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