Here are some hints that you should consider:
- Come to my office hours. If you are having trouble doing the
homework problems or understanding the material from class, 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.
- 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 similar to the
ones you will have on 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 the same as doing it; there may be complications
you don't recognize until you actually write it out.
- 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. It is
important to do the homework (or at least attempt it) before the next
class. Often the material in the following class will depend on your
having worked on the homework.
- Don't put off the problem sets 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 problems in one hour, or even in one sitting. The
programming assignments always take longer than you think they will, so be
sure to budget enough time for them. Start early enough to be able to
come to office hours in the event that you need help.
- 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" and you should 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. On the other hand, if it
appears that you think what you have done is right, even though it
isn't, I will take off credit for it, even if you end up with the "right"
- Don't turn in several different answers to the same problem, hoping
one will be right. Some students use this "shotgun" approach, hoping
that at least one answer will be correct and that I'll ignore the others.
I won't. If you write four answers and only one is right, that's probably
worth only 25% of the points, because 75% of what you said was wrong.
- 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 it 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.
- Redo your incorrect work until you get it right. When you get
an assignment back with correction on it, go over the corrections and
understand the mistake. I don't always write out all the details, so be
sure to go back and redo the problem carefully. Then put it aside for a
few hours and come back and do it again (without looking at your previous
work at first). Once you have that problem worked out, do some other ones
that are like it from the book.
- 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. When you work with other students, however, you should be
sure to note that fact; see the homework
policy for complete details.
- Don't work with others on problem sets. Problem sets are to be
done independently. If I suspect cheating occurred on a problem set, I do
not hesitate to take the issue to the Dean. Please see the college
statement on academic honesty for more information about what constitutes
cheating and the process followed when it occurs. See also my statement on
- Review your notes each night. This critical part of the
learning process often is neglected by college students who have been
successful in high school without it. Reviewing your notes daily 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. Don't expect that your understanding
will come during the lecture; learning simply doesn't work that way. You
need to spend time thinking about the course outside of class. Unless they
specifically plan for that, most students don't do this.
- 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 per 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.
LI>Understand the definitions first. The definitions and theorems
are the key to understanding mathematics (not the procedures to follow).
One can often do a computation without any real understanding of the
material, so that is not a good measure of comprehension. Your gaol is to
understand the concepts, so you need to consciously work at that. Most
students find that translating between symbols and ideas (or vice
versa) is one of the hardest aspects of mathematical thinking. One way
to get practice at this is to take each definition we produce in class and
write down how you use it in terms of mathematical symbols; if the
definition already includes symbols or formulas, try to write them down in
terms of words that say what the different parts of the formula are. This
is a critical skill that you need to develop. I would be happy to look
at your translations for you if you want advice on them.
- 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 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, you should think about other ways that the
material could be organized. This will help you recognized the
interconnections of the material. One good practice is to condense five or
ten pages of notes into one page by selecting the most important items.
This act of choosing helps you to organize the material in your head; you
determine what is important and what is not. Without this ability, you
will have way too much to study and will get hopelessly lost. Once you
have gone through all your notes and condensed them, you can go back over
the condensed ones and do it again. See if you can condense your notes
down to one or two pages by the end of the term.
- Don't forget to go over the homework and problem sets when you
study. These and homework are not just for practice of things we did
in class; they also should lead you to develop important concepts or
procedures that I will expect you to know. A good practice, particularly
when you are studying for an exam, is to look back at each problem from the
problem sets and the homework assignments (particularly the ones that are
not from the book) and try to give a one or two sentence statement that
summarizes what that problem is about. If it's a procedure for doing
something, make sure that it has been added to your notes.
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 on Math 127
outside of class each week. I expect the weekly problem sets to
take perhaps 6 to 8 hours, 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.
Some 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 I do want you to succeed at this course
(even when I am writing lots of corrections on your papers), 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
Good luck with the term!
||Math 127 (Winter 2000) web pages|
Created: 30 Dec 1998
Last modified: 31 Dec 1999 13:59:32