One of the most frequent questions I get in person or via e-mail is how I structure my class. There's a lurking frustration about the way people present material, Pre-Cal in particular. There seems to be a connection between higher level material and the need to explain explain explain. I find it to be the least successful method for conveying information, or at least a LOT of information. In talking with my students while doing classwork, it's pretty evident that they are highly likely to tune out during lengthy explanations. Students I've tutored share the same experience. Math is 50 minutes of note taking and that's that.
I need more from my students. I experienced math classes like that. Hundreds of hours of math classes like that. I was in cruise control and never figured much out until I got a chance to talk to someone during "homework time" in high school or meeting with my study groups in college.
This is my goal:
As frequently as possible, I want YOU doing something. I get bored talking. You get bored with me talking. I have a new concept for you, here's how it's going to go:
- introductory question or scenario
- questions about prior knowledge
- how can we extend your prior knowledge?
- new skill
- randomly assembled boardwork
- 10 minutes of work
- review prior introduction
- offer any new insights (special cases, errors to watch for)
- pass out classwork
- 20-25 minutes of work
That's about it. I was introducing function compositions the other day. I demonstrated some algebra. We rehashed expanding binomials, and they completed 3 exercises on their own. The following class day, I did some brief introductions and gave them an assignment. 25 minutes later we went over questions. On a block day with Calculus the other week, they had been prepped such that I gave them a variety of assignments and their job was to work for 80-90 minutes. I have many extension activities, but this is how I handle the nitty gritty skills.
Why is this so important? Kids will ask the questions that would stop them in their tracks at home. They'll turn to a neighbor. They'll confirm something with me. They'll offer a theory about something. They'll wonder if they're working the calculator correctly. When finished they'll find a neighbor to check with. They'll fight about stuff (I LOVE when they fight about stuff). Most importantly, I get to interact with them. Sidetrack them with a story, point out something weird, verify an assumption. I can have dozens of small moments, even if it's just to ask "are we ok?"
If I stand at the front all the time, I'll never know them.