Remembering problem solving knowledge

So, I just finished catching up on my flashcards of basic maths functions (mostly trigonometric formulas). I figured this wouldn’t be enough to remember how to solve analytical problems, but I opened my textbook and gave it a shot anyways.

Last time I did any of this was over a year ago, and I had marked what exercises I had done, so I basically just continued with the next exercise from where I had stopped. Turns out I can still do mathematical analysis!

To be fair, it was an easy problem, but even trying out the harder problems I could sort of figure things out. This made me think I should give some mock exam questions a shot next.

As I stated in my previous post, I think that the actual problem solving is how you can learn these skills. Psychologically, you’re building pathways and patterns between your neurons. Once these paths are built, you need to activate them from time to time to keep the knowledge. I think this is what I might have done when doing my flashcards, although I probably haven’t activated the whole neuron pattern for a certain kind of problem.

This got me thinking. What if I put in some actual exam problems as flashcards? After I’ve solved them of course, and the flashcard would contain just some general notes on how to solve the problem. Whenever I would do the flashcard I wouldn’t be trying to actually solve the maths problem, just quickly think about the problem solving steps and activate the neuron paths for it. Would that be a good way of retaining problem solving knowledge?

I think I’m gonna give this a shot, once I’ve done some mock exams.

Mathematical analysis & memorization

I’m going back to studying engineering again in a couple of months. So I’ve decided to brush up on my math skills before that. For now I’m focusing on Mathematical analysis in one variable and a little bit of linear algebra.

I’ve never finished a course in mathematics on a university level, but I used to study some. One thing I did remember was that in analytics, the trigonometry just completely got to me and put me in a deadlock. The issue being that I’m impatient, and there are a lot of trigonometric rules & shortcuts to remember.

One thing I did finish though was my courses is Japanese. Language is a complete different beast than maths, but I’ve been thinking that parts of how you learn language could be applied to maths.

When you’re learning maths, you’re really learning problem solving. The best way to do that is to start out by solving an easy problem, or a problem that you can be guided through (aka the problem your professor shows you how to solve on the blackboard). Once you can solve one problem, you move on to the next, similar problem, but with something more added on (this could be another mathematical rule or method you have to apply). As you progress through more and more complex problems, using more and more of the simple methods you learned in the first step, you should eventually be able to recognize and solve similar problems.

Now, this should still be your go-to way of learning maths. The trick is to balance solving problems where you challenge yourself to use the mathematical methods you need to learn, and not solve to easy problems using methods you already know how to use.

This is akin to how you would go about learning grammar in language, eg you start learning what a verb is, when you can identify different word classes you can start to conjugate them, then combine them into statements. But to learn words in the first place, we usually take a more repetitive approach, using flash cards or memory games.

I think the same can be applied for simpler math functions and methods. Your main method of learning should still be through problem solving, otherwise you wont know how to use the method you just learned, but using flashcards for repetition has been a huge boost for me in terms of remembering all those pesky trigonometric formulas.

Rather than breaking out a reference paper filled with formulae, or writing down a circle and a triangle every time you need to remember a certain formula, you just know it. What is hard to figure out however is how complex methods I can do this with?