Students (and the Teacher!) Learning From Students

I had a wonderful experience on Wednesday.

The PreCalculus question had to do with whether or not a larger area was possible. One group (each class has two groups made up of either 6 or 7 students each) disagreed as to the answer and I watched as an animated discussion took place, going back and forth with drawings on the chalkboard, IN ENGLISH! It was math, it was in English, it was problem-solving, it was learning from one another.

It was wonderful.

One of the things I love most about teaching is learning from the students. (During my five plus years of SAT math prep, I was always learning new ways to solve the same problem. It was just awesome.) In my case here in China, teaching at one of the best schools in this "medium-size" city of 10-12 million, I have some very bright students (especially true in a STEM subject). Allowing them to discuss ways of solving problems offers a FAR richer learning opportunity than I could ever do as "sage on the stage."

I read somewhere that teaching is listening (to which I'll add and asking good questions); learning is talking. Thus, if my job is to teach, my job is to listen and ask questions. This is difficult for me; it doesn't fit the standard definition of "teaching" as I know it. That said, the standard definition of teaching (I talk, you listen) is rapidly being shown to be ineffective, as learners need to talk, struggle, and make mistakes.

The Harkness Method has taken me out of my comfort zone (and I have a long way to go), but it has, so far, been SO rewarding. Seeing students learning from one another through discussion is incredibly satisfying.

A couple of notes:

1) Following in the footsteps of Johnothon Sauer, I took my two PreCalculus classes of 12 and 13 students and broke them into two groups each. I wanted more opportunity for discussion, which he was also looking for when he experimented and found that groups of 6-8 were pretty ideal. (This is particularly true in my situation with students for whom English is not their first language.)

2) In my classes, discussion will make up 10% of their grade. I'm not sure how'd I handle this in a class in the US (English speakers), but I wanted to emphasize the importance of speaking as a big goal for us is to develop their English.

3) I created a "Discussion Log" and each group has a Leader who keeps track of the presenter and who speaks (asks a question or presents another method) for each problem.

4) So far, we're going through one Exeter math page every two days. I'm hopeful that I'll be able to speed this up a bit as the English and presentation skills improve; however, I'm also teaching technology (using the TI-84 calculator) - brand new to these students - so that will take some time as well. Time well spent.