PromotingaProblemSolvingClassroomUsingGames
April2016NCTMConference;SanFrancisco,CA.
• SandyNiemieraSeniorProgramAssociateTeachingIntegratedMathandScienceProjectLearningSciencesResearchInsFtute,UniversityofIllinoisatChicago
• ElizabethCapeSeniorProgramAssociateTeachingIntegratedMathandScienceProjectLearningSciencesResearchInsFtute,UniversityofIllinoisatChicago
-ArthurJ.Baroody
WhyChildrenHaveDifficul3esMasteringtheBasicNumberCombina3ons&HowtoHelpThem
“Masterycanbestbeachievedbypurposeful,meaningfulinquiry-basedinstrucFon-instrucFonthatpromotesnumbersense.”
“Numbersense,criFcallyimportanttostudents’mathemaFcaldevelopment,isinhibitedbyover-emphasisonthememorizaFonofmathfactsinclassroomsandhomes.”
-JoBoalerFluencyWithoutFear:ResearchEvidenceontheBestWaystoLearnMathFacts
athRp://www.youcubed.org/fluency-without-fear/
SessionGoals• Discusshowtousegamestodevelopmodels,strategies,andflexibilitywithnumbersandoperaFons.
• DevelopcriteriaforanalyzingandselecFnggamesthatsupportconceptualdevelopment.
Fostera“GrowthMindset”
Fastlearningisnotalwaysthedeepestandbestlearning.
-CarolS.DweckEvenGeniusesWorkHard
HowtoLearnMath:4KeyMessagesJoBoaler,SanfordUniversityYoucubed.org/students
Whatisnumbersense?• ResearchtellsusthatthebestmathemaFcsclassroomsarethoseinwhichstudentslearnnumberfactsandnumbersensethroughengagingacFviFesthatfocusonmathemaFcalunderstandingratherthanrotememorizaFon.
7x8=?Iknow7x7is49
andthenIcanadd7moretomake56.
8x7=?10x7=70,butIonlyneedeightsevens.Isubtracttwosevenswhichis
70–14=56.
WhatisJluency?FluentlymulFplyanddividewithin100,usingstrategiessuchastherelaFonshipbetweenmulFplicaFonanddivision(e.g.,knowingthat8x5=40,oneknows40/5=8)orproperFesofoperaFons.BytheendofGrade3,knowfrommemoryallproductsoftwoone-digitnumbers.(3.OA.C.7)• “Skillincarryingoutproceduresflexibly,accurately,efficientlyandappropriately.”
-CommonCoreStateStandardsforMathemaFcs
Fluencyis• Fluencycomesaboutwhenstudentsdevelopnumbersense-whentheyaremathemaFcallyconfidentbecausetheyunderstandnumbers.
• Studentshavemasteredtheirfactswhentheyaresofluentatapplyingtheirstrategiesthattheydosoautoma3cally.
Studentscanapplystrategies,developnumbersense,and
learnandremembermathfactsastheyplaygames.
ConventionalWisdomvs.NumberSenseApproachtoLearningFacts
Conven1onalWisdom• Short-term,directapproach
• Masterycanbestbeachievedbyextensive,well-designeddrillandpracFce
• ChildrenhavedifficulFesduetothelearner’sdeficits
NumberSense• Longterm,indirectapproach
• Masterycanbestbeachievedbypurposeful,meaningfulinquiry-basedinstrucFon-instrucFonthatpromotesnumbersense.
• DifficulFesareduetotroublewithconvenFonalinstrucFon
“…ResearchevidencepointsinonedirecFon:Thebestwaytodevelopfluencywithnumbersistodevelopnumbersenseandtoworkwithnumbersindifferentways,nottoblindlymemorizewithoutnumbersense.”
-JoBoalerFluencyWithoutFear:ResearchEvidenceontheBestWaystoLearnMathFacts
AswepromotecomputationalJluency,wemustalso
fosterconceptual
understanding,
helpdevelopreasoningandproblem-
solvingskills,
encouragehardworkandperseverance,
Incorporatepracticethat• doesnotfeellikemindless,repeFFveexercises
• presentsnovelproblemsforstudentstosolve
• requirestheapplicaFonofwhatstudentshavelearnedinnewways
• stretchesstudentstothenextlevel
Howdostudentslearnfacts?
StagesforConceptualDevelopment
Direct Modeling
Counting Strategies
Reasoning from Known Facts
NaFonalResearchCouncil,2001
Phase3:MasteryFormalizaFon
6x#(ofladybugs)=#oflegs
MultiplicationFactsStrategies
DoublingStrategy
UseGamestoDevelopModels,Strategies,andFlexibilitywithNumbersandOperations
• NumberGoalGame-Baroody
