If you scan the high school academic landscape, the tallest peak — the Everest of them all — is calculus. And yet despite the fear factor, student demand for calculus has exploded at Lone Peak High School in Highland, Utah.

I recently sat knee to knee with Craig Smith who teaches seven straight periods of calculus at Lone Peak with an average class size of 34. (Disclosure: He has taught three of my children). Instead of meeting a jaded educator surrendered to the woes of American secondary education, I met a man brimming with enthusiasm for his students and his craft. Officially, Smith teaches calculus. Unofficially, he presides over a leadership laboratory, skunkworks and incubator of innovation.

A true outlier, Smith is widely regarded as one of the best secondary math teachers in the nation. Based on normalized data taken from the Utah State Office of Education, he may be the best calculus teacher in the country.

In 2006, the year before Smith began teaching calculus, 46 students per thousand took the AB calculus test at Lone Peak High School. Eight years later in 2014, 154 students per thousand took the AB calculus test at Lone Peak (a 235 percent jump), compared to 34 students per thousand statewide. The current Lone Peak participation rate is 353 percent higher than the statewide rate.

What about performance? In 2006, 13 students per thousand at Lone Peak passed the standardized AP calculus AB exam administered by the College Board, compared to a little higher rate of 22 per thousand among students throughout the state. In 2014, the state pass rate per thousand was still stuck at 22, whereas the pass rate for Smith’s students rocketed to 114 per thousand, a stunning 777 percent increase.

It’s one thing to make steady incremental improvement. It’s quite another to engineer a radical transformation. In an era when American teenagers don’t even crack the global top 20 among developed nations in math performance, Smith’s achievements are breath-taking.

A non-traditional track teacher, Smith graduated from Brigham Young University in electrical engineering on academic scholarship, worked for oil-giant Exxon and then spent several years at an instrumentation company as a design engineer. He began his second career as a high school teacher with no teaching experience. In my interviews with Smith, I discovered no single factor to explain his success, but rather a series of improvements. He has done for calculus what Dave Brailsford did for British cycling through the “aggregation of marginal gains,” or improvement in increments of one degree. However, there are a few unmistakable keys to his success:

Create a full-effort culture

Despite the buffered and often weak system of teacher accountability in public education, Smith creates a full-effort culture through his own modeling behavior. That modeling behavior sets the tone, the rhythm and the standard for his students. It’s both voluntary and infectious. For example, he learned quickly that normal effort and formal class time do not produce world-class levels of student performance. Consequently, Smith arrives at his classroom at 6:15 a.m. each day and stays for several hours after school, providing additional coaching sessions to help students learn the concepts.

He also conducts sessions on Saturdays and during breaks, including several during Christmas break. “If students are willing to learn, I’m willing to teach.” He once had 90 students in his room on a Saturday at 7 p.m. As one student put it, “You see the effort he puts in, so you want to do the same thing. This completely eliminates the motivation to cheat. No one thinks about cheating. You want to learn and you don’t want to let Mr. Smith down.”

Ensure psychological safety

Smith invites students to learn without adding fear to a subject that already creates its own. He recognizes that students who are emotionally distressed — anxious, angry or depressed — are cognitively impaired and don’t learn well, so he fosters a challenging and yet nurturing climate of psychological safety in which students become willing to engage in greater learning risk.

“There’s no embarrassment in Mr. Smith’s class,” one student said. “You never feel dumb even if you don’t understand something.” This requires low ego and uncommonly high emotional intelligence, traits which Smith possesses in abundance. He’s a man of great warmth who clearly seeks to bless rather than impress his students. He’s not competitive, combative or punitive. He’s not there to pontificate, display brilliance or duel with his students. Instead, he shows patience and intellectual humility.

“He never acts bothered or irritated when you ask a question,” another student said. “He’ll kneel down by your desk, find out what you know, and help you from there. But he doesn’t give you the answer. You have to explain where and why you’re stuck.” Finally, Smith learns the names of every student on the first day and can recall them years later.

Innovate and measure

Is Smith orthodox in his teaching methods? He is until he isn’t. Constantly hypothesis-testing, Smith is a disruptive innovator who employs lean start-up tools such as rapid-cycle-test-and-learn and A/B testing, and breaks with convention when he finds a better way. For example, he’ll teach a segment and then collect anonymous real-time feedback using a Promethean board and clickers.

Smith is a data junky who holds himself accountable to the results. “He’s totally open to feedback,” said one student, “he’s always trying new ways of doing things.” As one example, he’s debunked the conventional wisdom that “retakes don’t work” — not allowing students to re-test if they do poorly. “It’s a little more work for the teacher,” Smith observes, “but empirically speaking, re-testing clearly works, so I give endless chances. If you’re willing to work, there’s always mercy. You can try again.”

Guard against bias

Smith’s core belief is that all students can learn calculus. He rejects the notion that learning ability is fixed or implanted at birth. “I try never to judge a student’s aptitude or effort.” Smith maintains that slow students are not less intelligent students. They simply assimilate at a slower pace. “I had one student who failed every exam in my class, and yet passed the AP calculus exam.”

Another former student said, “Mr. Smith believes in you so much that you believe in yourself. I’ve never been good at math, and I mean never, but I learned calculus and passed the AP exam. How does that happen?”

Educate the whole student

Smith summarizes his philosophy this way, “I’m not big on rules and yet I’m also not the fun teacher. Calculus is not an easy subject. I also recognize that many of my students will never use calculus again. What we’re trying to do is build confident, self-reliant, mentally tenacious and unafraid students who are prepared for life. Calculus is a microcosm of life — if you’re willing to put in the effort, you can learn it. The journey makes you accountable. It makes you stretch. It makes you feel good about yourself. Yes, I teach calculus, but it’s not really about calculus, is it?”

Timothy R. Clark is founder of TRClark & Company, a management consulting and leadership development organization. He earned a doctorate degree from Oxford University. Email: trclark@trclark.net