Changes for the New Year

So, I had recently blogged about some ideas to change the pace of my Calc BC class and I want to report on how it is going so far. We are one (partial) week into the new year. We lost Tuesday to extreme cold and I am losing the second of my two BC classes today because I’ll be visiting another classroom. As department chair, it is one of my obligations (and one of my real pleasures) to visit my colleagues to watch them at work.

I have two very different sections of BC this year. My morning class has seven students and they are somewhat reluctant to work together. They get along fine, they are just much more independent workers by nature. My afternoon class has seventeen students and they are much more social and collaborative.

I want to summarize the past two days by section, rather than by day.

Yesterday we were in our computer lab for both sections working on the Desmos activity I slightly modified from Sam Shah’s Virtual Filing Cabinet. By the way, if you haven’t seen this resource, click on the link. You’ll be glad you did. My 1st period class was typically quiet and worked individually with only a little bit of collaboration. I started class with a quick exploration of the polar functions of the form r = 1/(1 – kcos(theta)) and r = 1/(1-ksin(theta)). After five minutes, I left them alone for the next half an hour. I wrapped up class with a verification that, when k = -2, the graph is a hyperbola. A Desmos graph shows this quickly and some recall from precalc days allowed us to convert this to a rectangular equation. It was not a pretty one and the process required recalling the standard form of a hyperbola as well as remembering how to complete the square. I was pretty much the lone voice (unfortunately) but it sure seemed like they were all fine. Today, they worked on the problem set that I also linked to in my last post. I sat and worked myself and had all 7 of them sit at one of my two big tables together. Normally they split themselves with five at one table and two at the other. I thought that this would encourage more collaboration. Instead, I sat working quietly for 30 minutes while they all worked quietly as well. No talking, no looking over each other’s shoulders, no recognition of each other at all that I could see. I must admit that I was getting kind of frustrated. At one point, I catch the eye of one of them and his attention seems to be wandering. I ask him why he’s not talking to anyone and he says he answered them all except for the first question. This is very surprising to me on a number of levels. I think that the first question is the most straightforward (and most related to Calculus) and I thought that this was the one that would seem the least intimidating. The next fifteen minutes were spent sharing solution ideas to that problem as well as the other problems (we only made it through the first five together) and I have to admit I was knocked out by their creativity. Especially on the question involving counting digits. Three of my students actively shared their solution ideas and they just knocked it out of the park. Frustration turned to a combination of delight and confusion. I’ll ask some of my questions later.

Yesterday, my afternoon class also met in the computer lab to work with Desmos. Again, I spent about three to five minutes looking at an animated drawing of the polar curves I mentioned above. For the next thirty minutes the class had a consistent hum of chatter, people arguing with each other about conclusions, kids looking at each other’s work. When I reconvened the class to focus on the same k = -2 case, they were engaged. telling me what the hyperbola equation was, catching a mistake I made in factoring, just a lively discussion. When class ended, I checked in with two students who were just packing up. One of them said something to the effect that my class made his head hurt a bit. He said it cheerfully and his neighbor said that my class was ‘interesting’ which is the word I use to describe difficult or challenging questions. He, too, said this rather cheerfully. I won’t be around to see them work on the problem sheet but I have asked the colleague who is subbing for me to collect their work so I can see what they can accomplish and how they approached these problems.

Now, I am left with these questions as I move forward.

1. How do I create a situation so that my first period class actually talks to each other?
2. Is it important enough to make that happen, given that they are productive workers? I have a pretty strong belief that talking about ideas is important, but I don’t know how to win this class over to that point of view. Is my personal bias important enough to try to change the nature of my learners in my 1st period class?
3. Can I build momentum for these problem solving days if they only happen once per week?

I’ll keep reporting on progress and I’ll keep an eye on any wisdom that you can share int he comments section.