THE HARKNESS SEMINAR & The Student-Led Learning Revolution

 THE HARKNESS MATH SEMINAR

& The Student-Led Learning Revolution

The Architecture of Thinking: Harkness MATH Seminars and Student-Led Learning Slide Deck 

 

A Complete Explainer for Educators

From Phillips Exeter to Your Classroom

By Sean Taylor | Reading Sage 

Introduction: A Method Almost 100 Years in the Making

What if the most powerful teaching revolution of the 21st century wasn't invented in Silicon Valley, or by an EdTech startup, or by a bestselling researcher? What if it was invented nearly a century ago — at a prep school in New Hampshire — and most educators still don't know it by name?

That's the story of the Harkness Seminar at Phillips Exeter Academy.

Today, educators talk excitedly about the Thinking Classroom, the Flipped Classroom, Project-Based Learning, and student-led inquiry. These are genuinely powerful frameworks — but they all trace their philosophical DNA, directly or indirectly, to what Edward Harkness funded and what Phillips Exeter pioneered starting in the 1930s.

This explainer is for teachers who have never heard of Harkness — or who have heard the name but don't truly understand what it means, how it works, what it looks like in a math classroom, and why it still matters. We'll walk through the history, the pedagogy, real classroom dialogue, sample problem sets, and how you can bring these ideas into your own classroom starting tomorrow. 

Part 1: Phillips Exeter Academy and the Birth of the Harkness Table

Who Was Edward Harkness?

Edward Stephen Harkness was a philanthropist and heir to a Standard Oil fortune. But unlike many wealthy donors of his era, Harkness was obsessed with a simple, radical idea: that the most powerful form of education wasn't a teacher standing at a lectern pouring knowledge into passive students. It was students sitting together, wrestling with ideas, teaching each other.

In 1930, Harkness donated $5.8 million to Phillips Exeter Academy (and later to other elite schools) with one condition: the school would redesign its classrooms and pedagogy around collaborative, discussion-based learning. He specifically envisioned a large oval table where every student could see every other student — where no one could hide, and no one could dominate without the group noticing.

That table became legendary. It's called the Harkness Table.

What Is the Harkness Table?

The Harkness Table is exactly what it sounds like: a large oval or round table, typically seating 12-15 students and one teacher, arranged so that every participant has equal visual access to every other participant. There is no "front" of the room. There is no privileged seat. Everyone is a contributor.

The physical design of the table is a pedagogical statement: learning is a shared, circular endeavor. Ideas belong to the group, not to the teacher.

The Key Insight The teacher sits at the table too — but not to lecture. The teacher's role is to listen, ask a clarifying question when things go off the rails, and then step back again. The students run the discussion.

 

From Humanities to Mathematics: The Harkness Math Seminar

Harkness seminars began in humanities — literature, history, philosophy. These are subjects where discussion feels natural. But Phillips Exeter did something radical: they applied the same model to mathematics.

The Exeter Math Seminar (often called the Harkness Math Seminar) completely reinvented how students learn math. Here's how it works:

•       Students are given a problem set the night before class — NOT a lecture on how to solve the problems.

•       They work on the problems at home, individually or informally with peers, doing their best with what they know.

•       They come to class having attempted the problems, with their own approaches, their own partial solutions, their own confusions.

•       In class, students share their solutions at the board (the Exeter classroom has chalkboards or whiteboards covering every wall).

•       Other students question, challenge, extend, or affirm the approach being shared.

•       The teacher observes, asks probing questions, and rarely intervenes with "the answer."

The Exeter Math Department has been developing and refining problem sets for this model since the 1990s — and notably, they publish their entire curriculum for free online. These are the famous "Exeter Problem Sets" that have influenced math teachers worldwide.

 

Part 2: What a Harkness Math Seminar Actually Looks Like

The Physical Environment

Walk into a Harkness math classroom at Phillips Exeter and you'll notice immediately: every single wall is a chalkboard or whiteboard. The room isn't set up for a teacher to stand and deliver. It's set up for students to stand and work. The message is physical and psychological: you are the workers here.

This is significant. Long before Peter Liljedahl wrote about "vertical non-permanent surfaces" in Building Thinking Classrooms, Exeter was using every square foot of vertical space to make student thinking visible, collaborative, and erasable (which reduces anxiety — a whiteboard invites risk-taking in a way that a graded worksheet never can).

The Harkness Math Problem Set: An Example

Let's look at the kind of problem a student might receive the night before a Harkness Math class. These problems are intentionally designed NOT to look like textbook exercises with a single clear procedure. They are designed to provoke thinking.

Sample Exeter-Style Problem Set (Introductory Algebra) 1. A train leaves Station A traveling east at 60 mph. Another train leaves Station B (240 miles east of Station A) traveling west at 40 mph. At what point do they meet? Before solving algebraically, draw a diagram of what is happening. What does each variable represent?  2. The sum of three consecutive even integers is 78. Find them. Now find three consecutive odd integers whose sum is 99. What do you notice about your methods?  3. A rectangle's length is three more than twice its width. Its perimeter is 54. Find the dimensions. Can you write this two different ways? Which way feels more natural to you, and why?  4. Jenna says that x = 4 is always the solution to 2x + b = 12 no matter what b is. Is she right? Explain.  5. Extension: Create your own problem that requires writing and solving a two-step equation. Swap with a classmate tomorrow and solve each other's.

 

Notice what these problems do: they demand visualization, metacognition ("what do you notice?"), justification ("explain"), comparison of methods, and creativity ("create your own"). They are not asking students to execute a procedure. They are asking students to think.

Real Classroom Dialogue: The Harkness Math Discussion

Here's what a Harkness Math Seminar discussion might actually sound like. The teacher is Ms. Rivera. Students are 9th graders working on the train problem above. Three students have put their solutions on the board — they don't all agree.

 

Ms. Rivera: Alright, we have three solutions on the board. Marcus, Priya, and DeShawn all worked on the train problem last night. They didn't all get the same answer. Let's start by just looking. Marcus, can you walk us through your thinking without explaining it — just describe what you drew?

Marcus: I drew a number line with Station A on the left and Station B on the right. I labeled the distance 240 miles. Then I put arrows for both trains.

Priya: I did something different. I wrote equations right away. I said Train 1 is at position 60t and Train 2 is at 240 minus 40t. Then I set them equal.

DeShawn: Wait — why does Train 2 subtract?

Priya: Because it's going west — it's getting closer to zero, so it's losing distance from Station B.

Ms. Rivera: Interesting. DeShawn, what did YOU do?

DeShawn: I guessed and checked. I tried t equals 2 hours. Train 1 goes 120 miles. Train 2 goes 80 miles west, so it's at 160. They haven't met. I tried t equals 3. Train 1 is at 180. Train 2 is at 120. Still haven't met. I got confused.

Priya: You were on the right track. What's 180 plus 120?

DeShawn: Oh... 300. That's more than 240.

Priya: So they passed each other between 2 and 3 hours!

Marcus: That matches my diagram. They meet somewhere in the middle.

Ms. Rivera: So Priya's algebraic method gives us an exact answer. What is it?

Priya: 60t equals 240 minus 40t. So 100t equals 240. t equals 2.4 hours.

DeShawn: And I found it between 2 and 3. So that checks out.

Ms. Rivera: Beautiful. Three methods — diagram, equation, guess-and-check — and they all confirm each other. Here's my question for the table: which method would you use first if you saw this on a test, and why?

Student (Aisha): Probably diagram first because it helps me see what's happening. Then algebra to get the exact answer.

Marcus: Same. I can't set up equations without the picture.

Priya: I go straight to equations. Pictures slow me down.

Ms. Rivera: That's a really important difference. Neither is wrong. Aisha and Marcus — you're visual-first thinkers. Priya — you're symbolic-first. Math needs both.

 

This dialogue illustrates something crucial about Harkness: the teacher asked one question at the beginning and one question at the end. Every insight in the middle came from students. The teacher's job was to create the conditions — not to deliver the content.

 

Part 3: The Thinking Classroom — Harkness Reborn (and Renamed)

What Is the Thinking Classroom?

In 2010, Canadian math education researcher Peter Liljedahl began studying what actually happens when students learn math — specifically, what conditions cause students to THINK versus what conditions cause them to mimic procedures without understanding.

After studying over 400 teachers and thousands of students over more than a decade, Liljedahl identified 14 "Building Thinking Classrooms" practices. His 2020 book Building Thinking Classrooms in Mathematics became a bestseller in education circles and sparked a global movement.

His core findings? Students think more, more deeply, and more collaboratively when:

•       They stand at vertical, non-permanent surfaces (whiteboards, chalkboards) rather than sitting at desks.

•       They work in visibly random groups of 2-3, assigned by the teacher each class.

•       Problems are given verbally, not as worksheets.

•       The teacher moves around and asks questions — answering student questions only with questions.

•       The classroom culture rewards the process of thinking, not just correct answers.

Sound Familiar? Every single one of these practices is embedded in the Harkness Math Seminar. Liljedahl's research gave us the empirical WHY behind what Exeter had been doing through instinct and tradition for 90 years.

 

Liljedahl's 14 Practices vs. Harkness: A Comparison

 

PRACTICE	THINKING CLASSROOM	HARKNESS (1930s–)
Vertical non-permanent surfaces	Whiteboards on every wall	Chalkboards on every wall at Exeter
Visibly random grouping	Random groups, changed frequently	Varied discussion groups; no assigned seats
Defronting the classroom	No single "front" of room	Oval table — no front, no hierarchy
Teacher moves, never stands	Teacher circulates constantly	Teacher sits at table as equal participant
Answer questions with questions	Never give direct answers	Teacher probes, never lectures to group
Students own the problem	Assign problems without prior instruction	Problem sets given night before; no lecture first
Build thinking culture	Norm-setting for risk and effort	Trust is foundational to Harkness method

 

Part 4: The Flipped Classroom — Another Child of Harkness

What Is the Flipped Classroom?

The Flipped Classroom became a mainstream buzzword around 2007-2012, when teachers Jonathan Bergmann and Aaron Sams began recording video lectures so students could watch them at home — freeing up class time for problems, projects, and discussion.

The model is simple: traditional homework (practice problems) becomes classwork. Traditional classwork (lecture/instruction) goes home, usually as video.

Bergmann and Sams are rightly credited with popularizing this for the modern era. But here's the thing: the PRINCIPLE — students do preparatory thinking at home and use class time for collaborative application — is the Harkness Math Seminar. Exeter was doing it with problem sets in the 1930s.

How Harkness Predates and Informs the Flipped Model

The Harkness Math Seminar assigns the problem (the intellectual challenge) before instruction — not after. Students must grapple with material they haven't been taught yet. This is actually MORE demanding than the modern flipped classroom, which typically still gives students instruction at home (via video) before they apply it.

Harkness trusts students with genuine intellectual struggle BEFORE instruction. The flipped classroom trusts students to manage instruction delivery independently (watch a video). Harkness goes further.

Key Distinction Flipped Classroom: Students receive instruction at home (video), practice in class. Harkness Model: Students attempt problems at home with NO instruction, discuss and construct understanding together in class. The Harkness model demands more cognitive struggle — and research strongly suggests that struggle (productive failure) produces deeper learning.

 

Part 5: The Family Tree — What Else Grew from Harkness Roots?

Many of today's most celebrated pedagogical movements share the Harkness DNA. Some explicitly acknowledge it. Others arrived independently at the same conclusions Exeter had already reached. Here is the landscape:

Project-Based Learning (PBL)

PBL places students at the center of solving a real-world problem or creating a genuine product over an extended period. Like Harkness, PBL positions the teacher as a facilitator, requires student collaboration, and values process over product. PBL gained momentum in the 1990s through the Buck Institute for Education and today is widely practiced through organizations like PBLWorks.

The Harkness connection: both center student agency. In PBL, students design the inquiry. In Harkness, students construct the mathematical understanding. In both, the teacher resists the urge to just give the answer.

Socratic Seminar

The Socratic Seminar, popularized in American schools through the Great Books Foundation and the work of Mortimer Adler, uses structured discussion to explore texts and ideas. Students sit in a circle, ask each other questions, and build on each other's thinking — with the teacher asking one opening question and then stepping back.

This is functionally identical to a humanities Harkness seminar. Many educators use the terms interchangeably, though purists note that Socratic Seminar has a more formal "fishbowl" structure (an inner and outer circle) that Harkness does not.

Visible Learning and High-Yield Strategies

John Hattie's landmark meta-analysis Visible Learning (2008) synthesized 800+ studies on what actually improves student achievement. His highest-effect strategies — student self-assessment, peer teaching, teacher feedback, classroom discussion — are all embedded in the Harkness model.

Hattie specifically found that peer tutoring has an effect size of 0.55, and classroom discussion has an effect size of 0.82 — both well above the 0.40 threshold he identifies as meaningful. The Harkness seminar is, in effect, an integrated implementation of Hattie's highest-yield strategies.

Collaborative Learning and Cooperative Learning

From Elizabeth Cohen's Complex Instruction to Spencer Kagan's Cooperative Learning structures, the research on student-to-student interaction as a driver of achievement has been building since the 1970s. All of it validates what Harkness instinctively built: when students teach each other, both the teacher and the learner benefit.

The Talking Curriculum / Oracy Movement

The oracy movement — teaching students to speak and reason aloud as a core academic skill — has gained significant traction in the UK and increasingly in the US. Schools like School 21 in London have made spoken communication a central academic outcome alongside reading and writing. The Harkness seminar was developing oracy before the word existed in education circles.

Expeditionary Learning / EL Education

Founded in 1991 in partnership with Outward Bound, EL Education (formerly Expeditionary Learning Outward Bound) emphasizes crew, character, and collaborative inquiry. Its emphasis on student agency, peer learning, and the teacher as guide aligns deeply with Harkness principles — though EL Education adds community and service as explicit pillars.

 

Part 6: How Students Build Their Own Teams — The Group Dynamics of Harkness

Why Team Structure Matters

One of the most underappreciated aspects of the Harkness seminar is what it does to group dynamics over time. Unlike traditional group work — where a dominant student often does the thinking and the others copy — Harkness creates accountability structures that make coasting nearly impossible.

Here's why: when you're going to stand at the board in front of your classmates and explain your solution, you have to actually have one. And when your classmates are empowered to ask you genuine questions — not just politely accept your answer — you have to understand your own thinking well enough to defend it.

How Groups Are Formed (The Harkness and Thinking Classroom Approaches)

At Phillips Exeter, the Harkness Table is the group. With 12-15 students, everyone is in one collaborative group. The class is the team.

In modern adaptations — particularly the Thinking Classroom — teachers create smaller groups (2-3 students) that rotate frequently. Liljedahl's research found that VISIBLE RANDOMNESS (using a deck of cards, a random name generator, etc.) accomplishes something crucial:

•       It prevents clique formation and social comfort zones that produce groupthink.

•       It signals that every student is expected to contribute — there is no consistent "smart group" to hide behind.

•       It builds the cultural norm that anyone can work with anyone — a deeply Harkness-aligned value.

The Norms That Make It Work

Whether you're running a Harkness seminar or a Thinking Classroom, certain explicit norms must be established and reinforced consistently:

•       Everyone's thinking is public and worth discussing — even wrong thinking.

•       Questions are valued as much as answers — asking a good question is a contribution.

•       We discuss the idea, not the person — "I see this differently" not "You're wrong."

•       The group doesn't move forward until everyone understands — not just the fastest thinkers.

•       The teacher is not the answer key — turn to each other before turning to the teacher.

Trust is the Foundation Both Harkness veterans and Thinking Classroom researchers identify the same #1 prerequisite: trust. Students must trust that their mistakes will be treated as learning, not as evidence of failure. Teachers must trust that if they step back, students will step up. And that trust is built slowly, deliberately, through repeated experiences of productive struggle.

 

Part 7: The Teacher's Role — Guide on the Side, Not Sage on the Stage

Redefining Teacher Authority

The hardest thing for most teachers trained in traditional pedagogy to accept about the Harkness model is this: when the discussion is going somewhere slightly off, when students are making an error, when the conversation is inefficient — the teacher does NOT intervene.

Or rather: the teacher intervenes strategically, minimally, and almost always through questions rather than corrections.

This requires an act of profound professional trust. It also requires experience, because knowing WHEN to let productive struggle continue and WHEN a misconception will compound into confusion is a high-level teaching skill.

What the Teacher Actually Does

•       Designs problem sets that are accessible enough to start but deep enough to generate real discussion. Before class:

•       Frames the task clearly, establishes randomized groups, and sets up the physical space. At the start of class:

•       Circulates, listens, takes mental notes about who has which approach, what errors are circulating, what connections students are missing. During student work:

•       Asks one good question at a time, names and validates contributions without evaluating them, manages turn-taking without dominating it. During whole-group discussion:

•       Synthesizes what the class discovered, fills in any critical gaps students didn't reach, assigns the next problem set. After discussion:

The Art of the Harkness Question

The teacher in a Harkness or Thinking Classroom is a master of question types. Here are the most important categories:

QUESTION TYPE	EXAMPLE	PURPOSE
Clarifying	"Can you say more about what you mean by that?"	Surfaces a student's thinking without judging it
Connecting	"Does anyone see a relationship between what Priya just said and Marcus's diagram?"	Builds intellectual community across contributions
Probing	"What would happen if the trains were going the same direction?"	Pushes thinking to the edge of current understanding
Redirecting	"Hold on — DeShawn, what do YOU think before we hear from someone else?"	Prevents dominance; ensures all voices are included
Synthesizing	"So it sounds like we've found three different methods that all give the same answer. What does that tell us?"	Moves discussion toward generalization and insight

 

Part 8: Bringing Harkness Into Your Classroom — A Practical Guide

You Don't Need a Fancy Table

One of the most common misconceptions is that "Harkness" requires a specific oval table or a private school budget. It does not. What it requires is a philosophical shift and a few structural changes that any classroom can accommodate:

•       Rearrange desks into a U-shape or circle so students face each other, not the teacher.

•       Designate at least one wall or section of wall as student workspace (whiteboard paint, paper on the wall, or a rolling whiteboard all work).

•       Create problem sets that require thinking before instruction — not after.

•       Practice not answering questions directly. Practice waiting.

Week 1: Starting the Cultural Shift

You cannot introduce Harkness practices on Monday and have a fully functioning seminar by Friday. The culture must be built. Here's a practical Week 1 sequence for any grade level:

1.     Day 1 — Establish norms explicitly. Have students co-create a list of discussion norms. What makes a discussion feel safe? What makes it feel dismissive? Write these on the wall and refer to them constantly.

2.     Day 2 — Try a low-stakes problem. Give students a problem they CAN do and have them put their solutions on the board. Celebrate all approaches, including wrong ones. Model how wrong thinking is just thinking that needs refining.

3.     Day 3 — Practice turn-taking. Explicitly teach students how to invite others into the discussion: "I'd like to hear what someone else thinks" or "Does anyone want to add to what I said?" These phrases feel awkward at first. Practice them.

4.     Day 4 — Try a problem they CANNOT fully do yet. This is the first Harkness-style problem set: assign work students will struggle with, tell them to try their best and bring their attempts to class, and then let the discussion happen. Resist rescuing them.

5.     Day 5 — Debrief the process, not just the content. Ask: What was hard about this week? What felt different? What helped you learn? Get students to see themselves as learners who are becoming more capable of productive struggle.

Assessment in a Harkness Classroom

Assessment is often the first objection teachers raise: "If students are constructing their own understanding, how do I know what they actually know?"

This is a genuine challenge, and Harkness schools handle it in multiple ways:

•       Observation and listening: The teacher circulates during group work and listens carefully. Who is contributing? Who is confused? Who is making a key conceptual error? This informs the next lesson immediately.

•       Individual problem sets: Regular individual problem sets (not discussed in class) ensure each student is building their own understanding, not just riding their group.

•       Exit tickets: A brief individual response at the end of class — "What is one thing you understand better today than when you walked in?" — provides quick formative data.

•       Presentations and portfolios: Students keep records of their work, their reasoning, their growth over time. These serve as evidence of learning in place of traditional tests.

•       Traditional assessments used sparingly: Tests and quizzes can still exist — but they measure what students have genuinely constructed, not what they've memorized.

 

Part 9: Common Misconceptions — And What the Research Actually Says

"Students will just give each other wrong answers."

This is the most common fear — and the research doesn't support it. In a well-structured discussion with norms that require justification and evidence, errors are surfaced and examined rather than silently accepted. Students are remarkably good at detecting when something doesn't make sense — when given the space and expectation to question it.

Moreover: a student who gives a wrong answer to a classmate and then discovers, through discussion, why it's wrong has learned something far more durable than a student who was told the right answer by a teacher and wrote it down.

"This only works for high-level students."

Phillips Exeter is a selective school, so it's tempting to assume Harkness only works with elite students. But the Thinking Classroom research was conducted in schools serving diverse student populations, including students with IEPs, English language learners, and students with significant gaps in prior knowledge. The findings held: all students, at all levels, think more when given appropriate problems and the expectation to think.

The key word is "appropriate." Harkness-style problems must be accessible enough for every student to begin — even if some go further than others. Problems that leave students completely stranded create anxiety, not productive struggle.

"The teacher isn't doing anything."

The guide-on-the-side teacher is doing an enormous amount — most of it invisible. Designing the problem set, reading the room, deciding when to let a misconception sit and when to address it, managing the social dynamics of 30 adolescents, and synthesizing a coherent mathematical concept from a chaotic discussion: these are extraordinarily skilled acts of teaching.

In fact, most teachers find that facilitating a Harkness-style discussion is significantly harder than delivering a well-prepared lecture. It demands improvisation, pedagogical knowledge, emotional intelligence, and the courage to be comfortable with uncertainty.

 

Part 10: Why This Matters Now

We are in a moment of educational history when the urgency of student agency has never been higher. In a world where AI can retrieve any fact in seconds, what students need isn't more information — it's the capacity to think, to argue, to collaborate, to construct meaning together.

The Harkness seminar, born in 1930, answers this need better than almost any contemporary framework. And it answers it not because it is old, but because it is profoundly right about how humans learn: together, through struggle, through dialogue, through the experience of being taken seriously as thinkers.

The teacher who trusts their students with a problem they can't yet solve, who steps aside and lets them wrestle and discuss and construct, who bites their tongue when the answer is right there — that teacher is doing something ancient and radical and essential.

"The role of the teacher is not to pour knowledge into the student but to draw it out — like Socrates. The table is just the shape of that invitation."
 — Edward Harkness, paraphrased

 

Whether you call it Harkness, Thinking Classroom, Flipped Learning, or just "good teaching," the core insight is the same: students learn by doing, by talking, by struggling, by teaching each other. The best classroom is one where the teacher's voice is the least frequent one in the room — and the students' thinking is loudest.

 

 

Resources and Further Reading

Primary Sources and Essential Reading

•       Phillips Exeter Academy Mathematics — exetermath.org (Free problem sets, department philosophy, curriculum resources)

•       Building Thinking Classrooms in Mathematics by Peter Liljedahl (2020) — Corwin Press

•       Visible Learning by John Hattie (2008) — Routledge

•       The Harkness Method: Teaching by Discussion — Phillips Exeter Academy official documentation

•       Flip Your Classroom by Jonathan Bergmann & Aaron Sams (2012) — ISTE/ASCD

For Deeper Exploration

•       "The Thinking Classroom" — Peter Liljedahl's website and research papers at buildingthinkingclassrooms.com

•       PBLWorks (Buck Institute for Education) — pblworks.org

•       EL Education — eleducation.org

•       The National School Reform Faculty — nsrfharmony.org (Protocols for discussion-based learning)

•       "The Exeter Math Problem Sets" — freely downloadable from Phillips Exeter Academy, searchable as 'Exeter Math Department Problem Sets'

For Sean Taylor / Reading Sage

This document is a full explainer suitable for a YouTube script, blog post, or professional development resource. The dialogue sections are designed to be naturalistic and usable as video script excerpts. The problem sets are original and classroom-ready. All content may be adapted, expanded, or illustrated as needed for the Reading Sage platform.

 

Reading Sage | Sean Taylor

Student-Led. Teacher-Guided. Community-Built.

Here’s a comprehensive explainer crafted for your blog and video script—structured, clear, and grounded in both history and classroom practice.

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:::writing block
The Harkness Method, Thinking Classrooms, and the Roots of Student-Led Learning

If you walk into a classroom at Phillips Exeter Academy today, it may look like a modern progressive learning space—but what you’re really seeing is nearly 100 years of instructional design in action. Long before terms like “flipped classroom,” “student-centered learning,” or “thinking classrooms” became educational buzzwords, Exeter was quietly refining one of the most powerful models of learning ever implemented: the Harkness Seminar.

This approach didn’t just influence modern pedagogy—it anticipated it.

What Is the Harkness Method?

The Harkness Method originated in 1930 when philanthropist Edward Harkness funded a radical shift in teaching at Phillips Exeter Academy. His vision was simple but transformative: students learn best when they are actively engaged in discussion, problem-solving, and collaboration.

Instead of rows of desks facing a lecturing teacher, students sit around an oval table. There is no “front” of the room. The teacher is not the center of attention—the students are.

Core principles include:

• Student-led discussion and inquiry

• Collaborative problem-solving

• Teacher as facilitator, not lecturer

• Emphasis on reasoning, dialogue, and evidence

In humanities classes, this looks like Socratic seminar. In math, however, it becomes something even more powerful: a Harkness Math Seminar.

Harkness Math: The Original Thinking Classroom

In a Harkness math classroom, students are not passive recipients of procedures. They are active constructors of mathematical understanding.

A typical cycle looks like this:

1. Students are assigned a problem set before class (the “flip”).

2. They attempt solutions independently or in small groups.

3. In class, students present, defend, and revise their thinking.

4. Peers question, challenge, and build on each other’s ideas.

5. The teacher guides discussion but does not dominate it.

This is strikingly similar to what we now call:

• Flipped classroom

• Thinking classroom (Peter Liljedahl)

• Vertical non-permanent surfaces (VNPS)

• Inquiry-based learning (IBL)

Exeter was doing all of this decades earlier.

Example: A Harkness Math Dialogue

Problem: Solve for all real solutions to $x^2 - 5x + 6 = 0$

Student A: “I factored it into (x - 2)(x - 3), so the solutions are 2 and 3.”

Student B: “Wait, how did you know it would factor like that?”

Student A: “I looked for two numbers that multiply to 6 and add to 5.”

Student C: “Could we also solve it using the quadratic formula?”

Student D: “Yeah, that would give the same result, but factoring is faster here.”

Teacher (facilitating): “What kinds of quadratics are easier to factor, and when might another method be more efficient?”

Notice what’s happening:

• Students explain reasoning

• Students question each other

• Multiple strategies emerge

• The teacher nudges, not tells

The “Flipped” Nature of Harkness

Long before the term “flipped classroom” existed, Harkness classrooms were already flipping learning.

Traditional Model:

• Teacher lectures in class

• Students practice at home

Harkness Model:

• Students explore problems before class

• Class time is for discussion, refinement, and synthesis

This inversion is critical. It shifts cognitive load to students and reserves class time for higher-order thinking:

• Analysis

• Evaluation

• Creation

Thinking Classrooms: A Modern Reinvention

Peter Liljedahl’s “Thinking Classroom” framework echoes many Harkness principles but adds specific structures:

• Vertical non-permanent surfaces (whiteboards, chalkboards)

• Random group formation

• Visibly random tasks

• Emphasis on student thinking over answer-getting

But here’s the key insight:
These are not entirely new ideas—they are refinements and codifications of practices long embedded in Harkness classrooms.

“Vertical surfaces” are simply a modern rebranding of what Exeter math classrooms have always used: walls covered in chalkboards.

Example: Thinking Classroom Meets Harkness

Students are given this problem:

“A rectangle has a fixed perimeter of 20 units. What dimensions maximize its area?”

Students stand at whiteboards in groups of three.

Group dialogue:

• “If the perimeter is 20, then 2L + 2W = 20.”

• “So L + W = 10.”

• “Let’s test values—if L = 5, W = 5, area is 25.”

• “If L = 6, W = 4, area is 24… smaller.”

• “So a square gives the maximum area.”

Teacher role:

• Circulates

• Asks probing questions

• Highlights patterns across groups

Building Student Teams and Trust

One of the hardest parts of this model is not the structure—it’s the mindset.

Teachers must:

• Trust students to struggle productively

• Resist the urge to “rescue” too quickly

• Allow productive confusion

Students must learn:

• How to collaborate

• How to explain thinking

• How to disagree respectfully

Team formation strategies:

• Random grouping (prevents tracking)

• Rotating groups (builds social flexibility)

• Assigned roles (facilitator, recorder, skeptic)

What Makes This Powerful?

This model works because it aligns with how people actually learn:

• Learning is social

• Understanding is constructed, not delivered

• Struggle is necessary for deep learning

• Teaching others reinforces mastery

It also builds skills far beyond content:

• Communication

• Critical thinking

• Intellectual humility

• Academic resilience

Common Pitfalls

This model can fail if:

• Teachers intervene too quickly

• Problems are too easy or too procedural

• Students are not trained in discussion norms

• Assessment still prioritizes rote answers

The biggest mistake?
Trying to control the learning instead of designing for it.

A Sample Harkness Math Problem Set

1. Solve $2x + 3 = 11$. Explain your steps.

2. Create a different equation with the same solution.

3. Compare two methods for solving linear equations.

4. Design a real-world scenario that models your equation.

5. Challenge: What happens if the equation has no solution?

Each question builds:

• Procedural fluency

• Conceptual understanding

• Application

• Metacognition

Final Thought

What we now call “innovative teaching” is often a rediscovery.

Phillips Exeter’s Harkness Method reminds us that powerful learning doesn’t come from new terminology—it comes from trusting students, designing meaningful problems, and creating space for thinking.

The tools may evolve—whiteboards, collaborative groups, flipped videos—but the core remains the same:

Students learn best when they are doing the thinking.

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Would you like me to adapt this into a tighter YouTube script with timestamps and visuals, or expand it into a full lesson series with downloadable materials?