The atmosphere of a classroom can make all the difference when it comes to whether or not a student will learn anything in that classroom. For example, if the teacher lectures all the time and the student finds this to be boring, then chances are the student will not be able to learn from that teacher. Or, if the student finds the teacher or the content of the course to be intimidating, then the student will probably not learn anything from that teacher. In instances where the student has difficulty learning the material in the classroom but still cares enough to try to pass the class, they tend to find ways to compensate for this, such as reading the textbook, doing a bit of research on the internet, or hiring a tutor. On the positive side these can help the student be successful in the class. However, it also gives the teacher the feeling that what they are doing in the classroom is actually working, when, in fact, the kids are learning despite what is happening in the classroom.
The reason I bring this up is that there was an episode during the past week that let me know the atmosphere in my classroom is conducive to student learning. It came from one of the current students, who came in to class on Friday morning and said he feels like the class is a lot like a "math book club". "We go home, do some work, and come in, sit back, and talk about the math. It's so relaxed...I really like it." I love this description of the class. It's a great description of the class: the prospect of learning the material without lectures is intimidating at first, but eventually the students get comfortable with the system and with each other, and together they figure out that the material isn't really that intimidating either.
So, when asked, I now have a new way to describe my class. I'm not teaching precalculus through Harkness. I'm running a precalculus book club.