This should come as no surprise to anyone, but most high school kids have never been taught any general-purpose techniques for problem-solving. Those of you who have been reading my journal might recall that I’ve been making an effort to give my classes challenging problems and give them just enough help to keep them from getting stuck, such as the smoke detector problem I gave a few months back.
The current topic (colligative properties) is a hodge-podge of equations that are almost the same as each other, but not quite. Rather than make a flowchart, which the kids would become dependent on, I’ve been trying to teach them the kind of analytical thinking that will allow them to set up these and other problems themselves. Today, I think (hope?) I’ve made a quantum leap in figuring out how to do this.
I’ve made the suggestion many times that it’s easiest to start from what the question is asking for and work backwards to what you’re given, but this instruction doesn’t seem to mean anything to most of them. Today, I tried doing each word problems by first coming up with a written strategy. Once the strategy was complete, we’d follow it, which would lead us right to the answer. The strategies came out something like this:
We’re looking for foo
We can get foo from the formula foo = bar x baz .
We know bar but not baz.We’re now looking for baz.
We can get baz from the formula baz = quux x blech
We know quux but not blech.We’re now looking for blech
We can get blech from the formula blech = bling x blang x blung.
We know bling, blang, and blung, so we’re ready to go!
For each problem, once we had the strategy written down, we used it as road map, starting from the bottom and working our way back to the top, checking off the steps as we completed them. After working a couple of problems this way, a bunch of the kids seemed to understand the process a lot better. I’ll still have to see how well they can do it by themselves, but the initial attempt seems to have come closer than anything else I’ve tried.
