I work as a tour guide at Phillips Exeter and one of the most common questions I get is, "how do students learn math at a Harkness table?" This is a very good question. For those of you unfamiliar with the Harkness method, it involves students sitting around an oblong table and is entirely discussion based. Students do not raise their hands to answer questions, but are expected to learn from and teach, the students around them.
Tim Wu answering the question How do I learn without memorising? on Quora.
It find it interesting that the collaborative model that Dan Meyer, Elizabeth Green and others are advocating in primary and secondary education is also being used at the university level. Even more interesting is that it's been used and refined at Phillips Exeter Academy since 1930.
After a bit of digging, I was able to find some more information on teaching with a Harkness Table.
There is never any busy work at the Harkness Table. Instead of a math book with an endless number of identical problems and the answers in the back of the book, your math teachers write their own text and design problems that will challenge you. In your history class, you move beyond dates – instead, you are asked to consider what “the facts” mean and why you think they are important. In your English class, your teacher wants to know which books you and your classmates have already read and which ones you want to read. Sometimes, the class syllabus may even grow out of everyone’s ideas. You go to school to challenge yourself with the unknown, not the known. That’s what makes class absorbing and keeps you immersed in it all.
I personally love the collaborative nature of a Harkness table. Working with other people on finding the answer to a problem is the way I learn and work best, but I can't help but wondering if it's the best approach for everyone. While I'm not an extravert, I'm certainly not an introvert either. I think I would thrive in an environment where this type of discussion is the norm, but I wonder about people who are more introverted than I am.
I suspect that like any good collaborative process, the Harkness Table is actually more about listening than about speaking, but I still wonder if introverts wouldn't find this type of learning overwhelming. In the case of Exeter, they could simply choose another university. But if this kind of collaborative learning becomes more commonplace, I'd like to know that it isn't solving one problem while creating an other.