《如何塑造优秀教师》（第九章）翻译项目报告.pdf

'旅六劈葡译专化学位硕丈论文＇《如何４連化£表巧》ｆ第先章＾｜？４｜巧《振告张晶莖巧导教巧Ｉ李龙泉巧巧专化巧巧：ｆｔ译额±研巧方巧Ｉ巧巧笔巧论文捷巧时巧：如１６年４巧论义巧辩时巧：２０１６年５月论义Ａ巧，２０化４奶＇？？■■－■■ SichuanInternationalStudiesUniversityATranslationProjectReportonBuildingaBetterTeacher(Chapter9)byZhangJingyingAthesissubmittedtotheGraduateSchoolinpartialfulfillmentoftherequirementsforthedegreeofMasterofTranslationandInterpretingunderthesupervisionofProfessorLiLongquanChongqing,P.R.ChinaMay2016 《如何塑造优秀教师》（第九章）翻译报告摘要随着经济发展与全球化程度的提高，教育显得日益重要。良好的教育是国家兴旺的基础，中国应借鉴西方先进的教育理念，发展自己的教育事业。鉴于此，本翻译报告所选原文为《如何塑造优秀教师》(BuildingaBetterTeacher)中的第九章。该书主要介绍了西方先进的教育理念与教学方法。本报告分为五部分。第一部分为引言，介绍项目背景和项目意义，说明本翻译报告的结构。第二部分为原作介绍，包括作者简介和原文本的主要内容及语言特点。第三部分介绍译者采用的翻译理论——目的论。第四部分介绍翻译难点及在翻译理论指导下的对应解决方法。译者以目的论为指导，通过分析译文中的典型例子，总结出翻译专业术语、长难句的方法和技巧,以及如何保持语篇连贯。第五部分对翻译中的经验教训进行了总结。关键词：目的论；术语翻译；长句翻译；语篇连贯；翻译技巧ii ATranslationProjectReportonBuildingaBetterTeacher(Chapter9)AbstractWiththedevelopmentofeconomyandglobalization,educationisplayingamoreandmoreimportantroleintheworld.Ifacountrywantstosurviveinsuchacompetitiveenvironment,ithastodevelopitsowneducation.GreateducationisthefoundationofaflourishingsocietyandChinashouldlearnforeignadvancededucationalconceptsandmethodstodevelopitsowneducation.Againstthisbackground,thetranslatorchosetotranslateChapter9ofBuildingaBetterTeachertointroducesomeadvancedteachingconceptsandskillstoChinesereaders.Thisreportisdividedintofiveparts.Thefirstpartisanintroductiontothetranslationproject,includingthebackgroundandsignificance,aswellasthestructureofthereport.Thesecondpartgivesanintroductiontothesourcetext,consistingoftheauthor,maincontentandlinguisticfeatures.Thethirdpartintroducesskopostheory—theguidingtheoryofthetranslationreport.Thefourthpartsummarizestranslationdifficultiesandcorrespondingsolutions.Basedontheskopostheory,thetranslatoroutlinestranslationmethodsandtechniquestodealwithspecializedterms,longsentencesandtextualcoherencethroughtheanalysisoftypicalexamplesinthetranslation.Thelastpartconcludestheexperienceandlessonslearnedfromtheproject.Keywords:skopostheory;specializedtermstranslation;longsentencestranslation;textualcoherence;translationtechniquesiii AcknowledgementsFirstandforemost,Iwouldliketoexpressmyheartfeltgratitudetomysupervisor,ProfessorLiLongquan,bothforhisintellectualguidanceandforhiswarmandconstantencouragementduringtheprocessofwritingthisthesis.Withpatienceandprudence,helaboredthroughdraftsofthisreportandpointedoutdefectstherein.Therefore,Ioweallthemeritsinthisthesis,ifany,tohim,thoughIamfullyawarethatitmightstillcontainsomemistakes,forwhichIbearthewholeresponsibility.Second,mysincerethankstoallthehonorableandrespectableprofessorswhohelpedmewithmystudyduringthepasttwoyears.Inaddition,manythankstomyclassmates,fortheirhelpinanalyzinglonganddifficultsentenceswithmeandtheirpersistentsupportwheneverIfacedwithproblems.Lastbutnotleast,bigthankstomyfamilywhosharedwithmemyworries,frustrationsandhappinessduringtheprocessofthisthesis.iv CONTENTS摘要.............................................................................................................................iiAbstract........................................................................................................................iiiAcknowledgements.......................................................................................................ivChapter1Introduction...................................................................................................11.1ProjectBackground........................................................................................11.2ProjectSignificance.......................................................................................11.3ProjectStructure............................................................................................2Chapter2AnalysisoftheSourceText..........................................................................42.1AbouttheAuthor...........................................................................................42.2AbouttheSourcetext....................................................................................42.2.1Content..............................................................................................42.2.2LinguisticFeatures............................................................................5Chapter3TranslationTheoriesandApplication...........................................................73.1IntroductiontoSkoposTheory......................................................................73.2ApplicationofSkoposTheory.......................................................................7Chapter4TranslationDifficulties&CorrespondingSolutions.....................................94.1TranslationDifficulties..................................................................................94.1.1SpecializedTerms.............................................................................94.1.2Long&DifficultSentences..............................................................94.1.3CoherenceoftheTargetText.........................................................104.2CorrespondingSolutions..............................................................................104.2.1SolutionstoSpecializedTerms.......................................................104.2.1.1FreeTranslation.................................................................104.2.2SolutionstoLong&DifficultSentences........................................114.2.2.1TranslatingintheOriginalOrder.......................................124.2.2.2TranslatingintheReverseOrder.......................................124.2.2.3Division..............................................................................134.2.2.4ComprehensiveMethod.....................................................154.2.3SolutionstoCoherenceoftheTargetText.....................................16Chapter5Conclusion...................................................................................................185.1Lessons.........................................................................................................185.2UnsolvedProblems.......................................................................................18References....................................................................................................................20AppendixISourceText...............................................................................................21v AppendixIITargetText..............................................................................................39vi Chapter1Introduction1.1ProjectBackgroundWiththedevelopmentofeconomyandsociety,educationisplayingamoreandmoreimportantroleintheworld.Greateducationisthefoundationofaflourishingsociety.Ifacountrywantstosurviveinsuchacompetitiveenvironment,ithastodevelopitsowneducation.Furthermore,withthedevelopmentofdifferentcountries,globalculturalblendinghasbecomeanunstoppabletrend.Therefore,learningtheadvancededucationalphilosophyandteachingmethodsfromforeigncountriesisbecomingincreasinglynecessary.AlthoughsometranslationsaboutforeigneducationhaveexistedinChina,thetranslationstudiesinthisareaarenotenough.HencetranslatorshavetheresponsibilitytotranslatemoreadvancedbooksabouteducationforChinesereadersanddofurthertranslationstudies,whichwillcontributetostrengthenthecommunicationbetweenChinaandforeigncountriesinthisfield.AsabookrecommendedbyNewYorkTimesBookReview,BuildingaBetterTeacherprovidesanopportunityforreaderstostudyadvancedteachingtheoriesandmethods.ForthesakeofmoreChinesereaders,thetranslatorchosetotranslateChapter9ofthisbookandmadeatranslationprojectreportonit.1.2ProjectSignificanceFirstofall,fromthemomentourchildrenstepintoaclassroom,thesinglemostimportantfactordeterminingtheirachievementisnotthecoloroftheirskinorwheretheycomefrom;it’snotwhotheirparentsareorhowmuchmoneytheyhave.It’swhotheirteacheris(BarackObama,2005).It’struethatteachersareplayinganincreasingimportantpartforthestudentsaswellasthecountry’sfuture.Henceweneedtotrainourteacherstobebetter.Meanwhile,Chineseteachersshouldlearnfromthewest,absorbtheessenceanddiscardthedrosstohelpChinesestudents.Throughthisbook,Chinesereaderscanknowmoreaboutwesterneducation,likeadvancedteachingmethods,andbeenlightened.1 Furthermore,greateducationisthefoundationofaflourishingsociety,anditdependsongreatteachers.Generally,thecommonviewofgreatteachersistheyarebornthatway.However,thetruthisthatteachersneedtobetrained.Teachingis“thegreatestartinalltheworld”;learningtodoitwellcouldtakealifetime.BuildingaBetterTeacherilluminateshowwecandevelopgiftededucatorswhopreparechildrenforabrighterfuture.Inthisfascinatingandaccessiblebook,ElizabethGreen,theauthorofthisbook,tellsthestoryofthecountry"sleadingresearchersontheall-importantquestionsofwhatmakesforaneffectiveclassroomteacherandhowteacherscanbetrainedtodotheirjobsbetter.ThatthestoryfeelscompletelyfreshistestamentnotonlytoGreen’sskillasareporterandwriterbutalsotohowbeside-the-pointmuchofthenationalconversationabouteducationis.Green’sbookoughttopersuadethecountrytofocusonwhatreallymattersineducation.Lastbutnotleast,thetranslatorwantstobeateacheraftergraduation.Intranslatingthisbook,shecannotonlyacquiresometranslationskillsandauthenticEnglishexpressions,butalsolearnhowtobeabetterteacher.Throughtheproject,thetranslatorhopesthatshecanimprovehertranslationability,getagoodtranslationundertheguidanceofhersupervisor,learnmoreaboutwesterneducationandprovideanopportunityforChinesereaderstolearn.Meanwhile,theexperienceandlessonsillustratedinthereportarehopedtoofferreferenceforthefuturetranslationinthisfield.1.3ProjectStructureThestructureofthereportisasfollows:Part1:Anintroductiontothetranslationproject,includingthebackground,significanceandstructure.Part2:Ananalysisofthesourcetext,includingtheauthor,contentandlinguisticfeatures.Part3:Anintroductiontoskopostheory—theguidingtheoryofthetranslationreport.Part4:Translationdifficultiesandcorrespondingsolutions.2 Part5:Conclusionofthetranslationreport,includinglessonsandproblemsremainedtobesolved.3 Chapter2AnalysisoftheSourceText2.1AbouttheAuthorTheauthorofthisbook,ElizabethGreen,isaco-founder,CEO,andeditor-in-chiefofChalkbeat,anonprofiteducationnewsorganization.GreenhascoverededucationforTheNewYorkSunandU.S.News&WorldReportandalsowroteabouteducationissuesforNewYorkTimesMagazineandotherpublications.GreenservesontheboardoftheEducationWritersAssociation.In2009-2010,shewasaSpencerFellowineducationjournalismatColumbiaUniversity,andin2011,shewasanAbeJournalismFellowstudyingeducationinJapan.2.2AbouttheSourceTextBuildingaBetterTeacherisaneducationbookwrittenbyElizabethGreenwhichwaspublishedinW.W.Norton&Companyin2014anditwasa2014NewYorkTimesBookReviewNotableBook.TheChineseversionofthisbookhasnotbeenpublishedinChina.Chapter9—theselectedtextfortranslationhas7,968words.2.2.1ContentPeopleallhavegreatteacherswhoopennewworldsorevenchangetheirlives.Whatmakesourteacherssogreat?Isitamatterofnatural-borncharisma?Ordoesexceptionalteachingrequiresomethingmore?Nowadays,teachereffectivenessisahottopicineducationcircles.Howtomeasureitandimproveitiscrucialforustodiscuss.Asamatteroffact,greatteachersarenotborn,they"remade.ElizabethGreen,whohasstudiedteachingmethodsinbothAmericanandJapaneseclassroomsoverthespanofsixyears,considersthatteachingmustitselfbetaughtandindividualtechniquesarekey.TheselectedtextintheprojectistheninthchapterofBuildingaBetterTeacher,whichisnamedasTheHolyGrails.Itintroducessomeadvancedteachingtheoriesandmethods,includingsometeachingcasestodemonstratetheteachingtechniquesspecifically.Itintroducesanewgenerationofeducatorsexploringhowto4 improveteachingquality,includingMagdalene’s“instructionalactivities”andPam’s“corepractices”.Theauthorfocusesonthequestionsthatreallymatter:Howtoprepareteachersandwhatshouldteachersknowbeforeenteringtheclassroom?Howtogetyoungmindstounderstand,reason,conjectureandprove?Howtomakeclassroomdiscussionsmoreexciting?Incorporatingnewresearchfromeducationspecialistsandclassroomentrepreneurs,sheprovidesanewwayforteacherstothinkabouthowtobeabetterteacher.Inthischapter,severalcompellingteachingcasesarepresentedtoreaders.Inamathclassofthefirst-gradestudentsinaBostonelementaryschool,theteacherSabineFerdinandmakeseffortstoinspirethestudentstograspthecoremathknowledge.AnotherexampleisaformerAmericanhighschoolteacher—PamGrossmanworkswithatopEnglishinstructor—PeterWilliamsontopinpointthekeyinteractionsateachermustfostertoinitiateafascinatingclassroomdiscussion.Thentheauthorstateswhataretheholygrailsinteaching—“academicdiscourse”,whichmeansfourthings.First,adultscouldn’tdoallthetalkingandthinking.Second,thestudentshadtotalkabouttheacademicideaathand.Third,theyhadtotalkusingacademicvocabulary.Finally,theyhadtodowhatAspirecalled“bringingevidencetobear”—quotingthetextinEnglishclass,citingaprimarysourceinhistory,reasoningthroughaproofinmath,pointingtoexperimentalevidenceinscience.Throughtheeducators’stories,ElizabethGreentakesusonajourneyintotheheartofaprofessionthatimpactseverychild.2.2.2LinguisticFeaturesThelinguisticfeaturesoftheselectedtextareasfollows:First,astheselectedbookisanacademicwriting,thelanguageinthesourcetextisquiteformalandacademic.InChapter9,therearemanyforeignspecializedtermsabouteducationwhichneedtobetranslatedfaithfullyandaccessibly,suchasmodeling,“turnaround”school,BostonTeacherResidencyandAspirecharternetwork.Second,theauthordemonstratesherideasbyalternatinglongandshortsentences.Somelongsentencesaredifficulttoanalyzebecausethewords,phrasesandstructuresarecomplicated.Alsotherearemanyparenthesesseparatedfromtherestofthesentencesbydashes.5 Third,therearemanyvividteachingcaseswhichhelpreadersunderstandtheteachingtechniquesbetter,inwhichthelanguageislivelyandnotsocomplicated.Intranslatingtheteachingcases,thecoherenceandvividnessshouldbenoticed.6 Chapter3TranslationTheoriesandApplicationSkopostheoryistheguidancetheoryofthetranslationproject.Thetranslatordealswithdifficultiesencounteredinthetranslationprocessonthebasisofskopostheory.3.1IntroductiontoSkoposTheorySkoposistheGreekwordfor“aim”and“purpose”andwasintroducedintotranslationtheoryinthe1970sbyHansJ.Vermeerasatechnicaltermforthepurposeofatranslationandoftheactionoftranslating(Munday,2008,pp.79-80).Accordingtoskopostheory,theaimorpurposeofthetranslationisfocusedaboveallinthewholetranslationalaction,whichdeterminesrelevanttranslationstrategiesandmethodsemployedinthetranslationprocess.Inotherwords,receiversofthetargettextplayaveryimportantrole.Notjusttranslatingthesourcetext,translatorsshouldconsiderthereceiver’ssituationandneeds.Therefore,inskopostheory,itiscrucialforthetranslatortoknowwhyasourcetextistobetranslatedandwhatthefunctionofthetargettextwillbe(Munday,2008,pp.79-80).Therearethreemajorrulesinskopostheory,namely,skoposrule,coherenceruleandfidelityrule.Themostimportantoneistheskoposrule,whichmeansatranslationalactionisdeterminedbyitsskopos.Thecoherencerule,linkedtointratextualcoherence,statesthat“thetargettextmustbeinterpretableascoherentwiththetargettextreceiver’ssituation”(Reiss&Vermeer,1984,p.113).Thatistosay,thetargettextmustbeinternallycoherentforthesakeofreceivers,giventheirsituationsandknowledge.Thefidelityrule,orintertextualcoherence,isthattheremustbecoherencebetweenthetargettextandthesourcetext,whichmeanstheinformationandemotioninthesourcetextshouldbetransmittedtothereceivers.Inotherwords,thetargettextmustnotbedivorcedfromthesourcetext.Whatcallsforspecialattentionisthatthefidelityruleisconsideredoflessimportancethanthecoherencerule,andbotharesubordinatetotheskoposrule.Allinall,inordertogetafunctionallyadequatetargettext,thetranslatorshouldtakealltheseintoconsideration.7 3.2ApplicationofSkoposTheoryWiththeadventofskopostheoryasdevelopedbyKatharinaReissandHansJ.Vermeer,ashiftinparadigmtookplaceinthe1980sinthecourseofwhichthelinguisticallyorientedtranslationstudiesmorphedintoanactionandfunctionfocusedtranslationsciencewhichexplicitlyincludestheculturalaspectsofthetransfer.Sincethattimetranslationisnolongerregardedmainlyasalanguagetransferconcernedpredominantlywiththeequivalenceatthewordlevel,butatargetedtransferintoanotherculturewherebyadequacyisthemainfocus.GreatachievementshavebeenmadeinitstheoreticalstudyandapplicationsinceskopostheorywasintroducedintoChina.Ithashadafar-reachinginfluenceontranslationstudiesinChinaanditiswidelyusedindifferenttypeoftranslations,suchasadvertisementtranslation,publicitytexttranslation,tourismtranslationandsoon.Asfortheselectedbook,thepurposeoftranslatingthisbookistointroducesomeadvancededucationalmethodsandtheorytoChinesereaders.Fortranslationstrategies,thetranslatormainlyuseddomesticationtranslationtomakethetextcloselyconformtothetargetculture.Shemadegreateffortstohelpthetargetreadersunderstandtheinformationeffectivelytomeetthestandardsoffaithfulness,readabilityandfluency.8 Chapter4TranslationDifficulties&CorrespondingSolutions4.1TranslationDifficultiesWhentranslatingtheselectedtext,thetranslatormetwithsomedifficulties,suchasthespecializedterms,longanddifficultsentences.Andalso,thecoherenceofthetargettextisanotherhardpartintranslating.4.1.1SpecializedTermsTheselectedtexthasmanyspecializedtermsineducationwhicharedifficulttohandle,suchasmodeling,“turnaround”school,BostonTeacherResidencyandAspirecharternetwork.Intranslatingspecializedterms,twopointsmustbeconsidered:oneistechnicaltransformation;theotherislinguistictransformation.Asthemeaningofatermisusuallycomplexandreferential,therelevantknowledgeisrequired.Inconsequence,moredifficultiesareaddedintranslating.4.1.2Long&DifficultSentencesTheselectedtexthasmanylonganddifficultsentencesinwhichtherelationamongthecomponentsisdifficulttounderstand.Thesentencestructureiscomplicatedandthewordsinitaredifficulttounderstand.Alsotherearemanyparenthesesseparatedfromtherestofthesentencesbydashes.Englishisahypotacticlanguage,whileChineseisparataxis.Insyntacticstructure,ChineseusesverbsandshortsentencestoexpresswhileEnglishusesnounsandrigorouslongsentences.Therefore,itrequiresvarioustranslationskillstoturnEnglishlongandcomplicatedsentencesintoChineseshortones.Intranslating,longsentencesshouldbeseriouslydealtwith.Example1:ThiswasacorepartofthebestEnglishteachers’repertoire,awayofwalkingstudentsthroughtheprocessestheyneededtoperforminEnglishclass—notjustreadingandwriting,buttheircomponentparts,likeannotatingatexttohelpunderstanditsmeaningorusingevidencetoconstructanexplanation.9 Example2:Nextcamea“readingresponseprompt”thateachstudentansweredindividually,completewithremindersaboutthebestwaytoread—“markupthetextinthewayyouchoose,”theinstructionssaid,“includingtheuseofhighlightersandmetacognitivemarking”—andinstructionsaskingthestudentstowritequestionsoftheirown.4.1.3CoherenceoftheTargetTextTheselectedtexthassomevividteachingcasesandtherearemanyshortsentencesanddialoguesintheteachingcases.It’sdifficulttotranslatethemfluently,accuratelyandvividly.Furthermore,thewholechaptershouldbetranslatedcoherentinternally.4.2CorrespondingSolutions4.2.1SolutionstoSpecializedTermsIntranslatingspecializedterms,thetranslatortriestofindtheiraccuratetranslationthroughinternetandrelevantbooksortranslatethemaccordingtothecontexttomakethemmoreaccessible.4.2.1.1FreeTranslationExample1:SourceText:Residentswereplacedinsomeofthecity"smostdifficultschools,includingseveral"turnaround"schools,representingBoston"sportionofthecountry"sfivethousandworst-performingmiddleandhighschools.TargetText:当地驻校教师被安排在市里最差的学校教学，其中包括一些“待改造(turnaround)”学校,这些学校是美国5000所状况最糟的初高中学校里的一部分，位于波士顿。Inthissentence,thespecializedterm“turnaround”isdifficulttodealwith.Intranslating,thetranslatorfirstcheckstheoriginalmeaningofitinEnglishandChinese.InEnglish,“turnaround”isacompletechangeinopinion,attitude,ormethod.InChinesetranslation,itisalwaystranslatedinto“转向，转弯处，回车道”.Sothekeypointisacompletechange.As“turnaround”istheattributeof“school”inthissentence,itmeansa10 kindofschool.Ifitmodifiesakindofschool,itmeansthattheschoolneedstobechangedoverall.Aftercheckingontheinternet,thetranslatorfindsithasestablishedtranslationversioninsomeforeignwebsites.Soshetranslatesitinto“待改造”accordingtothecontextandwebsite，whichmeanstheschoolhassomesevereproblems,suchastheoveralllevelofitsstudentsislowandthestructureofitneedstobeimproved,andneedstobechangedcompletely.Inthisway,thetranslationismoreaccurateandexplicit.Example2:SourceText:Finally,theyhadtodowhatAspirecalled“bringingevidencetobear”—quotingthetextinEnglishclass,citingaprimarysourceinhistory,reasoningthroughaproofinmath,pointingtoexperimentalevidenceinscience.TargetText:最后，学生需要按照艾斯派尔（Aspire）称作“运用证据支撑(bringevidencetobear)”的方法来学习，即在英语课上引用文章，历史课上引用第一手资源，数学课上通过证明推理，科学课上重视实验证据。Inthissentence,thespecializedphrase“bringingevidencetobear”isdifficultforthetranslatoratfirst.Afterunderstandingthewholesentences,thetranslatorknowsthatitmeanstheexamplesfollowingthephraseaccordingtothecontext.Itistheoutlineofthefollowingpart.Itmeanstousetheevidencetoprovesomethingthatyoubelieve.Sointranslatingthisphrase,thetranslatortriestoexplainitsmeaningtolettheChinesereadersunderstandtherealimplicationthewriterwantstotellthem.SothecorrespondingChinesetranslationis“运用证据支撑”.4.2.2SolutionstoLong&DifficultSentencesEverylanguagehasitsowncharacteristics.WhileEnglishischaracterizedbyhypotaxis,whichmeansthatEnglishspeakerstendtogivemuchattentiontoformalcohesion,Chineseischaracterizedbyparataxis,whichmeansthattherelationbetweensentencepartsisoftenlooseandunclear.Inotherwords,ChineseclausesareconnectedthroughmeaningwhileEnglishusesfunctionalwordstostringthemtogether(ChengZhaowei,2006,pp.72-73).Intranslatinglonganddifficultsentences,thetranslatortakesallthesecharacteristicsintoaccount.Sheknowsthattranslationisaprocessofunderstandingandexpression.Shefirstanalysesthestructureofthesentencesandfiguresoutthetrue11 meaningofthem.ThenthetranslatorusessometranslationmethodsandtechniquestomakethesentencesmoreaccessibletoChinesereaders.4.2.2.1TranslatingintheOriginalOrderExample3:SourceText:Thediscussionnowmovedintomoreimportantterrain:theshiftfromwhatthepsychologistJeanPiagetcalled“animism”—theideathatobjectshavetheirownconsciousnesses,likepeople,andsocanmoveandchange,ratherthanstayingstableandconstant—toamoreabstractunderstandingofasquareasacategorydescribingshapeswithfourequalsidesofunchanginglengths.TargetText:现在，讨论已进入到一个更重要的领域：从心理学家让·皮亚杰（JeanPiaget）称为“万物有灵论”的思想,即物体与人一样有自己的意识，可以移动改变，而不是一成不变，转移到了更抽象的理解正方形，即将其看做一个类别，有4个长度相等且不变的边。It’sacomplexsentencewithsubordinateclauses.First,thecorecontentshouldbefound.Throughanalyzingthissentence,thetranslatorfindsitis“Thediscussionmovedintomoreimportantterrain:theshiftfrom…to…”.Second,themeaningofdifferentlayersshouldbefiguredout.Inthissentence,thereisanobjectiveclause“whatthepsychologistJeanPiagetcalled‘animism’…”,andanappositiveclause“thatobjectshavetheirownconsciousness…”.Sotheshiftisfrom“心理学家让·皮亚杰（JeanPiaget）称为“万物有灵论”的思想,这个思想是物体与人一样有意识,可以移动改变，而不是稳定与持续”to….Then,thetranslatormovestothelastpart“toamoreabstract…”.Hereisanon-finiteverb“describing”and“with”asaccompanyingadverbial.Sotheshiftisfrom…to“更抽象的理解正方形，即将其看做一个类别，有4个长度相等且不变的边”.Third,thetranslatorfindsthemeaningofdifferentlayersisprogressiveandsequential.Whenthepartsofalongsentencearearrangedintheorderoftimeorlogicalconnections,thetranslatorcanfollowtheoriginalorderintranslation(ChengZhaowei,2006,p.73).Thus,thetranslatortranslatesthesentenceinitsoriginalorderandthetargettextisnaturalandfluent.4.2.2.2TranslatingintheReverseOrderExample4:12 SourceText:Itwasn’teasy,butwithawell-chosenproblemateachercouldmakethesubject’sbigideascomealive,eventolittlechildren.TargetText:要做到这一点并不容易。但是，即便是对低年级学生，老师通过精挑细选的问题也可以使学科的主要思想活灵活现。It’sacompoundsentence.Thelastpart“evento…”isanadverbialofconcessioninthesentence.Ifthetranslationisintheoriginalorderofthesourcetext,itdoesn’tconformtoChineseexpressionhabits.Hence,thetranslatorput“evento…”forwardinthetargettext.Inthisway,theexpressionismoresuitableforChinesethinkingmodeandcommunicativehabits.Example5:SourceText:JesseSolomonwasespeciallytakenwithanideathatwasatthecoreofMagdaleneLampert"sfindingsaboutItaliaidea:theconceptofinstructionalactivities,orIAs.TargetText:玛格达莱妮·兰佩特（MagdaleneLampert）对意大利语言学校（Italiaidea）的调研结果集中体现在教学活动（InstructionalActivities）理念上。对此，杰西·所罗门（JesseSolomon）非常赞同。It’sacomplexsentencewithasubordinateclause.First,thecorecontentisJessewastakenwithanidea….”.Second,thereisanattributiveclausetoexplainwhattheideais.Ifthetranslatortranslatesitinitsoriginalorder,“杰西·所罗门非常赞同玛格达莱妮·兰佩特对意大利语言学院调研中发现的核心,即教学活动理念。”,thetranslationversionistoolongandcomplicated.ItisgenerallyagreedthatthemostimportantdifferencebetweenEnglishandChineseisthatEnglishishypotaxis-prominent,whileChinese,parataxis-prominent.ThistranslationversionisnotfaithfultoChineseparataxis-prominent.Furthermore,whilethefocusofanEnglishsentenceisusuallyplacedahead,aChinesefocusoftenappearsattheendofasentence,hencethereverseorderintranslationisbetter(ChengZhaowei,2006,p.75).Therefore,thetranslatorchoosestoreversethesentencetotranslateandthefinaltranslationismorefluentandeffective.4.2.2.3DivisionExample6:13 SourceText:Steeringtheconversationdemandedacomplicatedsetofmaneuversforabeginningteacher,butDilitmadeiteasierbyspellingoutthestepsandhavingteacherstrythemout,firstwiththeprofessorandotherstudentsactingintheroleofstudents—theteacher-educatorthrowingoutcommonstudenterrors—andthenwithrealstudents.TargetText:对于一位新老师来说，掌控谈话情景需要一系列复杂技巧才能得以实现。但在迪里特（Dilit），通过详细说明步骤并让新老师去尝试，一切变的简单可行。首先，教授和其他学员一同扮演学生与新老师进行模拟训练。过程当中，教师教育者(teacher-educator)会抛出普通学生常犯的错误。之后，新老师与真正的学生进行训练。It’salongandcompoundsentence.Thecorecontentis“steeringtheconversationdemand…,butDilit…”.TherestofthesentenceistoexplainhowDilitmadeiteasier.Thepartusingtwodashesisaparenthesis.Englishgivesmuchattentiontoformalcohesionandthesentencesareoftenverylongandconnectedbyfunctionalwords,forexample,inthissentence,suchasby,with...,whileChinesesentencesareoftenshortandorganizedbythoughtgroups.AccordingtoChinesethoughtgroups,alongsentencemaybedividedintoseveralpartsintranslationsoastoachieveaclearandnaturalexpression(ChengZhaowei,2006,p.76).Hence,asthethoughtgroupsofthesentenceisrelativelyindependent,thetranslatordividesthisoneEnglishsentencestofiveChinesesentencesandthetargettextisnatural,logicalandeasytounderstand.Example7:SourceText:ThiswasacorepartofthebestEnglishteachers’repertoire,awayofwalkingstudentsthroughtheprocessestheyneededtoperforminEnglishclass—notjustreadingandwriting,buttheircomponentparts,likeannotatingatexttohelpunderstanditsmeaningorusingevidencetoconstructanexplanation.TargetText:它是优秀英语老师教学内容的核心部分，可引导学生在英语课堂上进行他们需要经历的过程。这个过程不仅包括阅读和写作，还有一些细分内容，如给文章加注时来帮助理解意思，以及使用例证来进行阐述。14 Itisalongcomplexsentencewithasubordinateclause.First,thecorecontentshouldbefound.Thesubjectofthissentenceis“this”,whichrefersto“modeling”inthelastsentence.Somodelingisacorepartof…andawayofwalkingstudents….Second,themeaningofdifferentlayersshouldbefound.Thereisanattributiveclause“theyneededtoperform…”tomodify“processes”.Sothetranslatortranslatesitinto“引导学生经历一个他们需要在英语课堂上经历的过程”.Thenthetranslatormovedtothepart“notjust…but…”.Itmeanstheprocessincludesreading,wringandtheircomponentparts.Andthelastpart“likeannotating…”isthedetailsofcomponentparts.Finally,thetranslatoroutlinesthemeaningofdifferentlayers.Thecorecontentis“模型是英语老师教学内容的核心部分，而且是一种方法，可引导学生经历一个教学过程”.Thesecondlayeris“这个过程是他们在英语课堂上需要经历的过程”.Thethirdlayeris“这个过程不仅包括阅读和写作，还包括他们的组成部分”.Thefourthlayeris“这个组成部分包括给文章加注释来帮助理解意思，以及使用例证来给与阐述。”Accordingtothemeaningofdifferentlayers,thetranslatordividestheEnglishsentenceintotwoChineseones.Inthisway,theoriginalmeaningisexpressedmoreclearandaccurateandthetranslationismorereadableandaccessibletoChinesereaders.4.2.2.4ComprehensiveMethodExample8:SourceText:Nextcamea“readingresponseprompt”thateachstudentansweredindividually,completewithremindersaboutthebestwaytoread—“markupthetextinthewayyouchoose,”theinstructionssaid,“includingtheuseofhighlightersandmetacognitivemarking”—andinstructionsaskingthestudentstowritequestionsoftheirown.TargetText:接下来是让每个学生独自回答的“阅读反应提示”（readingresponseprompt）。这些提示告诉学生可以自己选择最好的阅读方式，包括通过使用荧光笔及元认知标志在内的方式进行标注，以及指导学生写下他们自己的问题。It’salongandcomplicatedsentence.First,it’saninvertedsentence,whichmeans“areadingresponsepromptcame”.Second,thenextpart“eachstudentanswered…”isanappositiveclausetoexplainthe“responseprompt”.“Completewith”meansincluding—连15 同、包括.Therefore,thispartmeans“每个学生独自回答问题，包括提示学生可以自己选择最好的阅读方式”.Thenthesourcetextusesdashtoexplainthebestwaytoread,whichis“教学指导中说明的，通过使用荧光笔及元认知标志在内的方式进行标注”.Andthelastpart“instructionsaskingthestudents”isanotherpartof“completewith”,whichmeans“还包括教学指导要求学生写下自己的问题”.Atlast,throughanalyzingthewholesentence,ifthetranslatortranslatesitliterallyandsequentially,itisdifficultforreaderstounderstandandreaderswillbeconfused.Hencethetranslatorgraspsthecentralmeaningofthesentenceandtranslatesitfreely.Thefinaltranslationismoreeffectiveandreadable.4.2.3SolutionstoCoherenceoftheTargetTextAstherearemanyshortsentencesintheteachingcases,inordertotranslatetheteachingcasesvividly,thetranslationofsomeshortsentencesshouldbenoticed.Example9:SourceText:"You"resittingonyourbottoms,crisscrossapplesauce,"shesaid,warmly."Idon"twanttoremindyouagain.Thankyou."TargetText:她温和的说：“你们盘腿坐下，我不会再次提醒了哟。谢谢大家。”Example10:SourceText:Yetsomestudentsstillseemedconfused.BuildingonDanica’scomment,Oscar,theeagerboyintheback,hadproppedhimselfuponhiskneestoshareanidea.“Ifyouputitalittleup,andalittleup,”hesaid,motioningtoshowhowhecouldmovethetopandbottomsidesfartherapart,then,heexplained,“itwouldbelonger,becauseyou’reputtingitalittleupper.”Butwhiletherightandleftsidesthenwouldhavetogetlonger,thetopandbottomwouldbecomeshorter,hesaid.“Soareyousayingifweweretosquishthisshape?”Sabineasked,toconfirm.“Yeah,”hesaid,nodding.TargetText:不过，一些学生仍很疑惑。这时，后面那个很积极的男孩奥斯卡，接着达尼卡的观点，站起来与大家分享。他用手向大家展示如何让上下两边距16 离更远，解释道，“如果把这个正方形抬高一点，再高一点，正方形就会更长。因为你把它抬高了。但当左右两边变长时，上下两边就变短了。”萨拜恩跟他确认到，“所以你的意思是我们把这个正方形压扁？“对，就是这个意思”,他点头说道。Theabovetwoexamplesarebothfromtheteachingcases.Astherearemanydialogues,theselectedChineselanguageaswellastheexpressionsarelively,colloquialandeasytounderstand,suchastheabovedialoguestranslation.Furthermore,thetranslatornoticesthecoherenceofthecontexttomakethetranslationmoreaccessibleandletChinesereadershavethesamefeelingasnativereaders.InExample10,thetranslatornoticestheuseofassociatedwords,suchas“不过”,“这时”.Besides,therearrangeofwordorder(theboldedparts),theamplification(Yeah.→对，就是这个意思。)andomission（hesaid）ofsomewordsareallforthecoherenceandvividnessofthetargettext.Lastbutnotleast,thetranslationofthewholechaptershouldbecoherentinternally.Regardingthewholechapterasatranslationunit,logicalconnectioninitmustbeconsidered.Thetranslatormusttakeeachword’sorsentence’scontextintoaccount.Forthesakeofcoherenceoftheparagraphs,itiscrucialforthetranslatortonoticethechoiceofwords,suchassomelogicallinkers,thestructureofsentencesandtheexpressionofcentralidea.Forexample,therearesomeimportantwordswhichoccurrepeatedlyandtheconsistenttranslationofthemisamust,like“rigor—严谨”and“modeling—示范教学法”.Example11:SourceText:AmongthepracticesPamoutlinedwas“modeling”.TargetText:帕姆将英语教学练习总结归纳为“示范教学法（modeling）”。SourceText:Modelingworkedbestontextsthatresonatedwithstudents.TargetText:在引起学生共鸣的文本中，运用“示范教学法（modeling）”能达到最好效果。17 Chapter5Conclusion5.1LessonsThetranslatorlearntalotthroughthetranslationproject.Shehasmadegreateffortstoproduceagoodtranslationandsheknewthatlearningisanendlessprocess.Asuccessfultranslatormustbroadenhisorherhorizon,keeplearningandworkwith100%effort.First,backgroundknowledgeofthesourcetextiscrucialintranslating.Thetranslatormustreadmanyrelevantbooks,papersandjournals,surfonlineandaskteachersforadvicetoknowmoreaboutthebackgroundinformation.Second,skopostheory—theguidingtheoryofthetranslationreportshouldbetakenintoaccountinthewholetranslationprocessforthesakeofcohesionandcoherence.Ithasagreateffectonpointingoutthedirectionfortranslatorabouthowtoselecttranslationstrategiesandmethods.Third,bilingualcompetenceisamust.WhenreadingtheEnglishsourcetext,thetranslatormustgraspthemainideaandanalyzethesentencesskillfullyandaccurately.WhentranslatingEnglishintoChinese,thetranslatorshouldtransferwhatshehavelearnedfromthesourcetexttoproperChineseexpression.Hence,thetranslatorshouldreadmorebilingualbooksandpracticealot.Fourth,asasentencecanbetranslatedintodifferentversionsfromdifferentperspectives,thetranslatorshouldapplytranslationmethodsandtechniquesflexiblyinthetranslationprocesstomakethetranslationmoreacceptableandreadable.Lastbutnotleast,inordertogetabettertranslation,thetargettextshouldberevisedrepeatedly.Thetranslatorhadbetterreviseiteveryseveralweekstogetsomenewidea.Meanwhile,thetranslatorshoulddiscusswithherteachersandfriendswhoareexpertsinEnglishandeducation.5.2UnsolvedProblemsInthetranslationprocess,thetranslatormetwithalotofdifficultiesandobstacles,whichshetriedherbesttoovercome.ShehopeshertranslationwillhelpChinesereaderstoknowmoreaboutadvancedforeignteachingphilosophyandmethods.However,duetothe18 translator’sabilityandlimitedknowledge,someproblemsremaintobesolved.First,somevocabularytranslationmaynotbeaccurateenough.Second,astheunderstandingofthesourcetextisnotaccurateenough,theexpressionofthetargettextmaynotbeasclearandpreciseasthesourcetext.Therefore,thetranslatorwilllearnmoreanddomoretranslationpractice.19 ReferencesBarker,L.M.(2012).UnderDiscussion:ImprovisationalTheatreasaToolforImprovingClassroomDiscourse.PhDdissertation,StanfordUniversity.ChengZhaowei.(2006).AConciseCoursebookonTranslation.Beijing:NationalDefenseIndustryPress.Green,E.(2014).BuildingaBetterTeacher:HowTeachingWorks.NewYork:W.W.Norton&Company.Lampert,M.,&Graziani,F.(2009).InstructionalActivitiesasaToolforTeachers’andTeacherEducators’Learning.ElementarySchoolJournal,109(5),491-509.Lampert,M.etal.(2010).UsingDesignedInstructionalActivitiestoEnableNovicestoManageAmbitiousMathematicsTeaching.InM.K.Stein&L.Kucan(Eds.).InstructionalExplanationsintheDisciplines(pp.129-141).NewYork:Springer.Lemov,D.(2012).PracticePerfect:42RulesforGettingBetteratGettingBetter.SanFrancisco:Jossey-Bass.Lemov,D.(2010).TeachlikeaChampion:49TechniquesThatPutStudentsonthePathtoCollege.SanFrancisco:Jossey-Bass.Munday,J.(2008).IntroducingTranslationStudies:TheoriesandApplications.London:Routledge.Nida,E.A.,&Taber,C.R.(2004).TheTheoryandPracticeofTranslation.Shanghai:ShanghaiForeignLanguageEducationPress.Reiss,K.,&Vermeer,H.(1984).GrundlegungeinerallgemeinenTranslationstheorie.Tubingen:Niemeyer.Venuti,L.(2000).TheTranslationStudiesReader.London:Routledge.卞建华.(2006).关于翻译目的论相关问题的讨论.中国翻译，27(1),44-46.道格·莱莫夫.(2013).教无不胜.王佳佳译.上海：华东师范大学出版社.方梦之.(2005).英汉翻译基础教程.北京：中国对外翻译出版公司．郭建中.(2014).创造性翻译与创造性对等.中国翻译，35(4)，10-15.李长栓.(2012).非文学翻译理论与实践.北京：中国对外翻译出版有限公司.连淑能.(2010).英汉对比研究.北京：高等教育出版社.刘佳.(2012).功能目的论视野下的英汉长难句翻译策略.外交学院硕士学位论文.刘宓庆.(2012).文体与翻译.北京:中国对外翻译出版公司.孙致礼.(2003).新编英汉翻译教程.上海：上海外语教育出版社.叶子南.(2008).高级英汉翻译理论与实践.北京：清华大学出版社.原传道.(2005).英语“信息型文本”翻译策略.中国科技翻译,18(3),50-53.张培基.(2006).英汉翻译教程.上海：上海外语教育出版社.朱恒.(2015).语言的维度与翻译的限度及标准.中国翻译，36(2),5-10.20 AppendixISourcetextChapter9TheHolyGrailJesseSolomonwasespeciallytakenwithanideathatwasatthecoreofMagdaleneLampert"sfindingsaboutItaliaidea:theconceptofinstructionalactivities,orIAs.Thehardpartaboutgettingteacherstoteachatahighlevel,Magdaleneexplained,wasnottosacrificecomplexityforthesakeofaccessibility.Thiswasnotsodifferentfromthechallengeofhelpingstudentswhoknewverylittleaboutmathtoneverthelessgraspthebignessofit—gettingthemnotjusttomemorize,butalsotoreason,conjecture,prove,andunderstand.Itwasn"teasy,butwithawell-chosenproblemateachercouldmakethesubject"sbigideascomealive,eventolittlechildren.Thesameheldforteaching:focusononlythesimplerpartsofinstruction,andteacherswouldlearnonlysuperficialtechniques.Thetrickwastogetnewteachersteachingrigorouslyrightfromthestart.AtItaliaidea"strainingschool,aplacecalledDilit,teacher-educatorsdividedItalianteachingintofourteencoreinstructionalactivities.EachIAwaslikearichmathproblem.Evenabrand-newteachercouldtryitout,itcouldbeadaptedacrossanygradeorcompetencylevel,anditwasbothaccessibleandrigorous.TakeoneIA,called"ConversationRebuilding."Intheclassroom,theroutineresembledagameofcommunicationPictionary.Theteacherbeganbypantomimingaconversation,usingonlygesturesanddrawings.Shespokenowords.Then,lettingthestudentsspeakonlyItalian,sheinvitedthemtoimaginewhathadbeensaid.Whatwouldapersonorderingamealinarestaurantsaytogetthewaitertobringoverawinelist?Oncethelistarrived,howmightthepersonrespond,ifshestillwasn"tsurewhatshewantedtodrink?Asstudentsproposedhypotheses,theteacherhelpedsteerthemtowardanunderstandingofhowtheconversationcouldhaveactuallyproceeded.(Whenahypothesismadesense,theteachersignaledthatbyhavingthewholegrouprepeatit;whenitdidn"t,shesaid"excuseme,"mimedtheactagain,andgotthemtostartover.)Alongtheway,thestudentslearnednotjustnewvocabularywordsandgrammar,buthowtofeeltheirwayintothelanguage,tocommunicate.Steeringtheconversationdemandedacomplicatedsetofmaneuversforabeginningteacher,butDilitmadeiteasierbyspellingoutthestepsandhavingtheteacherstrythemout,firstwiththeprofessorandotherstudentsactingintheroleofstudents—theteacher-educatorthrowingoutcommonstudenterrors—andthenwithrealstudents.Duringrehearsals,Dilitteacher-educatorsgavelivesuggestionsinthemiddleofanactivity.Theyremindednewteachersnottoforgetkey21 piecesoftheIA,likealwaysmakingastudentrepeatacorrecthypothesis.Later,asthetraineeteachersbecamemoreadvanced,theylearnedtoanalyzestudents"thinking,ignorelikelydiversions,andguidestudentstowardincreasinglyaccurateresponses.Bytheendofasession,thewholegroupbegantochimein,givingeachotherremindersandsuggestionsabouthowtoproceed.BeforeshebeganworkinginBoston,MagdalenehadbeentryingtodothesamethingattheSummerLearningInstituteshehadbuiltinAnnArbor.IAs,shesaid,werelike"containers."Theyletnewteacherslearnwhattheyneededtoknow.Onepieceofthatlearningconsistedofpractices,theactionsrequiredtohelpchildrenlearn.Inthe"ChoralCounting"IA,forexample,teacherslearnedhowtoleadagroupofstudentsincountingaloudbyaparticularnumber(tens,say,ortwos);howtowritethesequenceontheboard(forinstance,usingcolumns,sothat,countingbytwos,2,12,22,and32wouldsitsidebyside,helpingthechildrenseeapattern);howtostopthecountatadeliberatelychosennumbertoaskaquestion,like"What"sthenextnumber?";howtohelpthestudentslookforpatterns;and,finally,howtofacilitateadiscussionleadingtothekeymathematicalidea.TheIAsalsoletnewteachersworkonthecoremathknowledgetheyneededtoteach—thestuffDeborahBallandHymanBasshadnamed"MathematicalKnowledgeforTeaching,"orMKT.(InChoralCounting,thisincludedanunderstandingofmathematicalpatterns,thecommonwaysstudentscometounderstandnumbers,andrepresentationsthatteacherscouldusetoadvancethestudents"understanding.)FollowingtheDilitmodel,theSummerLearningInstitutehadgroupsworktogetherbetweenrehearsalstogiveeachotherfeedbackandcontributeideasandtechniquestoimprovestudents"numbersense.Finally,theytriedtheIAswithlocalchildrenenrolledinthesummerprogram.JesseSolomonwantedtoincorporateIAsintotheBostonTeacherResidency.Withinayear,therestoftheBTRleadershadtraveledtwicetoMichigantowatchtheSummerLearningInstituteinaction.By2011,theyhadaskedMagdalenetocomeworkwiththemfulltimetoredesigntheentireBTRprogram.TheBostonprogramposedgreaterchallengesthanthesummerprograminAnnArbor.Residentswereplacedinsomeofthecity"smostdifficultschools,includingseveral"turnaround"schools,representingBoston"sportionofthecountry"sfivethousandworst-performingmiddleandhighschools.WhilethestudentsMagdalenehadworkedwithinMichiganwereraciallyandculturallydiverse,thestudentsinBostonweremorelikelytobeimpoverished,morelikelytobenewspeakersofEnglish,stilllearningthelanguage,andmorelikelytostrugglewithlearningandemotionaldifficulties(20percentofstudentsintheBostonpublicschoolsareclassifiedasneedingspecialeducation).22 Andyet,whentouringtheBostonschools,sittinginclassroomsthatwereoftenchaoticandunruly,Magdalenealwayshadthesamethought.Theproblemsshesaw,allthechallenges—theyweredifficult,buttheywerealsosolvable.TheBTRteachers,sheknew,couldgettheirstudentstolearn.Theyonlyneededtobetrained.So,whenJesseaskedhertoleaveMichiganandworkatBTRfull-time,Magdalenesaidyes.Twoyearslater,MagdaleneLampertfoundherselfstandinginthefirst-gradeclassroomofaBTRresidentnamedSabineFerdinand,holdingupaniPadtorecordalessonthatwouldhelpdeterminewhetherBTRwouldawardSabinethecertificationsheneededtoteachinMassachusetts.Technically,theclassroombelongedtoIleneCarver,afifteen-yearveteranteacher.Butoverthecourseoftheyear,Sabinehadtakenmoreandmoreresponsibility,becomingjustasmuchtheteacherasIlene,atleastintheeyesofthestudents.Thatday,shewasleadinganactivitycalled"QuickImages,"anIAadaptedfromthemathcurriculumusedthroughoutBostonelementaryschools.ThelessonbeganwithSabinecountingdown—"eight,seven,six,..."—asthestudentsarrangedthemselvesontheclassroom"srectangularrug,sittingonmaskingtapeX"swiththeirnameswritteninmarker."Three,two,one,"Sabinesaid,pausingpatientlybetweeneachnumber."Theexpectationisthatyou"reinyourrugspotwithyourpencil."Sabinesatintheusualteacherspot:thecornerclosesttothedoor,neartheplacewheretheclass"sclothcalendarhungonthewall."MARCH,"itsaid,countingoutthedaysinbrightredandwhite."You"resittingonyourbottoms,crisscrossapplesauce,"shesaid,warmly."Idon"twanttoremindyouagain.Thankyou."Thensheshiftedintotheworkofthemoment."Whohereremembersearlyon,whenweusedtodoQuickImages,withthedots?"Handsshotup.Onesquealingstudentgulpedandjumpedfromherbottomtoherkneesinglee.Theyreviewedtherules:Theteacherflasheseachimageonlytwice,andonlyverybrieflyeachtime.Aftereachflashoftheimage,thestudentswritedownwhatthey"veseen.Butwhiletheimageisup,theycanonlythink—nopencils.Onthisdaytheywereworkingongeometry,sotheimagesSabineshowedwouldn"tbedotstocount,butshapestodraw."Ready?"sheasked."One,two,three."Thestudentstookindeep23 breathsasSabineflashedthedrawing,rotatingitforeveryonetosee,VannaWhite-style.Aperfectsquareonawhitesheetofpaper.Afterthesecondviewing,shepinnedthedrawingtoaneaselonherleft."Allright,"shesaid."Somyquestionis,howcanwedescribethisshape?"Therewasanothershowofhands,butSabinewaitedpatiently,givingmorestudentsanopportunitytothink."Howcanwedescribethisshape?"sherepeated."Rafael?""Uhh,"Rafaelsaidthoughtfully.Hewasaheavysetchildwithabig,nervoussmile."It"sasquare."Sabinecouldhaveleftitthere—yes,asquare—andmovedontothenextshape.ButshecontinuedtoprobeasMagdalenewatched."WhoagreeswithRafael?"sheasked,holdingupamodelthumbtoherchesttosuggesthowstudentscouldsignaltheiranswer,upordown."Stephanie,"sheasked."Doyouhaveanythingyouwanttoaddon?Whatelse—howcanyoudescribeyourshape?"Stephanie,anenergeticgirlwhosatinaspecialchaironthesideoftherug,presumablytokeepherfocused,mulledthatover."Um,"shesaid,andthenannounced:"Itisnotlong!""Canyousaymoreaboutthat?"Sabineasked."What"snotlong?""Thesidesarenotlong,"Stephanieoffered.Malcolmhadhishanduptoo."Malcolm,whatdoyouwanttosay?"Sabineasked."Ithas"—hepausedtocount—"foursides!"Theyweregettingmorespecific,butSabinedecidedtheycouldsayevenmore."Now,"shesaid,"whatdowenoticeaboutthesesides?""They"remedium-sized,"offeredOscar,fromtheback."True,"shesaid."Danica,"shecontinued,turningtosomeoneelse,"whatdoyounoticeaboutthesides?""IwanttoaddontowhatOscarsaid,"Danicasaidthoughtfully.Magdalenetooknoteofherphrasing—herewasafirst-graderengaginginamathematicaldiscussion,intheclassroomofafirst-yearteacher.Itwasremarkable.Danicawenton."Theyarelarge,"shesaid,"butonthetopofit—theyarelarge—onthesides,they"reevenlonger."Danica"sdescriptionwasn"taccurate,ofcourse;theshapewasasquare,andsothesideswereactuallyequal.Butshewasthefirstintheclasstocomparethelengthsatall,andthatpulledthediscussioninanimportantdirection.Sabinerepeatedtheobservation,pointing24 tothedrawingontheboard:thesides,Danicawasarguing,wereevenlongerontheleftandrightthantheywereonthetopandbottom."Interesting,"Sabinesaid.Thestudentsweretreadingintosignificantmathematicalterritory,andatjusttherightdevelopmentalmoment.Bythespringoffirstgrade,thesestudentsclearlygraspedthedifferencebetweenbroadgeometriccategories,liketrianglesversussquares.Butgrapplingwithfinerdistinctions—thedifference,forinstance,betweenarighttriangleandanisoscelestriangle,orinthiscase,betweenarectangleandasquare—provedmoreofachallenge.Thechildren"sideassuggestedtheyhadsomeunderstandingofthedifference(therelationshipbetweenthesides),buttheywerestrugglingtodescribeit.Weretheleftandrightsideslongerthanthetopandbottomones,orweretheythesame?Thediscussionnowmovedintomoreimportantterrain:theshiftfromwhatthepsychologistJeanPiagetcalled“animism”—theideathatobjectshavetheirownconsciousnesses,likepeople,andsocanmoveandchange,ratherthanstayingstableandconstant—toamoreabstractunderstandingofasquareasacategorydescribingshapeswithfourequalsidesofunchanginglengths.Forchildrenstillthinkinganimistically,asquarewasnotasolidandpermanentfact,butanobjectthatcoulddecidetoexpandinanydirectionifitchosetodoso.NotlongafterDanica’smisguidedcommentaboutthesquare’slongerverticalsides,agirlnamedLuisamadetheobservationthattuggedtheclassinthecorrectdirection.Theshape,shesaid,actuallyhadfourequalsides.“Luisa,”Sabinehadasked,seizingtheopportunitytounderscoreanimportantpoint,“whywereyousuretosayequalsides?Whatdoesthatmean?”Clarifyingfortherestoftheclass’sbenefit,Luisahadrepliedthatequalmeant“thesameas.”Yetsomestudentsstillseemedconfused.BuildingonDanica’scomment,Oscar,theeagerboyintheback,hadproppedhimselfuponhiskneestoshareanidea.“Ifyouputitalittleup,andalittleup,”hesaid,motioningtoshowhowhecouldmovethetopandbottomsidesfartherapart,then,heexplained,“itwouldbelonger,becauseyou’reputtingitalittleupper.”Butwhiletherightandleftsidesthenwouldhavetogetlonger,thetopandbottomwouldbecomeshorter,hesaid.“Soareyousayingifweweretosquishthisshape?”Sabineasked,toconfirm.“Yeah,”hesaid,nodding.Onepurposeofstudyingmathinschool,Magdaleneknew,wastohelpchildrenwrestlewithjusttheideasOscarwasworkingon.Couldsquaresreallysquishthemselves?Orweretheymorestablethanthat?“But,”SabineaskedOscar,“whatdidLuisatellusaboutthisshape?Malcolm?”25 “Shesaidit’sfourequalparts,”Malcolmsaid.“Equalparts,”Sabinerepeated.“Equalsides.”Asamoreexperiencedteacher,MagdaleneknewthattherewereotherwaysSabinecouldhavehelpedthestudentsworkontheseideas.Togetthemclosertograspingthedistinctionbetweenarectangleandasquare,forinstance,shecouldhaveusedDanica’sincorrectobservationaboutthesidesasanopportunity.“Icouldhavepulledoutapictureofarectangleandsaid,‘Arethesethesameoraretheydifferent?Inwhatwaysaretheythesameandinwhatwaysaretheydifferent?’”Magdalenesays.Butthatkindofresponsetakeslongertocultivate(startingwithlearningtorecognizewhatallthisstrangesquishingwasabout—nosimplething),andshedidn’texpectafirst-yearresidenttofigureitoutonthefly.WhatSabinewasdoingwasexactlywhatMagdalenehopedfor.Usingaroutineshe’drehearsedmanytimesbefore,shewasabletokeepthestudentsfocused—and,atthesametime,tolistentotheirmath.Herpreparationhadhelpedherlearnnotonlywhattodo(thestepsofchoralcounting)buthowtomakesenseofthemaththestudentswereworkingon.Asaresult,shehadgottenthekidsthinkingaboutfundamentalconceptsingeometry,andwhenwrongideasarose,shedidn’tjustswatthemaway;sheputthemonthetablefortheclasstoprobe.Ultimately,shehadmanagedtoelicitthepivotalideaaboutfourequalsidesfromLuisa.SowhenOscarbroughtuphisanimisticideathattheshapecould“squish,”SabinecouldholditoutagainstLuisa’smoresophisticatedconjecture,helpingOscartoreconsiderwhatitmeanttobeasquare.Evenifthestudentsdidn’tendthatparticulardiscussionfullygraspingthedifferencebetweenarectangleandasquare,orthedifferencebetweenanabstractshapeandaliving,elasticobject,theyhadmadeimportantprogress.“They’restrugglingwithafundamentalconcept,andtheyshouldbe,”Magdalenesaid.Itwasmorethancouldbesaidofmanyfirst-gradeclassrooms.Itwasexciting.Later,aftertheyfinishedtheQuickImagesIA,Sabineintroducedaproblemaboutaddition.Sheshowedthestudentsapuzzleandthengavethemachartthattrackedtheblocksshe’dusedtocompleteit—“twohexagons,zerotrapezoids,onebluerhombus,zerosquares,threetanrhombuses,andsevengreentriangles,”shereadoutloud.Nowtheirchallengewastofindthetotalnumberofblocks.MagdaleneknewSabinehadselectedthenumbersdeliberatelytoadduptoasumgreaterthan10(13).They’dbeenworkingonmorecomplicatedmethodsofaddingnumbers,like“countingup”fromthelargestnumberorbreakinganunfamiliarproblemintofamiliarpartsorusinganumberlinetoskipfromonenumbertothenext.Aproblemwithasolutionlargerthan1026 wouldnudgethestudentstotryoutthenewmethodsforthemselves,ratherthanusingtheonethatmanyofthemstillpreferred:countingontheirfingers.Indeed,justasSabinehadhoped,thestudentswalkedthroughallkindsofnovelcombinationsofthemethodsthey’dbeenworkingon.Magdalenewatchedasonegirl,lyingonherstomach,wroteouttwonumbersentences—3+3=6and6+7=—andthenfilledintheemptyboxbystartingwith7andthendrawing6lines:Shecaughtanotherstudentwritingoutdifferentsetsofnumbersentences:Anotherstudent,Faith,tookasimilarapproach.“Thatisverycool,”Magdalenetoldher,asFaithshowedoffwhatshe’ddone:Later,asthelessonmovedfromindividualworktimetogroupdiscussion,SabineinvitedaquietboynamedKevintosharehisstrategy.“Ididthreeplussevenequalstenandthen—”hebegan,beforeSabineinterrupted.“Howdidyouknowthatthreeplussevenequalsten?”sheasked.“BecauseIknewmycombinationsoften,”Kevinreplied.“Sothreeandseven’sjustanothercombinationoften,”Sabinerepeated,turningtotherestofthestudentstomakesurethey’dunderstoodKevin’sstrategy.“Soyoucanusewhatyoualreadyknowtohelpyoufigureoutthisproblem.Soheknewthreeplussevenequalsten.”SheturnedbacktoKevin.“Goon.”27 Kevindescribedhisnextstep.Hewasleftwith2and1,andheknewthat2+1=3,soheaddedupthetwofinalsums,10and3.“Andyougot?”Sabineasked.“Thirteen,”hesaid.Sabineaddedthattotheboard,whereshewaschroniclingeachstudent’ssteps:Butbeforeshecouldsummarizetheimportantpoint—onceagain,Kevinhadusedacombinationhealreadyknewtofindthefinalsum—anotherboyblurtedoutanideafromthecarpet.Earlier,he’dbeensquirmingandtalkingoutofturn.ButnowhewasinterruptingwithanobservationaboutKevin’sstrategy.“Ifyoutakeawaythezero,”hesaid,pointingto10,“andputthethree,it’sthirteen!”SabinelookedatMagdalene.Acommoncourseforyoungchildrenwastosee“3+10”andmistakenlyaddthethreeandonetogether,sincetheoneisclosesttothethree,getting4.Then,notknowingwhattodowiththezero,andnotfullygraspingthedifferencebetweenthetensandtheonesplaces,theywouldwriteazeronexttothefour:3+10=40.Thisboy,stilljustafirst-grader,hadleaptheadfirstintothecorrectidea:threeonesandonetenmeantthatthethreecouldeffectivelyreplacethezero:13.Hehadintuitedplacevalue.SabineandMagdalenesmiledateachother.“Iseewhatyou’resaying,Sabinetoldtheboy.Andtheclassmovedon.JesseSolomonwasn’ttheonlyentrepreneurtoseekhelpfromtheacademics.HeatherKirkpatrick,aleaderattheAspirecharternetworkinCalifornia,cametotheLearningtoTeachsummitfocusedonthesameproblemastheothers.“Welookedsogoodonpaper;wewerekindofkillingit,”Heathersays.“Butweallfeltlike,jeez,whenwewalkintotheclassroom,we’renotwherewewanttobe.”Whattheywantedwasrigor—morespecifically,somethingtheycalled“academicdiscourse.”Tothem,discoursemeantfourthings.First,adultscouldn’tdoallthetalking(andthereforeallthethinking).Second,thestudentshadtotalkabouttheacademicideaathandand,third,theyhadtotalkusingacademicvocabulary.Finally,theyhadtodowhatAspirecalled“bringingevidencetobear”—quotingthetextinEnglishclass,citingaprimarysourceinhistory,reasoningthroughaproofinmath,pointingtoexperimentalevidenceinscience.28 “Itwasthosefourthings.Andwesaidweshouldbeabletoseethatinmath,science,Englishlanguagearts,history.Thatistheholygrail,”Heathersays.“Thenwesaid,okay,howdowegetthere?”HeatherwasstrugglingwiththisquestionwhensomeonesuggestedshetalktoPamGrossman,aprofessoratStanford’sedschoolandoneofLeeShulman’sfirststudentsafterLeeleftMichiganStateforStanford.PamhadcometogradschoolafternearlyadecadeofteachinghighschoolEnglish.DuringhertimeatStanford,Leedispatchedagroupofhisstudentstostudytheteachingofindividualacademicsubjects;PamselectedEnglish.Overtime,shecametothinkofLee’sstudentsinfamilyparlance.WithLeeastheirsharedmentor,DeborahBallandtheotherswerelikePamGrossman’sacademic“cousins,”workingonthesamequestions,justatdifferentuniversitiesandindifferentsubjects.TherewasoneotherdifferenceforPam:insteadofexperimentingwithherownteaching,shestudiedotherteachers’work.Oneepisode,caughtonvideotape,showedsevenstudentsatastrugglingurbanhighschoolinSanLorenzo,California,discussing“TheYellowWallpaper,”theshortstorybyCharlottePerkinsGilman.Theirteacherwasnotvisibleinthevideo,butthestudentscarriedonasifhewasrightthere,pagingthroughtheXeroxedstoryinfrontofthemandevencallingoneachothertospeak.“Whatdoyouhavetosay,Jim?”ablondegirlnamedAmywasaskingtheboyacrossfromherwhentheclipopened.“Myinterpretationofthis,”Jimsaid,“goesbacktowhatMs.McWilliams”—hisstudentteacher—“saidbeforeweevenreadthestory,abouthowitgaveherchills.”Jimworeglassesandhadaknackforthetheatricalpause.“Andactually,myinterpretationofthisisthatshewasdeadfromtheveryendofpagethirty.”Theotherstudentslookedupfromtheirpapers.Thestory,writtenasaseriesofdiaryentriesbyawomansufferingfromanxiety,usedtheworddeadonlyonce,andthatwastodescribethepaperonwhichthewomanwroteherdiary.Butwhilethediarydidchroniclethewoman’sworseningconditionafterherhusband,aphysician,orderedthatsheisolateherselffromworkandsociety,itnevermentionedthatthewomanwasnotalive.NowJimwassayingshe’dbeendeadsincepagethirty.“What?”onestudentasked.“Thatwholeconversation”onpagethirty,Jimcontinued,“theverylastlinesays,‘Iamsecurelyfastenednowbymywell-hiddenrope—youdon’tgetMEoutintheroadthere!’”Thelinedescribedhowthenarrator,afterfeelingtrappedbehindthewallpaperofherisolatedroom,hadusedaropetoescapeit.Jimcontinued,“Ithinkatthatpoint,she’sdead.ThisishertalkingtoJohn”—thenarrator’shusband—“asaghost.”29 “Ah!”exclaimedJade,agirlindenimwhohadbeenlisteningquietly,withoneeyeonthepageandanotheronJim.Sheboltedup,puttingahandoverhermouth.Thegirlnexttoher,Sariah,hadhermouthwideopentoo.“She’sfreeinthehouse,”Jimwenton,“butsheisnever,like,free—”“—OUTSIDEOFTHEHOUSE!”JadeandSariahshoutedinunison,astherestofthegrouptalkedovereachotherinanexcitedrush.ButAmy,theonewhohadcalledonJiminthefirstplace,wasn’tbuyingJim’sidea.“Sothen,wait,wait,”shesaid.Shepointedtoanotherpassagethatdidn’tseemtofitJim’sstory.Thelineaboutthe“securelyfastened”ropewasprecededbyanother,speculatingthatotherwomenmighthavemadethesameescapeasthenarrator,fleeingfrombehindtheroom’soppressivewallpaper.“Rightthere,”Amysaid,“itsays,‘IwonderiftheyallcomeoutofthatwallpaperasIdid?’”HowdidthatdescriptionjibewithJim’sinterpretation?“Doesthatrepresentthepeoplewhodiedjustbeforeher,orsomething?Otherpeoplewho’vedied?”AfewstudentsattemptedanexplanationbeforeJimspoke.“Iwonderifitsortofrepresentssociety,”hesaid.“Becauseshe’sfreeingherself,andshe’swondering,arealltheotherwomendoingthistoo?”“Soherwayoffreeingherselfwaskillingherself,”Amyreplied,repeatinghispoint.Youcouldconnectthetwopassages,Jimwassaying,byinterpretingallthewomen’sescapesfrombehindthewallpaperassuicides.SoonJadehadaquestion.“Butwhataboutthishouse?”sheasked.“Thishouse!Thishouse!Thishousehastorepresentsomethingtoo.”Amytooktheopportunitytoofferherowninterpretationofthestory.“Maybe,”shesaid,“maybethehouseandtheareacanrepresentlife,right?Therearepartsoflife,placesinlifeyouwanttogo,thingsyouwanttodo,right?Shewastalkingaboutthatoneroomshewanted,butherhusbandsaidno.”Jadenodded.Shewaspersuadedbythisinterpretationtoo.“Thedifferentroomscouldbedifferentlifestyles!”shesaid,jumpingin.“Ordifferentthingsshecanorcannotdo,”Amysaid.“Or,”Jimsaid,quietly,“differentpartsofherlife.”“Yeah,”Amysaid,pointingathimwithherpencilandnodding.Theyhaddifferentinterpretations,buttheywereonthesamepage.ThevideoshowedjustthekindofconversationHeatherandherteamwantedtocultivateatAspire—apristineexampleof“academicdiscourse.”Theteacher,PeterWilliamson,mightnothavebeenonthescreen,but,asPamexplained,hisworkwasalloverthelesson.More30 specifically,hehadsetthestudentsuptohaveaproductivediscussion,firsthavingthemwriteouttwotypesofquestions,literalandinterpretive;thenhavingthemgooverthequestionswitheachother,gettingfeedbackonhowtoimproveonthem;andfinally,afterthey’dfinishedtalking,leadingadebriefingoftheconversationcenteredonhowtheycouldhavegottenevenmoreoutoftalkingtoeachother.(ThatwasonereasonPeter,wholaterbecameaprofessorofteachereducationattheUniversityofSanFrancisco,hadvideotapedthesession—sothatthestudentscouldwatchitandthinkaboutwhattodobetternexttime.)AndthesestepswereonlywhatPeterhadtodotoprepareforthesingle“YellowWallpaper”lesson.Ithadtakenhimmoreworktogetthestudentstothatpoint.Eventually,PamandhergraduatestudentsbrokethepracticeofEnglishteachingdownintokeyparts—“corepractices,”Pamcalledthem,anEnglishcounterparttoMagdalene’sinstructionalactivities.AmongthepracticesPamoutlinedwas“modeling.”ThiswasacorepartofthebestEnglishteachers’repertoire,awayofwalkingstudentsthroughtheprocessestheyneededtoperforminEnglishclass—notjustreadingandwriting,buttheircomponentparts,likeannotatingatexttohelpunderstanditsmeaningorusingevidencetoconstructanexplanation.Toteachstudentseachpart,ateachernotonlyhadtowalkthemthroughwhat,forinstance,anannotationlookedlike(herearemyhighlights!)orshowthemanexplanation(thissentencerighthere!);shealsohadtobreaktheactivitydownintoitsinvisiblementalsteps.Pamcalledthis“makingyourthinkingvisible.”Modelingworkedbestontextsthatresonatedwiththestudents.Evenbetter,theteachercouldusethestudents’ownwork.Forinstance,ateachermighttakethedraftofastudent’spersuasiveessayanduseittomodel,say,thewritingofexplanations,walkingstepbystepthroughtheevidenceandnarratinghowawritermightthinkaboutusingthatevidencetosupportapoint.“‘Sowhat?’isthequestionIneedtoask,”theteachercouldtellthestudents.“Andmyanswershouldtellyou...oh,that’swhythisevidenceissoimportant!”AnothercategoryinPamGrossman’staxonomyofEnglishteaching,“classroomdiscourse,”helpedteachersworkwithstudentsontheirideas.Aclassroomdiscussionshouldn’toperateasafloatingalternatereality,theentertainmentbeforetherealworkbegins.Attheirbest,discussionswerethefirststepinthewritingprocess,verbaleditingsessionsinwhichstudentsworkedtogethertosharpentheirideas.Whatdidthetextliterallymean?Whatdiditmeansymbolically?Ifthediscussionwentwell,then,bytheendofthelesson,aclassroomfullofblandobservationswouldtransformintothirtywellarticulatedinterpretations.WhenPamstartedgradschool,scholarsofEnglishteachinghadwrittenabouttheimportanceofdiscussioninaliteraryclass.StudyingAmericanclassrooms,theyhadalsodiscoveredhowrareitwas.Butfewhadthoughtabouthowtohelpteachersdomoreofitanddoitbetter.Pamandherstudents“decomposed”discussion,breakingthepracticedownintoteachableparts.31 Whattheyfoundwasthatgreatdiscussionsdidnothappenbyaccident.Theyrequiredserious,deliberatepreparation.OneteacherwhosepracticePamstudied—YvonneDivansHutchinson,whotaughtintheLosAngelesUnifiedSchoolDistrictatahighschoollodgedbetweentheneighborhoodsofWattsandCompton—handedherstudentsdetailedlistsofwhatshecalled“stockresponses,”possiblewaysofparticipatinginadiscussion,includinghalfadozenalternativestoashrug:•Youdon’tknowtheanswer?Trysaying,“Idon’tknow,butIwilltrytofindouttheanswerandgetbacktoyou.”•Youdidn’tcomepreparedtotalk?“IregrettosaythatIamIamnotprepared.”•Youdidn’tunderstandthequestion?Justask,“Wouldyoupleaserepeat(orrestate)thequestion?”•Youdidthehomeworkandunderstoodthequestion,butstillcouldn’tcomeupwithananswer?Howabout,“Pleasecomebacktome;I’mstillthinking.”Thestockresponsesmightseemforced,butwithoutthemtherewasnoguaranteestudentswouldtalkatall.“You’renotbornwithagenethattellsyouhowtotalkaboutBeloved,”Pamsays.“Actually,that’ssomethingyoulearntodoovertime,andtherearethingsthatteacherscandotomakekidssuccessful.”Yvonnealsowroteoutsuggestionsforwaysofmakingacontribution.Todisagree,firstsayso:“Irespectfullydisagree.”Thengiveyouropposingidea—“andjustifyit.”Toagreeandthenextend,say,“Iwanttoaddtowhat(person’sname)said.”Otherrulesaddedtotheclass’sdiscursiverepertoire.Tomakesureawidevarietyofstudentsspoke,andtoincreasethelikelihoodofgettingananswer,Yvonnetookadvantageofpeerpressureandhadstudentscalloneachother.Askedforaresponsebyapeerratherthantheteacher,shefound,teenagersweremorelikelytocomply.Shealsopreparedforthecaseofastudentwithnothingtosay.Sheoftenremindedherclassestopause,givingthestudentsYvonnecalled“reticent”moretimetoputtheirthoughtstogether.Andthroughhermodeling,thestudentslearnedhowtocoacheachothertoo,coaxingcontributionsfromeventhequietestpeers.Thatwasjustthebeginning.InYvonne’sclass,everydiscussionbeganwithan“anticipationguide,”alistofquestionsdesignedtogetthestudentsthinkingaboutsubjectscoveredinareadingbeforetheybeganit.Nextcamea“readingresponseprompt”thateachstudentansweredindividually,completewithremindersaboutthebestwaytoread—“markupthe32 textinthewayyouchoose,”theinstructionssaid,“includingtheuseofhighlightersandmetacognitivemarking”—andinstructionsaskingthestudentstowritequestionsoftheirown.(InYvonne’sclass,evenquestionshadacarefultaxonomy,frombasicfactual“rightthere”questions[levelone]to“global”questions[levelthree]thattookatext’ssubstanceandexpandedbeyondit;foroneprompt,thestudentsweretowritetwolevel-onequestions,threeleveltwos,andoneortwolevelthrees.)Finally,intheminutesbeforethewhole-groupdiscussion,theyheldminiconversationsinsmallgroups.“Iftheycometotheworkwiththeirownframeofreference,thenthey’remuchmoreapttobeengaged,”Yvonneexplained.Theplanninggotthestudentstothestartingline,buttopulloffalivelyandproductivediscussion,Yvonnehadtoteachinthemomenttoo.Pamandanotheroneofhergradstudents,LisaBarker,usedvideosfromYvonne’sclassandotherstofurtherbreakdowntheartofleadingadiscussion.Drawingonatermcoinedbyearlyscholarsofclassroomdiscussions,PamandLisacalledoneofthepracticesYvonneoftendeployed“uptake.”Ateacherpracticeduptakewhenshelistenedtoastudent’scontributionandthenrepeateditinsomeway,bysummarizingtheidea(Soherwayoffreeingherselfwaskillingherself),elaboratingonit,orpushingthestudenttodothesame.WorkingwithPam,Lisabrokedown“uptake”intoninesubparts,whichteachersusedatdifferenttimes.“Restatement,”thesimplest,involvedsummarizingastudent’sclaim,butthistimeaddingacademiclanguage,suchasbettergrammarormorepreciseterminology.“Revoicing,”asubsetofrestatement,summarizedastudent’scontributionfortheevenmorespecificpurposeofaligningitwiththeparticularsideofthediscussionitbelongedto—AmyisclarifyingJim’sstatementabout“freeingherself”inordertosupporthisinterpretationthatthewomanisaghost.Othermoveshadtheteacherdirectlypushingstudentsforbettercontributions.A“challenge”moverespondedtoaclaimbytakingtheoppositestance,justforthesakeofargument.“Press”askedthespeakerformoreinformation—evidenceofaclaim,maybe,orclarificationofmeaning.“Post”heldupastudent’sclaimandsolicitedcommentsonit—WhothinkstheycanarticulatewhatJimistryingtosay?NotonlyhadPeterWilliamson,theteacherwhoassigned“TheYellowWallpaper,”masteredclassroomdiscoursehimself;hismasteryservedasamodelforhisstudents,whouseduptaketodiscussthestoryontheirown.Amyknewtoaskforclarification;JadeknewtorepeatJim’sclaimtomakesuresheunderstooditandtopresshimtoelaborateontheideawhenshewantedtochallengeit;andattheend,whenAmyputforwardherowninterpretation,Jimknewhowtouse“uptake”tobuildontheidea,listeningasshedescribedthehouse’ssymbolicmeaningandthenhelpingherburnishherexplanation.Theroomsrepresentednotjust“differentthingsshecanorcannotdo,”but“differentpartsofherlife.”33 HeatherKirkpatricklovedPeter’svideo.ShetalkedwithPam,andinnotime,PamandLisawerecomingtoAspiretoteachasessionatitssummerretreat.Onewaytothinkaboutwhattheacademicsofferedtheentrepreneurswas“content.”WhereastheentrepreneurslikeDougLemovlookedatteachinggenerically,acrossallkindsofsubjects,MagdaleneLampertlookedonlyatmathandPamGrossman,onlyatEnglish.Butjustasimportantastheircontentknowledge,andmaybemoreso,wastheacademics’theoryoflearning.Ironically,thiswasalegacyofthesameacademicstructurethathadoncehinderedresearchonteaching:thecloserelationshipbetweeneducationresearchandpsychology.Itwastrue,asLeeShulman’spredecessorNateGagehaddiscovered,thatthescienceofteachingwasnotsimplytheinverseofthescienceoflearning.Butthecorollarywasalsotrue.Itwasn’tpossibletounderstandteachingwithoutunderstandinglearning.Perhapsunintentionally,thecharterschooleducatorshadadoptedalinearmodeloflearning.Learners,theyassumed,startedwiththebasicfluencyskillsneededtodowhattheycalled“higher-order”work.Inmath,thatmeantmemorizingthemultiplicationtablesbeforeworkingonproblemsolving;inEnglish,itmeantmasteringsimplevocabularywordsbeforelearningtoconstructanargument.Theythoughtoflearningasifitwerearchitecture:afantasticdesignwasnothingwithoutthematerialstobuildit.Somethingcomplexandbeautifulcouldnotbeaccomplishedwithoutfirstmasteringthemundane.Theideathatfactslaidthefoundationforconceptsyieldedabasicallybehavioristtheoryoflearning.Iflearningbeganwithfacts,andfactsbeganwithmemorizing—becausememorizing(or“fluency”)wasseparatefromconcepts(“criticalthinking”)—thenthebestmethodtoteachchildrentolearnwasnotsodifferentfromwhatEdwardThorndikehadhopedtoaccomplishwithhiscats.Practice,practice,practice,withregularpunishmentandrewards.The“rigor”couldcomelater.Theresultingteachingstylewasespeciallyclearinthehandlingofmistakes.Inabehavioristmodel,everymistakeshouldbegreetedwithaquickandfirmcorrection.Otherwise,studentswon’tlearnthatanideaiswrong.Thebestcharterschoolteacherstookthismaximseriously.Onemathteacher,heraldedasoneofthebestintheKIPPnetwork,decidednevertogivehisstudentschancestopracticeproblemsathomesthattheyhadn’talreadybeentaughthowtosolve.Thedanger,heexplained,layinthelikelihoodthat,aloneathomewithouttheteachertostopthem,theywouldpracticedoingthestepswrong.Absentaresponsethatcorrectedorapprovedthestep,themistakemightbeingrainedinthecategoryofuncorrected,andthereforeaccurate,truths.34 SeveralofthetechniquesinDougLemov’staxonomy(forexample,“DoItAgain”)restedonthisbelief.Teachingbehavior,intheworldofthetaxonomy,oftenboileddowntotheimperativeofrespondingtoeveryvisiblemisbehavior.Ateacherwasboundtogiveaswiftandclearcorrectiontoeverymistake.Dougappliedtheideatoteachingacademiccontenttoo.Writingabouthowtoteachchildrento“decode,”theworkofdecipheringastringoflettersintoapronounceableword,heemphasizedtheimportanceoflettingnoerrorgounnoticed.“Giventhebedrockimportanceofdecodingateverylevel,”hewrote,“teachersshouldstrivetocorrectdecodingerrorswheneverpossible,nomatterwhatsubjectorgradeleveltheyteach.”“PunchtheError”wasthenamehegavethetechniqueofnotifyingastudentswiftlyofhermistake.ButbythetimePam,Deborah,andMagdalenestartedtheirstudyofteachinginthe1980s,researchhadbeguntoshowthelimitsofthisbehavioristview.Learningamonghumans,psychologistswerediscovering,wasmorethanjustasumofexperiencedstimulus-and-responseyes-nopairs,andconceptsdidn’twaitforfactstoaccumulate;thetwowereenmeshedtogether.Thebestmemorizers,forinstance,succeededbyembeddingtheirobjectofstudywithinamoreabstractmapofbigideas.Onepsychologist,studyingacollegestudenthecalled“S.F.,”foundthatthestudentcouldmemorizelongstringsofnumbersonlybyattachingthedigitstoothersthatheldmoremeaning.Acompetitiverunner,S.F.translatednumbersintoracetimes;3492,forinstance,became“3minutesand49point2seconds,nearworld-recordmiletime.”Just3.492wouldn’thavebeenenough;healsohadtoplacethenumberinacontextthatmadesensetohim.Afterayearandahalfofusingtheracingmnemonic,thenumberofdigitsS.F.couldmemorizehadgrownfrom7to79.Theonlycaseswherehestumbledwerenumbersthatsimplycouldn’tbemappedbacktoamemorablerace.Children,similarly,learnedtoaddandsubtractthroughstrategiesthatbuiltontheirintuitivesenseofnumbers,notwhattheirteachertoldthemwascorrect.LiketheBrazilianstreetchildrensellingfruit,whomanagedtomakemultidigitcalculationsintheirheads,theycounted,grouped,andregroupeduntiltheyarrivedatasolutionthatcorrespondedtowhattheyknewabouthownumbersworked.Humansappearedtopracticethisreasoning—“criticalthinking”or“rigor,”theentrepreneurialeducatorsmightcallit—practicallyfrombirth.Inexperimentafterexperiment,psychologistsstudyinginfantsshowedthattheylookedattheworldnotviaasystemofrewardsandpunishments,butthroughawebofgeneralizations,rules,andprinciplesderivedfromobservations.Inoneexperiment,psychologistspushedabluecylinderdownarampuntilithitatoybug.Theirsix-and-a-half-month-oldsubjectswatchedasthebluecylinderpropelledthebugforward,sothatittraveledallthewaytothemiddleofahorizontaltrack.Thentheresearchersrolleddowntwomorecylinders,alargeryellowoneandasmallerorangeone.Predictably,thelargeryellow35 cylinderknockedthebugfartheralongthetrack,allthewaytotheend.Buttheorangecylinder,althoughsmallerthanbothoftheothercylinders,neverthelessmovedthebugtotheendofthetrackaswell.Presentingthesamestrangeeventstoadults,researchersfoundthattheyreactedwithsurprise.Butwouldinfants,whohadneverbeentaughtthelawsofphysics,dothesame?Theydid.Shownthesurprisingcaseofthesmallerorangecylinderthatknockedthetoybugfartherthanmadesense,infantsstaredlongerthanacontrolgroupofinfantsshownasequenceofeventsthatdidnotviolatephysics.They’dbeenonEarthforunderayear,andcertainlyhadneverbeengivenagoldstarforknowingthatlargercylindershavegreatermassthansmallerones.Butaftertakingintheworld’sdata—allthetimesthatlargeobjectspushedthingsfartherthansmallerones—theyhadcomeupwiththeabstractmentalmodelthatmadesense.Thetakeawaymessagewasnotthatconceptualunderstandingismoreimportantthanmemorization;itwasthatthetwoareinextricablyenmeshed.Anysupposeddichotomybetweenthemwasfalse.Magdalenesummarizedthelessoninasinglephrase.Children,shesaid,were“sensemakers.”Likethebabiesstaringatthecylinders,theytookindataandreasonedaboutit,workingfromtheirownevolvinggraspofhowtheworldworked.Educatorswhoimaginedotherwise—assuming,forinstance,thatmemorizationtookplaceoutsidethecontextofconceptsandprinciples,orthatrepeatedrewardsandpunishmentswereenoughtohelpapersonlearn—didsoattheirownperil.Childrenwouldtrytomakesenseofrules,evenrulesthatmadenosense.Then,whenviolationsinevitablyarose,theywouldapplytherulesanyway,astheCaliforniateacherwhooveremphasizedsubtractionwithregroupingfoundwhenherstudent,toldoftheimportanceofborrowing,begandoingsooneveryproblem,nomatterwhatsizethebottomnumberwas.MagdaleneandPamandDeborah’skindofteaching,TKOT,wasmoreacademicallyrigorousnotbecausetheirproblemswereharder,ortheirexpectationshigher,ortheirgradingcurvesteeper,butbecausetheirvisionoflearningwasmorerefined.Notonlyhadtheyreadthegeneralresearchonlearning.Theyhadalsostudiedthespecificrulesof“knowing”—theepistemology—fortheindividualsubjectstheytaught.Eachfieldhaditsownspecializeddefinitionofwhatitmeanttoknowsomething—oftheway,inmath,conjecturesbuilttoproofs,or,inliterature,evidencebecameexplanationandfinallyinterpretation.Becausethedefinitionswerenotallthesame,neitherwastheteachingtheyarguedfor.Inmath,forinstance,the“You,Y’all,We”lessonpatternpopularizedinJapan(aswellasinMagdaleneandDeborah’smathclassrooms)madesenseforstructuringinvestigationsofbigideas,likethemeaningoffractionsornegativenumbers.InEnglish,meanwhile,wherestudentsneededtolearnspecificreadingandwritingstrategies—howtofigureoutthemeaningofanunfamiliarword,forexample,orhowtobuildideasforanessay—the“I,We,You”patternofmodeling36 followedbyguidedpracticewasmoreappropriate.Andwithineachsubject,differenttopicscouldcallfordifferentstructures.Drawingontheseveryspecifictraditions,Magdalene,Pam,Deborah,andtheircolleagueshadaneasiertimeachievingtheacademicrigorthatthenoexcusesteachersalsolongedfor.Theytaughtbyhelpingstudentsseetheworlddifferently,pushingtheirintuitiveknowledgeclosertothebankofunderstandingsandrulesofoperationthatmathematicians(andscientists,historians,literarytheorists,andsoon)havearrivedatovercenturies.Teaching,inthisview,beganwithlistening.“Partofinteractingwithkids,”Magdalenesaid,“isassessingwheretheyareandthinkingaboutwhatexperiencesyoucangivethemthatwillchallengetheirwayofseeingtheworld.”ThedifferentapproachtolearningalsoledMagdalene,Pam,andDeborahtotakeadifferentviewofchildren’smistakes.InTKOT,mistakeswerenotworrisomeillstostampoutonsight,butpreciousopportunitiestobeginthelongerprocessofcorrectingmisunderstandingsovertime.Onepurposeofteaching,intheirview,wastodrawoutmistakes.ThebestEnglishteachers,Pamsaw,helpedchildrenwritebetterbyshowcasingrealexamplesofstudentwritingthatneededwork—andthen,holdingweakmodelsupagainstthestrong,bydescribingexactlywhatstudentscoulddotoimprove.MagdaleneandDeborah,similarly,builttheirproblemsofthedayaroundthegoalofelicitingmisunderstandingsthatcouldmovetheclasstowardmoreaccurateideas.SomeJapaneseteacherstookthisnotionevenfurther.InJapan,theportionofthelessonthatMagdalenecalled“teachingwhilestudentsworkindependently”actuallyhadtwocompetingnames:kikan-shidoandkikan-junshi.Thefirst,kikan-shido,describedtheactofobservingstudents’effortstosolvetheproblemofthedayand,whennecessary,interveningtoresolvetheirconfusionbyofferingahintoranextrainstruction.Butthesecond,kikan-junshi,adoptedbyacontingentofpurists,describedobservingwithoutcomment.Whenastudentmadeamistakeorbecameconfused,theteachersimplynotedtheerror(maybeonapadofpaperormaybejustinherhead),nodded,andwalkedonby.AnEnglishtranslationclarifiedthedifference:kikan-shidomeant“betweendesksinstruction,”whereaskikan-junshimeant“betweendeskspatrolling.”Studentslearnedbetterwhentheysawtheerroroftheirideasontheirown,thekikan-junshipuristsfelt.Andtheteachermadesuretheydidseeit,inthecourseofthe“We”partofthelesson,thegroupdiscussion.Inthisregard,DougLemovseemedconflicted.Ononehand,asthe“PunchtheError”techniqueexemplified,muchofhistaxonomywasbuiltaroundtheeradicationofmistakes.YetDougalsowroteabouttheimportanceofmakingclassasafespaceforerrors.Indeed,“NormalizingError”wasTechniqueNo.49,thelastoneinthetaxonomy.Itdescribedhowteacherscouldgetstudentsfeelingcomfortablewithmistakes.Andso,inTeachlikeaChampion,37 onthesamepagethatDougemphasizedtheimportanceoffixingerrors“asquicklyaspossible,”healsocalledthem“anormalandhealthypartofthelearningprocess.”ThetensionwasmuchlessapparentinDoug’sworkteachingadults,histeachertraining.Inthisregard,theentrepreneursandtheacademicstookastrikinglysimilarapproach.Attaxonomyworkshops,attendeespracticedDilitinItaly.Dougalwaysemphasizedthatteachersshouldusetheseevolvingtechniquesonlyiftheymadesense.Thejobofadministrators,meanwhile,wasnottopunishbadperformersforpoorteaching.Itwastogivethemopportunitiestolearn.Toteachthem.Andovertime,evenwithoutdirectinterventionfromtheacademics,theentrepreneurs’approachtoteachingchildrenwasbeginningtobearmoreresemblancetotheirapproachtoteachingadults.In2013,Dougbegancrafting“Taxonomy2.0,”asecondeditionofTeachlikeaChampion,inwhichherevisedlargeportionsofhisapproachtoerror.Insteadoffocusingonwaysthatteacherscouldeliminatemistakesassoonastheyarose,thenewdocumenttriedtogivethemtoolstouseerrorsaslearningopportunities,namingnewtechniquestheycouldusetohelpstudentsfeelcomfortablemakingmistakes.AsDoug’schangingideasmadeclear,thebiggestquestionwasnotwhethertheentrepreneurs’teachingwouldevolveovertime.Theirteachingalreadywasevolving,evenwithouttheacademics’help.Thebiggestquestionwaswhethertherestofthecountry’steachingwouldchangetoo.AcademicslikePam,Magdalene,andDeborahstillmadeuponlyaminorityofedschoolprofessors.Theentrepreneurs,meanwhile,weregrowinginnumber,butby2011,charterschoolsstillreachedonly4percentofAmericanpublicschoolstudents.Andalthoughtheoutsideworldwaspayingmoreattentiontothecharters,thelessonsthatobserversdrewdidn’tnecessarilyreflecttherealityinside.Instead,asusual,theobserversfocusedontheideathathadspawnedcharterschoolsinthefirstplace:accountability.38 AppendixIITargetText第九章圣杯玛格达莱妮·兰佩特（MagdaleneLampert）对意大利语言学校（Italiaidea）的调研结果集中体现在教学活动（InstructionalActivities）理念上。对此，杰西·所罗门（JesseSolomon）非常赞同。玛格达莱妮解释说，“要想教好高水平学生，其难点并不是舍弃教学内容的难度而求易于学生理解。”其实这与帮助数学差的学生一样，不过是让学生理解更多知识点，不仅让他们牢记，而且可以推理，推测，证明和理解。要做到这一点并不容易。但是，即便是对低年级学生，老师通过精挑细选的问题也可以使学科的主要思想活灵活现。教学亦同理：如果老师们仅仅教授较为简单的内容，那么，他们必然只能学到一些肤浅的教学技巧。实际上，提高老师水平的诀窍就是让新老师从一开始就严谨教学。在一所名为迪里特（Dilit）的意大利语言学校里，教师教育者（teacher-educators）将意大利语教学分为14个核心教学活动，每个教学活动都像解一道步骤繁多的数学题。这些活动严谨缜密又易于理解，因此适用于不同年级和不同能力水平的学生，即使是新入职的老师也可以尝试。以一个被称作“会话重建”(ConversationRebuilding)的教学活动为例。课堂上，老师和学生之间的例行交流好似看图说词游戏。老师不说话，只通过打手势和画画与学生进行交流。之后，老师请同学们猜刚才说了什么，学生只能用意大利语回答。一个在餐厅用餐的人说什么能让服务员把酒单拿过来？酒单送来之后，如果她仍不确定想喝什么，要怎么回应？在学生提出假设时，老师引导学生在头脑中构思这段话进行的真实情境。（若假设讲的通，老师示意让整组重复；若假设不通，老师会说“继续努力”，再次模拟当时的场景，请学生重新假设。）通过这种方法，学生不仅学到了新的词汇和语法，而且也体会到了如何用语言去交际。对于一位新老师来说，掌控谈话情景需要一系列复杂技巧才能得以实现。但在迪里特（Dilit），通过详细说明步骤并让新老师去尝试，一切变的简单可行。首先，教授和其他学员一同扮演学生与新老师进行模拟训练。过程当中，教师教育者(teacher-educator)会抛出普通学生常犯的错误。之后，新老师与真正的学生进行训练。迪里特（Dilit）的教师教育者在39 过程中间会给出建设性意见，提醒新老师切勿忘记教学活动中的几个关键点，如不断让学生重复正确假设。之后，随着实习老师的不断进步，他们就会学着分析学生的想法，忽略一些可能出现的干扰因素，引导学生向着准确的反应不断迈近。训练课程结束后，整个教学团队开始交流，就如何取得进步给与彼此提醒及建议。去波士顿工作之前,玛格达莱尼一直在密歇根州安娜堡市其创立的暑期学习机构工作。当时，她已尝试运用教学活动理念。她说，教学活动就像“容器（containers）”一样，新老师可以在其中学到他们需要了解的东西。教学活动的一部分，由一些帮助学生学习的实践活动组成。例如，在“合唱数数（ChoralCounting）”中，老师学习如何引导一群学生大声数特定数字（如10的倍数，或者2的倍数）；如何在黑板上将数字排序（例如使用纵列，将2的倍数，2，12,22和32列为一列，以便学生发现规律）；如何在数到一个特定数字时停下来，然后提问，如：“下一个数字是什么？”；如何引导学生找出规律，最终，引出重要的数学概念。同时，教学活动也可促进新老师研究他们需要教授的核心数学知识。暑期学习机构的员工黛博拉·鲍尔（DeborahBall）和海曼·巴斯（HymanBass）将其称为“数学教学知识（MathematicalKnowledgeforTeaching）”，简称MKT。（在合唱数数中，MKT包括了解数学模式，学生理解数字的常见方式，及老师为了加强学生理解所使用的例子。）机构分小组运用迪里特（Dilit）模式，共同学习讨论，并在每次排练之间互相给予反馈，就如何提高学生数字敏感度给出建议与方法。最后，他们试着与当地暑期项目的学生进行教学活动练习。杰西想要把教学活动引入到波士顿教师驻校计划（BostonTeacherResidency，简称BTR）中。一年之内，其余的BTR领导两次去密歇根暑期学习机构观摩学习。2011年，他们邀请玛格达莱尼到波士顿工作来重新设计整个BTR课程。与安娜堡暑期项目相比，波士顿项目挑战更大，难度更高。当地驻校教师被安排在市里最差的学校教学，其中包括一些“待改造(turnaround)”学校，这些学校是美国5000所状况最糟的初高中学校里的一部分，位于波士顿。玛格达莱尼在密歇根教的学生种族不同、文化多样。而波士顿的学生质量则有可能更低，他们大部分都不会说英语，才刚刚开始学习。因此，学生的学习和情绪问题可能更大（波士顿公立学校20%的学生被归类为需要特殊教育）。在当地学校考察时，玛格达莱尼也发现，教室里经常乱成一团，毫无秩序。但她认为，所有挑战虽困难，但却可以战胜。她所认识的BTR教师能够指导学生学习，只是仍需训练。所以，当杰西邀请她离开密歇根去BTR做全职教师时，玛格达莱尼答应了。两年之后，有一天，玛格达莱尼在BTR一年级的教室里听课。当天上课的老师是萨拜恩·斐迪南（SabineFerdinand）。玛格达莱尼拿着iPad做记录，参与决定萨拜恩是否有资40 格获得马萨诸塞州教师资格证。按规定，这节课的老师是已有15年教学经验的艾琳·卡弗（IleneCarver），萨拜恩是其助教。但在这一年里，萨拜恩已担负起更多责任。至少在学生眼中，她成为了像艾琳一样的老师。那天，她正领着学生进行“快速图像（QuickImages）”教学活动。此活动适用于数学学习，且已广泛运用于波士顿小学中。课刚开始，萨拜恩倒数，“8、7、6⋯⋯”，这时学生马上跑到教室长方形地毯的相应位置坐下，位置上用记号笔写了他们的名字。萨拜恩喊道“3、2、1”，她在每个数字间有所停顿。“我希望大家把铅笔拿好，坐在自己的位置上。”萨拜恩站在老师平常站的位置：离门最近的角落，教室墙上的布艺日历附近。日历上写着“3月”，用红白两色标出了日期。她温和的说：“你们盘腿坐下，我不会再次提醒了哟。谢谢大家。”然后，萨拜恩切入主题，“谁记得以前我们做过“快速图像”活动？”大家纷纷举起手来。一个学生高兴地跳起来，大声答着。学生一起复述活动规则:老师快速展示图像，每个两次。图像闪过之后，学生写下他们看见的东西。但当全部图像展示完后，他们就只能思考，不可以用笔写了。今天是几何课，所以萨拜恩展示的图像并不是数数的点，而是画出来的形状。她喊道：“准备好了吗？1、2、3。”学生深吸口气，萨拜恩轮流展示正方形图像，并确保每一个学生看到。第二轮展示过后，她把图片钉在左边的架子上，说道：“好的，所以我的问题是，我们怎么描述这个形状？”这时，有人自告奋勇举手，不过萨拜恩耐心等待，让更多学生有机会思考。接着，她说，“我们怎么描述这个形状，拉斐尔？”“啊”，拉斐尔边思考边想。他是个魁梧的男孩，脸上带笑，略显紧张。“这是一个正方形。”萨拜恩本可以就此打住（因为它就是一个正方形），然后继续下一个图形。但玛格达莱尼注意到的是，萨拜恩继续与学生探讨。萨拜恩竖起大拇指，给与学生鼓励，示意其他学生回答问题。她说道，“谁同意拉斐尔的观点？史蒂芬妮，你想要补充什么吗？你会如何描述这个形状？”史蒂芬妮是个活泼的女孩。她坐在地毯角落一个专用椅子上，正全神贯注，仔细思考。她说，“恩，它不长！”“能再多说点吗？哪儿不长？”41 “边不长。”史蒂芬妮答道。马尔科姆也举起手。萨拜恩问道，“马尔科姆，你想说什么？”“它”，马尔科姆停下来数到，“它有4个边！”学生们观察的越来越仔细，萨拜恩想让他们说出正方形更多特点。她说道：“现在，大家看看这些边有什么特点？”后面的奥斯卡回答道，“他们都是中等大小。”“确实如此。”萨拜恩说道。“达妮卡，你看出了什么？”达妮卡想了想，说道，“我想补充两句。”玛格达莱尼对萨拜恩的话语作着记录。这是刚上任一年的老师带着一年级学生一起进行数学讨论的情景，非常有意义。达妮卡接着说，“这些边很长。但是，左右两边看起来比上下两边长。”显然，达妮卡的描述不够准确。因为这是个正方形，所以每个边长度相等。但她是班级里第一个比较长度的，这把讨论引到了一个重要方向。萨拜恩手指着画板上的图形，重复着达尼卡的话，“左右两边看起来比上下两边长，有意思。”学生进入了一个重要的数学领域，并且朝着正确方向发展中。一年级刚开始，这些学生就已理解几何图形的不同，如三角形和正方形。但是为了更好的区分不同，例如，区分直角三角形和等腰三角形、长方形和正方形，学生仍面临很大挑战。学生的理解表明他们会区分不同（边的关系），而且试着去描述。左右两边比上下两边长，还是一样长？现在，讨论已进入到一个更重要的领域：从心理学家让·皮亚杰（JeanPiaget）称为“万物有灵论”的思想,即物体与人一样有自己的意识，可以移动改变，而不是一成不变，转移到了更抽象的理解正方形，即将其看做一个类别，有4个长度相等且不变的边。因为学生相信万物有灵，所以他们觉得正方形并不是固定不变的事物，而是，如果物体自己想要改变，就可以任意变形。达尼卡的误导性评论说完没多久，一个叫路易莎的女孩就将整个班级引到了正确轨道上。她说，正方形四个边相等。萨拜恩马上抓住机会强调重点，“路易莎，你为什么确定四个边是相等的呢？这是什么意思？”为了让班级其他学生弄清楚，路易莎答道：“就是长度相同。”不过，一些学生仍很疑惑。这时，后面那个很积极的男孩奥斯卡，接着达尼卡的观点，站起来与大家分享。他用手向大家展示如何让上下两边距离更远，解释道，“如果把这个正42 方形抬高一点，再高一点，正方形就会更长。因为你把它抬高了。但当左右两边变长时，上下两边就变短了。”萨拜恩跟他确认到，“所以你的意思是我们把这个正方形压扁？”“对，就是这个意思”,他点头说道。玛格达莱尼认为，在学校学习数学的目的之一，就是帮助学生纠正奥斯卡持有的这种观点。正方形真能把自己压扁么？还是说，正方形很稳定？萨拜恩看着奥斯卡，“但是，路易莎是怎么说的？马尔科姆你说。”马尔科姆说：“她说它四个边相等。”“相等，”萨拜恩重复到，“四个边长度相等。”作为一位更有经验的老师，玛格达莱尼知道还有其他方法来帮助学生理解这个问题。例如，为了让学生更好的掌握长方形和正方形之间的区别，萨拜恩可以利用达尼卡的错误观点作为突破口。玛格达莱尼说道，“我会展示一张长方形图片。然后说，‘这两个形状相同还是不同？哪里相同，哪里不同？’”但是这种反应需要更长时间去培养（学生学习识别这些形状并不是件简单的事），而且玛格达莱尼并不期望刚教书一年的老师马上把它弄清楚。萨拜恩做的恰好是玛格达莱尼希望她做的事。萨拜恩排练过很多次的套路可使学生保持精力集中并且认真思考。萨拜恩准备很充分，她不仅学到了做什么（合唱数数的步骤），还学到了如何帮助学生理解数学知识。结果是，学生们对几何基本概念有了一定思考。当错误想法产生时，萨拜恩没有直接打击学生。相反，她让全班学生去思考。最终，萨拜恩从路易莎提出的四边相等成功引出了关键性概念。所以当奥斯卡把他万物有灵性的想法说出来，想要把四边形压扁时，萨拜恩可以用路易莎更复杂的推测，来帮助奥斯卡重新思考正方形是什么。即便学生在结束讨论时没有完全掌握如长方形和正方形、抽象形状和有生命物体之间的区别，他们也已经取得了重要进步。玛格达莱尼说：“他们在与一个基本概念斗争，他们应该这样的。”一年级学生能做到这样已经很好了。这非常令人激动。在完成“快速图像”教学活动之后，萨拜恩给学生出了一道加法题。她给学生一张图表，上面是完成这道题所需的各种形状的积木。她大声读出来，“两个六边形，零个梯形，一个蓝色菱形，零个正方形，三个棕色菱形以及七个绿色三角形。”现在学生需要算出这些积木的总数量。43 玛格达莱尼知道萨拜恩选择的数字加起来比10（13）大。学生已开始学习更加复杂的加法知识，像从最大数字开始相加、将并不熟悉的问题拆分成熟悉的部分、或利用数轴从一个数字跳到下一个数字。这个问题的答案比10大，这会引导学生尝试新的方法，而不是用大家仍会用的方法：数手指。如萨拜恩所望，学生运用各种方法、新奇组合。玛格达莱尼看到一个女孩趴在地上，写下两组数字——3+3=6、6+7=。之后她从7开始试着填空，写下了6行。她看到了另一个同学写出了不同的数字组合：另一名学生费丝选择了相似的方法。她给玛格达莱尼看她的算法，玛格达莱尼对她说，“这方法不错。”之后，课堂形式由个人学习转换为小组讨论，萨拜恩请一个安静的小男孩凯文来分享他的方法。凯文说道：“我知道3+7=10。而且，”萨拜恩打断道，“你怎么知道3+7=10的？”凯文答道：“因为我知道10是怎么组合成的。”“所以3和7是10的另一个组合，”萨拜恩重复道。她转头对其他的学生说，以确信他们听懂了凯文的方法。她转头对凯文说，“你可以用你知道的东西来解决这个问题。3+7=10，好，继续。”44 凯文接着说下一步。他留下2和1，他知道2+1=3，然后他将最后两个数字加起来，即10和3。萨拜恩问道，“然后，你得到了？”“13”，凯文回答道。萨拜恩把凯文的方法写在黑板上，黑板上还记录了其他学生的解题方法。凯文用他所知的数字组合找到了最后的答案，萨拜恩本想总结这个重点。这时，另一个坐在地毯上的男孩打断了她的话。他刚上课时还有些害羞，总把题目弄错。但是，现在他思路清晰，试着针对凯文的方法说出自己的观点。他指着10，说道“如果把0拿走，然后把3放在那，就是13。”萨拜恩看了一眼玛格达莱尼。儿童一般会错认为“3+10”，是把3和1加在一起，因为1与3最近，所以得到了4。之后，他们不知道怎么处理0。因为没有完全掌握十位和个位的区别，他们会把0挨着4写，得到3+10=40。而这个一年级男孩，已首先有了正确思路：3个1加1个10意味着3可以有效替代0，结果为13。他已凭直觉知道了位值。萨拜恩和玛格达莱尼相视一笑，对男孩说道，“我懂你的意思。”然后，课堂继续。杰西并不是唯一向专业学者寻求帮助的企业家。希瑟·科克帕特里克（HeatherKirkpatrick）是加利福尼亚州艾斯派尔特许学校网（Aspirecharternetwork）的领导人之一。她也来到教学峰会同他人一道学习。希瑟说道，“我们看上去不错，但事实却不是这样。当走到教室的时候，我们并没有真正体验到教学的快乐。”他们想要的是“严谨（rigor）”教学。具体来说，是一种叫做“学术话语（academicdiscourse）”的教学模式。他们认为，话语意味着四件事。第一，教师不能一直说话，应让学生独立思考。第二，学生必须交流当前的学术观点。第三，学生必须使用学术词汇来交谈。最后，学生需要按照艾斯派尔（Aspire）称作“运用证据支撑(bringevidencetobear)”的方法来学习，即在英语课上引用文章，历史课上引用第一手资源，数学课上通过证明推理，科学课上重视实验证据。希瑟说,“就是这四件事情，我们应试着在数学、科学、英语语言艺术、历史等学科中设法做好。这就是教学的圣杯。那么，我们怎么达到那个程度呢？”45 希瑟正思考这个问题的时候，有人建议她与帕姆·格罗斯曼（PamGrossman）一起探讨。1帕姆是斯坦福大学教育学院的一名教授。而且，在李·舒尔曼（LeeShulman）离开密歇根州去斯坦福大学教学之后，帕姆是其第一批学生中的一员。帕姆来斯坦福之前，在高中教了近10年的英语。她在斯坦福期间，李分派一组学生研究个人学科教学。帕姆选择的是英语。那段时间，她发现她的同学之间说话非常亲切。因为李是他们共同的导师，黛博拉和其他同学与帕姆像兄弟姐妹一样共同研究，只是大家的大学不同、科目不同。帕姆还有一点与众不同：帕姆不研究自己的教学方法，而是研究其他教师的教学方法。帕姆录下来的一个片断，展示了7个学生在加利福尼亚圣洛伦索的城市高中里讨论小说2《黄色墙纸》（TheYellowWallpaper）的情景。这是夏洛特·帕金斯·吉尔曼（CharlottePerkinsGilman）写的一个短篇小说。镜头里并没有出现老师，但学生非常认真，就像老师在他们前面翻着书，让每个学生发言一样。录像开始，一个叫艾米的金发女孩问他对面的男孩吉姆，“你有什么要说的吗？吉姆。”吉姆说：“我对这段内容的理解，要回到麦克威廉斯老师（他的实习教师）在我们阅读故事之前所说的话，即这个故事对她产生的巨大影响，阅读后的感想和产生的情绪（积极的还有消极的）。”吉姆带上眼镜，停顿了一下，说道，“其实，我对这段的理解就是她从第30页结束就死了。”其他学生抬起头来。这个故事以日记形式书写，女主人公饱受焦虑与沮丧。故事中只用过一次“死”字，是为了描述女主人公写日记的纸张。但当日记按时间顺序写到主人公的丈夫，一个物理学家要求她当全职家庭主妇这最坏的状况出现之后，就完全没有提到女人已经死了。现在吉姆说她从30页开始就已经死了。一个学生问道：“什么？”吉姆接着说：“第30页的整个对话，最后一行说道,‘我现在被一个隐藏的绳子牢牢拴住了，是你不让我出去！’”这行描述女主人公发现自己在黄色墙纸的小屋子里被困住之后，用绳子逃走的情景。吉姆接着说，“我想在那一刻，她是死了的。这是她死了之后与约翰——她丈夫的对话。”“啊！”杰德喊道，她穿着尼龙布衣服，刚才还坐在那静静地听。她一只眼睛看着书，一只眼睛盯着吉姆，捂住嘴，不再说话。挨着她的女孩，莎莉雅也张大着嘴。吉姆接着说，“她在屋子里是自由的，但她从来没有那么自由过，像在——。”“——屋子外面！”杰德和莎莉雅一起喊出来，组里其他人互相交流，非常激动。1李·舒尔曼，美国卡内基教学促进基金会荣誉退休主席，斯坦福大学查理·E·杜克曼教育学退休教授。2《黄色墙纸》，美国著名女权主义作家夏洛特·帕金斯·吉尔曼的代表作，它采用一位疯女人的第一人称叙述，讲述了19世纪女性在父权统治社会中受到的压迫，最终走向疯癫的悲剧故事。46 但是艾米不买吉姆的帐。她说道：“等等，等等，”她指着另一段内容，这段内容与吉姆的想法并不符合。这段写着“紧紧系着”的绳子那行已经预示，女主人公已经从房间令人喘不过气的墙纸后面逃了出来，其他女人可能也像女主人公一样已经逃脱。艾米说道：“就在那，‘我想知道他们是否像我一样都从墙纸里逃了出来？’这个描述怎么可能与吉姆的解读一致？”艾米接着说，“这意味着有人死在他前面了，还是其他的事？其他人死了？”在吉姆说话之前，几个同学尝试解释。吉姆说道，“我认为这在某种程度上代表社会，因为她自由了，她正想象，其他的女人也是这样做的么？”艾米重复吉姆的观点，“所以她获得自由的方式是自杀。”吉姆说道，“你可以将所有女人以自杀作为逃脱方式将两段内容连接起来。”很快，杰德有了疑问。她问道，“那这房子呢？”“这个房子，这个房子肯定也代表了某些东西。”艾米抓住机会表达自己对这个故事的解读。她接着说，“也许，也许这个房子和这个地方代表生活，对吧？人的一生有时候，你想去某些地方，你想做某些事情，是不是？她只是想要自己有一个空间，但她丈夫却拒绝了。”杰德点头，她被艾米的解释说服了。她激动的说，“不同的空间就代表不同的生活方式。”艾米补充道，“或者说是她能做或不能做的事。”“或者，”吉姆静静地说，“她生活的不同部分。”艾米用笔指着吉姆，边点头边喊，“耶！”这些学生虽有不同的解释，但他们互相理解，共同进步。这个视频片断正好展示了希瑟和她的团队想要在艾斯派尔（Aspire）培养的谈话方式，即“学术话语（academicdiscourse）”模式。当堂课的老师彼得·威廉姆森(PeterWilliamson)虽然根本没有出现在镜头里，但是，就像帕姆说的，他在整个课堂上起到了至关重要的作用。具体来说，首先他给学生机会讨论，讨论结果富有成效。讨论过程中，学生先写出两种类型的问题，字面问题和理解问题。接着，学生间就问题互相讨论，得到答案。讨论结束后，老师让学生做任务报告，以他们在互相交流中学到的东西为中心。（这也是后来成为旧金山大学教师教育学教授的彼得录这段视频的原因之一，以便学生观看之后思考下次如何进步。）这些步骤是彼得单为“黄色墙纸”这一课准备的内容。为了让学生更好的理解，彼得煞费苦心。最终，帕姆和她的研究生同学将英语教学实践分为了几个重要部分——帕姆将其称为“核心练习（corepractices）”。这与玛格达莱尼的教学活动非常相似。帕姆将英语教学练习总结归纳为“示范教学法（modeling）”。它是优秀英语老师教学内容的核心部分，可引导学生在英语课堂上进行他们需要经历的过程。这个过程不仅包括阅47 读和写作，还有一些细分内容，如给文章加注时来帮助理解意思，以及使用例证来进行阐述。为了让学生学习到每一个环节，老师不仅要教他们学基础，例如注释或者解释，还要将活动真正引入到学生的灵魂中去。帕姆将其称为“使思想显化”。在引起学生共鸣的文本中，运用“示范教学法（modeling）”能达到最好效果。而且，老师可以直接用学生作业评讲。例如，老师可以使用学生有说服力的作文做为解释写作的范例，通过证据一步一步深入，描述作者如何运用证据论证观点。老师可以问学生，“我要问的问题是‘所以呢’？我的答案会告诉大家⋯⋯哦，这就是证据的重要性！”帕姆的英语教学分类法中另一类别是“课堂话语（classroomdiscourse）”，它可以帮助老师理解学生的想法。课堂讨论不应该只是任务正式开始前的娱乐，不应远离现实。讨论应是写作过程和口语练习的第一步，学生通过协作进一步强化观点。这篇文章表面意思是什么？这篇文字象征着什么？如果讨论渐入佳境，在课堂结束时，乏味的观点就会转化成30个缜密的理解。帕姆刚在研究生院读书时，研究英语教学的学者就已经在强调讨论在文学课堂的重要性。通过研究美国课堂，学者也发现美国课堂在这方面很匮乏。但很少有人想到怎样帮助老师做的更好。帕姆和她的学生将这个“已被讨论过的”问题分解成几个可以教授的部分。他们得出的结论是，富有成效的讨论并不是偶然发生的，而是需要严肃而仔细的准备。帕姆研究的一位老师伊冯·迪万斯·哈钦森（YvonneDivansHutchinson），在洛杉矶联合学区沃茨与汤普顿附近的高中任教。伊冯将称为“备用回应（stockresponses）”的清单交给学生，其中包括参与讨论的可能方法，还包括几个不参与讨论的方法：•你不知道答案？试着说，“我不知道，但我会试着找到答案告诉你。”•你没有准备说什么？“很抱歉，我还没准备好。”•“你不懂问题？”那就问，“你能再说一遍吗？”•你做了作业也知道问题，但还是想不到答案？可以说，“请等一下，我还在想呢。”“备用回应（stockresponses）”看起来似乎是强制的，但若没有，就无法保证学生开口说话。帕姆说道，“人不一定天生都健谈。事实上，这需要时间学习，我们老师可以帮助学生进步。”伊冯也给出一些建议。如果你不同意某个观点，先这样说，“不好意思，我并不同意你的观点。”然后给出你的相反观点来反驳他。如果你同意某个观点并想要补充，可以说，“就某某刚才说的话，我想要补充⋯⋯”48 课堂内还包括其他规则。为确保大部分学生有机会发言，提高得到正确答案的可能性，伊冯利用同伴压力，让学生互相之间督促发言。伊冯发现，对学生来说，被同学叫起来回答问题效果似乎更好。她同样也想好了办法对付那些什么都不说的同学。她经常在课堂中停下来，让学生有充分时间思考来组织语言、整理思路。伊冯将这段时间称为“沉默（reticent）”时间。通过她的模型课堂，学生们学会了如何互相学习，即使最安静的同学也有机会表达自己的想法。这只是个开始。在伊冯的课堂上，每个讨论都由一个“预期引导（anticipationguide）”开始。预期引导包括一系列问题，旨在帮助学生在阅读之前思考这部分的主题。接下来是让每个学生独自回答的“阅读反应提示”（readingresponseprompt）。这些提示告诉学生可以自己选择最好的阅读方式，包括通过使用荧光笔及元认知标志在内的方式进行标注，以及指导学生写下他们自己的问题。（在伊冯的课堂上，即使问题也经过仔细分类，从基本的“事实”问题（第1级）到需要分析文章实质并拓展的“全面”问题（第3级）。例如，学生写下2个1级问题，3个2级问题，1个或2个3级问题。）最后，在整组讨论之前，先让学生进行小组微型讨论。伊冯解释道，“如果学生是以自己的理解为坐标，他们则更容易被理解与认可。”整个设计令学生们蓄势待发，讨论生动而富有成效。伊冯此时也开始参与教学。帕姆和她的另一个研究生同学丽莎·巴克（LisaBarker）一起通过研究伊冯和其他老师的教学视频，进一步分析引导讨论这门艺术。引用早期学者对课堂讨论总结出来的术语，帕姆和丽莎将伊冯经常展开的训练之一称作“吸收（uptake）”。其过程是，当老师听到学生回答时，总结观点（所以她以自杀的方式获取自由），加以说明，以某种方式重复，使所有学生理解。丽莎与帕姆一同将“吸收”分为9个部分，供教师在不同时期使用。“重述（restatement）”为其中最简单的一部分，包括总结学生看法，但要在其中加入学术语言，如使用更精炼的语法或更精确的术语。“重新表达(revoicing)”是重述的子项之一，概括学生因某一具体目的将讨论引入一定方向，就像艾米重新阐明吉姆为了解释女主人公已死，提出的“给自己自由”的观点。老师还有其他方法直接引导学生给出更好的见解。一种具有“挑战性”的方法，就是为了讨论持相反观点。比如，上课时老师要求学生提出更多信息，如某种说法或是意思解释。下课前根据某学生的观点，对本节课进行总结及评论——谁能驳倒吉姆说的话？彼得·威廉姆森（PeterWilliamson）不仅将自己的课堂话语恰到好处带入到“黄色墙纸”的教学课程中，同时，他也给学生做了良好示范，学生通过“吸收（uptake）”独立讨论问题。艾米知道主动问同学；杰德知道重复吉姆的观点加以理解，并且在她想要辩驳时，要求吉姆详细阐述观点。最后，当艾米说出自己观点的时候，吉姆知道如何“吸收”来重塑观点。49 他仔细听艾米对房子象征意义的描述，并且对艾米的见解加以补充。整个屋子代表的，不仅仅是“她能做和不能做的不同事情”，还有“她人生的不同部分。”希瑟非常喜欢彼得的教学视频。她与帕姆进行沟通。很快，帕姆和丽莎就一起来到艾斯派尔（Aspire）暑期课程中教学。从某一方面来说，学者教给企业家的是“内容（content）”。像道格·莱莫夫（DougLemov）这样的企业家就将教学放眼到各个科目。而玛格达莱尼只关注数学，帕姆只关注英语。但是，学者的学习理论与内容知识一样重要，或者说更加重要。讽刺的是，正是这同样学术结构的遗赠，曾经却阻碍了教学研究：教育研究与心理学的紧密联系。确实，就像李的前辈内特·盖奇（NateGage）发现的一样，教学和学习并不矛盾。不过，这种推论也是正确的。若不懂学习，也无法理解教学。也许，特许学校教育者无意中已采用了线性模型学习方式。他们假设，学习者以基础技能开始，以用来应付“更高层次”的工作。数学方面，其指的就是在解决问题之前记住乘法表。英语方面，则指在学习论证之前掌握基本词汇。他们将学习看成一项建筑：若没有材料去建造它那就什么都不是。只有把平凡的事做好，才能完成更加复杂和有意义的事。事实为概念奠定基础这一理念属于基本的学习行为理论。如果学习以事实开始，事实以记忆开始(记忆是与概念分开的)，那么教学生的最佳方法与爱德华·桑代克（EdwardThorndike）训练猫的方法是一致的。练习、练习、再练习，同时给与适当惩罚与奖励。这样下去，“严谨（rigor）”教学就会出现。结果导向的教学方式在处理错误上特别清晰明白。以行为主义者的角度，每个错误都应迅速改正。否则，学生将不会了解到某一观点是错误的。特许学校最优秀的老师则将其最大3化。其中一个数学老师是基普网络（KIPP）里数一数二的人物，他决定不让学生在家练习那些还没有教给他们如何解决的问题。他解释到，问题可能在于如果没有老师阻止学生，学生会一直犯错。没人去纠正错误，错误就会根深蒂固，更不容易改变，学生就忽略了真实。道格分类法中的几个技巧（例如，“再做一次”）就是以此观点为基础。教学行为，在分类学中经常被归结为对于每个明显错误行为的必要回应。教师必须对于每个错误给与迅速及明确的改正。道格也将这种观点应用于教学理论内容。在写到如何教学生“解码”，即如何去破译一连串的字母找出发音时，道格强调重视所有错误。他在书中写道：“老师应该在3KnowledgeisPowerProgram,美国开放招生的全国统一网络。它是一种大学预科公立学校,对生活在社区不完善地区的学生跟踪记录他们的学习与生活。50 任何可能情况下，努力改正并解码错误，不论他们教的是哪个科目或年级。”道格将这种技巧成为“直面错误（PunchtheError）”。然而，在20世纪80年代，帕姆、黛博拉和玛格达莱尼开始研究教学时，研究已展示出这种行为主义观点的局限性。心理学家曾经发现，人类学习不只是大量的经验刺激和“是与不是”的回答。而且，概念不等待事实去积累，两者相互渗透。例如，记忆力好的人通过将其研究对象植入于更为抽象的理解地图中记忆。一位心理学家在研究他称为“S.F.”的一名大学生时，发现这个学生仅通过将数字与帮助其理解的意思相联系就可以记住一长串数字。例如，S.F.将数字3492转换成运动员的跑步时间，即3分49.2秒（接近一英里赛跑的世界纪录）。仅是3.492是不够的，他还要将数字放在他可以理解的语境中。在使用比赛记忆一年半之后，S.F.可以记住的数字已从7个增长到79个。有困难的地方就是数字不可以映射成难忘的比赛。同样，孩子通过他们对数字的直觉去做加法或减法，而不是老师说的正确做法。就像巴西街头卖水果的孩子，可以直接用脑计算多述位题目，他们计算、分类，再分类，直到得到一个数字符合他们心里所想。人们似乎从出生就采用这个推理——企业教育者将其称为“批判性思维（criticalthinking）”或者“严谨（rigor）推理”。在反复实验中，心理学家发现婴儿不是通过奖惩系统来了解世界，而是通过观察得出总结、规则和原则来了解世界。在某实验中，心理学家将蓝色圆筒从斜坡上推下撞到一个玩具虫上。他们研究6个半月的婴儿看着蓝色圆筒推着玩具虫前进，直到水平通道中间。然后，研究者又滚下了两个圆筒，一个黄色大圆筒，一个橘色小圆筒。可以预见，黄色大圆筒将虫子撞得更远了，直接撞到了通道尾部。而橘色圆筒，虽然比另两个都小，但也将玩具虫撞到头上去了。研究者将这个奇怪现象展示给成人，成人很惊讶。那么，从没学过物理知识的婴儿会有同样的反应吗？是的，婴儿的反应相同。那些看到橘色小圆筒将玩具虫撞更远这一非合理现象的婴儿，比其他看到合理现象的婴儿注视时间更长。他们虽然6个月大，但从没有人告诉过他们大圆筒比小的重很多。但通过接受世界数据，那就是大物体比小物体推东西推的更远，他们想出了合理的抽象心理模型。由此得到的结论是，概念理解并不比记忆更重要，两者之间是相辅相成，不容分割的。玛格达莱尼将此课程概括为一个短语，就是儿童是“使合情合理者（sensemakers）”。就像当婴儿盯着圆筒时，他们接受数据并进行推理，通过自己对世界的了解进行分析。例如，教育者自己承担风险，假设记忆发生在概念和原则之外，或者说重复奖励或惩罚足以帮助学习。孩子试着将规则合理化，即使是那些不合理的规则。然后，当妨碍不可避免发生时，他51 们就会使用规则，就像一位加利福尼亚老师一样，他在给学生讲解借贷的重要性时，反复强调减法，不管底数是多少都将其运用到每个问题中。玛格达莱尼、帕姆以及黛博拉运用的教学方法被称为TKOT。它在学术上更加严谨，并不是因为他们设置的问题更难或期待更高，或者说是粒度曲线更深，而是因为他们对学习的愿景是精炼的。他们不仅阅读学习方面的一般研究，为了进一步了解教学个体，他们还要学习“认识(knowing)”的特殊规则，即认识论。当涉及到一个问题的时候，每个领域都有其专门的定义。如在数学中推测证明，在文学中通过证据解释并最终说明。因为定义并不全都一样，他们论证的教学也不尽相同。例如数学教学，“你，你们所有人，我们”的教学模式在日本已经很普遍（在玛格达莱尼和黛博拉的课堂上运用也十分普遍）。这种模式对构建大概念研究很有意义，如在理解分数和负数时。同时，在英语教学方面，学生需要学习具体的阅读和写作技巧，即如何分辨出陌生单词的意思或如何为文章确定主题，这时“我，我们，你们”的教学形式加上引导实践是非常合适的。在每个科目里，不同的主题都需要不同的结构。利用这些特定模式，玛格达莱尼、帕姆、黛博拉和他们的同事就更容易获得学术上的“严谨(rigor)”，这也是不喜欢找借口的老师所渴望的。他们教学生用不同的眼光看世界，将他们的直观知识与理解和操作规则紧密相连。其实数学家、科学家、历史学家、文学理论家等已在几个世纪之前达到这种境界了。按照这种观点，教学以倾听开始。玛格达莱尼说，“与孩子互动部分原因就是为了评估他们现在的程度，并考虑要给他们什么体验来挑战他们的世界观。”不同的学习方法也使他们对于孩子的错误有了不同的见解。在TKOT，错误并不是恼人的问题，一有苗头就要立即消灭，相反，这给学生提供了改正错误的机会，所以非常珍贵。在他们眼中，教学目的之一，就是让学生说出错误。帕姆看到，优秀的英语老师通过向学生展示他们自己的写作实例教学，并将好作文与一般作文进行对比，准确描述学生怎么做才能进步。同样，玛格达莱尼和黛博拉以引出对问题的错误理解为目标，最终使整个班级朝着正确思想前进。一些日本老师将这种观念更深入化。在日本，被玛格达莱尼称为“提高学生自学能力的教学”课程其实有两个矛盾的名字：kikan-shido和kikan-junshi。第一个描述的是这样一种行为，就是观察学生努力去解决问题，有必要的时候，老师会介入为学生解惑并给与暗示或额外指导。第二个则较为纯粹，为无评论观察。当学生犯错误或有疑惑时，老师只是记下错误（脑记或纸记），然后点头，轻轻走过。两者的英文翻译阐明不同：kikan-shido意思是“在课桌间指导”，kikan-junshi意思是“在课桌间巡视”。52 kikan-junshi的支持者认为，学生自己发现错误，记忆会更牢固。老师要确保在课堂“我们”部分的小组讨论中让学生发现错误。就这一点而言，kikan-junshi与道格的观点看起来互相矛盾。一方面，由于“直面错误（PunchtheError）”技巧例证，道格的分类学大部分是以消灭错误为基础建立的。不过道格也写到了课堂中存在安全错误的重要性。确实，“错误正常化（NormalizingError）”是第49条技巧，即分类法的最后一条。它描述了老师如何让学生更坦然的对待错误。而且在《教无不胜》（TeachlikeaChampion）这本书的同一页道格也强调了尽快改正错误的重要性，他将错误称作“学习过程中正常又健康的部分。”此矛盾在道格教成人的书里就没那么明显了。这一点，企业家和学者用的是明显相同的方法。在分类学工作坊中，参与者在意大利实行迪里特（Dilit）教学模式。道格多次强调只要合理老师就该使用这些改进技巧。同时，管理人员的工作并不是惩罚教学表现不好的人，而是该给新老师学习机会，去教他们。随着时间流逝，虽然没有学术界的直接干预，企业家教学生的方法也开始与他们教成人的方法越来越相似。2013年，道格开始制作“分类法2.0”，《教无不胜》的第二版，在其中他修改了处理错误的很多方法。道格不再希望老师发现错误就赶紧消灭错误，而是希望老师教会学生方法利用错误作为学习的机会，并提出新技巧引导学生合理看待错误。道格的观念已有所改变。现在，最大的问题已不是企业家教学是否要随着时间不断发展，因为他们的教学在没有学者的帮助下也在进步。最大的问题是国家教学的其他方面是否也会发生改变。像帕姆、玛格达莱尼和黛博拉这样的学者仍然只是学校教师中的一小部分。同时，企业家教育者在逐年增长。但是到2011年，特许学校仍仅占美国公立学校的4%。虽然外界对特许学校越来越关注，但关注的点并没有完全反应学校内部的真实情况。相反，他们照例关注特许学校起初引发的责任问题。53'