My pupils often remark on my enthusiasm for literature. They seem genuinely surprised to discover that someone who recently guided them through Pythagoras’ Theorem was also reading Kafka. Surely, they insist, it cannot be that an A-Level Maths teacher has ever read The Great Gatsby?!
Most mornings, however, before I arrive at work, I enjoy twenty to thirty minutes of reading on the number 41 bus as it creeps across North London, and often longer on the return journey slowed by evening rush hour. Monday morning reading during form time, I consider to be as important as many of the maths lessons I deliver. Asking pupils whether they are enjoying their current book—Why? Why not?—and letting them ask similar questions of me, is a valuable model for them to follow. The benefits of reading are significant and well-documented. Moreover, whilst its effects are not always easy to measure, literacy profoundly influences attainment in mathematics.
Among my favourite novels are those I consider truly unique, although perhaps all keen readers feel this way about their favourites. For example, The Master and Margarita by Mikhail Bulgakov is so otherworldly it defies comparison. Even more so, A Clockwork Orange—whether you love it or loathe it—is undeniably one of a kind.
In truth, however, I gravitate more toward nonfiction. Within this genre, I seek books that broaden and challenge my perspective. One such book is The Health Gap by Michael Marmot, which scratches beneath the surface of causes driving demand on the NHS. Another is The Righteous Mind by Jonathan Haidt, which will make you question your own decision-making processes. I suspect both books would broaden the horizons of the vast majority of readers. With this in mind, I plan to write (short) reviews of four maths books, each aligning with one of the categories above. The first is a classic of mathematical thought: How to Solve It by George Pólya.
A Classic of Mathematical Thought:
The best books often articulate what we already know—or suspect—in a distilled and coherent form. For me, this was the case with one of the above books, Jonathan Haidt’s The Righteous Mind, which explores the fallacy of believing in your own objectivity. Similarly, Why Nations Fail by Acemoglu and Robinson provided a framework to explain why some countries thrive while others falter. Both books enabled me to combine fragmentary ideas into a structured narrative, and both books I highly recommend to readers of this blog.
This is also true of How to Solve It. As maths teachers, we often suggest problem-solving strategies tailored to specific questions. What we may lack, however, is a comprehensive framework that enables us to coherently put forward these ideas: How to Solve It fills this gap. His four-step method—Understand the problem, Devise a plan, Carry out the plan, Look back—may seem simple, but its value lies in its adaptability. Each step will manifest differently to different problems, and thus careful guidance and a diverse repertoire of resources for effective teaching will be required if you are hoping to develop these approaches with your learners.
For any readers of this blog who are also regular users of Maths Advance, this approach will soon be a focus on the platform. I plan to develop year group-specific, curriculum-based problem-solving content, with teacher guidance on how to incorporate Polya’s strategies into lessons.
A Balanced Critique:
My only real criticism of How to Solve It lies in a common pitfall among university-level academics. Polya critiques primary and secondary education for focusing too heavily on procedural fluency and exam preparation, at the expense of creativity and genuine problem-solving. While this critique has merit, it oversimplifies a complex issue, ignoring systemic constraints that incentivise procedural fluency at the expense of problem-solving.
Final Thoughts:
How to Solve It remains a classic. Have you read it? What lessons have you taken from it, and how have you applied them in your teaching?
Another blog post in the form of a book review, coming soon.
George Bowman
Founder, Maths Advance
MATHS ADVANCE BLOG 
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