Bringing the Harkness Method to Math Class

Who is doing the majority of the talking in your math classroom? In a traditional secondary math classroom, the teacher is stationed at the front of the room demonstrating examples related to the topic of the day, as illustrated in the traditional model seen below.

However, consider an alternative method that fosters student discussion and engagement. In the Harkness model shown in the diagram, students and the teacher sit around an oval-shaped table called the Harkness table. The lines indicate connections between participants’ responses and comments.

Just a table?

Contrary to common belief, Harkness is not simply a change in furniture, nor is it the latest educational fad. The Harkness method began in 1930 at Phillips Exeter Academy in Exeter, New Hampshire, after a sizable donation by philanthropist Edward Harkness. Harkness’s donation outlined a “radical” approach to instruction and pedagogy.

A teacher wrote during the first term of Harkness in his class, “Now, there is a freedom of discussion, an eagerness to participate, that I never saw before, the value of which to both student and instructor is incalculable. And it comes mostly from sitting about a table.”

This approach is often still radical in many classrooms today. Kimberly Fradale writes in “Addressing Classroom Challenges With the Harkness Method” for The International Teacher, “Our students are reticent and our teachers, talkative. According to John Hattie, most teachers speak for 60–70 percent of a class period, leaving little time for students to ask questions, let alone verbally work out their own ideas.”

In Edutopia, Mark Wise explains that student-led discussions, such as Harkness, give students the skills to engage in respectful dialogue. “Students should be expected to bounce ideas off of their peers’ comments, paraphrase and extend the conversation, and, through inquiry, sharpen and deepen the points being raised—all without the teacher serving as the intermediary.”

Harkness in a Math Class

Harkness lends itself easily to the humanities. The National Council of Teachers of English offers lesson plans to discuss novels, and student discourse is paramount in learning about historical and current events. Harkness is also baked into the sciences with collaborative labs where the teacher is the facilitator of the students’ explorations.

However, math is a highly visible subject, requiring algorithms and diagrams; therefore, a whiteboard (or any vertical nonpermanent surface) is a necessary component of a Harkness math class.

Amy McAfee, a middle school math and science teacher in Houston, describes her Harkness math class, “On Mondays students would receive a problem set of five problems that consisted of word or puzzle-style problems that were challenging and required students to think in nonlinear ways. Thursday and Friday, at the start of class, students would work in groups of two to three to show how they worked the problems on the whiteboards. They would then do gallery walks around the room, return to their work to make changes, and finally as a class we would come to a consensus and share methods for solving.”

Phillips Exeter math teachers Sami Atif and Karen Geary write for Independent School magazine:

“The problem sets [homework] are only part of the story… Students bring their work to class and immediately go to the boards lining the walls to ‘put up a problem.’… After about 10 minutes, students gather back at the table to discuss each homework problem. The author of each solution presents her thinking, and the class responds. In a class where students have become comfortable with each other, with making mistakes and exposing misconceptions, what usually results is a lively conversation in which the teacher is on the periphery. The students are generating the work, the questions, and the answers for their classmates.”

Marianne Van Brummelen, chair of the Department of Mathematics at The Masters School in New York, describes the flexibility beyond the oval shape of the table: “Though we sit around a Harkness table, we are not always in our seats! Students go up to the board, sometimes I’m writing on the board, and students will move to different areas of the classroom to collaborate with one another. As for assessments, the tables have slides that you can pull out for privacy.”

Resources for Harkness in Math Class

The math department at Phillips Exeter decided to ditch textbooks in 1992 and develop rich problem sets instead. These problem sets are printed on spiral-bound notebooks and never published because they are perpetually updated each summer. Best of all, these problem sets are free. You can find problem sets for Math 1 (Algebra) to multivariate calculus on their website. The school also offers summer Harkness training for educators.

Getting Started

Since few math classrooms have 12 students sitting around a large oval table, math teachers have to get creative about classroom arrangement. One idea is to arrange student desks in two concentric circles, with an inner circle of 12. The 12 students in the center begin discussing a homework problem written on the board. The remaining students in the outer circle are assigned to observe one or two inner circle student(s) and keep notes on how they participated in the discussion or ask clarifying questions of the inner circle afterward. For the next problem, the inner and outer circles swap places. This is often called Socratic seminar or fishbowl.

Why consider Harkness for your math class?

Van Brummelen shares that her students see themselves as “mathematical thinkers” rather than simply doers of mathematics. As thinkers, the students gain a deeper understanding. She says, “The constructivist approach to math is essential to having students see themselves as mathematicians, and thus breaking down some of the barriers to equity and inclusion in our discipline.”

Harkness is more than a table—it is a pedagogy. Consider ways that you can promote discussion and collaborative learning among your students. How can you, as the teacher, step back from the “sage on the stage” lecture model? It doesn’t have to be an overnight shift; even small changes will promote student voice, equity, and deeper thinking.