Question

So how do you excel at problem solving in math? This is like that question about doing versus understanding math. I want that but I wanna also excel at the problem solving part specifically. I wanna make problems, not just solve those given to me too!

Answer 1

math just takes practice to master the concepts

Answer 2

Yeah, but it depends too. Like sometimes I don't interpret the problem right, sometimes I get stuck for too long (And I hate giving up, so there's wasting time there), I make silly mistakes in calculations and/or the algorithm i'm applying.
Do you know how to deal with all of that? and also maybe make problem solving pretty fun? because if i gotta do lots of it, it should be fun. but for some reason I get frustrated when I don't get things right, which is something i definitely need to deal with in order to excel here

Answer 3

http://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx

Answer 4

By slowing down, paying attention to what you’re doing and paying attention to proper notation you can avoid the vast majority of these mistakes!

Answer 5

Yeah I get it, you're right. I dunno why I'm expecting a magical answer to this, I do focus on understanding things intuitively. I think I just want to make this even more fun so I could prioritize it over other things, but it's hard to just ask someone "Hey how do I make this fun?"

Answer 6

XD

Answer 7

To me, the appeal of math has always been mostly collecting new ways of seeing and the joy of discovering and finding these ways. I think the main thing is most people just 'want the answer' and I was not too concerned with that. People for the most part are very good at lying to themselves when they see someone make a mathematical argument too. They can follow the steps one by one when someone holds their hand and at every step they'll agree, "Yeah, that makes sense!" but you ask them to explain what they were shown the next day and they'll be completely lost.

I think the only way to push past this is to have a very bad memory for math formulas. If you can't memorize formulas, then you are forced to create them. If you can't create it, then you don't understand it. This is great news because at any given moment you have a way of knowing what you need to study! Where you get frustrated and stop is where you need to try your hardest to see if you can surprise yourself with creative thinking. If you don't give it an honest shot and don't allow yourself to enjoy being frustrated, then you are cheating yourself. A big part of problem solving is being able to extend your comfort zone to where you don't know what's going on. After all, you're not solving a damn thing if you already know the answer.

So I'll be a little more succinct cause I'm getting winded here haha. When you get frustrated, after you've given it an honest shot, you have now successfully primed your common sense to adopt whatever the solution may be when you find it. In a lot of ways, you really learn what something is in math not by "what it is" but by "what it isn't" when you accustom yourself to the boundaries and make all the mistakes.

I could say much more, I have been literally frustrating myself with math problems every day for years and I've had a lot of bad and good experiences with it and my opinion of this has changed a lot. Maybe this helps?

Answer 8

The key to success is having sound basic skills.... a toolkit you can keep going back to.

like distributing, factoring, solving collecting like terms

Look at the problem and break it down to things you can do..

draw diagrams to help

Answer 9

@kainui yeah!! yeah I like your point of view there, it's like playing a video game. your obectives are like "beat the game, finish the enemy" but whaat's exciting about them is the process of meeting those objectives not just...meeting the objective.
I'm trying to get out of my comfort zone and feel positive about being frustrated, I think I just built many negative associations with that in the past so i'm trying to overcome them
When it comes to understanding concepts I think I always try to imagine the process, like, associating them to something concrete, and seeing how this object "X" changes to "Y" through a process. I wonder how I can apply that to "seeing what it isn't" rather than what it is?????
Thank you for that insight!

Answer 10

@campbell_st Ay, I get that!! I think my algebraic toolkit is sound but sometimes when I try to understand a concept I try to be intuitive with its process, so say, if Power = Current² times Resistance for objects in a circuit, I understand the basic operations (squaring, multiplying) but now how, or why, or what power is through this. I realized that if I manipulate the formula though I could put it in simpler forms since it can be put in any algebraic form that may be complex just so it's simpler to calculate with. But when I don't know any better form and still can't get the big picture there it gets frustrating

Answer 11

A good book for undergraduates is 'How to think like a mathematician' by Kevin Houston.

Answer 12

@welshfella Yes, will be checking that out thanks!