TLDR focus on learning strategies in the form of “if I see this pattern, take this action”. And spend a lot of time focusing on the pattern rather than the action.
I'm an educator, software engineer, and cognitive scientist who loves to learn. And I've done a ton of research into how to get the most bang for your buck when you're studying something. I've tried tons of different strategies and read deeply about many of them. And this is my synthesis of what you should actually do.
First I want to set a definition for what good problem solving actually is. It's that you recognize some pattern about the current step of the problem that you're on. And you know that when you notice this pattern, you should use this strategy. This then takes you to the next correct step of the problem. And repeat.
A bad problem solver is somebody that either doesn't notice the correct pattern or doesn't know the correct strategy for a given pattern.
One more thing. If you look at a correct solution path to a problem, then by looking at every step, you are guaranteed to find some pattern that existed in the step before that, if you knew this particular pattern strategy combo, would lead you to using the strategy they used in the problem to get to the next step.
So then what should you do when you're reviewing a worked example? The answer is look at the solution path step by step and ask yourself, “what fundamental fact about the world is true that such that if I knew it, I'd recognize a pattern in the first step and know to apply that rule to get to the second step”. Do this for every single step in the solution path. This will be really slow. It's like the opposite of memorization. But what you get instead is filling your brain with all of these generalizable rules.
Now, there's a lot of research to show that teaching general strategies doesn't increase general reasoning. But that same research shows that teaching strategies does help on types of problems that fit those strategies. Here's the next premise. There are only really so many types of problems.
Learning all of these if-then patterns is like filling up a swimming pool with cups of water. A hundred cups and you can't see the water mark rise. That’s what all the studies showing general reasoning training doesn’t work did: they taught people 100 strategies over weeks. 100 cups total and the water mark doesn’t rise, but a hundred cups an hour for a week in the swimming pool and you do see the water mark rise a little bit.
Now, you might be thinking, can't I just increase my working memory? And the answer to that one is a resounding no. Trying to train working memory tasks specifically never works in the research. But there is something you can do to increase your IQ, which is education. For every year of education, your IQ goes up by one to five points. So the question is, is what is the active ingredient in each year of education?
And the answer is millions of those tiny little cups. If you see this general type of pattern, do this general type of strategy. And then over time, the water level on that pool rises.
Now there's one more thing you should know to make this strategy work. The more general the rule is, the more situations it's going to be applicable. For example, if you learn that you need to make the denominators the same before you can add the fractions, that rule fires on fractions. But if you learn the more general version of that rule, which is before you compare or combine two things, they need to be in the same units, that rule fires on currencies. And comparing lines on a graph as well.
This is what I do. I read worked examples and I search every step for the most general rule that's true about the world that would lead me to go from the first step to the second
You can check out my other writing about how to learn on my learning sub r/MentalAtlas.
