problem solving: tips for teachers

3
Problem Solving: Tips For Teachers Author(s): Phares G. O'Daffer Source: The Arithmetic Teacher, Vol. 32, No. 3 (November 1984), pp. 46-47 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41192472 . Accessed: 12/06/2014 16:31 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 91.229.229.212 on Thu, 12 Jun 2014 16:31:15 PM All use subject to JSTOR Terms and Conditions

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Page 1: Problem Solving: Tips For Teachers

Problem Solving: Tips For TeachersAuthor(s): Phares G. O'DafferSource: The Arithmetic Teacher, Vol. 32, No. 3 (November 1984), pp. 46-47Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192472 .

Accessed: 12/06/2014 16:31

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 91.229.229.212 on Thu, 12 Jun 2014 16:31:15 PMAll use subject to JSTOR Terms and Conditions

Page 2: Problem Solving: Tips For Teachers

Problam Solving Tip> For Taachar^

By Phares G. O'Daffer Illinois State University, Normal, IL 61761

46 Arithmetic Teacher

7Г1 / QtrfltPfii/ ^nntliflht • Use data in the problem to begin a table. The table ' l' Wil^J J w|#WMl*|l U should be labeled so it will be useful. Write ' V 1 1 I numbers in sequence so that the patterns can more

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easily be observed. Check the entries in the table to IWIsilfO Sk nVlhlo see iï they accurately show the relationships given IViarVCCl laUIC in the problem.

Blue eyes 2

Make a table is a very useful strategy. Consider the Others 3 following problem to see how this stragegy might be Total 5 10 15 20 25 30 useo. I i

• Use these entries to extend the table to give new PROBLEM: Carlotta read that 2 out of every 5 people information. The relationship 2 to 5 is the key to have blue eyes. She decided to use this idea to extending the table. predict how many pupils in her class of 30 would have I I I I I I I I blue eyes. How many do you think she predicted? Blue eyes 2 4 6 81012

Although this problem can be solved using the Others 3 6 9 12 15 18 operations of division and multiplication, it can also be solved by making a table. | Total | 5 | 10 | 15 | 20 | 25 | 30 |

шШЕ^^ • Use the information in the table to solve the ^Щ^^к problem. When the total number of pupils is 30, ^^■ЕЯ^А about 12 should have blue eyes.

M ^ _M Blue eyes 2 4 6 8 10 12

yT^^^WL Others 3 6 9 12 15 18

/ ' tj A Totai 5 1° 15 2o 25 зо

/ /I ZlX '4Ȕvi' The make-a-table strategy is useful not only for / / j ~

- ' '^Sn4q>^^4 finding the solutions for certain problems directly but / / /

~ ' ' -^<TW?5s' often for organizing data when one employs other

/ ' / 7 I

V '

V N. strategies, such as guess and check and look for a f

' * I ' >> ^| pattern. Include the make-a-table strategy on your classrooms' Problem-solving Strategies poster or bulletin board, and compliment students when they use it effectively in solving a problem.

This content downloaded from 91.229.229.212 on Thu, 12 Jun 2014 16:31:15 PMAll use subject to JSTOR Terms and Conditions

Page 3: Problem Solving: Tips For Teachers

November 1984 47

I - ' The teacher's enthusiasm and what the teacher fl^^^SK^^^Bgf^^^ j^m ЩяЮш rewards play a major role in developing a special (l^^^^^^^^H^^SSì <Е|^шЕКшЁь "problem-solving spirit" in the classroom. A nonverbal '§^*!91^^ИШч^^^ fr jGaHÌHk_J . . acknowledgment or a special comment that rewards ^^^ХУ/ЙШа'^гЧг ^S^^BïnÏ

• Self-reliance - to trust one's own ability / ^y j. ^^^^"^^^^HBSBIÍ^Hw • Thinking - to think nonalgorithmically / ^apfer °°^ ^^^^^^^B^

' ^Wjhjy^il Give H a Try!

' ^Ш00Ш^0Яш^2*%~*~*0~^^ ' Use detective or mystery stories as an aid ' S^-^^^^^*^"^^^^^ ^^^^^t0 he|P students problem-solving skills!

' /^ ^^^^^^^^^^^^ The need t0 understand the situation, consider ' L--* ~'^^^^^^^^^^ 9iven data> collect additional data, discard

''~^^^0^^^^~_ ' irrelevant data, analyze and draw conclusions / Щ^

' - ' -- ^.^^^ " ' from the data> devise a plan for solving, and / eve'op/ng Proh/

^.^^^ " ' ' - ""^L^, f'nally> t0 solve and verify the reason-

/ / em"so/v/ng Skills ""Lableness of the solution are common to / Síudenís deve/on u- Isolving both mysteries and math problems.

/ ^//Üí/eS t0

understand u- ln projb/er^ solvin fHere are some references to help you begin.

¿ÏS'^&a?"* understand solvin

/°5Ä"tusasÄS.sar """* " / í-* AT$¿t -^Äss? ° To data' ^pand I sř~"" """* " (November 1975l:59e"

/ • wff .W/řh/^ fhe statore ° data' Ш Ripley, Austin. Minute Mysteries. New York: Harper &

/ • obro ' he same nan I Scalzittl, Joyce. "Wanted Dead or Alive: Problem- / • w,* On a paoe Hiff 9 as ř^e I solving Skills." In Mathematics for the Middle I • w,* °afa from an nT.f

Hiff • reni from tho I Grades (5-9), 1982 Yearbook of the National

/ maP, tax teb/ urs/cte Source /V * рг°Ыет- I Council of Teachers of Mathematics, edited by • 25^?^,^ tax

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This content downloaded from 91.229.229.212 on Thu, 12 Jun 2014 16:31:15 PMAll use subject to JSTOR Terms and Conditions