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.