A few weeks ago, high school students began to gather before their honors math class. They began pulling their homework, a set of math problems, out of their binders, actively discussing the places that they had become stuck or were able to move forward. One student excitedly exclaimed, “I got it!” as she began to explain her discovery of Cavalieri’s principle describing the volume of solids to the rest of her peers. (See example below).
At San Francisco Waldorf High School, all Honors math classes are taught using a cutting edge methodology that has been developed by the Phillips Exeter Academy since the early nineties. Other math classes at SFWHS use a combination of the Exeter method and the standard skill-building that is more common at college preparatory schools.
In math classes taught based on the student-centered method developed at Philips Exeter, students receive a carefully chosen series of math problems in lieu of a textbook or a set of lectures. They work on these problems throughout the year, working on problems at home and presenting them in class to their peers. The problem sets were developed in a collaborative and open-source process by the Phillips Exeter math department, a group of about 30 faculty members. Together, they came up with a series of problems that spreads throughout the year. Through the careful sequencing of the problems, the core math theorems gradually emerge through the students’ own work.
Dr. Cynthia Reneger and Mr. Kevin Farey in our high school math department are very clear about the benefits that the Philips Exeter method provides for students. They say that the problems help the students develop ownership and responsibility around their understanding of math. The students become used to asking questions and talking about the problems—sometimes before the class has even started! Because the problem set is so carefully structured, the learning can be student centered rather than teacher centered, and the teacher can facilitate the problem solving without interfering with the deeper learning.
There is also a deeper learning that happens in a class like this. Dr. Reneger points out that more than simply developing a confidence in math, a program like this develops an understanding that it is ok to be stuck with a problem! Not always knowing the outcome, or even the “textbook” way of doing a problem, allows the student to become comfortable with the process of learning and doing math. The method requires that the students bring their own ideas about the problems to the classroom, view each others approaches and collaborate on finding the solutions. This, of course, fits beautifully with the way so much is taught at Waldorf—observe the phenomena, make your own observation, collaborate with your classmates. It is perhaps these skills, even more than the advanced math, that the students take away with them when they graduate.
Editors note: Students in our honors math classes (culminating with AP Calculus) take the AP calculus test. The AP exams are graded on a 1 – 5 scale, with 5 being the highest score and one that is accepted for college credit almost everywhere. A 4 is also a strong score and is awarded college credit at many schools (for example Stanford). Last year 8 students took the AP test—five of them earned 5’s and three earned 4’s.