Finally, something to talk about!

Have I committed blog suicide by not posting in several months? I'll take the fact that you're actually reading this as a plus (thank you!) and start with a feeble excuse: I moved across the country this past summer and began teaching at a new school whose culture has taken some ... getting used to. This school's driving mission is to close the achievement gap between low-income, urban students and the rest of the country. This is an important task in a city where only 4% of high school freshmen will ever graduate from college, and they do an incredible job at it. The flip side is that my days of dedicating several class periods to wacky problems or to projecting balls off the roof seem to have come to an end, at least for the foreseeable future. For this reason I've felt at a loss for what to write - I'm teaching a fairly standard and very rigid Precalculus curriculum to juniors and seniors, with very little time for exploration or out-of-the-box discovery. What could I possibly blog about?

Well, finally with a few hours to collect my thoughts over Thanksgiving break I now realize that the same rigid nature of the school that has forced me to bite my philosophical tongue for several months has actually allowed me to experiment with some cool ideas that I'd love to get more input on, even if they're not as (dare I say?) glamorous as projecting balls off the roof.

Idea #1: Study groups. This is by no means novel, but I had never used study groups in my own classroom until my students were studying for their big end-of-quarter assessment a few weeks ago. I put them into groups of four and gave them a choice of six activities; their first item of business was to set their agenda and pick 3 activities that they would prioritize. They had 20 minutes for each activity and had to stick to their agenda, even if they weren't completely finished with an activity after the allotted time. Two options included reviewing previous exams, and I provided them with solution guides that they could use. A few of the activities were practice sets on particularly difficult topics that I knew most students were struggling with (like graphing transformed sinusoids - does anyone have a great way of teaching this?). The remainder of the activities involved making study materials of some sort. One such idea came from one of my seniors, who struggles tremendously in math but has found success in other classes making "process cards" and wanted to give it a try. Process cards are similar to flashcards, but instead of emphasizing one fact or formula each card provides a quick reminder of how to execute a particular process or solve a recurring type of problem (like graphing a transformed sinusoid). These are great for those complicated problems that involve a series of steps of which students invariably forget one (like factoring out the period to find the phase shift), because they can tailor the cards to their needs with individualized reminders using language that makes sense to them.

In any case, students were on task for the entire time and the illusion of choice (I mean, let's be honest - in the end, they were just doing practice problems) seems to have been effective. I also like that once I set them up, the remainder of the period was entirely student-led. To add a measure of accountability, I had students complete an exit ticket in which they graded their peers according to a study group rubric and wrote down one specific thing they learned during each activity.

Idea #2: Hands-down discussions. I stole this idea from an English teacher colleague whose room I share and whose classes by default I spend a lot of time observing. I adapted it to my math class as follows: Students solved a problem as a class while I served only as the "scribe", writing exactly what they said on the board. As an example, one problem was to simplify the expression cot(arcsin(1/5)). Students had to take turns providing steps or asking clarifying questions. As the name of the activity implies, they didn't need to raise their hands but instead took their turn when they felt they had something to contribute. Removing myself from the action, so to speak, had some positive effects:

• Students were forced to direct questions at each other and to be critical of each others' work, since I gave little indication as to whether a particular step was right or wrong;

• They had to be precise and specific with their language; I was obnoxiously literal in transcribing what they said, which was handy in getting them to struggle with algebraic nuances.

On the other hand, it took an awfully long time to do just one problem, so I'd like to find ways to speed up this process while preserving its organic nature. My English teacher colleague uses the hands-down discussion as a way to review several questions that students have had time to work on individually, which is nice because it gives the weaker students a chance to process their ideas and decide what they want to contribute to the discussion beforehand. He also sets a timer (we set a timer for everything at this school), and the students only have the allotted time to complete the problems. Turning the hands-down discussion into a race against the clock by offering some sort of class points as a reward also increases the sense of urgency.

Seeing as this is the time of year to give thanks and not to complain, I need to remember that there was a reason I came to this school, and that there is so much I can learn within their framework if I stop harping on what I am not able to do.

Happy Thanksgiving!