Indigenous Knowledge and Ethnomathematics PDF
Preview Indigenous Knowledge and Ethnomathematics
Eric Vandendriessche Rik Pinxten Editors Indigenous Knowledge and Ethnomathematics Indigenous Knowledge and Ethnomathematics · Eric Vandendriessche Rik Pinxten Editors Indigenous Knowledge and Ethnomathematics Editors EricVandendriessche RikPinxten NationalCentreforScientificResearch CulturesandLanguages Paris,France GhentUniversity Ghent,Belgium Thisworkcontainsmediaenhancements,whicharedisplayedwitha“play”icon.Materialin theprintbookcanbeviewedonamobiledevicebydownloadingtheSpringerNature“More Media”appavailableinthemajorappstores.Themediaenhancementsintheonlineversion oftheworkcanbeaccesseddirectlybyauthorizedusers. ISBN 978-3-030-97481-7 ISBN 978-3-030-97482-4 (eBook) https://doi.org/10.1007/978-3-030-97482-4 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Introduction 1.PreliminaryRemarks Thepresentvolumeaimstooffersomemoreinsightsontherelationshipsbetween indigenousknowledgeandethnomathematics.Theserelationshipshaveahistory,as someofthetextsremindus(e.g.Almeida,Vandendriessche).Wethinkitisimportant to elaborate on the possible links between both domains because of the richness involved, and because mathematics education on a global level is likely to benefit from such lines of research. In the conclusions to this volume, we indicate some pointswhichmayhavepotentialforthefuture.Itisgoodtoquestionoldviewsinboth disciplines:manymathematicianswillregardtheirthinkingascontextorculture-free, ontheonehand,whilesomeanthropologistswillclaimthattheethnosciencestudies ofrecentdecadesareuncriticaltypesofreductionism,stereotypingthinkinginother traditionsasparticularisticandweakerinstancesofwhatwasdevelopedinWestern history.Althoughclassificationstudiesandthelaterethnoscienceapproachescanbe arguablydescribedasemanatingfromsuchframesinthe20thcentury,thecombined interdisciplinaryworkbymathematicallyliterateanthropologicalresearchersinthe presentvolumequestionsthissortoftypecasting.Whatwascalledethnomathematics inthe‘70sand‘80softhepastcenturyhassincematured,mainlythankstoanin- depthcollaborationofknowledgeableresearchersinbothdisciplines.Itappearsthat themereevaluationoftherelationshipsbetweenIndigenousKnowledgeandwhatis nowadayscalledEthnomathematicscannotbereducedtoa“culturalist”biasonnative knowledge(asitwastosomeextentintheearlydaysoftheAmericanethnoscience scene:Descola2015).Itisthehopeofthisbook’seditorsthatthecontributionsto thisvolumewillallowforarenewedandsubstantiallydeepeneddiscussiononthese issues. Mostofthechaptersinthisvolumewerethesubjectofapresentationinasympo- sium, as part of the “18th International Union of Anthropological and Ethnolog- ical Sciences (IUAES) World Congress”, Florianopolis, Brazil, 2018.1 However, 1Theideaofelaboratingthisbookon“IndigenousKnowledgeandEthnomathematics”hasemerged duringthePanel“IndigenousMathematicalKnowledgeandPractices:(Crossed-)Perspectivesfrom Anthropology and Ethnomathematics”, coordinated by Eric Vandendriessche, Rik Pinxten, and v vi Introduction the texts have been thoroughly reworked in order to become substantial contribu- tionstothefieldweworkin.Afewtextsarenewandwereinvitedafterwards:M. Baker,A.Chronaki,L.Tiennot,S.Oliveiraetal.Theeditorsaddedacomprehensive introductionandconclusiveremarks. Thestructureofthebookhasbeendiscussedthoroughlyamongtheeditors,since abookis,ofcourse,altogetherdifferentfrommereproceedingsataconference. 2.TheBook’sStructure PartI“EthnographyandMathematics” This part presents papers focusing on particular ethnographic studies, in order to revealtheobviousandvisible,butalsothehiddenordeepstructuralmathematical featuresinparticularanddivergingculturalphenomena. CélinePetitoffersthefirstethnographictextunderthetitleCreating‘Evocative Images’sunannguanikiqqaigutinik:ProceduralKnowledgeandtheArtofMemory in the Inuit Practice of String Figure-Making. This study begins with the amazing fact that string figure making can be found around the world. It proves to be a widespreadactivityofproceduralknowledge.Thechapterfocusesprimarilyonthe Inuittradition. The meanings of String Figure-Making are diverse, ranging from cosmological andecologicalreferencingtomorestrictlysocialrolesanduses:indeed,itisoften foundasameansofsocializing,intheguiseofstorytellingwhilemakingthefigures. Petitanalyzesstringfigure-makingasakindofproceduralactivity,whichisimportant in knowledge transfer, memory training and to frame cultural learning processes. Moreoverthistraditionhassymbolicmeaningindifferentgroups:thefigurescanbe ahindranceduringhuntingendeavors,causingtroubleduringthehunt. Petitthengoesontorevealthestructuringandrecurringpatternsandrelations, whichcanbeidentifiedasmathematicalrelations.Especiallygeometricformswith their hidden or explicit symmetry relationships are highlighted. In the final para- graphs, the impact of the recognition of this tradition for mathematics teaching is explained. InModelingofImpliedStrategiesofSoloExpertPlayers,LucTiennotmakesan in-depth analysis of several forms of sowing games. These games were probably inventedinAfrica,buttraveledtoalargerareaaroundtheworld,throughoutEastern SouthAmerica,andSouthernAsiainparticular.Theyarecombinatorialboardgames fortwoplayersthatconsistinmovingseeds—organizedintheboard’s“cups”—,thus CélinePetit,aspartofthe18thInternationalUnionofAnthropologicalandEthnologicalSciences (IUAES)WorldCongress”,Florianopolis,Brazil,2018.Theorganizationofthispanelandthereafter theimplementationofthisbookprojectwouldnothavebeenpossiblewithoutthefinancialsupport oftheFrenchNationalResearchAgency(“ETKnoS”Project,2016–2021). Introduction vii “sowing and capturing” the latter seeds through precise rules and procedures. The chapter concentrates on a particular complex form of these sowing games, called Solo,thatareplayedfromCentraltoSouthernAfrica,includingMadagascar,where theauthorhascarriedoutfieldresearch.AmongthedifferentkindsofSolo,Tiennot studiesthesowinggamesbao,originatingfromZanzibar,andthedifferentvariants of this game that he has observed throughout Madagascar. The different forms of the game show the complex use of mathematical operations. The author manages to show how systematic ethnographic work on these games can reveal the mathe- matical algorithms which are hidden in them. To this end, Tiennot also introduces differentmodelingtools(symbolicwriting,andmathematicalgraphsinparticular) for encoding and analyzing the procedures implemented by the players during the game.Thismodelingapproachallowsustogainabetterunderstandingofhowthe sowing game experts can play so fast, by anticipating the outcome of each move (without “overloading their short-term memory”) through the implementation of “optimizedmovements”. InSandDrawingVersusStringFigure-Making,EricVandendriesschecompares twoactivitiesoftheNorthernAmbrymIslandersinVanuatu,whicharebothseenas formsof“writing”inthelocalknowledge.Oneisthemakingofstringfigureswith hands,feetand/ormouth.Theotherisdrawingacontinuouslineinaloopwiththe fingerinthesand(ordustyground).Bothexpressandrecordknowledgeoneither particularmythicentitiesorspecificenvironmentalphenomenainthearea. Inthesecondplace,andmostimportantly,theauthorinvestigateswhatnotions, termsandconceptsofoperation,procedure,sub-procedure,symmetryanditeration canbefoundinbothtypesofpracticesandhowtheserevealsharedgeometricand algorithmic properties. In this way, ethnographic detail and in-depth analysis on mathematicalthinkinginthesepracticesareofferedasmaterialforthebasicdiscus- sion in this volume, going from a particular ethnographic context to the general interdisciplinaryfieldofinvestigationtheeditorshaveinmind. PartII“ImpactofIndigenousCultureonEducation inGeneral,andonMathematicsClassesinParticular” HerethereaderwillfindtwoBrazilianstudies.BothrightlyclaimthatBrazilhasa particular and very interesting history with regard to the impact of native cultures on educational programs. Apart from these two articles, a chapter is included that focusesonprojectsinthenorthofGreece. In Indigenous School Education, Sérgia Oliveira, Liliane Carvalho, Carlos MonteiroandKarenFrançoisfirstgiveasyntheticoverviewofthehistoryofIndige- nouspeoplesinBrazil,fromthebeginningoftheinvasion/colonization(from1500 on),whenthesepeopleshavebeendecimatedbytheinvaders,andthereaftersubjected tocolonialauthoritiesandreligiousinstitutions.Afterindependence(1822),different educational programs have attempted to acculturate these populations. It will take viii Introduction more than 150 years, through different Indigenous movements’ struggles, to see public policies emerge in Brazil, and the creation of the Indian’s National Foun- dation—FUNAI, finally granting civil and political rights to Brazilian indigenous people,includinglegalregulationsoftheirlands,education,culture,andhealth.Our authorsshowthatthedevelopmentoflocaleducationalsystems,progressivelytaking intoaccounttheculturesofthevariousBrazilianIndigenoussocieties,hasbeendone throughalongprocesswhichfinallyledtolegalrecognition.Recently,thesepolitical andeducationaladvanceshavebeendeliberatelydismantled,bythefederalgovern- ment,seekingto“deconstructtherightsandguaranteesofsocialpoliciesaimedat indigenouspeoples.Educationwasthehardesthitbytheseconstraints.” However,variousBrazilianindigenouscommunitiescontinuetostruggleforan interculturaleducationbasedontherespectofdiversity.Itisindeedthecaseofthe XukuruofOrorubápeoplesettlingindifferentvillagesinthestateofPernambuco. They“strengthentheirethnicidentityandreinforcetheirstrugglesthroughasocio- political organization”. In particular, the Council of Xukuru Indigenous Teachers ofOrurubáwhichseekstodiscussissuesrelatedtointerculturaleducation,helping indigenousteacherstoentwinetheofficialcurriculumwiththeirownlocalculture.It isincollaborationwiththelattercouncilthatourauthorshaveundertakenacollab- orativeresearchprogramrelatedtotheteachingofstatistics.Thechapterendswith thedescriptionofthisexperiment:Atfirst,Oliviera’steamcarriedoutaparticipant- observer ethnographic research, in order to better understand the Xukuru cultural context.Thereafter,acollaborativeworkinggroupwasformedwithbothindigenous teachers and our researchers, in order to determine how teaching statistics could be correlated with the Xukuru’s concerns, while implementing a (locally based) course plan on statistics (related to the use and preservation of water resources in these communities). Indeed, the results of this local experiment suggest that such pedagogicalprojects(whencarriedoutincollaborationwithlocaleducationalinsti- tutions)canenhancetherelationshipbetweenthelocalcurriculumandindigenous communities’challenges. Theroleofso-callednon-westernworldviewsandformalreasoningproceduresin thegeneraleducationallandscapeofalargeandintenselydiversecountrylikeBrazil illustratesapointthatwillhavemuchrelevanceinthefuture,formanycountriesin thisprogressivelymixedworld. In Indigenous Mathematical Knowledge and Practices, Cecilia Fantinato and KetioLeitefocusonaparticulartopic:withinthecontextofBrazil’sstudiesofmath- ematicsandeducation,onefindsaseriesofsixconsecutivecongresses(2000–2016). Theauthorsanalyzeformatsandpresentationsduringthesenationwideconferences andindicatehowtheygottobeprogressivelymoreinterestedinandmarkedbynative perspectivesinmathematicseducation.Theyshowhowthepoliticalfocusallowed for this shiftover the years, combined with the successful development of cohorts of“native”teachers.BrazilianethnomatheticiansMariaCeciliaFantinatoetKecio LeitegiveanoverviewoftheresearchinethnomathematicscarriedoutinBrazilover thepast20years,dealingwithissuesrelatedtoindigenousknowledgeandculturally based education. Since the seminal works by Ubiratan D’Ambrosio in the 1980s, theethnomathematicsresearchfieldhassignificantlydevelopedinthiscountry(as Introduction ix nowhereelseintheworld)andinstitutionalizedinmanyBrazilianUniversities.In ordertodrawapictureoftheimpressiveBrazilianproductioninethnomathematics, theauthorsfirstanalyzethedifferenttopicsaddressedthroughoutthefiveeditionsof theBrazilianCongressofEthnomathematics(CBEm),from2000to2016.Notably, this brings to light an increasing interest—over this period—for research devoted toindigenousmathematicalpracticesandknowledgeandtheirpedagogicalimplica- tions.Thechapterdemonstratesthatthereasonsarethreefold;first,thereareover300 differentindigenoussocietiesinBrazil.Thisgreatlinguisticandculturaldiversityin thiscountryoffersinvaluableopportunitiesforcarryingoutsuchresearch,whichfew ethnomathematicianshaveundertakensincethe1980s.Secondly,in2008,alawwas adopted,establishingtheguidelinesforNationalEducation,whileincludinginthe officialcurriculumthemandatorytopic“HistoryandAfro-BrazilianandIndigenous Culture”. Consequently, this led to an increase of the number of works on indige- nousmathematicalknowledgeandtheirpossibleusesfortheelaborationofcultur- allybasedcurricula.Thirdly,thedevelopmentofIndigenousInterculturalLicentiate University Courses implies an increasing “capillarization of Ethnomathematics in teacher training courses” from undergraduate to graduate education. As a conse- quence, Brazilian academic research in ethnomathematics is conducted by indige- nousresearcherswhobelongtothesocieties/communitiesunderstudy.Thechapter thusraisessomeissuesregardingtheresearchmethodologyimplementedbythese new generations of researchers arguing that they do not need to carry out genuine ethnographies—asnon-nativeresearchersdid—sincetheyaredealingwiththeirown cultures. InSubvertingEpistemicideThrough‘TheCommons’:Mathematicsasare/making space and time for learning, Anna Chronaki and Eirini Lazaridou focus on the global—and the Greek—push towards detached and presumed universal mathe- maticsandmathematicseducationalprograms,emanatingfromtheneoliberalthink tanks of our time. With an in-depth ethnographic research on alternative develop- ments in one particular region of Greece (bordering on Macedonia) the authors characterizetwoopposingeducationallinesofdevelopment. Thefirsttrendyieldswhatiscalled“epistemicide”,resonatingwithcriticalstudies withinmathematicseducationandschoolingingeneral.Thetermepistemiciderefers to the destruction of local, but also of situated learning processes and contents, replacingthemwithso-calledglobaluniversallypowerfulalternatives.Theauthors describe what this trend allows for and is producing in the local community: the destructionofknowledge(hencethespecificterm“epistemicide”)andtheuprooting of the local people who are enduring this trend. The second trend is observed as a local alternative and goes by the name of “radical pedagogy of commons”. It is linked to a profound criticism of mathematics education, as it is emerging in for exampleSouthAmerica,withanontologicalshifttowardsa“pluriverse”insteadof thewestern-dominatedso-calleduniversalknowledge.Inthatsensethestudyrelates to the project of this book, and it prefigures some of the theoretical critiques in Baker’s chapter (part III).Also, it exemplifies what was precedingly referred to in thisfieldas“streetmathematics”,whichmaybeinterpretedasethnomathematicsin westernculturalcontexts.Theauthors’studyshowshowtheexplicitexplorationsof
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