Problem Solving: Tips For Teachers

  • Published on
    19-Jan-2017

  • View
    213

  • Download
    0

Embed Size (px)

Transcript

  • Problem Solving: Tips For TeachersAuthor(s): Phares G. O'Daffer and Randall I. CharlesSource: The Arithmetic Teacher, Vol. 33, No. 8 (April 1986), pp. 34-35Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194168 .Accessed: 12/06/2014 13:36

    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 support@jstor.org.

    .

    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 195.78.108.147 on Thu, 12 Jun 2014 13:36:53 PMAll use subject to JSTOR Terms and Conditions

    http://www.jstor.org/action/showPublisher?publisherCode=nctmhttp://www.jstor.org/stable/41194168?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp

  • Problem >oh>lng Tip) For Tacichao

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

    Prepared by Randall I. Charles, Illinois State University, Normal, IL 61761

    9 4 I www

    f if |_^ Your parents will give you all the water, ice, and I Ik Strategy Spotlight fL K.:- You have t0 buy "" rest ot I I '1-7^^^^^^^^^^^^^^^^^^^ I Paper cups are 12 for $0.39. I ^' n ^^^^^^^^^^^^^^^^^^^^ Paper cups hold 8 ounces. I n Solvi no Add I Gel I Lemonsare2r$o-35'andsu9ar;sabout$o-25 1

    ProbIfinS I " You need 4 lemons and 1 CUP of sugar for each L^^^JJJJ^^^^^^^^^^^B pitcher of lemonade. ^^^^^! Your pitchers hold 8 cups each. I

    Students need experience in solving a variety of You estimate that you will have between 50 and problems fully to develop their problem-solving 75 customers for each game. abilities. Applied problems are an important type of A valuable characteristic of applied problems is problem that should be included at all grade levels. their connection with situations that are realistic to Applied problems are realistic situations that require students. However, the solutions to most applied students to collect and analyze data to make a problems involve several computational steps that decision. Here's an example of an applied problem can quickly become "messy" unless a calculator is appropriate for the intermediate grades: used. So that all students can work realistically with

    applied problems, consider allowing the use of Problem: Your house is across the street from the calculator at all times. For the applied problem given I playing field of a semiprofessional baseball team. earHer> here are some of the subproblems (that I You and a friend think you can earn money selling nv0|ve computations) that would have to be solved. I lemonade before and after the games. How much will you charge for each glass of lemonade? How many pitchers should you make?

    How many lemons will you need? What will they The solution to an applied problem is similar to, yet cost? different from, the procedures we typically use to B What s the cost of each cup? solve story problems. The following phases are a What win the tota, cost be t0 you for each g|ass of involved in the solution of an applied problem: lemonade? ^^^^^^^^^^^ I 1. Understand the problem. ^ ~^' M 2. Identify the conditions to be satisfied, the ^^^ ^^

    M

    assumptions you will make, and the needed data. f^^^^^^l Jr*" ^^ 11 3. Select or collect the needed data. | lr^

    ^^ ^*^L III 4. Identify and solve subproblems. ' W 'i M I 5. Check your work. iT^^Tm

    /7 I 6. Make a decision. I c^0^l if I M I

    The second and third phases are crucial in the j^^^^^nM II ' ' ' ^ I solution of applied problems. To solve the applied fn' 7 [Arm ' I V v4 I problem given, students might proceed according to iHj II '/ M l^4^

    v4

    I

    the following assumptions and collect the following '^^^O^f ^^ ^ ~^

    I

    34 Arithmetic Teacher

    This content downloaded from 195.78.108.147 on Thu, 12 Jun 2014 13:36:53 PMAll use subject to JSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsp

  • given amounts as different as $0.15 and $1.25, but each answer has "made sense" given the conditions

    they set for the situation. Finally, helping students deal with an applied problem,

    like other problems, is not complete until the students reflect on their work for the purpose of improving their skills in solving applied problems in the future.

    The "Applied Problem-Solving Guide" on the Tip Board shows some tasks that will help students work through the procedures of solving an applied problem and evaluating their work.

    With students who have had little experience with applied problems, you might provide a list of things to consider and a list of some questions to answer to help them get started. Then, as they gain experience, they will be able to generate these types of questions on their own.

    Good applied problems do not have only one correct answer. Many answers may be correct, depending on the assumptions and information with which the students started. For the applied problem given here, students in the same classroom have

    Tip Boarel^^^-^- - - " U TiPs from Readers I

    _ r - " co er

    To help students gain more practice H I l ^ problem

    co er e at^PieS usin9 Problem"solvin9 strategies,

    I H I i - i I

    ^ ii^vMina are some

    e at^PieS assign a problem on Monday that is H I i

    - i I

    l ^'^.^^^ I ii^vMina P

    are or

    M to

    assign be solved

    a problem by Friday.

    on Monday Many

    that of my

    is

    ' ot app I P ' w be appropriate or

    students eagerly await "Friday's I 1 modmee

    le ' w

    orK wrth a app"cie ve iQf problem," which I try to make both I

    i - . ' grade le

    provide a ve

    ano ^ motivating and challenging. Peer and H I i

    U 1 problerns 9 athematics ano

    parental help on the problem is I l integra n

    9 curriculum. a d Uip encouraged! On Friday we discuss I U I topics n te g0-,ng on

    a oi the S0|uti0ns and strategies used. I

    1 #V"'ocationwrthtn t0 ^destination a a Two points are awarded for use of I

    1 t0

    r school- Select a a

    ^ ^ 1 strategy with correct I 1 ' ^0Vm

    r decide when you w" back solution,

    and one point is given for I

    ' what time you receive w" M an appropriate strategy with an I

    I what

    class has receive roorn. incorrect answer. H I '

    * Lssiontopai^j rtw"cos osttodo

    The students' problem-solving I

    ' per^e ^eC how much rtw"cos abilities grow, and parents have I ' ^eC a P oicnic- How ^B

    commented on how much they enjoy H I 1 tnnr class is having

    a oicnic- P ach helping their children. I add new I

    ' * should you cna Iy.hpr other problems to my files with each new I ' ^mbior

    should tood you

    and Iy.hpr other copy

    problems of the

    to /'rrtftmef/c my files with

    Teacher/ each new

    ' Tenses? exp _^^^^ Eleanor W.Dearolph I

    ' exp ^^^^^^^^^^^ Woodward Academy I I 1 - ^-^ College Park, GA 30337 I

    Take a Look H ^^^^^^^^^^^^^^^^ I These books have useful ideas to help H I you create some applied problems that H i i Part o* the ^ Board- 1 are appropriate for your students. Developing Skills for Solving U is reserved for I

    Applied Problems *"^ I _. .. , _, . . ,_ _, . ^m you've found useful I Sharron, _. Sidney, .. and , _, Robert . . E. ,_ _, Reys, eds^ .

    As readiness activities for solving m teaching problem I ^^^979

    eds^

    applied As readiness

    problems, activities

    students for

    should solving

    | m .^=SL Send

    teaching

    Idea

    problem

    to Kaplan, Lucy, Jeff Nusbaum, Kathy Otto, Sally H have experience collecting data from Send your Idea to I

    Tucker, and Georgine Voghch. Applied Problem sources SUCh as the following: !^ eciion. I i Solving. This teacher s resource guide was ^ . .. . . . eciion. i developed as part of a National Science tables,

    . .. Charts, . .

    graphs, .

    maps, I Foundation Honors Teachers Project at Illinois ^m reference books, menus, I State University. (Contact Carol Thornton, advertisements, product labels, Mathematics Department, Illinois State University, ^ . x ' , . _ H I Normal, il 61761.) H experiments,

    . x catalogs,

    , checkbooks, . _ I

    and newspapers. I I

    April 1986 35

    This content downloaded from 195.78.108.147 on Thu, 12 Jun 2014 13:36:53 PMAll use subject to JSTOR Terms and Conditions

    http://www.jstor.org/page/info/about/policies/terms.jsp

    Article Contentsp. 34p. 35

    Issue Table of ContentsThe Arithmetic Teacher, Vol. 33, No. 8 (April 1986), pp. 1-59Front MatterOne Point of View: Curricular Improvement versus StandardizedTesting [pp. 3-3]Readers' Dialogue [pp. 4-5, 41]Correction: Problem Solving: Tips For Teachers [pp. 41-41]Let's Do ItCoordinate Geometry for Third Graders [pp. 6-11]

    Geometry Links the Two Spheres [pp. 13-16]Talking with Young Children aboutMultiplication [pp. 18-21]Multiplication Games [pp. 22-25]Verbal Multiplication and Division Problems: SomeDifficulties and Some Solutions [pp. 26-33]Problem Solving: Tips For Teachers [pp. 34-35]Teaching the Process of MathematicalInvestigation [pp. 36-38]Mathletics: Adding Activity to Arithmetic [pp. 39-40]Computer Corner [pp. 42-43]Research ReportIndividualizing Mathematics Instruction [pp. 44-45]

    Reviewing and ViewingComputer MaterialsReview: untitled [pp. 46-46]Review: untitled [pp. 46-47]Review: untitled [pp. 47-47]Review: untitled [pp. 47-47]

    New Books for PupilsReview: untitled [pp. 47-48]Review: untitled [pp. 48-48]

    New Books for TeachersReview: untitled [pp. 48-49]Review: untitled [pp. 49-49]

    EtceteraReview: untitled [pp. 50-50]Review: untitled [pp. 50-50]

    NCTM Affiliated Group Officers [pp. 51-59]Back Matter