HOW TO STUDY MATH AND SCIENCE
Before class briefly preview the text material that will be covered in the lecture.
- Get an overview of the material by reading the introductory and summary passages,
section headings and subheadings, and diagrams.
- Look at the problems at the end of the chapter.
- Make note of new terms and theorems.
- Review (if necessary) old terms and definitions referred to in the new material.
- 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
When taking notes in class, listen actively; intend to learn from the lecture.
- Write down the instructor's explanatory remarks about the problem.
- Note how one gets from one step of the problem to another.
- Note any particular conditions of the problem.
- Note why the approach to the problem is taken.
- Try to anticipate the consequences of a theorem or the next step in a problem. During a
proof, keep the conclusion in mind.
- Note any concepts, rules, techniques, problems that the instructor emphasizes.
- Question your instructor during class about any unclear concept or procedure.
- 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.
- 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 omissions.
- 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
- 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
- Review your notes at regular intervals and review them with the intent to learn and
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
- Briefly preview the material. Get an overview of the content and look at the questions
at the end of the chapter.
- Read actively and read to understand thoroughly.
- Formulate questions before you read (from lecture notes or from previewing) and read to
answer those questions.
- Know what every word and symbol means.
- Translate abstract formulas to verbal explanations.
- Analyze the example problems by asking yourself these questions:
- What concepts, formulas, and rules were applied?
- What methods were used to solve the problem? Why was this method used?
- What was the first step?
- Have any steps been combined?
- What differences or similarities are there between the examples and homework problems?
- Further analyze the example problems by using the following procedures:
- Explain each step using your own words. Write these explanations on paper.
- Draw your own diagrams to illustrate and explain problems.
- 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 you are having trouble with.
- Check to see how the material relates to previous material. Ask yourself these
- How was the material different from previous material?
- How was it the same?
- What totally new concepts were introduced and how were they applied?
- Where does this material "fit" within the overall structure of the course?
- Stop periodically and recall the material that you have read.
- 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
- Read through the problem at a moderate speed to get an overview of the problem.
- 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.
- If appropriate, draw a diagram and label the givens.
- Read each phrase of the problem and write down (symbolically or otherwise) all
information that is given.
- Devise a tentative plan to solve the problem by using one or more of the following
- Form relationships among all facts given. (Write an equation that includes your
- 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
- 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.
- Once you have a plan, carry it out. If it doesn't work, try another plan.
- 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.
- 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? Can I simplify what I did?
- Explain each step using your own words. Write these explanations on your paper.
If you have followed an approach to study as suggested in this handout, your
preparation for exams should not be overly difficult. Consider these procedures:
- Quickly review your notes to determine what topics/problems have been emphasized.
- Look over your notes and text. Make a concept list in which you list major concepts and
formulas which will be covered.
- Review and rework homework problems, noting why the procedures applied.
- Note similarities and differences among problems. Do this for problems within the same
chapter and for problems in different chapters.
- 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.
- 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.
- Begin to work the problems which seem easiest to you. Also give priority to those
problems which are worth the most points.
- Maximize partial credit possibilities by showing all your work.
- If you have a lapse of memory on a certain problem, skip the problem and return to it
Analyzing returned tests can aid your studying for future tests. Ask yourself the
- 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, you should seek help early, if you
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