Problems with Conventional Approaches to Building Knowledge
I use the phrase “building knowledge” instead of the word “learning” because I want to focus on the building aspect. When I think of learning, I imagine my mind building an ever more complex network of ideas and experiences. It’s the “network” part that is so important—everything is interconnected.
Yet so often it is the case that students learn concepts in isolation of any broader context. My experience developing online versions of textbook math problems has made this quite clear. Each lesson covers a particular topic, like how to find the median of a set of numbers. This lesson is likely to follow the one on how to find the range of a set of numbers, and a lesson on how to find the mean will probably come the next day. The progression is nicely organized and each lesson is careful not to intrude on the territory of any other.
The problem is that the real world is not so nicely organized. The complex tasks we perform everyday require us to pull from a diversity of experiences in order to accomplish them. Few would argue this point, yet many are complacent about the segregation of knowledge that exists both within their own minds and within society. Specialization is rewarded in school and in the workplace, leading to a world in which everyone knows a lot about something but few understand how it all comes together.
The Harkness Teaching Philosophy
Enter Harkness. Harkness is a teaching philosophy made popular by Phillips Exeter Academy that replaces textbooks and lectures with problem sets and group discussions. In most cases this is not a casual replacement in the sense that “you have a textbook but we try not to teach from it” but a strict replacement in the sense that you literally don’t have a textbook. An example of one of their math “textbooks” can be found here.
In their math courses, Exeter students solve problems every night that they may have never seen before and which may not fit into any single category (note the contrast with the textbook layout described above). Students then bring their solutions to class and present them to one another. The teacher facilitates a group discussion rather than giving lectures. This format is made possible by small classes (of 8 to 12 students, typically) in which students and teacher sit together around a “Harkness table.”
Why Harkness is Well-Suited for SAT Prep
When I began developing a curriculum for my SAT prep classes, I set out to offer an alternative to the rote memorization of formulas, to brainless tips and tricks, and to the simple mimicry of a solution process shown in a textbook or a teacher’s lecture. This decision was informed by my degree in physics, which trained me to derive formulas and concepts from first principles.
I wanted to design an SAT course that trained students to work from the ground up on every problem they solved. A course that treated math concepts, grammar rules, and vocab as a toolkit for problem solving rather than as an end in-and-of themselves.
It was therefore natural to adopt the Harkness teaching philosophy. Students in my SAT classes solve problem sets that force them to think critically, while helping them to integrate elements of the core toolkit in a more functionally useful way. Rather than solving only problems that are obvious applications of a particular concept or formula, students solve problems for which the correct solution process is not obvious (as is the case for many SAT questions). Problem sets follow a non-linear progression that aspires to profundity and elegance. The result is a preparatory experience that builds knowledge through an understanding of the functional relationships between concepts.
The Harkness style would not be complete without a Harkness table. Indeed, The Knowledge Roundtable would not be complete without a Harkness table. Giving students difficult problem sets without the supportive roundtable discussion that occurs around the Harkness table in my classroom would be unproductive. But the group discussion enables students to experiment collectively on ways to answer a question. This is a creative process that imparts a sense of ownership (in stark contrast to the faithful following of a prescription from a textbook or a lecture). This further enhances the vitality of the knowledge that is built.
The Reasoning Test
Finally, in case you have any lingering doubts about the suitability of Harkness for the SAT, I should point out the often overlooked official name of the SAT: The SAT Reasoning Test. Notice it’s not called the “SAT Algebra Test” or the “SAT Vocabulary Test.” The SAT is specifically testing a students ability to reason. This is why it’s important for any SAT course to emphasize the fact that the content of the test (math, reading, or writing) is secondary. These elements are merely, as mentioned above, a toolkit for problem solving.
The College Board, and colleges for that matter, are not particularly interested in whether you can solve an equation; they want to know that you can analyze a situation and use logic to arrive at an answer. In other words, knowledge of a particular topic is necessary but not sufficient. Therefore, it should be the objective of any good test prep course to provide training sufficient for students to build integrated knowledge and to creatively solve problems. In my opinion, anything less falls short.