Madder 'n Hell

Actually, I'm not mad at all, but it fits in with the word problem for this week. As mentioned in a previous post, I had decided to do the Math Forum problem #3340 with the students. It was the first word problem I've done since returning from break, and had quite varied success with. I also assumed that the students would be less interested in charity donations, so the problem was altered to be about the Madden video game. The rewritten version can be found here.

In both classes, I decided not to go through the explicit process of Noticing & Wondering. The students did not really seem to buy into it. I replaced it with a nearly equivalent process where I projected the problem statement on the board. I then had the students prompt me to circle what they thought was important. The process more closely emulates what they might do on a homework assignment or test, and reduces the amount they have to write which lead to a noticeable improvement in participation. On the flip side, if they're not writing are they still learning?

After the last attempt at encouraging the students to work out a solution themselves, I did not feel that allowing them to work together would be fruitful. Instead, I tried to lead the entire class to a solution. I accomplished this in different ways for each class, and the results were similarly different.

During third hour, with a total of 10 students, I threw them into the deep end without floaties. After having them read the problem statement, I immediately tried to convince them that the number of donors and total budget represented a coordinate point. I found the step to be logical, but if anything, I've learned that you can't force students to reach a result. Instead, you have to leave a trail of breadcrumbs and let them arrive to the result themselves. As soon as I talked about replacing the x-y plane with a donors-budget plane, I had lost nearly everyone. Trying to connect the problem to y = mx + b, was also futile. Usually, the quicker students can help to pull the class along, but most of them were missing on this day. It got to the point where I asked one student a simple question and he ignored me. For several uncomfortable minutes. Last year I taught a lab class at the undergrad level, and the NCRTL told us that you just have to wait it out. I don't think they considered a case where you only have 15 minutes to make your point. I pushed ahead, but had lost any momentum that I had started with.

Determined to correct my mistakes in third hour, I spent the lunch break rethinking my approach to the problem. This time, I deliberately ignored the linear relation. Instead, I had them rewrite the statement,

The company started by setting aside  a  certain  amount  of  money  to  produce  the  game.  To  encourage  their 60  richest  fans  to make  individual contributions, the company pledged to also provide an additional fixed amount for each fan who made a personal donation to the budget.

in the form of an equation. We ultimately ended up at something like B = FA+C, where B represented the company's part of the budget and F was the number of fans who donated. All it took to convince them that this was the same as a line was writing the slope-intercept form directly beneath it. Despite the success in this initial portion, I still think many of the students had difficult thinking of the data in as coordinate points. However, there were definitely several students that grasped the concept and helped move the class forward. While we were able to find A, time ran out right before we could finish the calculation for C. Nevertheless, change in the students' attitudes was palpable.