So, we are almost done with our deep and quick tour of AB topics in my BC class. We use the Stewart text which has an interesting section at the end of each chapter. The section is called Problems Plus and I have been browsing through these sections for class examples. On Friday I picked a problem that looked pretty challenging. The set up is this – Imagine a square region with sides measuring two units. In the square a region is shaded. This region is the set of all points that are closer to the center of the square than to the nearest side. What is the area of this region? I did not try this problem first, I had confidence that we could work our way through it. In each of my two sections this was the second problem of the day. Each group dispensed with the first problem in about 5 minutes. Each class spent almost 40 minutes discussing/debating/arguing over this square problem. What thrilled me was that both classes (the small morning class of 8 and the large afternoon class of 18) stayed engaged offering ideas, questioning each other, thinking about circles, etc. We looked at GeoGebra to try and sketch some regions. We thought about the distance formula and circles since the kids were convinced that the region where the distance to the center and the side was equal would be somehow circular in nature. None of our ideas came to find a final solution. To me, this fact is SO tiny in comparison to the fact that they fought, they were engaged, and some of the afternoon kids stayed after to share new insights. I am so proud of this group for being willing to engage and not being at all angry or visibly annoyed when we did not come to a solution. I can’t wait until Monday to see what ideas they bring to the table.
Sounds like a great problem, I have tried this in my AB class, but some students were steadfast on their assumptions, and tuned out to others’ ideas. I allowed each group of students to make a presentation to convince the others in the class they were correct. Some of the best error analysis and problem solving solutions I have seen.
PERSEVERANCE! If there is one thing we (any teacher, but especially math teachers) can help students develop, it is perseverance. If they are willing to try stuff, and mess stuff up, and KEEP TRYING stuff, they will have success!! Good luck!
Thanks Noah. As part of the MTBoS challenge I have been reading a boatload of blogs today. Just got out from under midterm comments so I can breathe today.
Read the following along the lines of my post and want to share the link here
Well worth a read.