Problems with Words

Almost all Teaching Fellows have the same set of responsibilities; we all do presentations, a field trip, demonstrations, and several other things. As a math TF, I have the added fun of integrating new ways of teaching problem solving. Last week was my first attempt at using some of the methods provided by the Math Forum. Herein, you will find out how well that attempt went.

For those counting, I chose Problem #3520 to try. Simply put, it involves solving a system of five simple algebraic equations. I wanted to try this one because the development of the equations was simple, but the problem was long enough that it'd be difficult for the student to see the immediate conclusion. Each class began with a session of Noticing and Wondering. Here we all wrote down and discussed what we noticed and wondered about the problem (without yet knowing the question). This was followed by some attempts to prompt suggestions from the class on solution techniques. Finally, we ended with a discussion of the actual solution.

The Noticing and Wondering did not go entirely smoothly. Many of the students didn't see the importance to thinking about the problem statement, and instead tried wisecracking their way through the section with silly suggestions. In response, I decided the best thing to do was to write down their silly suggestions on my list. After this, I was glad to hear the students start chastising each other over meaningless statements. Unfortunately, this led to only two or three very forward students saying anything, and the rest quickly became detached from the lecture.

While I tried to get some discussion going on how to solve the problem, no one was willing to say anything, even after some hints on how to approach the problem. When I was teaching a college lab, this is the point at which I'd stand around saying nothing until someone volunteered a solution no matter how long it would take. With less than an hour to do practice problems, the starter, take attendance, hand back papers, and lecture, each minute not spent teaching feels like one lost. By the second class there was little more than a brief pause and comment between the noticing/wondering and the solution. Thankfully, I got some help from the students on writing out the equations.

At the end of the class, Mrs. Porter and I picked up the problems from each student. I've just finished grading them; you might ask,"Ben, how do you grade a problem that you solved for the students?" I would reply, "I treated them like notes, and the students who wrote down all major steps of the solution got full credit." This might seem like an easy grade for most students, but I counted a total of 29 papers when there are 48 students enrolled in these classes. How can I convince the students that there's a reason behind all that's going on? I wish I could have two hours with them to answer all the questions they have, but don't feel like asking.

As an epilogue, I'll be trying another word problem tomorrow. This one should be a bit shorter and I actually worked through this one with the instructors from Drexel. Counting ostriches and llamas, maybe I can come up with a slightly more interesting alternative...