Suggestions
and Tips for Success in Calculus A
*By failing to prepare,
you are preparing to fail.*
~
Benjamin Franklin
Learning mathematics takes consistent practice. Much of the opportunities for practice are
furnished by the homework problems that you need to turn in regularly. In
addition to homework problems, you should also honestly “test” yourself with
extra problems in the textbook, and exam reviews. Your performance in these
“self-tests” could give you a good gauge of your understanding of the material
taught in class.
Aim to achieve ownership of mathematical knowledge.
By that we mean you could:
(1) Identify the tools needed to
solve a given problem.
(2) Carry out the process of
solution in a reasonable time frame without help from a tutor or peer.
(3) Give a reason for each step
in the solution of the problem.
(4) Obtain insights from your
computation besides giving a number.
Although we recognize that some
individuals are more gifted in mathematics, consistency in your learning is still required to improve
your chance of success. Mathematics is a hard subject; for many, much has
to be done just to get by. However, the skills you gain and the opportunities
opened to you from your training in the subject will make the challenges you face
worthwhile. These skills are required in your future employment. For instance,
see:
http://www.businessweek.com/magazine/content/06_04/b3968006.htm
http://news.bbc.co.uk/2/hi/uk_news/education/6954666.stm
Meet with your instructors (professor and TA) whenever
you feel that you are falling behind or have trouble understanding the material
to the level listed above. In addition to your instructors, you could also get
help from Math department tutoring, and the LRC. For details look up:
http://www.nd.edu/~b1hu/math10350-07F/index.html
http://www.nd.edu/~b1hu/math10350-07F/lrc.htm
Ultimately, students need to be
able to solve the problems by themselves. But you will be helped by the guided
experience provided by the course. Use the resources available to you to
support your learning. These resources include your instructor, tutoring
services, and practice problems.
Many students in the past have
been successful in Calculus.
With that said, we wish to give
advice on how you should manage your time, and tips for handling various
learning activities of the course, including the examinations.
Getting the Most of Classroom Instruction
Be in class and be prepared to listen attentively and take notes.
Work out all examples discussed in class. You should be able to
work these out on your own in a reasonable time frame. Most problems should
take no more than 20 minutes if you have grasped the material. You should be
able to reason out and explain each step of your work.
Identify the material that you do not understand, and examples
that you have a hard time working out or take a long time to complete.
Ask for help immediately. We highly encourage that you speak with
your instructors about this material before the next class or at least on the
same day as the next class. The point is to promptly resolve
any confusion as soon as possible.
You may still need to “test” yourself with a few similar problems after meeting
with your instructor.
Completing Your Homework
Start working on your homework by the end of each lesson since
homework is collected every class day. At least have an idea of how much time
and help you need to complete your homework.
Getting
started early gives a good margin of time to complete on your homework.
Mark out those you have confidence doing and those you do not
know how to start. Work on at least a couple of them to know how much help you
need. You are expected to complete about 8 to 10 problems every day.
Attempt those problems that you are confident in completing
first. Work on those that you are unsure of. Give yourself a full 20 minutes to
seriously attempt these problems.
Ask for help promptly if you still cannot do your homework. Bring
along your scratch work.
File your homework immediately when it is returned. You will
need it for reviewing.
Preparing for Exams
Give yourself a
week to prepare for each midterm (or
final) exam. Get all the material you need to go through: (1) Sample exams, (2)
Class Notes, (3) Homework, and (4) Quiz.
There
is obviously a lot of material to be covered. However, learning the course material should be a consistently on-going process and should NOT take place merely the week before the
exam.
Start with the
sample exam. Mark out all the problems
that you are confident of solving, those for which you need to refresh your
memory, and those you totally do not know how to attack.
Attempt as many problems as possible before review sessions.
Ask for help promptly from tutors and instructors. Bring along your
attempts and scratch work; they help us see how to best facilitate your
learning.
Attend review sessions. Please note that going to reviews
session alone does not mean that you are ready for the test.
Test yourself with an exam from a previous year. You need to be able
to solve a problem by reasoning out each step of the solution.
Look for more practice problems in topics
that you are still uncomfortable with. It is a good idea to work out those
problems in the notes and text for these topics. See your instructor.