As a first year students you should know that there is a fundamental difference between a high school and university.
Please read carefully following thoughts (courtesy of Prof. Steven Zuker) about different styles of learning and try to follow these closely.
What follows is what an entering freshman should hear about the academic side
of university life [in mathematics (and the sciences)].
The underlying premise, whose truth is very easy to demonstrate, is that most
students who are admitted to a university were being taught in high school
well below their level. The intent here is to reduce the time it takes for the
student to appreciate this and to help him or her adjust to the demands of
working up to level.
. . . . . 1. You are no longer in high school. The great majority of
you, not having done so already, will have to discard high school notions of
teaching and learning, and replace them by university-level notions. This may be
difficult, but it must happen sooner or later, so sooner is better. Our goal is
for more than just getting you to reproduce what was told to you in the
classroom.
. . . . . 2. Expect to have material covered at two to three times the
pace of high school. Above that, we aim for greater command of the material,
esp. the ability to apply what you have learned to new situations (when
relevant).
. . . . . 3. Lecture time is at a premium, so must be used efficiently. You
cannot be "taught" everything in the classroom. It is your
responsibility to learn the material. Most of this learning must take place
outside the classroom. You should willingly put in two hours outside the
classroom for each hour of class.
. . . . . 4. The instructor's job is primarily to provide a framework, with
some of the particulars, to guide you in doing your learning of the concepts
and methods that comprise the material of the course. It is not to "program" you
with isolated facts and problem types, nor to monitor your progress.
. . . . . 5. You are expected to read the textbook for comprehension. It gives
the detailed account of the material of the course. It also contains many
examples of problems worked out, and these should be used to supplement those
you see in the lecture. The textbook is not a novel, so the reading must often
be slow-going and careful. However, there is the clear advantage that you can
read it at your own pace. Use pencil and paper to work through the material, and
to fill in omitted steps.
. . . . . 6. As for when you engage the textbook, you have the following
dichotomy:
. . . a) [recommended for most students] Read, for the first time, the
appropriate section(s) of the book before the material is presented in
lecture. That is, come prepared for class. Then, the faster-paced college-style
lecture will make more sense.
. . . b) If you haven't looked at the book beforehand, try to pick up what you
can from the lecture. Though the lecture may seem hard to follow (cf. #2),
absorb the general idea and/or take thorough notes, hoping to sort it out later,
while studying from the book outside of class.
. . . . . 7. It is the student's responsibility to communicate clearly in
writing up solutions of the questions and problems in homework and exams. The
rules of language still apply in mathematics, and apply even when symbols are
used in formulas, equations, etc. Exams will consist largely of fresh problems
that fall within the material that is being tested.
. . . . . 8. Solving problems to learn. Mathematics is learned through
practice. For students, this means solving as many problems as one can find.
Here many students fall into the trap. While it is relatively easy to find
simple problems, it is rather hard to find more advanced problems which an
average student can solve in a reasonable time. So any good problem someone
solves for you, or you read a solution actually will hurt your chances to learn.
Never ask for a solution, never read a solution of a good problem before you
spent few hours/days thinking about it.