Thursday, September 30, 2010

Problem Solving Hints - Stick With It!

During my Calculus II class on Wednesday, we were working an example with integration by partial fractions.  We had broken down the integral into three different integrals.  The one that I did not know how to do is below.

The nasty integral.

We worked on it in class on Thursday, and used Maxima to find the antiderivative.  However, at the time I was not able find out how to do it by hand.  So the students, one other faculty member, and I worked on it off and on for two days.  Today, we finally found the solution.

To find the solution, it took an integration table and one differential equation to set up the integration by parts.  I do not believe that a normal Calculus II student could have found the answer, which is why I could not find it worked out in either of the calculus texts I used as a reference.

The moral of the story is:
  1. Stick with a problem until it is finished.
  2. Do not be satisfied with an answer that technology gives you.  You do not learn anything by letting the computer do the work for you.
  3. Do not be afraid to use the tools available to you.  You should learn to do the problem by hand, but books and technology can get you started in the right direction.
  4. Learn to work and talk math with other people.  It is a valuable skill because very few people can survive learning math alone.
P.S.  I am not sharing the answer.  You will have to work it out for yourself.

    Wednesday, September 29, 2010

    Students Behaving Badly - One Way to Always Fail a Test

    I got the following e-mail from a student after his class had a test.
    I am having difficulty understanding what we have been going over. I am not for sure what would be best thing to do about it. Thought about dropping the class. It would be best for me to take class over next semester, but still take it this semester. Didn't take test today because I didn't know what the result of a bad exam score would do to my over all grade. Let me know what you advise. Thanks.
     My response was the following.  I didn't really say precisely what I meant in the first sentence of the second paragraph, but I hope I got the point across.
    [name omitted],

                    Since you didn’t take the test, your score will be zero.  You can use your final exam score to replace the missing grade, but that will only work for one test.

                    As far as dropping the class because you are not following the material, remember that you will have the same trouble next semester.  You need to get help in the tutoring lab or in my office hours to catch up in the class.
     So, college students should remember the following.

    1. Not taking a test will always result in a bad grade (0 to be precise).
    2. Dropping a course will not get you ahead the next time you take the course.  In fact, you will forget more of the prerequisite material, and you may need to retake the prerequisite course.  That will put you behind two semesters.
    3. Getting help from the professor or tutors is better than sitting at home and trying to figure it out yourself.