How can one effectively solve difficult homework problems?

[ADMO]

I was working on a homework problem today and I got stuck, so I tried manipulating the equation as many different ways as I thought possible hoping that rearranging and substitution would allow me to see something that I was not taking into account. No luck, so then I took a break as is often recommended and I am still stuck. I gave an honest attempt for about two hours. One hour before the break and one hour after it. I then did a google search and found the problem and an explanation, and I understood what I did wrong which was "factoring out a negative sign"....

When one is struggling with a homework problem should one look for the answer or work at it till one gets it?

 

[jedishrfu]

That's one way to solve a problem. It can be very satisfying knowing you have the skill and patience to solve the toughest of problems and that's how it was done in times before the internet. When I went to school, we sometimes searched in books for how other authors may have attacked the problem and would spot something that would lead us to the solution.

I think its good that you worked at it and then found and appreciated the online solution. In some sense, you had the sense to know the online solution was reasonable and you learned something too. If you remember it then the problem became yours and someday you'll get to use the same method to solve a new and different problem.

Do just what you did now, work at it, don't give up but be realistic and manage your time. Skip to another problem and come back later. Finally, search online and see if that gives you more insight. Lastly, do a post-analysis to see where you went wrong and why. Sometimes we have wrong notions of how to apply rules or constraints to a problem or we make mistakes in our checks that lead us astray.

 

[haruspex]

I was working on a homework problem today and I got stuck, so I tried manipulating the equation as many different ways as I thought possible hoping that rearranging and substitution would allow me to see something that I was not taking into account. No luck, so then I took a break as is often recommended and I am still stuck. I gave an honest attempt for about two hours. One hour before the break and one hour after it. I then did a google search and found the problem and an explanation, and I understood what I did wrong which was "factoring out a negative sign"...

When one is struggling with a homework problem should one look for the answer or work at it till one gets it?

Without seeing your erroneous working it's hard to say. It sounds like you were getting an answer, but it was wrong.
If so, there are various tricks you can try to pin down the error.
First, I hope you were working purely symbolically. Plugging in numbers early is a novice error.
Plug in (simple) values (don't need to match given values) for the variables and constants at various points in the working and see where things change. (Do you know what I mean by a binary chop?)
Check sanity of dimensions. In physical problems, the variables represent dimensions like time, distance, mass... Check whether the equations are internally consistent, e.g. that you don't have a force equated to an acceleration.

 

[ADMO]

That's one way to solve a problem. It can be very satisfying knowing you have the skill and patience to solve the toughest of problems and that's how it was done in times before the internet. When I went to school, we sometimes searched in books for how other authors may have attacked the problem and would spot something that would lead us to the solution.

I think its good that you worked at it and then found and appreciated the online solution. In some sense, you had the sense to know the online solution was reasonable and you learned something too. If you remember it then the problem became yours and someday you'll get to use the same method to solve a new and different problem.

Do just what you did now, work at it, don't give up but be realistic and manage your time. Skip to another problem and come back later. Finally, search online and see if that gives you more insight. Lastly, do a post-analysis to see where you went wrong and why. Sometimes we have wrong notions of how to apply rules or constraints to a problem or we make mistakes in our checks that lead us astray.

Thank you. Can you recall any common error that would constantly come up when having difficulty solving a problem?

 

[ADMO]

Without seeing your erroneous working it's hard to say. It sounds like you were getting an answer, but it was wrong.
If so, there are various tricks you can try to pin down the error.
First, I hope you were working purely symbolically. Plugging in numbers early is a novice error.
Plug in (simple) values (don't need to match given values) for the variables and constants at various points in the working and see where things change. (Do you know what I mean by a binary chop?)
Check sanity of dimensions. In physical problems, the variables represent dimensions like time, distance, mass... Check whether the equations are internally consistent, e.g. that you don't have a force equated to an acceleration.

 

[ADMO]

Thank you. Binary Chop; is that to work out a problem as if all the values were given, and the only thing to do is to plug them in and see how variables (dimensions) and unit respond? Can you recall any common error that would constantly come up when having difficulty solving a problem?

 

[ADMO]

Thank you. Binary Chop; is that to work out a problem as if all the values were given, and the only thing to do is to plug them in and see how variables (dimensions) and unit respond? Can you recall any common error that would constantly come up when having difficulty solving a problem?

 

[jedishrfu]

Depends on the problem and your understanding of math notation. Sometimes it can be as simple as misunderstanding the precedence of operations.

A recent example I saw was someone who mistook 3*3^3 to be 729 (ie 9^3) instead of 81 (ie 3*27). Sometimes it can be doing an operation and not realizing you may be dividing by zero.

There as many ways and more to make a mistake in a problem as there are operational steps to get the solution. Thats why its important to understand and question every step you make.

 

[haruspex]

Thank you. Binary Chop; is that to work out a problem as if all the values were given, and the only thing to do is to plug them in and see how variables (dimensions) and unit respond? Can you recall any common error that would constantly come up when having difficulty solving a problem?

Binary chop is a process for homing in on something in a linear sequence in logarithmic time. In this case, it would consist of plugging in example values of the variables at the start and end of a manipulation sequence. If the results mismatch, try the same half way through the sequence. That should show whether the error is in the first half or the second half. And so on.
Common errors... any step can introduce an error. When cancelling out or extracting a factor, failing to do it consistently to all terms; when moving terms to the other side, getting a sign wrong; when distributing (multiplying out through parentheses) multiplying inconsistently or getting a sign wrong...
I would hazard that nearly half of all algebraic errors are wrong signs. Often this comes right at the start, when converting from the physical set up to an equation.