Another thing that I did well this year, was getting guesses before we delve into the problem, or find a solution.

Asking students to put down a guess did a whole lot of things, all informative and only some really helpful.

1) It revealed to me that they had never considered using their own experience to determine if an answer is reasonable. I spend a substantial part of the year trying to divorce them from the idea that the teacher has a magical ability to know the answer. At first I would just walk through their math and reasoning. Over the last month, I’ve started thinking out loud some estimation calculations (things like g = 10 m/s/s, round everything off to 1 sig fig, do the mental math out loud)

2) I found that they had never gone through the thought process of determining a range of reasonable answers. Even the Hi/Low was a real struggle at first. I have to think this one through a bit more, because I pretty much limited myself to talking about more/less than 0 most of the time.

3) One thing I should have done, is to create a page in their notebooks of useful quick and dirty conversions. Things like 60 mph ~ 30 m/s. You can roughly double any speed in m/s to get mph. 10 Km = 6 miles. 2.2 lbs = 1 kg, but also .5 kg ~ 1 lb. I think those might have helped.

4) At the very least, by forcing a guess I was able to find out if anyone in the class had a logical thought process. I could toss out a ridiculous number and the students would all guess around my number. I did this with estimating how far up a ramp a cart would roll during a gravitational potential energy / kinetic energy demonstration. All of the guesses in the first situation scattered around my ridiculous guess. In the second situation they jumped all over the map (at least they didn’t trust me anymore). In the third and last situation, they did the calculations, and adjusted for friction. Just by their guesses I could assess how much they understood about that situation.

5) The last part is that forcing a guess (along with a diagram) forced them to think about a physical situation – or at least read the problem – before jumping off into math world. Also, having that guess to check against caused more students to bring back that answer from “math world” and see if it actually fit before moving forward.