research-informed instruc2onal prac2ces: the non … · 11/19/17 1 research-informed instruc2onal...

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Research-InformedInstruc2onalPrac2ces:The

Non-nego2ableCore

Ma<hewR.LarsonNCTMPresident

Goals

•  Provideanoverviewoftheeightresearchinformedinstruc<onalstrategiesfromNCTM’sPrinciplestoAc.ons.

•  ConnectsomeofthesestrategiestoAMATYC’sBeyondCrossroads

•  Engageyouinobservingsomeofthestrategiesintheclassroom.

“TheprimarypurposeofPtAistofillthegapbetweentheadop<onofstandardsandtheenactmentofprac<ces,policies,programsandac<onsrequiredforsuccessfulimplementa<onofthosestandards.”

PrinciplestoAc.ons:EnsuringMathema.calSuccessforAll

―NCTM,PrinciplestoAc.ons:EnsuringMathema.calSuccessforAll(2014),p.4

Addi.onalPrinciplestoAc.onsResources

TeachingandLearning

1.AccessandEquity

2.Curriculum

3.ToolsandTechnology

4.Assessment

5.Professionalism

GuidingPrinciplesforSchoolMathema2cs

(NCTM,2014)

“Theoverarchingmessageisthateffec<veteachingisthenon-nego<ablecorenecessarytoensurethatallstudentslearnmathema<cs.Thesixguidingprinciplescons<tutethefounda<onofPtAthatdescribehigh-qualitymathema<cseduca<on.”

PrinciplestoAc2ons:EnsuringMathema2calSuccessforAll

―NCTM,2014,p.4

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“TeachingandLearning.Anexcellentmathema<csprogramrequireseffec<veteachingthatengagesstudentsinmeaningfullearningthroughindividualandcollabora<veexperiencesthatpromotetheirabilitytomakesenseofmathema<calideasandreasonmathema<cally.”

TeachingandLearningPrinciple

―NCTM,2014,p.9

Instruc<onStandard:Mathema<csfacultywilluseavarietyofteachingstrategiesthatreflecttheresultsofresearchtoenhancestudentlearning.

—AMATYC.BeyondCrossroads:Implemen.ngMathema.csStandardsintheFirstTwoYearsofCollege.(2006).p.51

AMATYC:BeyondCrossroads

•  Establishmathema<csgoalstofocuslearning.

•  Implementtasksthatpromotereasoningandproblemsolving.

•  Useandconnectmathema<calrepresenta2ons.

•  Facilitatemeaningfulmathema<caldiscourse.

EightResearch-InformedInstruc2onalPrac2ces

―NCTM,2014,p.10

•  Posepurposefulques2ons.•  Buildproceduralfluencyfromconceptual

understanding.

•  Supportproduc2vestruggleinlearningmathema<cs.

•  Elicitanduseevidenceofstudentthinking.


―NCTM,2014,p.10

“Establishmathema2csgoalstofocuslearning.

“Effec<veteachingofmathema<csestablishescleargoalsforthemathema<csstudentsarelearning,situatesgoalswithinlearningprogressions,andusesgoalstoguideinstruc<onaldecisions.”


―NCTM,2014,p.12

“Establishingcleargoalsthatar<culatethemathema<csthatstudentsarelearningasaresultofinstruc<oninalesson,overaseriesoflessons,orthroughoutaunit.”

WhatAreTeachersDoing?

―NCTM,2014,p.16

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“Implementtasksthatpromotereasoningandproblemsolving.

“Effec<veteachingofmathema<csengagesstudentsinsolvinganddiscussingtasksthatpromotemathema<calreasoningandproblemsolvingandthatallowformul<pleentrypointsandvariedsolu<onstrategies.”


―NCTM,2014,p.17 ―NCTM,2014,p.20

“[T]ypicalclassroommathema<csteachingintheUnitedStatestendsnottousechallengingtasks,nortopromotestudents’thinkingaboutandengagementwithmathema<calideas,andthusfailstohelpstudentsdevelopunderstandingofthemathema<cstheyarelearning.”

Cogni2vely-DemandingTasksAreAtypical

—Silver,“ExaminingWhatTeachersDoWhenTheyDisplayTheirBestPrac<ce:TeachingMathema<csforUnderstanding,”Journalof

Mathema.csEduca.onatTeachersCollege,2010,1(1),p.1

TypeandQualityofInstruc2onMa<ers

“Greaterexposuretopuremathema<cstasksandconceptshasastrongrela<onshipwithhigherperformance.

“Thedatasuggestthatexposingallstudentstochallengingproblemsandconceptualknowledgeinmathema<csclassescanhavealargeimpactonperformance.”

—OECD,2016,p.3

“Selec<ngataskwithhighcogni<vedemanddoesnotensurethatstudentswillbeprovidedopportuni<estoengageinrigorousmathema<calac<vity.”

—Jackson,etal.,“ExploringRela<onshipsBetweenSehngUpComplexTasksandOpportuni<estoLearninConcludingWhole-ClassDiscussionsinMiddleGradesMathema<csInstruc<on,”Journalfor

ResearchinMathema.csEduca.on,2013,44(4),651.

Selec2ngaQualityTaskIsNotEnough

“Supportproduc2vestruggleinlearningmathema2cs.

“Effec<veteachingofmathema<csconsistentlyprovidesstudents,individuallyandcollec<vely,withopportuni<esandsupportstoengageinproduc<vestruggleastheygrapplewithmathema<calideasandrela<onships.”


―NCTM,2014,p.48

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StudentLearningandtheLearningEnvironmentImplementa<onStandard:

“Studentswillbeexpectedtoconscien<ouslypersistineachmathema<cscourse.”



“Thecogni<vedemandofahigh-leveltaskcanbeloweredifateacherorstudentsuggestsasolu<onpathbeforestudentsbegintosolveaproblemorifateacheraltersthedirec<onsofthetasksuchthatstudentsarenolongerrequiredtojus<fytheirthinkingorsolvethemorechallengingaspectsofthetask.”

Selec2ngaQualityTaskIsNotEnough

—Jacksonetal.,2013,p.651

“Acommonsitua<oninmathema<csclassesoccurswherebyteachersarecalledovertostudentswhoaskforhelp;thestudentsexpecttobehelped,andteachersknowitistheirroletohelpthem,sotheteachersbreakdowntheproblemandmakeiteasier.Indoingsotheyemptytheproblemofitscogni<vedemand.”

—Boaler,Mathema.calMindsets:UnleashingStudents’Poten.alThroughCrea.veMath,Inspiring

Messages,andInnovatedTeaching(2016)

The“Didac2cContract”

SupportProduc2veStruggleinLearningMathema2cs

“Teacherssome<mesperceivestudentfrustra<onorlackofimmediatesuccessasindicatorsthattheyhavesomehowfailedtheirstudents.”

―NCTM,2014,p.48

Strugglevs.Frustra2on

—Hiebert&Grouws,“TheEffectsofClassroomMathema<csTeachingonStudents’Learning,”inLester(Ed.),SecondHandbookofResearchon

Mathema.csTeachingandLearning(2007),p.387

“Struggledoesnotmeanneedlessfrustra<onorextremelevelsofchallenge.Itmeansstudentsexpendsomeefforttomakesenseofmathema<cs.”

Researchindicatesthatteacherswhocloselyaoendtohowstudentsaremakingsenseofthetask(e.g.,pressingstudentstojus<fy,explainand/ormakemeaning)and/orac<velyassis<ngstudentthinkingwithouttakingoveranddoingthethinkingforstudentsarethosewhomaintainahighlevelofcogni<vedemand.

(Kisa&Stein,“LearningtoSeeTeachinginNewWays:AFounda<onforMaintainingCogni<veDemand,”AmericanEduca.onalResearch

Journal,2015,52[1],105–136

Produc2veStruggle

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SuccessfulProduc2veStruggle

(Emerling,Hiebert&Gallimore,“BeyondGrowthMindset:Crea<ngClassroomOpportuni<esforMeaningfulStruggle,”

Educa.onWeekTeacher,December7,2015)

•  Engagesstudentswithaworthwhiletask—onethatcapturesthecentralideaofalesson.

•  Stretchesstudents’thinkingandperformancejustbeyondtheleveltheycandoontheirown.

•  Teachersprovide<melyassistance.

•  “An<cipa<ngwhatstudentsmightstrugglewithduringalessonandbeingpreparedtosupportthemproduc<velythroughthestruggle.”

•  “Praisingstudentsfortheireffortsinmaking

senseofmathema<calideasandperseveranceinreasoningthroughproblems.”


―NCTM,2014,p.52

(Boaler&Staples,“Crea<ngMathema<calFuturesThroughanEquitableTeachingApproach:TheCaseofRailsdaleSchool,”

TeachersCollegeRecord,2008,110,608–645)

TheImportanceofProduc2veStruggle(Perseverance)

Thegreateststudentlearninggainsoccurinclassroomsinwhichthehigh-levelcogni<vedemandsofmathema<caltasksareconsistentlymaintainedthroughouttheinstruc<onalepisode.

“Ifyourstudentsaregoinghomeattheendofthedayless<redthanyouare,thedivisionoflaborinyourclassroomrequiressomeaoen<on.”

—Wiliam,2011,p.49

“Useandconnectmathema2calrepresenta2ons.

“Effec<veteachingofmathema<csengagesstudentsinmakingconnec<onsamongmathema<calrepresenta<onstodeepenunderstandingofmathema<csconceptsandproceduresandastoolsforproblemsolving.”


―NCTM,2014,p.24

UseandConnectMathema2calRepresenta2ons

―NCTM,2014,p.25

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•  Presentmul<plerepresenta<onsofmathema<calconcepts.



•  “Focusingstudents’aoen<ononthestructureoressen<alfeaturesofmathema<calideasthatappear,regardlessoftherepresenta<on.”

•  “Alloca<ngsubstan<alinstruc<onal<mefor

studentstouse,discuss,andmakeconnec<onsamongrepresenta<ons.”


―NCTM,2014,p.29

“Facilitatemeaningfulmathema2caldiscourse.

“Effec<veteachingofmathema<csfacilitatesdiscourseamongstudentsinordertobuildsharedunderstandingofmathema<calideasbyanalyzingandcomparingstudentapproachesandarguments.”


―NCTM,2014,p.29

FacilitateMeaningfulMathema2calDiscourse

—Carpenter,Franke,&Levi,ThinkingMathema.cally:Integra.ngArithme.candAlgebrainElementarySchools(2003)

“Studentswholearntoar<culateandjus<fytheirownmathema<calideas,reasonthroughtheirownandothers’mathema<calexplana<ons,andprovideara<onalefortheiranswersdevelopadeepunderstandingthatiscri<caltotheirfuturesuccessinmathema<cs.”

An2cipa2ng•Monitoring•Selec2ng•

Sequencing•Connec2ng

(Smith&Stein,5prac.cesforOrchestra.ngProduc.veMathema.csDiscussions,2011)

FivePrac2cestoPromoteProduc2veMathDiscussions

StudentLearningStrategies:

•  Discussconceptswiththeinstructorandotherstudents.

•  Listentoclassmates’explana<ons.

•  Explainhowtosolveaproblemtoaclassmate.



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“Posepurposefulques2ons.

“Effec<veteachingofmathema<csusespurposefulques<onstoassessandadvancestudentreasoningandsensemakingaboutimportantmathema<calideasandrela<onships.”


―NCTM,2014,p.35

Effec2veTeachersAreEffec2veQues2oners

“Effec<vemathema<csteachers...posemoreques<onswithhighercogni<vedemandandaskmorefollow-upques<ons.”

—McREL,WhatWeKnowAboutMathema.csTeachingandLearning(2010),p.22

“Iftheques<onsarenotcausingstudentstostruggleandthink,theyareprobablynotworthasking.

“Mistakesareevidencethattheques<onsaskedaretoughenoughtomakestudentssmarter.”

—Wiliam,“TheRightQues<ons,theRightWay,”Educa.onalLeadership,2014,71,16–19

WeNeedMoreChallengingQues2ons

Teachers,throughqualityques<oningtechniques,cantransformtypicalmathema<csclassroomsintomorestudent-centered,inquiry-basedclassroomsinwhichstudentsarethinkingandreasoningathighlevels.

(Walsh&Saoes,QualityQues.oning:Research-BasedPrac.cetoEngageEveryLearner,2005)

Ques2oning

Makeclassroommantrasfrom:•  “Why?”

•  “Howdoyouknow?”•  “Canyouexplain?”•  “Doyouagreeor

disagree?”

(Leinwand,AccessibleMathema.cs:10Instruc.onalShi[sThatRaiseStudentAchievement,2009)


•  Askques<onstoguidestudentstosolu<onstoproblems.



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“Buildproceduralfluencyfromconceptualunderstanding.

“Effec<veteachingofmathema<csbuildsfluencywithproceduresonafounda<onofconceptualunderstanding....”


―NCTM,2014,p.42


•  Engagestudentsinac<vi<esthatleadthemtodevelopconceptualunderstandings.



“Elicitanduseevidenceofstudentthinking.

Effec<veteachingofmathema<csusesevidenceofstudentthinkingtoassessprogresstowardmathema<calunderstandingandtoadjustinstruc<oncon<nuallyinwaysthatsupportandextendlearning.”


―NCTM,2014,p.53

“Assessment.Anexcellentmathema<csprogramensuresthatassessmentisanintegralpartofinstruc<on…andinformsfeedbacktostudents,instruc<onaldecisions,andprogramimprovement.”

GuidingPrinciplesforSchoolMathema2cs:Assessment

―NCTM,2014,p.89

AssessmentofStudentLearningStandard:

Assessmentofstudentlearningisaprocessofhelpingmathema<csfacultyadaptinstruc<ontotheneedsofstudents…assessmentisanongoingac<vitythatleadstoimprovementinstudentlearningbyprovidingdatanecessaryformakinginformeddecisionsattheclass,course,andprogramlevels.


AMATYC:BeyondCrossroadsWhatInstruc2onalStrategies

DoYouObserve?

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WhatInstruc2onalStrategiesDoYouObserve?

•  Establishmathema<csgoalstofocuslearning.

•  Implementtasksthatpromotereasoningandproblemsolving.

• Useandconnectmathema<calrepresenta2ons.

•  Facilitatemeaningfulmathema<caldiscourse.Posepurposefulques2ons.

• Buildproceduralfluencyfromconceptualunderstanding.

•  Supportproduc2vestruggleinlearningmathema<cs.

•  Elicitanduseevidenceofstudentthinking.

WhatInstruc2onalStrategiesDidYouSee?

Goals

•  Provideanoverviewoftheeightresearchinformedinstruc<onalstrategiesfromNCTM’sPrinciplestoAc.ons.

•  ConnectsomeofthesestrategiestoAMATYC’sBeyondCrossroads

•  Engageyouinobservingsomeofthestrategiesintheclassroom.

FromMetoYou…SavingsonaNewNCTMMembership!

•  EnterBML0616foradiscount@Checkout•  $20–FullIndividualMembership•  $10–e-Memberships•  $5–StudentMemberships

•  Explicitlybroadenthepurposesforteachinghighschoolmathema<cs.

•  Catalyzeaseriousdiscussionofthe

challengesfacinghighschoolmathema<cs.

•  Defineimpera<vesforhighschool

mathema<csintheareasofstructures,instruc<onalprac<ces,curriculum,andpathways.

•  Iden<fyessen<alconceptsforfocus

thatallhighschoolstudentsshouldlearnatadeeplevelofunderstanding.

•  Provideexamplesof4-yearpathways

thatinclude2.5yearsofmathema<calstudyexpectedofhighschoolstudentsfollowedby1.5ofalternatepathsofstudy.

research-informed instruc2onal prac2ces: the non … · 11/19/17 1 research-informed instruc2onal...

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