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Visualizing
is one of the best ways to help you out in solving mathematical
problems. It is probably easiest to
relate this to the ever favorite word problem you run into over and over
again. Every time you read a word
problem you probably think to yourself — “ How am I going to solve this
one?” This strategy helps you be able
to put together the pieces of the word problem puzzle in your head down on
paper. Even
if the problem does not involve words you are still visualizing. There are many ways you may visualize a
problem. The easiest way is probably
to draw a picture. If the problem is not one where it would
be easiest to draw a picture then you may be able to think aloud and
follow the steps to the problem. Which
ever is easiest for you would be the route to go. Here are Polya’s (Teaching Reading in
Mathematics, 2000) problem-solving steps that include both drawing pictures and thinking aloud. A. Understand the problem. (MAKING
CONNECTIONS) 1. Ask yourself if you have done a similar problem before. 2. Determine what is given and if
any information is not needed. 3. You may want to draw a sketch of
the problem. B. Devise a plan. (QUESTIONING and
VISUALIZING and MAKING INFERENCES) 4. Ask yourself if there are any
hints in words to how you should solve this problem. 5. Look at the key words in the problem and see if the simplest plan would
be to select the correct operation. 6. If you are not sure what to do, then see if there is a problem that is
similar to the one you are working on. 7. You can also restate the problem to make
sure that you understand what the problem is asking for. 8. Make sure you have taken into account all
aspects to the problem so you can carry out your plan. C. Carry out your plan. (DETERMING IMPORTANCE) 9. Check to make sure you are
doing each step correctly. 10. Ask yourself, “Why is this the best way to solve it?” D. Examine the solution. (SYNTHESIZING INFORMATION) 11. Check the solution to see if you have correctly answered the
question. 12. Ask yourself — “Is this
solution a reasonable answer for this problem?” If not then check your plan again. Let’s
look at a word problem and use the first two steps to get started solving a
word problem. After
you are done reading the problem go to the assignment and answer the
following questions. |
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