Math IV A. College Prep has a distinctive math tradition, with students working in groups through complex problem binders. Really worth visiting the course description posted online; it has long been my understanding that the math curriculum is College Prep’s greatest distinction. I love the way the description states the first course goal: “problem solving as the central means of instruction” which is exactly what this blogger thinks should be every high school course’s approach! Second is a good command of basic facts based on understanding as well as memorization; third is clear communication, both oral and written [which is great to see in a math course, and should again be a goal universally]; fourth is the appropriate use of technology.
After a one minute demonstration on the whiteboard, our student groups are off and running, working at tables of four while the teacher circulates. The room in animated, upbeat, despite the fact that the sun is beating on it and it must be nearly 80 degrees in here. The classroom walls display posters celebrating the power and history of Math: one is headed A World of Mathematics, Science, and Technology; another Harmonious Connections: Math and Music.
Tim tells me that he finds this mode of learning very different from the traditional lecture format, and very different from his experience learning math prior to College Prep. He says though that after a “learning curve” (his term), it is a better way to learn. You really have to work together with your table group, you can ask them things that you might not ask a teacher at the whiteboard, the team really supports each other. The teacher still does, he hastens to point out, offer some lectures to help students, but they are most intermittent and responsive to the problems the students are working on. The students here have no textbook; they have a rich binder containing a large number of problems and some brief instructional overviews, which the College Prep teachers have written themselves. These students learn by doing these problems, rather than being taught how to do them and then separately trying to do them.
The students are doing a problem that goes like this: “The ancient Babylonians loved 60; they made 60 minutes in an hour, and 60 minutes in an arc…. Questions: 1. What did the Babylonians like about 60 and 360? 2. Why might time units and angle units be so closely related? 3. Convert a provided example of a geographical location from “babylonian” degrees to decimal degrees. 4. Here’s another reason for the definition of a degree: every day the Earth revolves round the sun through a central angle (measured at the sun) of about 1 degree. Explain how you know this is true.” I love these “Math” questions; they are rich, real world, and require students to explain their thinking and reasoning. The teacher offers some insight to the second question by projecting topographical maps on the board, and showing how the angles work there, in a very nice, real-world way.
It is great to watch Tim help a table-mate with a problem; she says she thinks she understands the concept but can’t figure out the problem. Tim jumps in and very helpfully explains it to her (”it looks like I was mixing up the xs and ys”). I can’t help but think that he is going to come away with a much more lasting understanding of this himself, because of the processing he has had to do to explain it to another, and encoding it in his brain in ways that are underscored by the social experience of explaining it. The kids really, really pay attention to each other as they receive their explanations, giving their full attention in a way I just don’t see happening so much when they listen to a teacher at a blackboard. As they are getting the explanation, they are talking, repeating the logic, exclaiming things like “oh that is why I did that,” or “noooo, I still don’t see it”– none of which students can easily do when a teacher is explaining it from the whiteboard. This is really good stuff. I like watching the way they lean– reaching across the table (these tables I think are about a foot too wide for the way they are being used, but it really requires them to lean far forward, which is a great learning posture) and as they reach they use their mechanical pencils to point out things on their partner’s graphs: pointing, drawing, sketching, gesticulating: wielding these pencils as extensions of their fingers (and hence as the ultimate powerfully “digital” tool) and as adeptly as a fencer wields a sword, and here this is indeed a mighty pen. As students help each other to solve a problem, they high five each other. This is an after-lunch, hot room (I am boiling), but every single student here is fully engaged and on-task.
Now, the teacher is using a graphing calculator program, projected on the whiteboard; the formula he is using isn’t quite working, but the students are quite attentive, offering advise and trying to assist. It is a good energy.