How to Study Math Science

How to Study Math Science
Adapted from a handout from
Learning Skills Center
The University of Texas at Austin
Before class briefly preview the text material that will
be covered in the lecture.
1. Get an overview of the material by reading the
introductory and summary passages, section headings and
subheadings, and diagrams.
2. Look at the problems at the end of the chapter.
3. Make note of new terms and theorems.
4. Review (if necessary) old terms and definitions referred
to in the new material.
5. Formulate possible questions for class.
Remember, the purpose of previewing is not to
understand the material but to get a general idea of
what the lecture will cover. This should not be a very
time-consuming process.
When taking notes in class, listen actively; intend to
learn from the lecture.
1. Write down the instructor's explanatory remarks about
the problem.
• Note how one gets from one step of the problem to
• Note any particular conditions of the problem.
• Note why the approach to the problem is taken.
2. Try to anticipate the consequences of a theorem or the
next step in a problem. During a proof, keep the conclusion
in mind.
3. Note any concepts, rules, techniques, problems that the
instructor emphasizes.
4. Question your instructor during class about any unclear
concept or procedure.
5. If you miss something in the lecture or don't understand
what's being presented, then write down what you can
catch--especially key words. Be sure to skip several lines
so you can fill in the missing material later.
6. As soon as possible after class, summarize, review, and
edit your notes.
• Quickly read through your notes to get an overview
of the material and to check for any errors or
• Fill in any information--especially explanatory
remarks (see #1 above)--that you did not have time to
write down or that the instructor did not provide.
• Use the margin or the back of the opposite page to
summarize the material, list key terms or formulas,
and rework examples. You can also use this space to
take notes from the textbook.
• Note any relationship to previous material; i.e., write
down key similarities and differences between
concepts in the new material and concepts in
previously learned material.
7. Review your notes at regular intervals and review them
with the intent to learn and retain.
If your class lectures provide a good overall structure
of the course, you can use your text to clarify and
supplement your lecture notes. In order to create a
single study source, insert the notes you take from
the text into your lecture notes themselves as well as
in the margin or the back of the opposite page.
If your text provides the best overall structure of the
material, then you can use your lecture notes as the
supplementary source. In either case consider the
following procedures:
1. Briefly preview the material. Get an overview of the
content and look at the questions at the end of the chapter.
2. Read actively and read to understand thoroughly.
• Formulate questions before you read (from lecture
notes or from previewing) and read to answer those
• Know what every word and symbol means.
• Translate abstract formulas to verbal explanations.
• Analyze the example problems by asking yourself
these questions:
a) What concepts, formulas, and rules were applied?
b) What methods were used to solve the problem?
Why was this method used?
c) What was the first step?
d) Have any steps been combined?
e) What differences or similarities are there between
the examples and homework problems?
f) Further analyze the example problems by using
the following procedures:
g) Explain each step using your own words. Write
these explanations on paper.
h) Draw your own diagrams to illustrate and explain
i) For practice, write down example problems from
your book, close your book, and try to work the
problems. Check your work with the example to
find what concepts, rules, or methods are difficult.
j) Check to see how the material relates to previous
material. Ask yourself these questions:
k) How was the material different from previous
l) How was it the same?
m) What totally new concepts were introduced and
how were they applied?
n) Where does this material "fit" within the overall
structure of the course?
3. Stop periodically and recall the material that you have
read. No peeking!
4. Review prerequisite material, if necessary.
Solving problems is usually the most important aspect
of math or science courses. You must, therefore,
spend much of your study time either working or
studying problems. When working a problem, follow
these steps:
If you have followed an approach to study as
suggested in this handout, your preparation for
exams should not be overly difficult. Consider these
1. Read through the problem at a moderate speed to get
an overview of the problem.
2. Read through the problem again for the purpose of
finding out what the problem is asking for (your unknown).
Be able to state this in your own words.
3. If appropriate, draw a diagram and label the givens.
4. Read each phrase of the problem and write down
(symbolically or otherwise) all information that is given.
5. Devise a tentative plan to solve the problem by using
one or more of the following tactics:
• Form relationships among all facts given. (Write an
equation that includes your unknown.)
• Think of every formula or definition that might be
relevant to the problem.
• Work backwards; ask yourself, "What do I need to
know in order to get the answer?"
• Relate the problem to a similar example from your
textbook or notes.
• Solve a simpler case of the problem using extremely
large or small numbers; then follow your example as if
it is an example from the text.
• Break the problem into simpler problems. Work part
of the problem and see if it relates to the whole.
• Guess an answer and then try to check it to see if it's
correct. The method you use to check your answer
may suggest a possible plan.
• If you are making no progress, take a break and
return to the problem later.
6. Once you have a plan, carry it out. If it doesn't work, try
another plan.
7.Check your solution.
• Check to see if the answer is in the proper form.
• Insert your answer back into the problem.
• Make sure your answer is "reasonable."
During the problem solving process, it is often helpful
to say out loud all of the things you are thinking. This
verbalization process can help lead you to a solution.
After you have worked a problem, analyze it. This can
help sharpen your understanding of the problem as
well as aid you when working future problems.
1. Focus on the processes used (not the answer) and ask
yourself these questions:
• What concept, formulas, and rules did I apply?
• What methods did I use?
• How did I begin?
• How does the solution compare with worked
examples from the textbook or my notes?
• Can I do this problem another way?
2. Explain each step using your own words. Write these
explanations on your paper.
1. Quickly review your notes to determine what
topics/problems have been emphasized.
2. Look over your notes and text. Make a concept list in
which you list major concepts and formulas which will be
3. Review and rework homework problems, noting why the
procedures applied.
4. Note similarities and differences among problems. Do
this for problems within the same chapter and for problems
in different chapters.
5. Locate additional problems and use them to take a
practice test. Test yourself under conditions that are as
realistic as possible (e.g., no notes, time restriction,
random sequence of problems, etc.). Also try to predict test
questions; make up your own problems and practice
working them.
1. Glance over the whole exam quickly, assessing
questions as to their level of difficulty and point value. Also
get a sense of how much time to spend on each question.
Leave time at the end to check your work.
2. Begin to work the problems which seem easiest to you.
Also give priority to those problems which are worth the
most points.
3. Maximize partial credit possibilities by showing all your
4. If you have a lapse of memory on a certain problem,
skip the problem and return to it later.
Analyzing returned tests can aid your studying for
future tests. Ask yourself the following questions:
• Did most of the test come from the lecture, textbook,
or homework?
• How were the problems different from those in my
notes, text, and homework?
• Where was my greatest source of error (careless
errors, lack of time, lack of understanding of material,
uncertainty of which method to choose, lack of
prerequisite information, test anxiety, etc.)?
• How can I change my studying habits to adjust for
the errors I am making?
IMPORTANT: The knowledge of most math/science courses is
cumulative. Many concepts build on previous concepts, and a poor
understanding of one concept will likely lead to a poor
understanding of future concepts. Consequently, master the
content as you go, and seek help early.
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