Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
PrinciplestoAc.ons:
BuildingaTeachingFrameworkwithHigh-leverageMathema9csTeachingPrac9ces
Dr.DeAnnHuinkerUniversityofWisconsin–Milwaukee
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Na.onalCouncilofTeachersof
Mathema.cs(NCTM)
ReleasedApril2014
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
OurAgenda
q Background
q IntroducetheMathema9csTeachingPrac9ces
q Lens:TheBandConcertTask
q ResourcestoSupportImplementa9on
q ClosingThoughts
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Background
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
25-yearHistoryofStandards-BasedMathema.csEduca.onReform
1989CurriculumandEvalua.onStandardsforSchoolMathema.cs
2000PrinciplesandStandardsforSchoolMathema.cs
2010CommonCoreStateStandards
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
RigorousContentStandardsdefinestudentlearningexpecta.ons,but...
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
TeachingandLearning
AccessandEquity
Curriculum
ToolsandTechnology
Assessment
Professionalism
GuidingPrinciplesforSchoolMathema.cs
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
OverarchingMessage
Effec9veteachingisthenon-nego9ablecorethatensureseachandeverystudentisabletolearnmathema9csathighlevels.
PrinciplestoAc.ons(NCTM,2014,p.4)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
GuidingPrinciple:TeachingandLearning
Anexcellentmathema9csprogramrequireseffec.veteachingthatengagesstudents
inmeaningfullearningthroughindividualandcollabora9veexperiencesthatpromotetheirabilitytomakesenseofmathema9calideas
andreasonmathema9cally.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Visualizeforamoment...
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Visualizeoneofthebestmathlessonsyou
evertaught.
• Whatmathema9cswasbeingexamined?
• Whatmadethelessonsosuccessful?
• Whatwereyoutheteacherdoing?
• Whatwerestudentsdoing?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Effec9veMathema9csTeachingPrac9ces
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Iden&fyingasetofprac&cesthataimsatcomplexoutcomesforallstudentsisafirststeptowardstrengtheningtheteachingprofession.
Theseprac.cescouldprovide• acommonfounda.onforteachereduca.on,• acommonprofessionallanguage,and• aframeworkforappraising&improvingteaching.
BallandForzani(2010,p.45)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Aresearch-informedconsensusonwhatcons9tuteseffec9veteachingaccumulatedoverthepast25years.
PrinciplestoAc&ons:EnsuringMathema&calSuccessforAll
Na9onalCouncilforTeachersofMathema9cs.PrinciplestoAc.ons:EnsuringMathema.calSuccessforAll.Reston,VA:NCTM,2014.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
“Thoseprac9cesattheheartoftheworkofteachingthataremostlikelytoaffectstudentlearning.”
(Ball&Forzani,2010,p45)
Ball,D.L,&Forzani,F.M.(2010).Teachingskillfulteaching.Educa.onalLeadership,68(4),40-45.
High-leverageMathema.csTeachingPrac.ces
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Establishmathgoalstofocuslearning
Implementtasksthatpromotereasoning&
problemsolving
Useandconnectmathema9calrepresenta9ons
Facilitatemeaningfulmathema9caldiscourse
Posepurposefulques9ons
Buildproceduralfluencyfromconceptualunderstanding
Supportproduc9vestruggleinlearningmathema9cs
Elicit&useevidenceofstudentthinking
Effec.veMathema.csTeachingPrac.ces
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Mr.Harrisand TheBandConcertTask
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
TheBandConcertTask
Thethird-gradeclassisresponsibleforseangupthechairsfortheirspringbandconcert.Inprepara9on,theyneedtodeterminethetotalnumberofchairsthatwillbeneededandasktheschool’sengineertoretrievethatmanychairsfromthecentralstoragearea.Theclassneedstosetup7rowsofchairswith20chairsineachrow,leavingspaceforacenteraisle.Howmanychairsdoestheschool’sengineerneedtoretrievefromthecentralstoragearea?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
• Whatmightbethemathlearninggoalsinusingthistask?MathGoal
• Whatrepresenta9onsmightstudentsusetoreasonthroughandsolvetheproblem?
TaskandRepresenta9ons
• Howmightwebuildfromunderstandingtowardaspectsofproceduralfluency?
FluencyfromUnderstanding
• Howmightwestructureclassdiscourseofstudentstrategiestofocusonkeymathideas?
Discourse&Ques9ons
• Howmightwecheckinonstudentthinkingandstrugglesanduseittoadjustinstruc9on?
Struggles&Evidence
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Mathema9cs LearningGoals
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
MathTeachingPrac9ce
Establishmathema9csgoalstofocuslearning.
Formula.ngclear,explicitlearninggoalssetsthestageforeverythingelse.
(Hiebert,Morris,Berk,&Janssen,2007,p.57)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Establishmathema9csgoalstofocuslearning
LearningGoalsshould:
• Clearlystatewhatitisstudentsaretolearnandunderstandaboutmathema9csastheresultofinstruc9on.
• Besituatedwithinlearningprogressions.
• Beusedtoframethedecisionsthatteachersmakeduringalesson.
Daro,Mosher,&Corcoran,2011;Haae,2009;Hiebert,Morris,Berk,&Jensen.,2007;Wiliam,2011
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Whatmathlearninggoalsmighttheteacherhavehadinmindinselec9ngtheBandConcerttaskforhisthirdgradestudents?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
BandConcertTaskMathLearningGoals
Studentsarelearningto:
• Understandthestructureofmul9plica9onasequalgroupsinafamiliarcontext.
• Recognizeequalgroupswithinandamongdifferentrepresenta9ons.
• Dis9nguishthenumberofequalgroupsandthesizeofeachgroupwithincollec9onsorarrays.
• Understandthatonecandecomposeandrecomposegroupstofindsolu9ons(informalknowledgeofthedistribu9veproperty).
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
BuildingConceptualUnderstanding...Standard3.OA.3.Usemul9plica9onanddivisionwithin100tosolvewordproblemsinsitua9onsinvolvingequalgroups,arrays,andmeasurementquan99es,e.g.,byusingdrawingsandequa9onswithasymbolfortheunknownnumbertorepresenttheproblem.--------------------------------------------------------------------------MovingtoFluency...Standard3.NBT.3.Mul9plyone-digitwholenumbersbymul9plesof10intherange10–90(e.g.,9x80,5x60)usingstrategiesbasedonplacevalueandproper9esofopera9ons.
StateStandards
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
PrinciplestoAc.ons(NCTM,2014,p.13)
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.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Student-friendlyVersionoftheMathGoalstatedasaLearningTarget
Wearelearningtorepresentandsolvewordproblemsandtoexplainhowdifferentrepresenta.onsmatchthestorysitua.onandthemathopera.ons.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
TasksforReasoningandProblemSolving
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Implementtasksthatpromotereasoningandproblemsolving.
Studentlearningisgreatestinclassroomswherethetasksconsistentlyencouragehigh-levelstudentthinkingandreasoningandleastinclassroomswherethetasksarerou.nelyproceduralinnature.
(BoalerandStaples2008;SteinandLane1996)
MathTeachingPrac9ce
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Implementtasksthatpromotereasoningandproblemsolving.
Mathema9caltasksshould:
• Provideopportuni9esforstudentstoengageinexplora9onorencouragestudentstouseproceduresinwaysthatareconnectedtoconceptsandunderstanding.
• Buildonstudents’currentunderstanding.
• Havemul9pleentrypoints.
Boaler&Staples,2008;Hiebertetal.,1997;Stein,Smith,Henningsen,&Silver,2009
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
InwhatwaysdoestheBandConcerttaskprovideopportuni9esforstudentstoengageinreasoningandproblemsolving?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
• Studentswerenottold“how”tosolvethetask,butweregiven.meandspacetouseapproachesthatmadesensetothem.
• Studentswereencouragedtorepresentthesitua9onusingvisualandphysicalrepresenta9ons.
• Studentshadopportuni9estoshare,compare,anddiscusstheirrepresenta9onsandapproaches.
Scenario:BandConcertTask
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Thereisnodecisionthatteachersmakethathasagreaterimpactonstudents’opportuni9estolearnandontheirpercep9onsaboutwhatmathema9csis...thantheselec9onorcrea9onofthetaskswithwhichtheteacherengagesstudentsinstudyingmathema9cs.
Lappan&Briars,1995
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Mathema9cal Representa9ons
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
MathTeachingPrac9ce
Useandconnectmathema9calrepresenta9ons.
Becauseoftheabstractnatureofmathema.cs,peoplehaveaccesstomathema.calideasonlythroughtherepresenta.onsofthoseideas.
(Na9onalResearchCouncil,2001,p.94)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
PreetyTripathi(2008)p.439
Tripathi,PreetyN.“DevelopingMathema9calUnderstandingthroughMul9pleRepresenta9ons.”Mathema.csTeachingintheMiddleSchool13,no.8(2008):438–45.
Whyfocusonmul&plerepresenta&ons?
“Usingdifferentrepresenta.onsislikeexaminingtheconceptthroughavarietyoflenses,witheachlensprovidingadifferentperspec.vethatmakesthepicture(concept)richeranddeeper.”
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Contextual
Physical
Visual
Symbolic
Verbal
TypesofRepresenta.ons
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Contextual
Physical
Visual
Symbolic
Verbal
Importantmathema.calconnec.onsbetweendifferenttypesofrepresenta.ons
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Contextual
Physical
Visual
Symbolic
Verbal
Importantmathema.calconnec.onswithintypesofrepresenta.ons
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
InwhatwaysdidMr.Harrisfocushisteachingondevelopingstudents’representa9onalcompetence?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Scenario:BandConcertTask
Aqerintroducingthetask,Mr.Harrisstated,“Beforeyoubeginworkingonthetask,thinkaboutarepresenta9onyoumightwanttouseandwhy,andshareyourideaswithapartner.”
ThenMr.Harrisaskedstudentstosharesomeoftheirideasinabriefwholegroupdiscussion.
Nextthestudentsworkedindividuallyonthetask.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Laterinthelesson,thestudentsweretoldtofindaclassmatewhousedadifferentrepresenta9onandtotaketurnsexplainingandcomparingtheirworkaswellastheirsolu9ons.
Moststudentssketchedequalgroups.Someusedconnec9ngcubesorcutanarrayoutofgridpaper.AfewstudentsmadeatableorT-chart.Somestudentswroteequa9ons.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
TheBandConcertTask
Kenneth
TyrellCorrineAnanda Elijah
Sam
Jasmine
Molly
MarcusTeresa
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Whatmightstudentsno&ceasbeingsimilarordifferentamongtheserepresenta&ons?
Howmightthissharinginpairssupportafocusondevelopingrepresenta&onalcompetence?
Jasmine Maria
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Marshall,A.M.,Superfine,A.C.,&Canty,R.S.(2010).Starstudentsmakeconnec9ons.TeachingChildrenMathema.cs,17(1),39–47.
Representa9onalcompetenceincludesknowinghowandwhentousepar9cularmathema9calrepresenta9onsandbeingabletomakeconnec9onsamongthem.
(Marshall,Superfine,&Canty,2010)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Purposeful Ques.ons
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
MathTeachingPrac9ce
Posepurposefulques9ons.
Teachers’ques&onsarecrucialinhelpingstudentsmakeconnec.onsandlearnimportantmathema.csandscienceconcepts.
Weiss&Pasley,2004
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Posepurposefulques9ons.
Effec9veQues9onsshould:
• Assessandadvancestudents’understanding.• Revealstudents’currentunderstandings.• Encouragestudentstoexplain,elaborate,orclarifytheirthinking.
• Makethemathema9csmorevisibleandaccessibleforstudentstoexamineanddiscuss.
Boaler&Brodie,2004;Chapin&O’Connor,2007;Herbel-Eisenmann&Breyfogle,2005
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
What“key”ques9onsdidMr.Harrisaskduringthelessontoelicitstudentthinkingandtopressorpromptthemtoconsiderideasrelatedtothemathlearninggoal?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Asstudentsworkedindividually,Mr.Harrisaskedques9onstoassesstheirunderstanding:
• Howdoesyourdrawingshow7groups?• Howmanytwen9esareyouadding,andwhy?
• Whyareyouaddingtens?Howdoesthatrelateto20?Howdoesthatrelatedtotheproblem?
Scenario:BandConcertTask
MathGoal:Studentswillrecognizethestructureofmul9plica9onwithinandamongdifferentrepresenta9ons.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Duringthewholeclassdiscussion,Mr.Harrisaskedques9onsthatmadethemathema9csvisibletoadvancestudentunderstanding:“Someofyouwrotethisequa9on,7x20=140,onyourpaper,soI’mwonderinghowthisequa9ondoesordoesn’tmatchtherepresenta9onsthateachofyouused?”
Scenario:BandConcertTask
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Mathema9cal Discourse
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
MathTeachingPrac9ce
Facilitatemeaningfulmathema9caldiscourse.
Teachersmustdeterminehowtobuildonandhonorstudentthinkingwhileensuringthatthemathema.calideasattheheartofthelessonremainprominentinclassdiscussions.
(Engle&Conant,2002)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Facilitatemeaningfulmathema9caldiscourse.
Mathema9calDiscourseshould:
• Buildonandhonorstudents’thinking;
• Providestudentswiththeopportunitytoshareandcompareideas,clarifyunderstandings,anddevelopconvincingarguments.
• Advancethemathema9callearningofthewholeclass.
Carpenter,Franke,&Levi,2003;Fuson&Sherin,2014;Smith&Stein,2011
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Howmighttheteacherhavestructuredthewholeclassdiscussionofthevariousstudentapproachestomovestudentstowardtheintendedlearninggoals?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
TheBandConcertTask
Kenneth
TyrellCorrineAnanda Elijah
Sam
Jasmine
Molly
MarcusTeresa
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Instructuringthewholeclassdiscourseofthetask,Mr.Harriswasstrategicin:
• Selec9ngspecificstudentrepresenta9onsandstrategiesfordiscussionandanalysis.
• Sequencingthevariousstudentapproachesforanalysisandcomparison.
• Connec9ngstudentapproachestokeymathideasandrela9onships.
Scenario:BandConcertTask
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Jasmine Kenneth
Sequence#1ofStudentApproaches
Teresa
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Elijah AnandaTyrell
Added20s. Skipcountedby10s. Reasoned7tensis70and7moretensis70.
Sequence#2ofStudentApproaches
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
ConceptualUnderstandingandProceduralFluency
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Buildproceduralfluencyfromconceptualunderstanding
ProceduralFluencyshould:
• Buildonafounda9onofconceptualunderstanding.
• Over9me(months,years),resultinknownfactsandgeneralizedmethodsforsolvingproblems.
• Enablestudentstoflexiblychooseamongmethodstosolvecontextualandmathema9calproblems.
Baroody,2006;Fuson&Beckmann,2012/2013;Fuson,Kalchman,&Bransford,2005;Russell,2006
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Whatdoesitmeantobefluentwithcomputa.onalprocedures?
Takeamomentandjotdownyourresponsetothisques9on.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
PrinciplestoAc&onsdefinesfluency:
PrinciplestoAc.ons(NCTM,2014,p.42)
Beingfluentmeansthatstudentsareabletochooseflexiblyamongmethodsandstrategiestosolvecontextualandmathema9calproblems,theyunderstandandareabletoexplaintheirapproaches,andtheyareabletoproduceaccurateanswersefficiently.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
PrinciplestoAc.ons(NCTM,2014,p.42)
Beingfluentmeansthatstudentsareabletochooseflexiblyamongmethodsandstrategiestosolvecontextualandmathema9calproblems,theyunderstandandareabletoexplaintheirapproaches,andtheyareabletoproduceaccurateanswersefficiently.
PrinciplestoAc&onsdefinesfluency:
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Whatdoesitmeantobefluentwithcomputa.onalprocedures?
Takeamomentandrevisityourresponsetothisques9onandreviseoraddtoyourearlierresponse.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Fluencydevelopsover.me...anditbuildsfrom
conceptualunderstanding.
PrinciplestoAc.ons(NCTM,2014,p.42)
Ini9alexplora9on
anddiscussion
Informalreasoningstrategies
Eventualuseofgeneralmethods
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
HowmightMr.Harrisdevelopconceptualunderstandinginwaysthatallowhimtobuildtowardproceduralfluency?
What“fluency”expecta9onsmightthestudentsbeworkingtoward?
Howmightthislessonestablishafounda9onforfluency?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
BandConcertSetup7rowsofchairswith20chairsineachrow,withacenteraisle.Howmanychairsareneeded?
Standard.3.NBT.3.Mul9plyone-digitwholenumbersbymul9plesof10intherange10–90(e.g.,9×80,5×60)usingstrategiesbasedonplacevalueandproper9esofopera9ons.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Mr.Harrishadaclearplanforlayingafounda.onofconceptualunderstandingfromwhichhecouldhelphisstudentsbuildtowardfluency.
Tyrell Ananda
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Tyrelldecomposedeach20into2tens.Skipcountedbytens.
Opportunity:Connect14tens=140.
Tyrell
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Anandaexplained,“Ifiguredout7tensis70...”Opportunity:Wheredidthosetenscomefrom?Anandadecomposed20into2tens.
7x20=7x(10+10)= (7x10)+(7x10)=70+70=140
Ananda
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Tousemathema9cseffec9vely,studentsmustknow:• whichprocedureisappropriateandmostproduc9ve
inagivensitua9on,• whataprocedureaccomplishes,and• whatkindofresultstoexpect.
Whyisitimportanttobuildproceduresfromconceptualunderstanding?
Mechanicalexecu.onofprocedureswithoutunderstandingtheirmathema.calbasisodenleadstobizarreresults.
GaryMar9n(2009,p.165)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Produc.veStruggle
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
MathTeachingPrac9ce
Supportproduc9vestruggleinlearningmathema9cs.
Studentswithagrowthmindsetarelikelytoperseverethroughastrugglebecausetheyseechallengingworkasanopportunitytolearnandgrow.
(Dweck,2008)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Thestrugglewehaveinmindcomesfromsolvingproblemsthatarewithinreachandgrapplingwithkeymathema9calideasthatarecomprehendiblebutnotyetwellformed.
(Hiebertetal.,1996).
Bystrugglingwithimportantmathema9cswemeantheoppositeofsimplybeingpresentedinforma9ontobememorizedorbeingaskedonlytoprac9cewhathasbeendemonstrated.
(Hiebert&Grouws,2007,pp.387-388)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Supportproduc9vestruggleinlearningmathema9cs.
Produc9veStruggleshould:
• Beconsideredessen9altolearningmathema9cswithunderstanding;
• Developstudents’capacitytopersevereinthefaceofchallenge;and
• Helpstudentsrealizethattheyarecapableofdoingwellinmathema9cswitheffort.
Black,Trzesniewski,&Dweck,2007;Dweck,2008;Hiebert&Grouws,2007;Kapur,2010;Warshauer,2011
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
HowmightMr.Harrissupportstudents’effortinusingstrategieswhilemovingthentowardthelearninggoalofthelesson...withouttakingoverthethinkingforthem?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Supporteffort...Allowgrapple...
Buildtowardunderstandingandfluency...
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Evidenceof StudentThinking
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
MathTeachingPrac9ce
Elicitanduseevidenceofstudentthinking.
Teachersusingassessmentforlearningcon.nuallylookforwaysinwhichtheycangenerateevidenceofstudentlearning,andtheyusethisevidencetoadapttheirinstruc.ontobeeermeettheirstudents’learningneeds.
(Leahy,Lyon,Thompson,&Wiliam,2005,p.23)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Elicitanduseevidenceofstudentthinking.
Evidenceshould:
• Provideawindowintostudents’thinking.
• Helptheteacherdeterminetheextenttowhichstudentsarereachingthemathlearninggoals.
• Beusedtomakeinstruc9onaldecisionsduringthelessonandtoprepareforsubsequentlessons.
Chamberlin,2005;Jacobs,Lamb,&Philipp,2010;Sleep&Boerst,2010;vanEs,2010,Wiliam,2007
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Whatmightbesomeindicatorsofstudentthinkingthattheteacherwouldwanttoelicitanduseduringthelessonandtoprepareforsubsequentlessons?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Inplanningforthelesson,Mr.Harriscreatedalistofkeyindicatorsofstudentthinking.Heplannedtolookandlistenfor:
• Representa9onsthatshowed7groupsorrows.
• Strategiesthatdecomposedgroupsorinformallyusedthedistribu9veproperty.
• Useofconcept-basedlanguage,suchasmakingequalgroupsorrowsoftensortwen9es,intheirexplana9onsanddiscussions.
Scenario:BandConcertTask
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Forma9veassessmentisanessen9allyinterac9veprocess,inwhichtheteachercanfindoutwhetherwhathasbeentaughthasbeenlearned,andifnot,todosomethingaboutit.Day-to-dayforma9veassessmentisoneofthemostpowerfulwaysofimprovinglearninginthemathema9csclassroom.
DylanWiliam(2007,pp.1054;1091)
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
BuildingaTeachingFrameworkforMathema.cs
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Huinker,DeAnn,andVictoriaBill.TakingAc.on:Implemen.ngEffec.veMathema.csTeachingPrac.cesinGradesK-5.Reston,VA:Na9onalCouncilofTeachersofMathema9cs,2017.
Movingfromalistofmathema.csteachingprac.cestoateachingframeworkformathema.cs...
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
PtAResources
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
PrinciplestoAc.onsWebsite
www.nctm.org/PtA/
PtABookoreBook
Execu9veSummary(English&Spanish)
PowerpointOverviewsw/Narra9veCases
Reflec9onGuide
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Descrip.on:Duringthissessionyouwill
• watchavideoclipofafourthgradeclassengagedinawholediscussionofaseriesofrelatedmul9plica9onequa9ons.
• Discusswhattheteacherdoestosupportthestudents'learning.
• Relateteacherac9onsinthevideototheEffec9veMathTeachingPrac9ces.
GradeBand:Elementary
Effec.veTeachingPrac.ces:•Buildproceduralfluencyfromconceptualunderstanding.•Implementtasksthatpromotereasoningandproblemsolving.
CaseofKatherineCaseyandtheMul.plica.onStringsTask
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
GradesK–5
DeAnnHuinker
VictoriaBill
NewNCTM
Resource
TakingAc&on
Series
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Chapter1: SeangtheStage
Chapter2: EstablishMathema9csGoalstoFocusLearning
Chapter3: ImplementTasksthatPromoteReasoningandProblemSolving
Chapter4: BuildProceduralFluencyfromConceptualUnderstanding
Chapter5: PosePurposefulQues9ons
Chapter6: UseandConnectMathema9calRepresenta9ons
Chapter7: FacilitateMeaningfulMathema9calDiscourse
Chapter8: ElicitandUseEvidenceofStudentThinking
Chapter9: SupportProduc9veStruggleinLearningMathema9cs
Chapter10:PullingItAllTogether
Achapterfocusedoneachmathteachingprac.ce.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
• AnalyzingTeachingandLearning(ATL)ac9vi9esuseclassroomar9factsto:-studyeachteachingprac9ce.-seeitsenactmentinclassrooms.-reflectonwhatmakesiteffec9veforstudentlearning.
VideoClips
Narra.veCases----ClassDiscussions
• WhattheResearchSays
• Promo.ngEquitythroughtheMathema9csTeachingPrac9ce
• TakingAc.oninYourOwnClassroom StudentWorkAnalysis
ChapterSec.ons
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
AudiencesfortheBook
• Teacherstoreadontheirown.
• Colleaguesworkingtogetheringradelevelteamsoracrossgradebands.
• Professionaldevelopersandteachereducatorsworkingwithpreserviceorinserviceteachers.
• Onlineorface-to-facebookstudy.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
ClosingThoughts
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
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
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
WhyfocusonimprovingourTeachingPrac.ceinMathema.cs?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Studentlearningofmathema9cs“dependsfundamentallyonwhathappens
insidetheclassroomasteachersandlearnersinteractoverthecurriculum.”
(Ball&Forzani,2011,p.17)
Ball,D.L,&Forzani,F.M.(2011).Buildingacommoncoreforlearningtoteach,andconnec9ngprofessionallearningtoprac9ce.AmericanEducator,35(2),17-21.
BecauseTeachingMamers!
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
Ms.Robinsonaskedhersecond-gradestudentstowriteabouta9mewhentheyfeltreallysmartinmath.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
SecondGradeStudent
Whendoyoufeelsmartinmathclass?
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
SecondGradeStudent
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
SecondGradeStudent
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
TheMathema9csTeachingPrac9cessupportdailyayen9ontoaccess,equity,andempowermentinthe
mathema9csclassroom
Space&choicetoengagein
mathreasoning.
Voiceinamathclasscommunity.
Posi.vemath
iden..es.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
CalltoAc.on• Readit.Readitagain.
• Haveconversa9onswithyourcolleaguesandwithyouradministrators.
• Makeaplantoworktogetherwithcolleaguestowardcommonandconsistentimplementa9onoftheeight,high-leverageMathema&csTeachingPrac&cesinclassroomsinyourschool.
• Supportdeep,meaningfullearningofmathema9csandensuremathema9calsuccessforeachandeverystudent.
Dr. DeAnn Huinker, University of Wisconsin-Milwaukee; Build Math Minds Virtual Summit, July 31-August 2, 2017
ThankYou!
Dr.DeAnnHuinkerUniversityofWisconsin–Milwaukee
www.nctm.org/ptawww.nctm.org/ptatoolkit
Top Related