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Math 15 Study Suggestions:
Many incoming freshman have not developed good study habits and find the
transition to college work to be quite difficult. You may find some
aspects of this course to be frustrating to you; this is natural, but you
should try not to let that block you from succeeding at the course. Try
to remember that part of what you are learning is how to learn
effectively; find out what works for you and what doesn't.
Here are some hints that you should consider:
- Come to my office hours. If you are having trouble doing the
homework problems, please come see me during my
office hours or ask questions in class
(everyone will be thankful that you did).
- If you have trouble with a homework problem, do more problems like it
from the book. There usually are others nearby that are similar. If not,
there are lots of calculus books in the library and in the lounge in the
Math Department; these will have problems similar to the ones we do, so you
can use these as additional practice. Our calculus book is organized in a
traditional way, so you should be able to locate the proper section in
just about any calculus text by looking through the table of contents for
a similar section title.
- Make sure you continue to work on a problem until you get it
right and understand why it's right. It does not do you much good
to work through many problems but get them all wrong. It is better to
get one right in the end than to do ten incorrectly.
- If you still can't get it right, come see me. Many students
attempt, but do not complete, the harder problems. These are the most
important ones to work through, and are more likely to be like the ones you
will have on quizzes and exams. Be sure you know how to do all the
homework problems. Looking them over and saying to yourself "I know how
to do that one" is not always the same as doing it.
- Don't get behind in the homework. You have many demands on your time,
and you will not be able to catch up once you start to fall behind.
- Don't put off the homework until the last minute. Some of the
problems may require considerable thinking, and you will need to come back
to them several times over several days. This is to be expected,
and does not mean you are not understanding the material. It is simply
part of the process of doing hard problems. Do not expect to be able to
do all the homework problems in one hour, or even in one sitting.
- Don't turn in work that you know is wrong but pretend that you think it
is right. It is far better not to finish a problem than to continue on and
produce a wrong answer, or make some other error to compensate so as to get
a reasonable-looking answer; that just makes you look like you
really don't know what you are doing. No answer at all is better
than an answer you know to be wrong. You should say something like: "I
know that something has gone wrong at this point, but I can't figure out
what." You might also say why you think something is not right, and what
you would have done if you could have continued on. There is no shame in
admitting you don't know how to do something. If it appears that you don't
know what you're doing, I will take off credit for it, even if you end up
with the "right" answer.
- Don't do your homework in front of the TV or with the radio or
stereo going. These are distractions and will prevent you from
concentrating on the material you are studying. Some students say: "But I
work better with music going"; they are deluding themselves. What they
actually mean is "I enjoy it more when there's music going". That may be
true, but studies indicate that is takes students longer, and the results
are worse, if there are distractions like music and television when they
are working on their homework. If you must listen to music while
studying or doing homework, at least listen to classical music; studies
show that this makes you smarter.
- Work with other students on homework. This is one of the best
ways to learn the material. If you don't understand it, another student
frequently can help out; if you do know how to do a problem,
explaining it to someone else frequently helps to clarify and solidify the
process for you.
- Don't work with others on take-home exams or quizzes. Quizzes
and exams are to be done independently, including take-home portions. If
I suspect cheating occured on an exam or quiz, I do not hesitate to take
the issue to the Dean, and have done so at least once each semester I have
been at Union College. Please see the college statement on academic
honesty for more information about what constitutes cheating and the
process followed when it occurs.
- Review your notes between classes. This is a critical part of the
learning process, and should not be overlooked. This will help you to
organize the material for yourself, and to locate areas
where you may have questions. It is especially important if you spend most
of your class time taking down notes and find it difficult to think about
the material and write at the same time.
- Form note-sharing groups. If you are having trouble taking
notes and listening at the same time in class, you might consider forming a
note-sharing group with two or three other students in the class. For
example, if there were three of you in the group, each would take notes
one class each week while the other two could pay full attention to the
lecture. After the class, the note-taker would photocopy his or her notes
and give copies to the other members of the group.
- Come to class prepared. Do the homework before the next class,
if you can, and be prepared with questions if not. Look over your
notes briefly in the few minutes before class starts, so you that you
remember where we left off and what we were trying to accomplish. I will
not go over homework problems that people don't have questions about, so if
you want to know how to do the hard ones, you need to ask about them.
- Organize the course material as you study. When you go to
review for exams or quizzes, you should think about other ways that the
material could be organized. This will help you recognized the
interconnections of the material. For example, we will study parametric
surfaces and then implicit surfaces; in both cases we will work out
formulas for tangent planes, but the formulas for these tangent planes will
appear several weeks appart in the course. Your notes will be organized by
the type of surface (parametric or implicit) and will have sub-topics for
tangent planes. You may wish to reorganize your notes the other way
around: make a category for tangent planes with sub-topics for parametric
and implicit surfaces.
The most important job you have as a student is not the memorization of
isolated facts, but the building in your head of a network of connected
information. It's the connections that are crucial. The more ways you
have of organizing the information that you know, the better off you will
be. This takes practice, and you need to do it consciously, at least at
When determining how much time you should spend on your course work,
consider the following analogy: if you were working a full-time job,
you would be putting in 40 hours a week (at least). Think of your
class work here as your job. Since you are probably taking three courses,
that means you should spend about 13 hours a week on each course. Of
that, 3 will be in class, so you should expect to put in about 10
hours of work outside of class each week. I do not expect the weekly
homework to take you that much time, so the remainder should be spent
reviewing your notes, coming to office hours with questions, and
trying to internalize the material from class. On the course
evaluation at the end of the term you will be asked to estimate how
much time you spent per week on the course. Many students end up
saying 2 to 4 hours, which is not enough; however, if you find you
are spending more than 12 hours a week, then something is probably
wrong, and you should come see me.
Finally, I want to remind you that (although it may not always seem like
it), I do want you to succeed at this course, and I will do whatever
I can to make that happen for you. Your role in that is to do
whatever you can to make that happen, and to come to me for
help when it's not working. It is far better to admit that there is
a problem than to brazen it out and hope it gets better; it usually
doesn't on its own.
Good luck with the term!
Up: Math 15 Home Page
Created: Jan 1 1998 ---
Last modified: Jan 4, 1998 3:09:43 PM