Jason Garofalo’s students are all in their teens. But to teach them the importance of taking mental risks in the classroom, he reaches for a lesson he learned from his 3-year-old daughter’s favorite PBS television show, “Daniel Tiger’s Neighborhood.”

“It’s OK to make mistakes,” reads the quotation that hangs on the wall above his classroom at Marble Hill International HS in the Bronx. “Try to fix them and learn from them, too.”

Garofalo’s dogged cultivation of his students’ critical thinking skills earned him a 2017 Sloan Award for Excellence in Teaching Science and Mathematics.

“Jason’s biggest goal is teaching students to become great thinkers themselves,” says fellow Marble Hill math teacher Scott Wohl. “He almost never misses an opportunity for students to discover something new on their own.”

Garofalo, who studied both engineering and psychology in college, is acutely aware of how most of his students have experienced math in the past.

“In other classes, you might have different viewpoints, but in math, there’s one right answer and a bunch of wrong answers, and no one likes to be wrong,” he says. “Most of the time in math, it is students who have it right who get called on; the kids who get the engagement are the kids who were right.”

Garofalo, who has been teaching for 13 years — the past 10 of them at Marble Hill — strives to turn this paradigm on its head by “celebrating great mistakes.” Instead of modeling the steps to get to a correct answer, he makes a point of prizing students’ wrong ones.

“I want them to view math as a puzzle they can figure out,” he says. “When students say, ‘I’m no good at math,’ I tell them, ‘Then you’d be a great math teacher.’”

In Garofalo’s classroom, the first step toward being comfortable with wrong answers in math is becoming comfortable discussing math in the first place.

“Students in his class are constantly talking about math,” says Jeff Hamilton, a fellow math teacher.

“We know to get everyone else’s opinion before we ask him for help,” agrees 11th-grader Akina.

Garofalo designs his lessons to promote interaction and discussion. In one lesson, students worked in groups of three. One student acted as a scribe, who was allowed to write but not speak; the other two students were permitted to discuss the problem, but they were not allowed to write at all.

“I’m uncomfortable when it’s too quiet,” Garofalo says. “I try to instill that math is a workout to exercise your brain, and talking is very important.”

The animated student conversation is the product of Garofalo’s careful planning outside the classroom, from choosing engaging problems that all students will be able to tackle to anticipating what misconceptions students might have.

“He has a knack for creating challenging yet achievable activities in the classroom,” says Wohl. “Rarely is an idea, strategy or formula simply presented to his kids.”

This year, Garofalo brought his interest in puzzles and games to a new course called “The Math of Games,” in which students practice using mathematical probability rules and strategic decision-making.

On the last day of algebra class before the end of the semester, Garofalo and his students are reviewing a run-of-the-mill Regents worksheet with a twist: Garofalo distributes a playing card to each student and periodically instructs each suit to move to a new group. As students discuss their answers — sometimes several times with different groups — Garofalo finds ways to prompt even more discussion.

“Try to find at least two ways to find the answer,” he tells one group.

Even when students are in agreement about a correct answer, Garofalo continues to press them to explain why other answers must be incorrect.

“Sometimes even if they have the right answer, they lack a conceptual understanding of the problem and can’t explain why the other choices are not right,” he notes.

When the majority of students are ready to move on from a particular question, Garofalo is met with a sea of shaking heads from one group in the corner.

“Hold on, we’re not OK,” one student objects. “I don’t think anyone understood that.”

The frank admission is music to Garofalo’s ears. “I want the students to be unafraid to make mistakes, because that’s what math is all about,” he says. “The whole process of making mistakes is how we learn.”