I’m approaching the end of the school year and I’ve been pretty negative almost the entire time. Because I don’t know where I’m teaching next year (due to my spouse’s career), there are a lot of changes that I didn’t make based on my perception of investment/return. Those problems have occupied my mind, pushing out the problems that I have solved and addressed. So I’m going to spend this week documenting one thing per day on this blog that I changed this year for the positive.
Today I’m going to talk about less structured problem solving.
In the math & physics blog-o-twittersphere there is a strong discussion about how to make our students better at applying this wonderful math that they’ve spent so long learning. I’ve even noticed this in my own teaching, how a slightly novel situation throws my students for a complete loop. If the information in a problem was not explicitly listed, they weren’t sure where to start.
In the past week, I’ve noticed that this is no longer the case. I can’t take all of the credit, but it seems reasonable that certain teacher moves contributed to their increased flexibility.
1. From the beginning of the year, I refused to nail down a particular explanation or calculation as correct. It was always: “What assumptions are you making?” “What Jane said seems to be assuming X, is that a valid assumption?” “I can’t say if that’s correct, but I can listen to your thought process and tell you if something doesn’t match up.” I also tried to remove myself as the expert with all the answers, going so far as to not even know the final calculation so I couldn’t react with body language.
2. Presenting situations first with a bare minimum of information. And by bare minimum, I mean just enough to understand the physical situation, but not enough to make all of the calculations. Students are then prompted to ask for the information they need. I could always add in more prompting or help in figuring out what information they need later.
3. Presenting situations with an excess of information that is unnecessary. This was really eye-opening for students when they were doing gravitation problems where I would give them planetary radii and orbital radii and they had to figure out which radius/distance to use.
4. Forcing them to draw diagrams and list variables. I taught them to do this from the beginning, but many students refused. “Drawing a diagram is too much work!” They were very focused on the step immediately in front of them. I -think- many of them weren’t thinking 2-3 steps ahead in a path to solutions. Once I forced the issue and refused to grade their work unless they drew a diagram (I offered to help them figure out a diagram if they didn’t know what to draw), the quality of work and accuracy improved drastically.
DISCLAIMER: I’m not saying I came up with any of this, or that anything is groundbreaking. I just wanted to make sure I have a record of things that I’m doing that seem to be working well.