CALCULUS III
MATH 283
Southwestern   
Adventist University 
 
   Distance Education Lawrence E. Turner, Jr., Ph.D.  


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Success in Mathematics Courses


Success in a math course is defined primarily in terms of being able to solve mathematical problems efficiently and correctly in a test situation or in practice after you complete the specific math course. In order to do this you must:
  1. learn specific mathematical concepts,
  2. learn techniques of problem solving,
  3. be able to apply these correctly and quickly.
There are two primary keys to learning the concepts presented:
  1. spend the necessary time,
  2. keep up to date.
Mathematics is best learned by doing—not memorizing. Indeed, often there are very few basic concepts—you can derive everything from those! However, in practice you will need to become familiar with a number of derived concepts so that you can work problems in an efficient manner.

There is no substitute for spending the necessary time required to learn the concepts. The expectation for the average student is two hours outside of class studying and working problems for each class period. Of course, some students can do well by spending less time than this average, and others may need considerably more time. However, time spent is not the only contribution to the learning process. It is important that you spend the appropriate time for you to learn the concepts and methods so that you can work problems efficiently.

It is important also that you do not attempt to put in all the necessary hours the night before a test. Spend some time each day. Keep up to date. Mathematics is like a language—later concepts build upon previous ones. It is virtually impossible to study effectively calculus without a good understanding of algebra. However, as the semester progresses you may come to feel that you are always behind even though you get all the assignments done and turned in on time. This is typical! It often seems just as you finally have figured out all the nuances of a topic, the class has moved on to something new. Do not worry—you are exactly right on schedule!

The best way to study involves a several phase program:
  1. Read through the material that is to be covered in the next lecture. Do not try to understand everything. Mark those things that you do not understand with a question mark in pencil as you read.
  2. Go back through the material quickly. You may find that many of the questions that you had have now been answered—erase them.
  3. Listen in class and take notes. The class presentation will often approach the subject somewhat differently than the text which may fill in gaps or make more sense to you than the written approach.
  4. Go back through the material quickly. Hopefully, you will find that most of the original questions that had remained marked are now answered—erase them.
  5. Ask the teacher, tutor, classmate, or anyone else you can find about the remaining ones. Erase the marks as you finally understand them.
  6. Mark your notes and/or the text as to the important points—you may wish to write out your summary as a review sheet for the next test.
Even though you feel you have a good understanding of the material, applying it to working problems can be another thing.

To work the problems efficiently:
  1. Study the material as presented above.
  2. Attempt the problem.
    1. Write down what is known.
    2. Think about what is being asked for.
    3. Write down all the steps—add a word or two explaining what you are doing with each step.
    4. Mark the final answer prominently.
  3. Do not be afraid of using paper—trees are a bio-renewable resource! It is often faster to take the time to write out each step so that you can check back through your work to find an error than to take shortcuts to save paper.
  4. To assist you with difficulties, study the examples in the text—often an example may be similar to the problem you are attempting.
  5. Give each problem at least some time before you ask for help. Somewhere between the extremes of spending hours on a single problem before asking for help and asking for help before you have even read it probably is best. Learning comes from struggling with problems, but not beating your head against a brick wall.
  6. Do not ask the teacher, tutor, or friend to do the problem for you—ask for specific help on specific points. Having the homework done for you may "feel good" at the time, but you will have real trouble during the tests. Keep in mind that the homework is to help you to become proficient so that you can do well on the tests.
The assignments are designed with two goals in mind:
  1. to provide a minimal set of practice and experience, and
  2. to furnish a set of exercises for grading and feedback.
While a good student may learn all the material with a minimum of time and practice, many will find that extra practice on a daily basis is helpful. Work extra problems—especially the ones with answers in the back of the book.

Keep in mind that the text and the teacher can do only so much. These components cannot "make" you understand the material. That only comes from within. It is the role of the teacher to help you learn.

The "bottomline" key is work lots of problems daily as primary study and for preparation for the tests!
 
© 1999, 2000, 2001, 2002, 2003 by Lawrence Turner