Improving Problem Solving Skills: Tips and Strategies

[cs23]

When solving problems i always solve it the trivial way, the only way i know how to.I usually follow the procedure outlined in the examples of the book. I rarely am able to come up with a solution myself that is correct/ without looking at the solution manual.

When i see the solution to a problem, i usually say,"i would never have thought doing that."

I know some of you may say, I am just following a recipe. But i do read the book aswell, and use the worked examples as templates.

I need help learning how to come up with more complex solutions my self.O

 

[micromass]

Wait, why are trivial solutions bad? I mean, if the solution is trivial and correct, then I prefer it to any overly complex solution. Are do you mean that your solution is often incorrect.

Well, in my opinion, there is only one way to being able to solve complex problems: do a lot of problems! At first, you will probably not be able to solve the question. So it's probably OK to look it up somewhere (but only after you have attempted it yourself!). However, try to learn from it: try to know why the solution is correct, try to see a general method, try to solve thesame problem a day later to see if you can do it now. After you've done loads of problems, then you'll see that you can now come up for solutions to complex problems yourself!

Many of the complex problems require tricks and methods that are not known if you've never solved that problem. The good thing is, that there are not many of such tricks. So if you do a lot of problems, then you will be exposed to all the available tricks.

 

[cs23]

Wait, why are trivial solutions bad? I mean, if the solution is trivial and correct, then I prefer it to any overly complex solution. Are do you mean that your solution is often incorrect.

Correct. I try to solve as many questions as i can, but i can get over a 'bump' so to speak. For example, at the end of section problems, i can solve the first 10 problems which are relatively simple. But once i get to the later problems, that's when i get into trouble. I just don't know how start or what to do for those. When i look at the solutions for those problems, i say ' i wouldn't have thought of that'

 

[Klockan3]

Which kind of course are we talking about?

 

[cs23]

Which kind of course are we talking about?

Mostly physics based courses. However for math courses that require more than solving differential equations, derivatives i have trouble with.The application type questions

 

[Klockan3]

So basically you have problems solving text questions rather than the questions where you are just given an equation to solve? This is a very widespread problem and there is no easy solution, it seems like some just magically gets it while others struggle tremendously with exactly the same problems.

How to solve the harder problems? First you need to be able to solve the easy problems without utilizing others solutions, you must be able to come up with the solution yourself. That is why the problems ramp up, first you learn how to come up with a solution to an easy problem and then they tack on more and more so that you just have to take a small extra step every time. However doing it like you do by finding already done solutions and then applying them to all the easy problems you basically don't leanr anything and when you then face the harder problems where you can't find any solution strategies that fits you hit a wall. That wall as made with the intention that you had already built a set of stairs from all the earlier problems so that it is just another small step to solve.

 

[cs23]

How to solve the harder problems? First you need to be able to solve the easy problems without utilizing others solutions, you must be able to come up with the solution yourself. That is why the problems ramp up, first you learn how to come up with a solution to an easy problem and then they tack on more and more so that you just have to take a small extra step every time. However doing it like you do by finding already done solutions and then applying them to all the easy problems you basically don't leanr anything and when you then face the harder problems where you can't find any solution strategies that fits you hit a wall. That wall as made with the intention that you had already built a set of stairs from all the earlier problems so that it is just another small step to solve.

So basically, if i have a hard problem and strip it down it should resemble one of the easier problems i solved before.

 

[thegreenlaser]

I'd say the best way is not to just blindly do problems, but to gain a deep understanding of why a given method works. When you solve a problem, don't just copy what you've done before, force yourself to say "Why does this method work here? How can I justify using this method?" If someone were to come up to you and say "I think what you did is wrong," you should be able to justify exactly why that method works, and not just say "Well, it's what we always do for this type of problem" or "Well, the answer's right so I obviously did it right". When you understand why, you'll know exactly when you can and can't apply a given method to a complex problem. Teachers like to throw wrenches into those "cookie cutter" questions because it separates out the people who really understand from the people who blindly copy a method. When you understand the reasoning behind the method, those 'wrenches' that make most people stumble will start to seem like no problem to you.

 

[hylander4]

When solving problems i always solve it the trivial way, the only way i know how to.I usually follow the procedure outlined in the examples of the book. I rarely am able to come up with a solution myself that is correct/ without looking at the solution manual.

When i see the solution to a problem, i usually say,"i would never have thought doing that."

I know some of you may say, I am just following a recipe. But i do read the book aswell, and use the worked examples as templates.

I need help learning how to come up with more complex solutions my self.O

I tend to run in this problem when I'm overtired or burnt out. Basically, I have to want to focus on a hard problem before I can solve it myself. Do you listen to music or watch TV when you do math homework? I never understood how anybody could learn while double-tasking like that.

 

[contramundum]

Do you listen to music or watch TV when you do math homework? I never understood how anybody could learn while double-tasking like that.

Have you tried Mozart?