How to Get Good At Problem-Solving ?

[soccer123]

Hey guys I am taking a calculus course that is mainly on computation, no proofs. For the most part the computation is easy, but I struggle to solve "challenging" problems and I don't know how to practice for these problems.

An example is I will attempt a solution to the problem but get no where even close in getting the answer. It seems no matter how long I sit and stare at the problem it's impossible to solve, unless I look at the solutions manual.

That's the problem. I don't want to reference the solutions manual to "hard" problems because come exam time, there will be some "hard" problems and I want to be able to tackle them with ease.

Are there any tips to being able to solve these challenging problems? Thanks.

 

[symbolipoint]

Does your book have any "word" problems and applications problems? Work on more or many of those kinds. Your book must have a few of these; otherwise, look for another book which does have many of these word and applications problems.

You also need to try to solve the example exercises yourself. Do what you can as much as you can before looking at any of the solution of any example. Any GOOD Calculus book will have a few example exercises in each section.

People improve at problem-solving through other courses such as Physics and Chemistry. In those courses, symbolic mathematical conceptual exercises are not the goal, but applications problem solving for the particular subject are the goal.

 

[Mute]

Solve lots of problems. Lots of them. The more experience you get, the easier solving problems will be. (The problems, of course, may still be hard, but you'll be able to tackle them because you've built up a toolbox of approaches to use against various kinds of problems).

Looking at the solution manual isn't bad - sometimes there's a trick that maybe you wouldn't have thought of otherwise - but you don't want to ween yourself off of looking at the solutions. To this end, it really helps if you have someone to discuss problems with. Bouncing ideas on how to solve problems off other people really helps you think about things from different angles and gives you new insights. Plus, if a book uses a trick, it might not explain it, whereas your friend can.

 

[Edgardo]

Problem solving is about asking the right questions. Polya, a famous mathematician, described these questions in his book "How to solve it". A summary can be found here:

http://www.math.grin.edu/~rebelsky/ProblemSolving/Essays/polya.html
http://www.math.utah.edu/~pa/math/polya.html

 

[pierce15]

Hey guys I am taking a calculus course that is mainly on computation, no proofs. For the most part the computation is easy, but I struggle to solve "challenging" problems and I don't know how to practice for these problems.

An example is I will attempt a solution to the problem but get no where even close in getting the answer. It seems no matter how long I sit and stare at the problem it's impossible to solve, unless I look at the solutions manual.

That's the problem. I don't want to reference the solutions manual to "hard" problems because come exam time, there will be some "hard" problems and I want to be able to tackle them with ease.

Are there any tips to being able to solve these challenging problems? Thanks.

1. Figure out exactly what the question is asking (i.e. what exactly you have to show/find).
2. Figure out what in the problem relates to something you studied (example: if you studied differentiation a whole chapter and you received a basic optimization problem- you need to figure out how the problem applies to what you studied. In this case, you need to find the local max of a function).
3. Apply the concept and be happy when you get the problem right