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Problem Solving: Tips For TeachersAuthor(s): Phares G. O'DafferSource: The Arithmetic Teacher, Vol. 32, No. 6 (February 1985), pp. 62-63Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192564 .
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Problam Solving Tip> For Taachar>
By Phares G. O'Daffer Illinois State University, Normal, ¡L 61761
ЗД Strategy Spotlight
Use Logical Reasoning
Use logical reasoning is a more general strategy than such strategies as make a table, guess and check, or make an organized list. The following problem gives one type of situation where this strategy might be used.
Problem: Ann, Ben, Carlos, and Dina like different types of books: humor, mystery, sports, and adventure. One of Ann's classmates in the group likes mystery books best. Carlos and Dina do not like adventure books. Ben's favorite type of book is sports. Dina did like humor books but has changed her favorite. What is Dina's favorite book?
• First, use a chart to organize the data given in the problem.
Ann Ben Carlos Dina
Humor no
Mystery no
Sports yes
Adventure no no
• Then use the information given and logical reasoning to extend the chart.
For example, since Ben's favorite type of book is sports, we can write "no" in Ben's column for every other type of book. After doing this step, we see that Ann is the only possible person to have adventure books as her favorite.
Ann Ben Carlos Dina
Humor no no yes no
Mystery no no
Sports no yes
Adventure yes no no no
• Use the chart to solve the problem. (Since mystery books are the only type not yet chosen, they are Dina's favorite.)
Some forms of logical reasoning that might be used in solving this problem are these:
1. Since A, then В
2. A or В and not A, so В
3. Not both A and B, and A, so not В
Can you find where each form of reasoning was used in the example?
Use logical reasoning is a general strategy useful in problem solving. Praise your students when they гч reason logically when solving any problem, ц w * J
62 Arithmetic Teacher
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additional ideas and other strategy games, | •aniq jou see the following sources: %
p9j jeqiieu 8jb ^ SJBO sjjods uei t Kru(jk Stephen, and Jesse Rudnick. A Sourcebook for % ujoiqojd ЭЧ1 p Teaching Problem Solving. Newton, Mass.: Allyn & Ba- '
suoujpuoo эц] щ con, 1984, pp. 55-66. ;; sujbj6b!P aseqi 2. Gallagher, Kevin. "Problem Solving through Recreational f.
Mathematics." In Problem Solving in School Mathemat- ^ ics, 1980 Yearbook of the NCTM, pp. 169-77. щ S
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Part of the Tip Board is reserved for techniques that you've found useful in teaching problem solving in your class. Send your ideas to the editor of the section.
February 1985 63
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