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Problem Solving: Tips For TeachersAuthor(s): Phares G. O'Daffer, Stephen Krulik and Jesse A. RudnickSource: The Arithmetic Teacher, Vol. 33, No. 3 (November 1985), pp. 34-35Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194075 .
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Problem totoing Tip> For Teacher}
Edited by Phares G. O'Daffer, Illinois State University, Normal, IL 6I761
By Stephen Krulik and Jesse A. Rudnick, Temple University, Philadelphia, PA 19122
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34 Arithmetic Teacher
^ ̂ Strategy Spotlight |b ^ аа^Ц ' Experimentation I III ^^шЗг | and Simulation I 'l.Be^ty^^^A /
|
Experimentation and simulation are very important n' ^^^^^^^^^^^^W / related strategies in problem solving. Some problems 'чУ ^^^^^^^^^^^^V у can only be solved by actually doing them! (For ex- WÊIS^^S^ÍB^tmi^meK^^^^^^^^B^ ample, are more red cars or blue cars in a parking lot?) Others can often be solved by simulating the Replace every other coin with a nickel: action with a drawing or other objects. The following ^^^ problem gives a situation where either strategy can пи (5с) Me) (5c)
^^^ Сн) (5c) Сн) (5с)
Eight pennies are placed in a row on a table top. • Next, replace every third coin with a dime: Every other coin is then replaced with a nickel. ^-^ ^-^ ^^^ ^^ ^^^ ^_^ ^_. Every third coin is then replaced with a dime. Fi- 00 ^-^
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OO ^^^
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nally, every fourth coin is replaced with a quarter. ^-^ vil/ ^-^ VU/ VU/ ч/ ч1/ '^у What is the value of the 8 coins now on the table? ,_. „ . • ,_.
Finally, „
replace every fourth .
coin with a quarter: We could actually do this problem. That is, we could >*- ч >^^ч ^->^ /^ ' >■- >, ^-^ ^->v / - 4 actually place the eight pennies on the table and 00 Í5<m
^-""^ (wý ^->^ Í
^-^ 25c
J Mcj (юс) ^-^
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( ̂ 25c) make the replacements indicated. For some stu- ^-""^ ^-^ ^ - ' dents, this strategy is the best one to use when solv- ф The tota, va|ue of the coins ¡s now 78c ing this problem.
As your students work on the problem, several other It is also possible, however, to simulate the action questions can be explored and the results shown with a series of drawings: graphically: • Start with 8 pennies:
What is the value of the 8 coins after each step of
(и) (н) Сч) (h) (h) (h) (h) (ч) the Problem? Which coin(s) are not touched?
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November 1985 35
D Tip Board /5"^^- --^_ I Ш
■ Classroom Climate L / • Proofed so^^'^'^^Sknl 1 I О • Encourage your students to solve problems. I / term* *Hh a /©¿f pr°ceSs. Jhe Ш n U
To become a good problem solver, one must ■ / behalt?' h°*ever î'"^^!?^ И n U constantly practice. I / *J***^^^&]* ГПе f
Щ • Find problem situations that will interest your ■ ш ГПе Words, stu Ш I students and make them want to solve the ■ /
* ег$'апс( the Proh/
stu ■ I
U problem. Students are always interested in ■ / * Understand th e
Proh/ Ш I
sports, television shows, rock groups, and ■ / * D¡nLr th e Question- Ш I
D food. sports, groups,
I I
/ 9™0Utthe * D¡nLr
°9Шге > Pertinent facts. S' f • Ask questions that help students to focus I / °9Шге extrañen.
facts. S' Ш I
their thinking. I I /
/ # ■
^сОдп/ге ̂ extrañen.
^°Us a are data; and
Щ • Do not solve the problems for them! I / #
discuss proble a are
hissing, Щ • Do not reject guesses-pursue them!
Щ^^ш!^ ^Í!£¡l^' ° the Ma/ce Щ • Have your students work in groups. This ар- Г^^^^^^^^^_ ° the a°tion Щ
proach enables them to talk through their ■ ^^^^^^^^^^^^^^^^ m ideas before presenting them to the class. I ^^^^^^^^^^^^^^И
/"S^i"- y fïszz^- шаг
The 1980 NCTM Yearbook. РгоЫегТШ ^ГнЙЗ^ di«erenUypes oui o |Г^1
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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.
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