do?**Pershan acknowledges that worked examples are not some magic bean to understanding: ‘students learn when they think actively and deeply about a worked example’ (p.20). He suggests a process of Analyse – Explain – Apply when approaching a worked example and that made me think about how I show workings to pupils. One of the things I want to try out is focusing attention on a completed example.**Focusing on completed examples can help all pupils.**Imagine a scenario where you flummox a class with a problem, wondering why they just don’t get it. Providing a worked example for pupils to engage with, followed by a similar example, is – according to Pershan and his research – likely to lead to more success and more learning. I also think this approach can be great for my higher attaining pupils – can they reason and explain the example? Can they articulate the need for each step?**Part- and whole-task practice may be something we miss in primary.**Teaching Math with Examples dedicates Chapter 5 to this idea so I won’t go into too much detail. Essentially I read part-task practice as working on the small steps to answer a problem e.g. how to add, how to find an equivalent fraction, how to simplify. We do a lot of this in primary and many of us do it well. But what happens next? Do we ask them to do Step B while still thinking about Step A? Step C that relies on Step A? I’m not sure how often I explicitly help my pupils to connect the dots of part-practice.

I think you should read this book if…

… you teach secondary mathematics.

… you are a Maths Lead or someone with responsibility for curriculum / pedagogical decisions in teaching maths in primary

… you have read about worked examples and want a more detailed look.