Paul's Online Math Notes
How To Study Math / Problem Solving  
Notice

On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

I have spent the better part of the last year or so rebuilding the site from the ground up and the result should (hopefully) lead to quicker load times for the pages and for a better experience on mobile platforms. For the most part the update should be seamless for you with a couple of potential exceptions. I have tried to set things up so that there should be next to no down time on the site. However, if you are the site right as the update happens there is a small possibility that you will get a "server not found" type of error for a few seconds before the new site starts being served. In addition, the first couple of pages will take some time to load as the site comes online. Page load time should decrease significantly once things get up and running however.


Paul
August 7, 2018


How To Study Math
Doing Homework Previous Chapter   Next Chapter Studying For an Exam

Problem Solving

In the previous section there were some general tips in regards to homework sets as a whole.  Here are some tips to help you actually work the problems.  Note that some of the ideas were important enough that they are actually in both sections.

 

  • Read the Problem.  Read the problem to get an idea of what you’re being asked to do.  This one of the biggest sources of point loss that I’ve seen in grading.  Too many students just skim the problem and assume they know what’s going on and what they are being asked to do.
  • Read the Problem Again.  Now that you know what you’re being asked to do, read the problem again.  This time around make note of what you are given and what you need to find.  Also make sure that you understand just what you’re being asked to do.
  • Clearly Note What You Are Asked to Find.  Clearly write down somewhere what you’re being asked to find.
  • Clearly Note What You Know.  Clearly write down somewhere all the information you’ve been given.
  • Draw a Diagram.  If appropriate draw a diagram and label what you know and what you need to find.  Often diagrams will suggest the solution technique, so it’s a good idea to get into the habit of drawing them.
  • Devise a Plan.  Try to figure out what you’re going to need to work the problem.   Identify formulas that may help you.  See if there are any intermediate steps/answers that will be needed in order to arrive at the final answer.
  • Work a Similar Problem.  If you can’t figure out how to work the problem find a similar problem that is simpler.  Work this then go back and compare what you did in the simpler problem to the problem you’re asked to do.
  • Work the Plan.  Once you’ve got the plan, work it out to get the answer.
  • Check Your Solution.  Is the answer in proper form?  Does your answer make sense?  If possible, plug your answer back into the original problem as a check.
  • Go Back Over the Problem.  Once you’re satisfied that you’ve got the correct answer go back over the problem.  Identify concepts/methods/formulas that were used for the problem.  Try to understand why these concepts/methods/formulas were used on this problem. Look for identifying characteristics that will help you identify this kind of problem in the future.

Here is a great problem solving flow chart by Eric Austin (a Mechanical Engineer from Clemson University). This flow chart really encompasses all the ideas here in a nice easy to remember process!

Doing Homework Previous Chapter   Next Chapter Studying For an Exam

How To Study Math / Problem Solving   

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