Lessons learned

Here are two problems I encountered while teaching problem-solving:

1). My students aren't attuned to what I'm trying to teach. When they see a problem, they're immediately filtering for "what are the steps for this problem type?" There's a lot of resistance to the idea that there is no algorithm to learn, and even more to the idea that we won't look at a single "type" of problem over and over again; instead each problem will look totally new every time.

2). Even when they get better at problem-solving, they feel adrift because there's nothing concrete they can point to and say "THIS is what I learned". As a result, they feel anxious and unsatisfied, because it's hard for them to know what they're doing or if they're getting better.

To address these problems, I'd like to give students a general algorithm for problem-solving. This will give them steps to follow when facing a new problem, but also be what I want them learn. I can introduce it early and have it appear (to start) on quizes as pure regurgitation. The goal is for the problem-solving steps to be so internalized as to become habits of mind (eventually). I can introduce heuristics a few at a time, and ideally have some accountability structure that will make students feel like they're making progress towards improvement on those heuristics.

Hopefully this will give them a cognitive reference point so they feel (and can explain to others) exactly what they're getting better at.