Helping ELLs Reach Their Potentials: Thinking Maps ?· Using Thinking Maps to Assess ... Mathematics…

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<ul><li><p>HelpingELLs </p><p>ReachTheirPotentials: UsingThinkingMapstoAssess</p><p> ConceptualUnderstanding</p><p>LolitaGerardoHSMathTeacher&amp;Dept.ChairPharrSanJuanAlamoISD</p><p>SylviaTaubeMathEducationProfessor</p><p>SamHoustonStateUniversity</p><p>MathematicsforEnglishLanguageLearners[MELL]AnnualConference</p><p>TexasStateUniversity,SanMarcos,TXJuly31August2,2008</p></li><li><p>ObjectivesofMELLSession</p><p> Shareactivitiesandexperiencesinteaching mathematicstoEnglishLanguageLearners;</p><p> ExplorealternativetoolsthatcanassesstheELLs conceptualunderstandinginmath;</p><p> Constructdifferenttypesofmaps,anddesignrubric toscorestudents</p><p> conceptmaps.</p></li><li><p>WARMUP: Canyoucomeupwithdifferent</p><p> representations?Problem:Inmanyparades,flowersareusedto</p><p> decoratethefloats.Thelistbelowshowsthe numberofflowersusedineachrowofa</p><p> paradefloat.</p><p>{(1,54),(2,58),(3,62),(4,66)}</p></li><li><p>Summarizethedifferent representationsoffunctions</p><p> Usegraphicorganizers</p></li><li><p>Recent State Data on ELLsand Achievement in Algebra</p></li><li><p>End-of Course Algebra 1Testing Date: Spring 2008</p><p>Number of students tested = 52,462</p><p>Commended Performance = 11%</p><p>Met standards = 56%</p><p>Current LEP = 17% (# of students tested=1,104)</p><p>Low SES = 43% (# of students tested=21,932)</p><p>Hispanic = 47% (# of students tested=20,270)</p><p>White = 66% (# of students tested = 22,020)</p></li><li><p>21</p><p>1 </p></li><li><p>AKickoffSummerProgramforELLs</p></li><li><p>ThinkingMapsin Algebra1</p></li><li><p>MultipleRepresentations Why?</p><p> Usingandunderstandingdifferentformsof representationsarecriticaltolearningmath;</p><p> Implementationandflexibilityinusingvaried representationsprovideastrongevidenceofdeeper</p><p> understandingofmathematics;</p><p> Thisunderstandingisrichwithconnectionsand relationships.</p></li><li><p>Bringinstudentsculture</p><p>Promoteequity</p><p>Whatcanrepresentationsinclude? Physicalobjects Drawings,graphs Symbols,numbers Verbal ContextualTheseareusedtoorganize</p><p> andrecordstudents thinkingaboutmathideas</p><p> andproblemsolving.</p><p>Predominant</p><p>Representations Numeric Geometric Algebraic</p></li><li><p>Adaptedfrom:AnInteractiveModelforUsingRepresentationalSystemsby:Behr,Lesh,Post,&amp;Silver</p><p>Written Symbols Spoken</p><p>Symbols</p><p>Real-WorldSituations Manipulative</p><p>Aides</p><p>Pictures</p></li><li><p>AssessmentStrategies</p><p>If multiple representations is being valued, then the teacher should include questions or problems that involve a variety of representations.</p></li><li><p>WilltheELLs </p><p>haveadvantagesin thistypeofassessment?</p></li><li><p>VisualRepresentations</p><p>Example:TakingStockProblem</p><p>Father </p><p>has19animalsonhisfarmsomechicken andsomecows.Hetoldmethathecounted</p><p> 62legsaltogether.Howmanyofeachanimal werethere?</p></li><li><p>Canyoucomeupwithatleast3different representations?</p></li><li><p>Usingphysical(human)graphs</p></li><li><p>ConceptsMaps&amp;ThinkingMaps</p><p>Arrowsindicatethedirectionsofthe relationshipsbetweenconcepts;</p><p>Linesarelabeledwithlinkingwordsto specifyrelationship;</p><p>Conceptsareplacedinovalsoranyshape</p><p>Concept map an instrument for explicitly describing concepts and the relationship among them. It is a way to organize a learners knowledge.</p></li><li><p>Graphicorganizers</p><p>VennDiagram</p><p>Chart</p><p>Web</p><p>Timeline</p><p>Combinebothlinguisticand nonlinguisticinformation(e.g.,circles,</p><p> linesthatshowrelationship)</p></li><li><p>Type:Hierarchical Purpose:Promotemathematicalconnection</p><p>Quadrilateral</p><p>includes</p><p>rectanglerhombus</p><p>Trapezoid</p><p>square</p><p>includes</p><p>includes</p><p>parallelogram</p><p>is also a </p><p>Isosceles</p><p> trapezoid</p></li><li><p>TYPE:Web</p><p>Linear Equations</p><p>Graph shows a straight line</p><p>Form: y=mx+ b</p><p>has slope</p><p>ordered pairs</p><p>Crosses either x or y-axis</p><p>first - degree functions</p><p>domain/range</p><p>m is the slope</p><p>b is where line crosses y-axis</p><p>zero or undefined </p><p>That is + or -</p></li><li><p>Whatteachersmustdotofacilitatestudents useofMultipleRepresentations?</p><p>By listening, questioning, and making a sincere effort to understand what they are trying to communicate with their drawings and writings, especially when they are using personal [use of invented strategies] representations. [Tarlow, L. D. (2008), MTMS, Vol 13, #8.]</p><p>Step back to give students freedom to test their ideas; observe students work and decide when to intervene or pose questions to clarify ideas.[Tarlow, L. D. (2008), MTMS, Vol 13, #8.]</p><p>Give clear, comprehensible, useful, relevant feedback.[Hill, J.D. &amp; Flynn, K. M (2006). Classroom instruction that works with ELLs, ASCD publication]</p></li><li><p>HowtoassessthinkingmapsTask</p><p>Drawaconceptmaprelatingthefollowing concepts:</p><p>Parabolas </p><p>Domain</p><p>Standardequation </p><p>Range</p><p>Apex </p><p>Symmetry</p><p>QuadraticfunctionTranslate/Slide</p><p>Maximumpoint </p><p>Minimumpoint</p></li><li><p>Participantswillcreatetheirown conceptmap</p><p>Then . . .design a rubric for scoring the concept map</p></li><li><p>RecommendationsfromResearch</p><p>Findings mostly from science, psychology, reading, and college math</p><p>J. Novak (1984) early researcher in science education</p></li><li><p>A scoring rubric should be able to assess the breadth and depth of students knowledge transformation as they progress from novice to expert. (Edmonson, 2000)</p></li><li><p>Scoring can be done by comparing experts (criterion) with students maps</p><p>Findings:Maps that focus heavily on concept relationship has strong correlations with scores in standardized tests.</p></li><li><p>Therubricshouldbeabletomeasure studentprogress(understanding)over</p><p> time. </p><p>Novice </p><p>Expert </p><p>Eventually, learnersdocometothinklike</p><p> teachers</p></li><li><p>THERUBRICMUSTBEABLETOINFORM INSTRUCTION</p><p>Recommendeduseduringformative assessmentorfordiagnosticpurpose</p></li><li><p>LearningStrategiesforMathELLs</p><p> Mustbeengagedwithvariedcollaborative activities</p><p> Usemultiplerepresentations Useactivitiesthatpromotecommunication Challengestudentsinsolvingproblemswith</p><p> openendedquestions Usegraphicorganizers</p></li><li><p>LearningStrategies</p><p> Integrationofmanipulativematerialsand graphingtechnology</p><p> Handsonapproachofdevelopingconceptual understanding</p><p> Establishhomeconnection Questioningstrategies Richconnectionsincontext</p></li><li><p>References Bartels,B.(1995).Promotingmathematicsconnectionswithconcept</p><p> mapping.MathematicsTeachingintheMiddleSchool,1542549. Bolte,L.(Jan1999).Usingconceptmapsandinterpretiveessaysfor</p><p> assessmentinmathematics.SchoolScienceandMathematics,</p><p>99(1).</p><p> Hill,J.D.&amp;Flynn,K.M(2006).ClassroominstructionthatworkswithELLs.</p><p> ASCDpublication. Novak,J.(1984).Learninghowtolearn.NewYork:CambridgeUniversity</p><p> Press. Rye,J.(Jan2002).Scoringconceptsmaps:Anexpertmapbasedscheme</p><p> weightedforrelationship.SchoolScienceandMathematics. Focusissue(April2008)MathematicsTeachingintheMiddleSchool</p><p> publishedarticleson:DevelopingMathematicalUnderstandingthrough</p><p> Representations.</p><p>Helping ELLs Reach Their Potentials: Using Thinking Maps to Assess Conceptual UnderstandingObjectives of MELL SessionWARM-UP:Can you come up with different representations?Summarize the different representations of functionsSlide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Thinking Maps inAlgebra 1Multiple RepresentationsWhy?What can representations include?Slide Number 15Assessment StrategiesWill the ELLs have advantages in this type of assessment?Visual RepresentationsCan you come up with at least 3 different representations?Using physical (human) graphsSlide Number 21Slide Number 22Concepts Maps &amp; Thinking MapsSlide Number 24 Type: Hierarchical Purpose: Promote mathematical connectionTYPE: Web What teachers must do to facilitate students use of Multiple Representations?How to assess thinking mapsParticipants will create their own concept mapRecommendations from ResearchSlide Number 31Slide Number 32The rubric should be able to measure student progress (understanding) over time.Novice ExpertEventually, learners do come to think like teachersTHE RUBRIC MUST BE ABLE TO INFORM INSTRUCTIONLearning Strategies for Math ELLsLearning Strategies References</p></li></ul>

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