Students Take Charge with Problem-Based Learning

THE CONCEPT OF LEADERSHIP may conjure images of a drill sergeant leading a squad of new recruits. The captain of a basketball team. A CEO or a president.

But what about a math student?

At Peck, being a leader doesn’t just mean being at the front of the line. It means making the people around you better.

And when the concept of leadership is anchored in that idea, a straight line is drawn between Peck’s dedication to ‘consideration of others’ and an inclusive view of leadership developed throughout the K-8 experience.

“There’s a component of listening in our view of leadership,” said Chris Weaver, director of curriculum and faculty development. “Gathering information, generating new ideas, incorporating feedback, making adjustments—those processes all develop a sense of agency in learning.”

Leadership, then, is not about having a particular role; it is using critical thinking, analysis, and persuasion to cause a group to take action.

Leadership Through Math

So how does a teacher take something like learning math—which may traditionally be seen as an independent study—and turn it into a practical exercise in team leadership?

They set the stage and give students the tools to continually guide each other toward different problem-solving techniques.

Upper School math teacher Amy Papandreou is accomplishing that using a technique called “problem-based learning,” which she picked up several summers ago at the renowned Anja S. Greer Conference on Mathematics and Technology, presented by Phillips Exeter Academy.

“I was blown away by the concept,” Papandreou said. “It just resonated with me as a better way to teach.”

Problem-based learning (PBL) is a student-centered approach in which students learn about a subject by working in groups to solve an open-ended problem.

In math class, this means flipping the typical concept of learning through lecture in class and practicing through homework assignments. Homework assignments are discovery-based, with five or six problems that require students to think critically about their approach and tackle new concepts independently.

Then, they come together in the classroom, present their process to their classmates, and dissect the problem as a group—offering feedback, untangling knotty issues, and gaining deeper insight into various ways to solve it. In essence, they’re the ones leading the charge and, as a team, tackling problems the way they occur in the real world: without an answer key.

“The goal is not to come in with a perfectly completed assignment, but to leave class understanding it after the discussion with your classmates,” said Papandreou.

The approach requires vulnerability on the part of students, and the willingness to make mistakes in front of their peers. But when they learned that Papandreou had created an environment with a trusting, friendly tone, math class became a safe place to take risks.

The difficulty level of the problems meant that mistakes were frequent, and therefore, not stigmatized. Students soon cue into the fact that the conversations with their peers are part of what they are learning about: establishing norms, contributing meaningfully in varying roles, disagreeing politely, being clear and concise, and focusing on big ideas.

“With problem-based learning, you cede a lot of the control to the kids. You assign problems, but they decide how the conversation goes. It works because students invest the energy and dig deeper into math concepts,” said Papandreou.

She remembers a student who struggled to present a problem confidently and articulately in seventh-grade math and then blossomed into a leader in eighth grade.

“Through conversations, he realized that in his dream job, as a CEO, he’d need to be able to face a room full of people and explain his ideas and their merit. And he suddenly understood the life skill that this work was really shaping in him,” she said.

“It’s easy for a teacher to push back, but when their peers do it, that really inspires them at a different level. They realize that there’s great knowledge all around them, not just from the teacher.”

Around the same time students are digging into PBL in math class, Harkness discussions in English classes are ramping up, reinforcing the notion that this type of conversational protocol is itself part of what they are learning.

Around the Harkness table, they are exchanging ideas in an encouraging, supportive environment with minimal teacher intervention.

“They run into the same challenges there, and their reasoning, discussion, and collaboration skills in one class certainly help them in the other,” said Papandreou.

As more classes experience the PBL model and enter secondary school with skills that transcend math, the benefits of the approach become all the more clear.

Says Papandreou, “Yes, I want to teach them all these specific things, these math concepts, but ultimately, I want to teach them how to explain their thought processes and lead conversations so that they can collaborate and be part of a learning community.”