Problem Solving
3
straightforward way to solve that type. Recognition of the problem (not the
mechanics of the solution) often is the biggest difficulty to be overcome. In most
cases, there are only a few types of problems associated with a given topic.
8. Be sure that you understand material, rather than just being familiar with
it (there's a huge difference!). See if you can write something about the topic in
a clear, concise, and convincing manner, without any outside assistance. The
act of writing is one of the best ways to fix an idea in your mind, and it is the
same process that you use on an exam. Many students feel that repeated reading of an assignment is all that is needed to learn the material; unfortunately,
that is true for only a few students. Most people will read the words the same
way each time; if real understanding has not occurred by the second or third
reading, further readings probably are a waste of time. Instead of going on to a
fourth reading, search through the text and jot down on a piece of paper the
words representing new concepts, principles, or ideas. Then, with the book
closed, see if you can write a concise "three-sentence essay" on each of these
topics. This is an oversimplified approach (and not nearly as easy as it sounds),
but it does sharpen your view and understanding of a topic. It helps you to
express yourself in an exam-like manner at a time when, without penalty, you
can look up the things you don't know. If you need to look up material to write
your essays, then try again a few days later to be sure you can now do it without
help.
PROBLEM SOLVING
1. Understand a problem before you try to work it. Read it carefully, and
don't jump to conclusions. Don't run the risk of misinterpretation. Learn to
recognize the type of problem.
2. If you don't understand some words or terms in the problems, look up
their meaning in the text or a dictionary. Don't just guess.
3. In the case of problems that involve many words or a descriptive situation, rewrite the problem using a minimum number of words to express the
bare-bones essence of the problem.
4. Some problems give more information than is needed for the solution.
Learn to pick out what is needed and ignore the rest.
5. When appropriate, draw a simple sketch or diagram (with labels) to show
how the different parts are related.
6. Specifically pick out (a) what is given and (b) what is asked for.
7. Look for a relationship (a conceptual principle or a mathematical equation) between what is given and what is asked for.
8. Set up the problem in a concise, logical, stepwise manner, using units for
all terms and factors.
3
straightforward way to solve that type. Recognition of the problem (not the
mechanics of the solution) often is the biggest difficulty to be overcome. In most
cases, there are only a few types of problems associated with a given topic.
8. Be sure that you understand material, rather than just being familiar with
it (there's a huge difference!). See if you can write something about the topic in
a clear, concise, and convincing manner, without any outside assistance. The
act of writing is one of the best ways to fix an idea in your mind, and it is the
same process that you use on an exam. Many students feel that repeated reading of an assignment is all that is needed to learn the material; unfortunately,
that is true for only a few students. Most people will read the words the same
way each time; if real understanding has not occurred by the second or third
reading, further readings probably are a waste of time. Instead of going on to a
fourth reading, search through the text and jot down on a piece of paper the
words representing new concepts, principles, or ideas. Then, with the book
closed, see if you can write a concise "three-sentence essay" on each of these
topics. This is an oversimplified approach (and not nearly as easy as it sounds),
but it does sharpen your view and understanding of a topic. It helps you to
express yourself in an exam-like manner at a time when, without penalty, you
can look up the things you don't know. If you need to look up material to write
your essays, then try again a few days later to be sure you can now do it without
help.
PROBLEM SOLVING
1. Understand a problem before you try to work it. Read it carefully, and
don't jump to conclusions. Don't run the risk of misinterpretation. Learn to
recognize the type of problem.
2. If you don't understand some words or terms in the problems, look up
their meaning in the text or a dictionary. Don't just guess.
3. In the case of problems that involve many words or a descriptive situation, rewrite the problem using a minimum number of words to express the
bare-bones essence of the problem.
4. Some problems give more information than is needed for the solution.
Learn to pick out what is needed and ignore the rest.
5. When appropriate, draw a simple sketch or diagram (with labels) to show
how the different parts are related.
6. Specifically pick out (a) what is given and (b) what is asked for.
7. Look for a relationship (a conceptual principle or a mathematical equation) between what is given and what is asked for.
8. Set up the problem in a concise, logical, stepwise manner, using units for
all terms and factors.