Review of: How I Wish I’d Taught Maths


Craig Barton, a British math teacher, introduces his topic in a humble fashion—unusual among educators. He endeavors to talk about being a math teacher, and so he begins with his qualifications. While he notes his bona fides as an “Outstanding” teacher with a national and international reputation, including work in Thailand and Cambodia, he does so to say that his awards were on the basis of his own opinions and experience, not research. His thesis follows: we should not rely on what we know works or on our experience, and we should not teach in ways that are obvious; we should read and apply The Research. When Barton did this, his results were surprising. He says, “We were getting through more work in class. My students seemed more confident with the concepts we tackled. I felt like I was actually teaching” (19).

Before I continue, it is worth noting that Barton doesn’t stop being humble. At the end of his introduction, he notes that “the more I know, the less I understand” and asks us to join him in confronting our weaknesses head-on and “striv[ing] to improve.” He finishes with this admonition: “I am not sure I agree with all of it myself” (23)! This book explores a variety of research with broad application.[1]  Read it as such and prepare to be amazed and even transformed as a teacher—whether you teach “maths” or not. This approach has even changed my own presentation modes as an educational leadership consultant!


The book has twelve themes, including focused thinking, deliberate practice, and long-term memory and desirable difficulties. Each themed chapter has four sections:

  1. What Barton used to do
  2. Sources of inspiration (i.e., a short review of the research)
  3. Barton’s takeaway
  4. What Barton plans to do from now on

Key Aspects

I will share key aspects of three chapters, with the hope that you will be inspired to buy this book, put it on your bookshelf, and thumb through it regularly. While it is an academic text, it is very readable. There is no bibliography at the back to prove how clever the author is, and there are no footnotes to distract. The language is technical without being pedantic, and the argument flows with mostly short sentences. He attempts to share with the reader, not impress them.

The first important moment comes from the chapter “How Students Think and Learn,” where Barton says that “engagement alone does not imply learning” (39). Attempting to engage students can become the primary goal of teaching, but engagement, interest, and even motivation cannot automatically be equated with learning. Instead, he quotes Peps Mccrea, the dean of learning design: “Students remember what they attend to” (38). So, Barton reflects on what he used to do and progresses to what he does now.[2] 

  1. What he used to do: be entertaining to get engagement
  2. What research says: that engagement is not necessarily learning
  3. His takeaway: he needs to focus on “attending” rather than engaging
  4. From now on: he declares that “engagement comes a far distant second when planning lessons to considerations of learning” (41)

The second moment is from the chapter “Motivation,” where Barton talks about the tough problems he used to give his students to struggle with. To him, the difficulty was good because it was “obvious” that struggle and failure bring about brain growth. He quotes Middleton and Spanias, explaining that “the effort a person is willing to expend on a task is determined by the expectation . . . [of] a successful outcome” (79). In other words, humans—even children—constantly do cost-benefit analyses to see whether an action is worth it. Failure, Barton finds, does not result in a growth mindset but in disillusionment.[3]  He quotes a student: “It’s kind of hard to have a growth mindset when I keep doing s— on tests, sir” (80). Barton again reflects on what he used to do and progresses to what he does now.

  1. What he used to do: rejoice in making his students struggle and fail
  2. What research says: that the growth mindset is hard to support
  3. His takeaway: students need the experience of past success to continue to put in effort
  4. From now on: he believes that success is key to learning; students need immediate success—within twenty seconds—and enough challenge to keep them thinking hard

The third moment comes from the chapter “Deliberate Practice.” One of Barton’s old teaching objectives was to “introduce complex processes as a whole” (261). He showed students the whole problem, such as a simultaneous equation, and then went through the steps necessary to solve it—a very common teaching method. And if the student gets it, it “obviously” works. But when a student doesn’t get it, how does the teacher help? “Deliberate practice” starts from a different place: it aims to isolate individual skills and provide regular and specific feedback to improve performance. Barton points out that musicians don’t practice by playing whole pieces; instead, they focus on difficult phrases and tricky jumps[4] . Ultimately, he realized that practice is not the same as final performance (274). So:

  1. What he used to do: teach with whole processes, since they provided context and were presumably the same as the “final performance”
  2. What research says: that “deliberate practice,” breaking down the process into subprocesses, is far more effective
  3. His takeaway: to implement the five stages of “deliberate practice”
  4. From now on: he writes, “By isolating, developing, assessing, performing, and practicing retrieval later, I can help students transition along the path to expertise” (271)

If you are an academic administrator, please buy a copy of this book for each of your math teachers and even one for every other department. You don’t have to read it cover to cover, as each chapter stands on its own. If you do read the entire book, the chapters cross-reference and support each other for a holistic pedagogical study. For those who like synopses, you can turn to the end of each chapter for an “If I only remember three things” section. You can also review the two-page conclusion of each chapter, where Barton explains ten takeaways of his journey as an educator. He even gives extremely detailed examples throughout the book, which could serve as lesson plans!

Is there a Christian twist to this? I believe so. Our schools are full of dedicated and intelligent Christian teachers. In my experience, most do not believe that each of their students can succeed. [5] Books like this help us confront the secular pessimism of the bell curve and reject the belief that some children are doomed to fail. As Christians, we believe that every child can and will succeed; the biggest obstacle for our students is ourselves. Craig Barton’s How I Wish I’d Taught Maths gives us the tools to reach every child in our classrooms with God’s blessing of salvation.

Work Cited

Middleton, J. A., and P. A. Spanias. “Motivation for Achievement in Mathematics: Findings, Generalizations, and Criticisms of the Research.” Journal for Research in Mathematics Education, vol. 30, no. 1, 1999, pp. 65–88.

Work Reviewed

Barton, Craig. How I Wish I’d Taught Maths: Lessons Learned from Research, Conversations with Experts, and 12 Years of Mistakes. John Catt Educational Ltd., 2018.

Simon Jeynes began teaching in 1977 and got his first Commodore 64 in 1981. He has consistently advocated for a child-centered approach and, when he joined Facebook in 2007, was gratified to gain former students as followers. Now, he is executive director of Christian School Management, a research and biblically infused consulting group composed of Christian school leaders who help schools increase enrollment, implement the best emerging practices in governance/operations/academic leadership, and put resurrection hope back into the Christian school movement. Feel free to contact Jeynes at or visit him online at