It wasn’t too long ago—not even three years—that I finished reading David Didau’s terrific book (this one), so I still remember the excitement that I felt reading it, and watching all of the silly certainties of common wisdom in education being dismantled in front of my eyes, making way—I could only hope—for pedagogical practices informed by a real science of learning.

I felt a similar excitement reading Craig Barton’s book How I Wish I’d Taught Maths, because in this book, at long last, are many of those practices in one place, constructed, as readers will see, next to the debris of familiar canards and shallow reasoning that once guided parts of Barton’s teaching.

It is not a book full of proclamations about “best” practice. But you will find in this book a beautiful translation of the science of learning to the classroom. And far from the drudgery that one may imagine this to be, the joy of effective explicit instruction, for both teacher and students, comes through in every chapter of the author’s writing. It is serious, thorough, humble, and humane. And accessible: perhaps the greatest pleasure in reading it is knowing that you could turn around and start to implement many of these practices in short order—or, perhaps, that you already do these things, but don’t know why you should stick with them or how you could improve on them.

I have a lot of underlines and margin notes, but I think these three snippets together, from the chapter on problem solving and independence, are my favorites. The section starts, as they all do, with what the author used to think:

I used to love the sight of my students struggling through problems. Scratching heads, heavy sighs, and even the snap of a pencil thrown down in frustration were the soundtrack to learning. . . .

And then we are introduced to one of these problems, Question 23 from this paper (PDF), along with a deep concern for how novices will handle it. Contrast Barton’s new diagnosis below with common wisdom—that students ask why they are doing math because it is boring, tedious, procedural, or not relevant to their lives.

The task of choosing cards and calculating their totals may prove so cognitively demanding that novices do not have any spare cognitive capacity to recognise patterns. They do not realise that it is not the actual totals that matter, but whether those totals are odd or even. They just carry on regardless. Moreover, students are so consumed with the minutiae of the problem that no cognitive capacity remains to consider the global picture—why are they doing this? The result is that the novices may end up with an assortment of lists and totals, but not actually do anything with it—the fact that this is a probability question was pushed out of working memory long ago when the first set of cards was being processed.

As you might imagine, since the diagnosis is different from that received from common wisdom, the prescribed treatment is different too:

Before I set students off to work independently, I ensure they have enough domain-specific knowledge to solve problems on their own.