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1、TheLanguageofMathematicsMathematicsEducationLibraryOLUME4V6ManagingEditorA.J.Bishop,MonashUniversity,Melbourne,AustraliaEditorialBoard.P.Becker,JIllinois,U.S.A.C.Keitel,Berlin,GermanyF.Leung,HongKong,ChinaG.Leder,Melbourne,AustraliaD.Pimm,Edmonton,CanadaA.Sfard,Haif
2、a,IsraelO.Skovsmose,Aalborg,DenmarkThetitlespublishedinthisseriesarelistedattheendofthisvolume.BillBartonTheLanguageofMathematicsTellingMathematicalTales123BillBartonUniversityofAucklandAucklandNewZealandb.barton@auckland.ac.nzSeriesEditor:AlanBishopMonashUniversity
3、Melbourne3800AustraliaAlan.Bishop@Education.monash.edu.auLibraryofCongressControlNumber:2007936207ISBN-13:978-0-387-72858-2e-ISBN-13:978-0-387-72859-9Printedonacid-freepaper.¬2008SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedin
4、wholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnec-tionwithanyformofinformationstorageandretrieval,electronicadapt
5、ation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyare
6、subjecttoproprietaryrights.987654321springer.comDedicationThisbookisdedicatedtomywife,Pip.AcknowledgementsIwishfirsttoacknowledgetheacademicinspirationandguidanceIreceivedfromUbiratanD’Ambrosio,AlanBishop,MariadoCarmoDomite,andAndyBegg.Manyoftheideasinthisbookemerge
7、dfromtheirwritingorindiscussionwithoneorotherofthem.Iamindebtedtothemfortheirmentoringand/orinsights.Therearemanyotherswhohavecontributedtomythinkingaboutlanguageandmathematics:mycolleaguesandstudents,reviewersofpapers,andthemanyres-pondentsatseminarsorconferencepre
8、sentations.Thankyouforyourcriticalquestions,originalideas,andhelpfulsuggestions.Specialthanksalsogotomylanguageadvisers,inparticular:Shehe
