There Is No Perfect Teacher (Just a Bunch of Great Ones)

I’ve taught at two schools in my career.

The first, in California, had a dozen teachers in total. I adored my colleagues, but we each had our own domain. I handled Trig, Precalc, Calculus, and Stats. Soon I fell into unquestioned habits, built on assumptions I didn’t know I was making.

My second school, in England, had a dozen *math* teachers. It was as if, after years of playing bass in my empty garage, I had suddenly been recruited into an actual band.

My first winter, I took myself on a tour of the department, observing a lesson from each of my new colleagues. I came away convinced that there’s no one way to teach mathematics, that our methods are necessarily as diverse as our goals.

Take two very different teachers: Simon and Tom.

Whereas I’m always fretting about students who can execute procedures without understanding them, Simon wastes no such worrying; he simply weaves the two together far better than I do. His notes at the board model clear and disciplined thinking, and he gives written comments every bit as careful and analytical as the work he expects. (He is also one of the two most competitive sportsmen I have ever met.)

Tom couldn’t be more different. At the front of the room, he’s less a lecturer than a provocateur: the mischief-maker in chief, whose highest goal is to create space for mathematical exploration.  That means open-ended problems, and multiple days spent wrestling with a single provocative question. He incites debates, sets traps, and shines a spotlight on the students’ own thinking. (He is also one of the two most competitive sportsmen I have ever met.)

But the diversity in math teaching runs deeper than the Simons vs. the Toms, traditionalists vs. progressives.

Take Beccy. She’s a master of rapport, and a motivator of even the most reluctant. Whereas many mathematicians prefer working with top students, Beccy is a fierce guardian of the strugglers and the stragglers, needling and teasing them even while radiating warmth.

Tim C. takes another angle. At a school with some of the most precocious mathematicians in the United Kingdom (one of my 14-year-olds invented proof by induction for himself, I kid you not) Tim finds ways to challenge them all, drawing from a bottomless supply of devilish problems. An immensely creative problem-solver himself, he knows how to incubate this sort of thinking in students. It’s a skill I thought was essentially unteachable until I saw Tim teaching it.

By now you get the idea, but I can’t resist going on:

Richard is, quite simply, my hero: a cultivator of deep, rigorous thinking who brought to his classroom an erudition and philosophical depth rarely found in university teaching, much less at the secondary level.

Neil (my boss and foremost Twitter abuser) orchestrates lessons around grand, simple questions, unveiling favorite pieces of mathematics with a conductor’s flair.

Like other veteran teachers I’ve known, Chris makes his mark not only in the classroom, but in the extracurricular life of the school. He organizes myriad trips and expeditions, including the annual three-day camping adventure for sixth graders (who are known, lovingly, as “Shells”).

It was always a treat talking with Tim M. Our classroom practices differed, sometimes sharply (whereas I put a lot of value on oral communication, he wanted students to express their understanding through careful written work) but our goals enjoyed an uncanny synchronicity. I suspect that my mathematical thinking resembled his more than any of my other colleagues.

Laurence is a modern-day James Brown: the hardest-working man in show business. One of my greatest pleasures last year was building the 7th-grade curriculum with him, watching the enormous-yet-lightning-fast gears of his mind spin to solve the pedagogical problems we encountered. (He also single-handedly built a virtual Library of Alexandria for the students on the school’s internal computer system, known as Firefly.)

Peter, who came to teaching after a career in the Royal Air Force, reminded me of Dwight Eisenhower: a nearly omnipotent strategist who always seemed to get the results he sought.

Becky, the department’s youngest member, showed an uncanny knack for the classroom, quickly developing an arsenal of pedagogic moves that outstripped my own.

My fellow Ben, arriving midyear from Brazil, showed extraordinary calm under conditions of perpetual chaos.

Ed is perhaps the most centered person I know. His pedagogy modeled patience and persistence, seeking out errors and uprooting misconceptions. Our 35-minute lessons always felt like a sprint to me. Ed, despite being a top-tier 800-meter runner, never showed an ounce of rush or haste.

And Robin (whom I’ve written about before) was all gruffness on the outside, all gold on the inside. (Sometimes, if you could trick him into wearing a Hawaiian shirt, you’d see the gold on the surface, too.) Observing his lesson, I watched him cut straight to the deep, conceptual heart of the matter, and thought, “That. That’s what I’m aiming for.”

It’s not just the variety of methods that I love. It’s the variety of goals. If I had a kid moving through the school, I’d want him to have a different teacher every year, soaking up lessons from each.

This is one reason why standardization, of almost any kind, spooks me. To keep mathematics rich and robust, we need to maintain genetic diversity. We need smart, independent educators tackling what appears most urgent and resonant to them. I wouldn’t want every teacher to conform to single style any more than I’d want all bands to issue a song-by-song cover of Abbey Road.

I’m back in America now. Today they start another year of teaching, this one without me. I’ll miss the heck out of these guys (not to mention my dear friends Caz and James, who helped to shape my teaching from the safe distance of the English department).

I don’t think “perfection” is a meaningful concept in teaching. The job is too varied, too ill-defined. But “greatness” – now, that’s something I’ve seen firsthand.