Principles to Acons

Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017

PrinciplestoAc.ons:

BuildingaTeachingFrameworkwithHigh-leverageMathema9csTeachingPrac9ces

Dr.DeAnnHuinkerUniversityofWisconsin–Milwaukee

[email protected]


Na.onalCouncilofTeachersof

Mathema.cs(NCTM)

ReleasedApril2014


OurAgenda

q  Background

q  IntroducetheMathema9csTeachingPrac9ces

q  Lens:TheBandConcertTask

q  ResourcestoSupportImplementa9on

q  ClosingThoughts


Background


25-yearHistoryofStandards-BasedMathema.csEduca.onReform

1989CurriculumandEvalua.onStandardsforSchoolMathema.cs

2000PrinciplesandStandardsforSchoolMathema.cs

2010CommonCoreStateStandards


RigorousContentStandardsdefinestudentlearningexpecta.ons,but...


TeachingandLearning

AccessandEquity

Curriculum

ToolsandTechnology

Assessment

Professionalism

GuidingPrinciplesforSchoolMathema.cs


OverarchingMessage

Effec9veteachingisthenon-nego9ablecorethatensureseachandeverystudentisabletolearnmathema9csathighlevels.

PrinciplestoAc.ons(NCTM,2014,p.4)


GuidingPrinciple:TeachingandLearning

Anexcellentmathema9csprogramrequireseffec.veteachingthatengagesstudents

inmeaningfullearningthroughindividualandcollabora9veexperiencesthatpromotetheirabilitytomakesenseofmathema9calideas

andreasonmathema9cally.


Visualizeforamoment...


Visualizeoneofthebestmathlessonsyou

evertaught.

•  Whatmathema9cswasbeingexamined?

•  Whatmadethelessonsosuccessful?

•  Whatwereyoutheteacherdoing?

•  Whatwerestudentsdoing?


Effec9veMathema9csTeachingPrac9ces


Iden&fyingasetofprac&cesthataimsatcomplexoutcomesforallstudentsisafirststeptowardstrengtheningtheteachingprofession.

Theseprac.cescouldprovide•  acommonfounda.onforteachereduca.on,•  acommonprofessionallanguage,and•  aframeworkforappraising&improvingteaching.

BallandForzani(2010,p.45)


Aresearch-informedconsensusonwhatcons9tuteseffec9veteachingaccumulatedoverthepast25years.

PrinciplestoAc&ons:EnsuringMathema&calSuccessforAll

Na9onalCouncilforTeachersofMathema9cs.PrinciplestoAc.ons:EnsuringMathema.calSuccessforAll.Reston,VA:NCTM,2014.


“Thoseprac9cesattheheartoftheworkofteachingthataremostlikelytoaffectstudentlearning.”

(Ball&Forzani,2010,p45)

Ball,D.L,&Forzani,F.M.(2010).Teachingskillfulteaching.Educa.onalLeadership,68(4),40-45.

High-leverageMathema.csTeachingPrac.ces


Establishmathgoalstofocuslearning

Implementtasksthatpromotereasoning&

problemsolving

Useandconnectmathema9calrepresenta9ons

Facilitatemeaningfulmathema9caldiscourse

Posepurposefulques9ons

Buildproceduralfluencyfromconceptualunderstanding

Supportproduc9vestruggleinlearningmathema9cs

Elicit&useevidenceofstudentthinking

Effec.veMathema.csTeachingPrac.ces


Mr.Harrisand TheBandConcertTask


TheBandConcertTask

Thethird-gradeclassisresponsibleforseangupthechairsfortheirspringbandconcert.Inprepara9on,theyneedtodeterminethetotalnumberofchairsthatwillbeneededandasktheschool’sengineertoretrievethatmanychairsfromthecentralstoragearea.Theclassneedstosetup7rowsofchairswith20chairsineachrow,leavingspaceforacenteraisle.Howmanychairsdoestheschool’sengineerneedtoretrievefromthecentralstoragearea?


• Whatmightbethemathlearninggoalsinusingthistask?MathGoal

• Whatrepresenta9onsmightstudentsusetoreasonthroughandsolvetheproblem?

TaskandRepresenta9ons

• Howmightwebuildfromunderstandingtowardaspectsofproceduralfluency?

FluencyfromUnderstanding

• Howmightwestructureclassdiscourseofstudentstrategiestofocusonkeymathideas?

Discourse&Ques9ons

• Howmightwecheckinonstudentthinkingandstrugglesanduseittoadjustinstruc9on?

Struggles&Evidence


Mathema9cs LearningGoals


MathTeachingPrac9ce

Establishmathema9csgoalstofocuslearning.

Formula.ngclear,explicitlearninggoalssetsthestageforeverythingelse.

(Hiebert,Morris,Berk,&Janssen,2007,p.57)


Establishmathema9csgoalstofocuslearning

LearningGoalsshould:

•  Clearlystatewhatitisstudentsaretolearnandunderstandaboutmathema9csastheresultofinstruc9on.

•  Besituatedwithinlearningprogressions.

•  Beusedtoframethedecisionsthatteachersmakeduringalesson.

Daro,Mosher,&Corcoran,2011;Haae,2009;Hiebert,Morris,Berk,&Jensen.,2007;Wiliam,2011


Whatmathlearninggoalsmighttheteacherhavehadinmindinselec9ngtheBandConcerttaskforhisthirdgradestudents?


BandConcertTaskMathLearningGoals

Studentsarelearningto:

•  Understandthestructureofmul9plica9onasequalgroupsinafamiliarcontext.

•  Recognizeequalgroupswithinandamongdifferentrepresenta9ons.

•  Dis9nguishthenumberofequalgroupsandthesizeofeachgroupwithincollec9onsorarrays.

•  Understandthatonecandecomposeandrecomposegroupstofindsolu9ons(informalknowledgeofthedistribu9veproperty).


BuildingConceptualUnderstanding...Standard3.OA.3.Usemul9plica9onanddivisionwithin100tosolvewordproblemsinsitua9onsinvolvingequalgroups,arrays,andmeasurementquan99es,e.g.,byusingdrawingsandequa9onswithasymbolfortheunknownnumbertorepresenttheproblem.--------------------------------------------------------------------------MovingtoFluency...Standard3.NBT.3.Mul9plyone-digitwholenumbersbymul9plesof10intherange10–90(e.g.,9x80,5x60)usingstrategiesbasedonplacevalueandproper9esofopera9ons.

StateStandards



Themathema&calpurposeofalessonshouldnotbeamysterytostudents.

Classroomsinwhichstudentsunderstandthelearningexpecta9onsfortheirworkperformathigherlevelsthanclassroomswheretheexpecta9onsareunclear.

Haae,J.A.(2009).Visiblelearning:Asynthesisofover800meta-analysesrela.ngtoAchievement.NY:Routledge.

Haystead,M.W.,&Marzano,R.J.(2009).Meta-analy.csynthesisofstudiesconductedatMarzanoResearchLaboratoryoninstruc.onalstrategies.Englewood,Colo.:MarzanoResearchLaboratory.


Student-friendlyVersionoftheMathGoalstatedasaLearningTarget

Wearelearningtorepresentandsolvewordproblemsandtoexplainhowdifferentrepresenta.onsmatchthestorysitua.onandthemathopera.ons.


TasksforReasoningandProblemSolving


Implementtasksthatpromotereasoningandproblemsolving.

Studentlearningisgreatestinclassroomswherethetasksconsistentlyencouragehigh-levelstudentthinkingandreasoningandleastinclassroomswherethetasksarerou.nelyproceduralinnature.

(BoalerandStaples2008;SteinandLane1996)

MathTeachingPrac9ce


Implementtasksthatpromotereasoningandproblemsolving.

Mathema9caltasksshould:

•  Provideopportuni9esforstudentstoengageinexplora9onorencouragestudentstouseproceduresinwaysthatareconnectedtoconceptsandunderstanding.

•  Buildonstudents’currentunderstanding.

•  Havemul9pleentrypoints.

Boaler&Staples,2008;Hiebertetal.,1997;Stein,Smith,Henningsen,&Silver,2009


InwhatwaysdoestheBandConcerttaskprovideopportuni9esforstudentstoengageinreasoningandproblemsolving?


•  Studentswerenottold“how”tosolvethetask,butweregiven.meandspacetouseapproachesthatmadesensetothem.

•  Studentswereencouragedtorepresentthesitua9onusingvisualandphysicalrepresenta9ons.

•  Studentshadopportuni9estoshare,compare,anddiscusstheirrepresenta9onsandapproaches.

Scenario:BandConcertTask


Thereisnodecisionthatteachersmakethathasagreaterimpactonstudents’opportuni9estolearnandontheirpercep9onsaboutwhatmathema9csis...thantheselec9onorcrea9onofthetaskswithwhichtheteacherengagesstudentsinstudyingmathema9cs.

Lappan&Briars,1995


Mathema9cal Representa9ons


MathTeachingPrac9ce

Useandconnectmathema9calrepresenta9ons.

Becauseoftheabstractnatureofmathema.cs,peoplehaveaccesstomathema.calideasonlythroughtherepresenta.onsofthoseideas.

(Na9onalResearchCouncil,2001,p.94)


MathTeachingPrac9ce

Useandconnectmathema9calrepresenta9ons

Effec.veteachingofmathema.csengagesstudentsinmakingconnec.onsamongmathema.calrepresenta.ons:

•  todeepenunderstandingofmathema.csconceptsandproceduresand

•  astoolsforproblemsolvingPrinciplestoAc.ons(NCTM,2014,p.25)

Lesh,Post,&Behr,1987;Marshall,Superfine,&Canty,2010;Tripathi,2008;Webb,Boswinkel,&Dekker,2008


Collins,A.(2011).Representa9onalcompetence:ACommentaryontheGreenoanalysis.InT.Koschmann(Ed.),Theoriesoflearningandresearchintoinstruc.onalprac.ce(pp.105-112).NewYork:Springer.

“Theteachingofrepresenta&onalcompetence

shouldlieatthecenterofclassroomprac.ceinmathema.cs.”

AlanCollins(2011,p.105)


PreetyTripathi(2008)p.439

Tripathi,PreetyN.“DevelopingMathema9calUnderstandingthroughMul9pleRepresenta9ons.”Mathema.csTeachingintheMiddleSchool13,no.8(2008):438–45.

Whyfocusonmul&plerepresenta&ons?

“Usingdifferentrepresenta.onsislikeexaminingtheconceptthroughavarietyoflenses,witheachlensprovidingadifferentperspec.vethatmakesthepicture(concept)richeranddeeper.”


Connectbothbetweenandwithin

typesofrepresenta9ons.

Thedepthof[student]understandingisrelatedtothestrengthofconnec.onsamongmathema.calrepresenta.onsthatstudentshaveinternalized.

Physical

Visual

VerbalContextual

Symbolic

Lesh,R.,Post,T.,&Behr,M.(1987).Representa9onsandtransla9onsamongrepresenta9onsinmathema9cslearningandproblemsolving.InC.Janvier,(Ed.),Problemsofrepresenta.onsintheteachingandlearningofmathema.cs(pp.33-40).Hillsdale,NJ:LawrenceErlbaum.


Contextual

Physical

Visual

Symbolic

Verbal

TypesofRepresenta.ons


Contextual

Physical

Visual

Symbolic

Verbal

Importantmathema.calconnec.onsbetweendifferenttypesofrepresenta.ons


Contextual

Physical

Visual

Symbolic

Verbal

Importantmathema.calconnec.onswithintypesofrepresenta.ons


InwhatwaysdidMr.Harrisfocushisteachingondevelopingstudents’representa9onalcompetence?



Aqerintroducingthetask,Mr.Harrisstated,“Beforeyoubeginworkingonthetask,thinkaboutarepresenta9onyoumightwanttouseandwhy,andshareyourideaswithapartner.”

ThenMr.Harrisaskedstudentstosharesomeoftheirideasinabriefwholegroupdiscussion.

Nextthestudentsworkedindividuallyonthetask.


Laterinthelesson,thestudentsweretoldtofindaclassmatewhousedadifferentrepresenta9onandtotaketurnsexplainingandcomparingtheirworkaswellastheirsolu9ons.

Moststudentssketchedequalgroups.Someusedconnec9ngcubesorcutanarrayoutofgridpaper.AfewstudentsmadeatableorT-chart.Somestudentswroteequa9ons.


TheBandConcertTask

Kenneth

TyrellCorrineAnanda Elijah

Sam

Jasmine

Molly

MarcusTeresa


Whatmightstudentsno&ceasbeingsimilarordifferentamongtheserepresenta&ons?

Howmightthissharinginpairssupportafocusondevelopingrepresenta&onalcompetence?

Jasmine Maria


Marshall,A.M.,Superfine,A.C.,&Canty,R.S.(2010).Starstudentsmakeconnec9ons.TeachingChildrenMathema.cs,17(1),39–47.

Representa9onalcompetenceincludesknowinghowandwhentousepar9cularmathema9calrepresenta9onsandbeingabletomakeconnec9onsamongthem.

(Marshall,Superfine,&Canty,2010)


Purposeful Ques.ons


MathTeachingPrac9ce

Posepurposefulques9ons.

Teachers’ques&onsarecrucialinhelpingstudentsmakeconnec.onsandlearnimportantmathema.csandscienceconcepts.

Weiss&Pasley,2004


Posepurposefulques9ons.

Effec9veQues9onsshould:

•  Assessandadvancestudents’understanding.•  Revealstudents’currentunderstandings.•  Encouragestudentstoexplain,elaborate,orclarifytheirthinking.

•  Makethemathema9csmorevisibleandaccessibleforstudentstoexamineanddiscuss.

Boaler&Brodie,2004;Chapin&O’Connor,2007;Herbel-Eisenmann&Breyfogle,2005


What“key”ques9onsdidMr.Harrisaskduringthelessontoelicitstudentthinkingandtopressorpromptthemtoconsiderideasrelatedtothemathlearninggoal?


Asstudentsworkedindividually,Mr.Harrisaskedques9onstoassesstheirunderstanding:

•  Howdoesyourdrawingshow7groups?•  Howmanytwen9esareyouadding,andwhy?

•  Whyareyouaddingtens?Howdoesthatrelateto20?Howdoesthatrelatedtotheproblem?


MathGoal:Studentswillrecognizethestructureofmul9plica9onwithinandamongdifferentrepresenta9ons.


Duringthewholeclassdiscussion,Mr.Harrisaskedques9onsthatmadethemathema9csvisibletoadvancestudentunderstanding:“Someofyouwrotethisequa9on,7x20=140,onyourpaper,soI’mwonderinghowthisequa9ondoesordoesn’tmatchtherepresenta9onsthateachofyouused?”



Mathema9cal Discourse


MathTeachingPrac9ce

Facilitatemeaningfulmathema9caldiscourse.

Teachersmustdeterminehowtobuildonandhonorstudentthinkingwhileensuringthatthemathema.calideasattheheartofthelessonremainprominentinclassdiscussions.

(Engle&Conant,2002)


Facilitatemeaningfulmathema9caldiscourse.

Mathema9calDiscourseshould:

•  Buildonandhonorstudents’thinking;

•  Providestudentswiththeopportunitytoshareandcompareideas,clarifyunderstandings,anddevelopconvincingarguments.

•  Advancethemathema9callearningofthewholeclass.

Carpenter,Franke,&Levi,2003;Fuson&Sherin,2014;Smith&Stein,2011


Howmighttheteacherhavestructuredthewholeclassdiscussionofthevariousstudentapproachestomovestudentstowardtheintendedlearninggoals?


TheBandConcertTask

Kenneth

TyrellCorrineAnanda Elijah

Sam

Jasmine

Molly

MarcusTeresa


Instructuringthewholeclassdiscourseofthetask,Mr.Harriswasstrategicin:

•  Selec9ngspecificstudentrepresenta9onsandstrategiesfordiscussionandanalysis.

•  Sequencingthevariousstudentapproachesforanalysisandcomparison.

•  Connec9ngstudentapproachestokeymathideasandrela9onships.



1.  An.cipa.ng

2. Monitoring

3. Selec.ng

4. Sequencing

5. Connec.ng

5Prac.cesforOrchestra.ngProduc.veMathema.csDiscussions

(Smith&Stein,2011)

Smith,M.S.,&Stein,M.K.(2011).Fiveprac9cesfororchestra9ngproduc9vemathema9csdiscussions.Reston,VA:Na9onalCouncilofTeachersofMathema9cs.


Jasmine Kenneth

Sequence#1ofStudentApproaches

Teresa


Elijah AnandaTyrell

Added20s. Skipcountedby10s. Reasoned7tensis70and7moretensis70.

Sequence#2ofStudentApproaches


ConceptualUnderstandingandProceduralFluency


Buildproceduralfluencyfromconceptualunderstanding.

Arushtofluencyunderminesstudents’confidenceandinterestinmathema.csandisconsideredacauseofmathema.csanxiety.

(Ashcraq2002;Ramirezetal.2013)

MathTeachingPrac9ce

Ashcraq,M.H.(2002).Mathanxiety:Personal,educa9onal,andcogni9veconsequences.CurrentDirec.onsinPsychologicalScience,11(5),181-185Ramirez,G.,Gunderson,E.A.,Levine,S.C.,&Beilock,S.L.(2013).Mathanxiety,workingmemory,andmathachievementinearlyelementaryschool.JournalofCogni.onandDevelopment,14(2),187-202.


Buildproceduralfluencyfromconceptualunderstanding

ProceduralFluencyshould:

•  Buildonafounda9onofconceptualunderstanding.

•  Over9me(months,years),resultinknownfactsandgeneralizedmethodsforsolvingproblems.

•  Enablestudentstoflexiblychooseamongmethodstosolvecontextualandmathema9calproblems.

Baroody,2006;Fuson&Beckmann,2012/2013;Fuson,Kalchman,&Bransford,2005;Russell,2006


Whatdoesitmeantobefluentwithcomputa.onalprocedures?

Takeamomentandjotdownyourresponsetothisques9on.


PrinciplestoAc&onsdefinesfluency:


Beingfluentmeansthatstudentsareabletochooseflexiblyamongmethodsandstrategiestosolvecontextualandmathema9calproblems,theyunderstandandareabletoexplaintheirapproaches,andtheyareabletoproduceaccurateanswersefficiently.



Beingfluentmeansthatstudentsareabletochooseflexiblyamongmethodsandstrategiestosolvecontextualandmathema9calproblems,theyunderstandandareabletoexplaintheirapproaches,andtheyareabletoproduceaccurateanswersefficiently.

PrinciplestoAc&onsdefinesfluency:


Whatdoesitmeantobefluentwithcomputa.onalprocedures?

Takeamomentandrevisityourresponsetothisques9onandreviseoraddtoyourearlierresponse.


Fluencydevelopsover.me...anditbuildsfrom

conceptualunderstanding.


Ini9alexplora9on

anddiscussion

Informalreasoningstrategies

Eventualuseofgeneralmethods


HowmightMr.Harrisdevelopconceptualunderstandinginwaysthatallowhimtobuildtowardproceduralfluency?

What“fluency”expecta9onsmightthestudentsbeworkingtoward?

Howmightthislessonestablishafounda9onforfluency?


BandConcertSetup7rowsofchairswith20chairsineachrow,withacenteraisle.Howmanychairsareneeded?

Standard.3.NBT.3.Mul9plyone-digitwholenumbersbymul9plesof10intherange10–90(e.g.,9×80,5×60)usingstrategiesbasedonplacevalueandproper9esofopera9ons.


Mr.Harrishadaclearplanforlayingafounda.onofconceptualunderstandingfromwhichhecouldhelphisstudentsbuildtowardfluency.

Tyrell Ananda


Tyrelldecomposedeach20into2tens.Skipcountedbytens.

Opportunity:Connect14tens=140.

Tyrell


Anandaexplained,“Ifiguredout7tensis70...”Opportunity:Wheredidthosetenscomefrom?Anandadecomposed20into2tens.

7x20=7x(10+10)= (7x10)+(7x10)=70+70=140

Ananda


Tousemathema9cseffec9vely,studentsmustknow:•  whichprocedureisappropriateandmostproduc9ve

inagivensitua9on,•  whataprocedureaccomplishes,and•  whatkindofresultstoexpect.

Whyisitimportanttobuildproceduresfromconceptualunderstanding?

Mechanicalexecu.onofprocedureswithoutunderstandingtheirmathema.calbasisodenleadstobizarreresults.

GaryMar9n(2009,p.165)


Produc.veStruggle


MathTeachingPrac9ce

Supportproduc9vestruggleinlearningmathema9cs.

Studentswithagrowthmindsetarelikelytoperseverethroughastrugglebecausetheyseechallengingworkasanopportunitytolearnandgrow.

(Dweck,2008)


Thestrugglewehaveinmindcomesfromsolvingproblemsthatarewithinreachandgrapplingwithkeymathema9calideasthatarecomprehendiblebutnotyetwellformed.

(Hiebertetal.,1996).

Bystrugglingwithimportantmathema9cswemeantheoppositeofsimplybeingpresentedinforma9ontobememorizedorbeingaskedonlytoprac9cewhathasbeendemonstrated.

(Hiebert&Grouws,2007,pp.387-388)


Supportproduc9vestruggleinlearningmathema9cs.

Produc9veStruggleshould:

•  Beconsideredessen9altolearningmathema9cswithunderstanding;

•  Developstudents’capacitytopersevereinthefaceofchallenge;and

•  Helpstudentsrealizethattheyarecapableofdoingwellinmathema9cswitheffort.

Black,Trzesniewski,&Dweck,2007;Dweck,2008;Hiebert&Grouws,2007;Kapur,2010;Warshauer,2011


HowmightMr.Harrissupportstudents’effortinusingstrategieswhilemovingthentowardthelearninggoalofthelesson...withouttakingoverthethinkingforthem?


Supporteffort...Allowgrapple...

Buildtowardunderstandingandfluency...


Evidenceof StudentThinking


MathTeachingPrac9ce

Elicitanduseevidenceofstudentthinking.

Teachersusingassessmentforlearningcon.nuallylookforwaysinwhichtheycangenerateevidenceofstudentlearning,andtheyusethisevidencetoadapttheirinstruc.ontobeeermeettheirstudents’learningneeds.

(Leahy,Lyon,Thompson,&Wiliam,2005,p.23)


Elicitanduseevidenceofstudentthinking.

Evidenceshould:

•  Provideawindowintostudents’thinking.

•  Helptheteacherdeterminetheextenttowhichstudentsarereachingthemathlearninggoals.

•  Beusedtomakeinstruc9onaldecisionsduringthelessonandtoprepareforsubsequentlessons.

Chamberlin,2005;Jacobs,Lamb,&Philipp,2010;Sleep&Boerst,2010;vanEs,2010,Wiliam,2007


Whatmightbesomeindicatorsofstudentthinkingthattheteacherwouldwanttoelicitanduseduringthelessonandtoprepareforsubsequentlessons?


Inplanningforthelesson,Mr.Harriscreatedalistofkeyindicatorsofstudentthinking.Heplannedtolookandlistenfor:

•  Representa9onsthatshowed7groupsorrows.

•  Strategiesthatdecomposedgroupsorinformallyusedthedistribu9veproperty.

•  Useofconcept-basedlanguage,suchasmakingequalgroupsorrowsoftensortwen9es,intheirexplana9onsanddiscussions.



Forma9veassessmentisanessen9allyinterac9veprocess,inwhichtheteachercanfindoutwhetherwhathasbeentaughthasbeenlearned,andifnot,todosomethingaboutit.Day-to-dayforma9veassessmentisoneofthemostpowerfulwaysofimprovinglearninginthemathema9csclassroom.

DylanWiliam(2007,pp.1054;1091)


BuildingaTeachingFrameworkforMathema.cs


Huinker,DeAnn,andVictoriaBill.TakingAc.on:Implemen.ngEffec.veMathema.csTeachingPrac.cesinGradesK-5.Reston,VA:Na9onalCouncilofTeachersofMathema9cs,2017.

Movingfromalistofmathema.csteachingprac.cestoateachingframeworkformathema.cs...


PtAResources


PrinciplestoAc.onsWebsite

www.nctm.org/PtA/

PtABookoreBook

Execu9veSummary(English&Spanish)

PowerpointOverviewsw/Narra9veCases

Reflec9onGuide


Effec.veTeachingPrac.ces

Elementary School

NCTMPtAToolkit20+PDmodules,K-12www.nctm.org/ptatoolkit/

Establish mathematics goals to focus

learning.

Implement tasks promote reasoning and

problem solving

Use and connect

mathematical representations

Facilitate meaningful

mathematical discourse.

Pose purposeful questions.

Build procedural fluency from conceptual

understanding.

Support productive struggle in

learning math.

Elicit and use evidence of

student thinking.


Descrip.on:Duringthissessionyouwill

•  watchavideoclipofafourthgradeclassengagedinawholediscussionofaseriesofrelatedmul9plica9onequa9ons.

•  Discusswhattheteacherdoestosupportthestudents'learning.

•  Relateteacherac9onsinthevideototheEffec9veMathTeachingPrac9ces.

GradeBand:Elementary

Effec.veTeachingPrac.ces:•Buildproceduralfluencyfromconceptualunderstanding.•Implementtasksthatpromotereasoningandproblemsolving.

CaseofKatherineCaseyandtheMul.plica.onStringsTask


GradesK–5

DeAnnHuinker

VictoriaBill

NewNCTM

Resource

TakingAc&on

Series


TakingAc.onSeries

Huinker,DeAnn,andVictoriaBill.TakingAc.on:Implemen.ngEffec.veMathema.csTeachingPrac.cesinGradesK-5.Reston,VA:Na9onalCouncilofTeachersofMathema9cs,2017.Smith,Margaret,MichaelSteele,andMaryLynnRaith.TakingAc.on:Implemen.ngEffec.veMathema.csTeachingPrac.cesinGrades6-8.Reston,VA:Na9onalCouncilofTeachersofMathema9cs,2017.Boston,Melissa,FredrickDillon,MargaretSmith,andStephenMiller.TakingAc.on:Implemen.ngEffec.veMathema.csTeachingPrac.cesinGrades9-12.Reston,VA:Na9onalCouncilofTeachersofMathema9cs,2017.

GradesK-5

Grades

6-8

Grades

9-12


Chapter1: SeangtheStage

Chapter2: EstablishMathema9csGoalstoFocusLearning

Chapter3: ImplementTasksthatPromoteReasoningandProblemSolving

Chapter4: BuildProceduralFluencyfromConceptualUnderstanding

Chapter5: PosePurposefulQues9ons

Chapter6: UseandConnectMathema9calRepresenta9ons

Chapter7: FacilitateMeaningfulMathema9calDiscourse

Chapter8: ElicitandUseEvidenceofStudentThinking

Chapter9: SupportProduc9veStruggleinLearningMathema9cs

Chapter10:PullingItAllTogether

Achapterfocusedoneachmathteachingprac.ce.


•  AnalyzingTeachingandLearning(ATL)ac9vi9esuseclassroomar9factsto:-studyeachteachingprac9ce.-seeitsenactmentinclassrooms.-reflectonwhatmakesiteffec9veforstudentlearning.

VideoClips

Narra.veCases----ClassDiscussions

•  WhattheResearchSays

•  Promo.ngEquitythroughtheMathema9csTeachingPrac9ce

•  TakingAc.oninYourOwnClassroom StudentWorkAnalysis

ChapterSec.ons


AudiencesfortheBook

•  Teacherstoreadontheirown.

•  Colleaguesworkingtogetheringradelevelteamsoracrossgradebands.

•  Professionaldevelopersandteachereducatorsworkingwithpreserviceorinserviceteachers.

•  Onlineorface-to-facebookstudy.


ClosingThoughts


Establish math goals to focus learning

Implement tasks that promote reasoning &

problem solving

Use and connect mathematical

representations

Facilitate meaningful mathematical

discourse

Pose purposeful questions

Build procedural fluency from conceptual

understanding

Support productive struggle in learning

mathematics

Elicit & use evidence of student thinking

Effec.veMathema.csTeachingPrac.ces


WhyfocusonimprovingourTeachingPrac.ceinMathema.cs?


Studentlearningofmathema9cs“dependsfundamentallyonwhathappens

insidetheclassroomasteachersandlearnersinteractoverthecurriculum.”

(Ball&Forzani,2011,p.17)

Ball,D.L,&Forzani,F.M.(2011).Buildingacommoncoreforlearningtoteach,andconnec9ngprofessionallearningtoprac9ce.AmericanEducator,35(2),17-21.

BecauseTeachingMamers!


Ms.Robinsonaskedhersecond-gradestudentstowriteabouta9mewhentheyfeltreallysmartinmath.


SecondGradeStudent

Whendoyoufeelsmartinmathclass?


SecondGradeStudent


TheMathema9csTeachingPrac9cessupportdailyayen9ontoaccess,equity,andempowermentinthe

mathema9csclassroom

Space&choicetoengagein

mathreasoning.

Voiceinamathclasscommunity.

Posi.vemath

iden..es.


CalltoAc.on•  Readit.Readitagain.

•  Haveconversa9onswithyourcolleaguesandwithyouradministrators.

•  Makeaplantoworktogetherwithcolleaguestowardcommonandconsistentimplementa9onoftheeight,high-leverageMathema&csTeachingPrac&cesinclassroomsinyourschool.

•  Supportdeep,meaningfullearningofmathema9csandensuremathema9calsuccessforeachandeverystudent.


ThankYou!

Dr.DeAnnHuinkerUniversityofWisconsin–Milwaukee

[email protected]

www.nctm.org/ptawww.nctm.org/ptatoolkit

Principles to Acons

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Transcript of Principles to Acons