mathematics funds of knowledge: sotmaute and sermaute fish ... · mathematics funds of knowledge:...

Australian Journal of Adult Learning Volume 52, Number 1, April 2012

Mathematics funds of knowledge: Sotmaute and Sermaute fish in a Torres Strait Islander community

Bronwyn EwingYumi Deadly Centre, Queensland University of Technology

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through adopting a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can also be used as foundations for future learning for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

Mathematics funds of knowledge 135

Keywords: Torres Strait Islands, Torres Strait Islander parents, Indigenous Knowledge Centre, funds of knowledge, sorting, partitioning.

What can be learned from Torres Strait Islander parents’ funds of mathematical knowledge and incorporating into the transition to formal school?

AtatimewhenanumberofstrategieshavebeenimplementedtoincreaseTorresStraitIslanderparents’participationineducationwiththeirchildren(seeforexample,DepartmentEducation,EmploymentandWorkRelations2011;TorresStraitIslanderRegionalEducationCouncil2011),Iarguethatgoingbeyondthesimpledichotomybetweenparents’fundsofknowledge(experience,out-of-school,intuitive,tacit)andacademic(in-school,linear,deliberate)iscritical.Forchildrenintheearlyyearsofschooling,instructionmustbeunderpinnedwithauthenticengagementinproductiveactivities,drawingonpriorknowledgeandcomplexityandthedialogicalemergenceofinstruction.Whatthismeansforeducationalpracticeisthatbyinvitingchildrenintoaworldofmotivatingactivitieswheretheeverydayandspontaneouscomesintocontactwithschool,thechildren’sandtheirparents’engagementwithboththeactivityandthesocialcontextareforegroundedsothatquestionsandinquirycanoccur(Gonzalezetal.2005).Thatis,theclassroombecomesaninformationexchangethatdrawsonmultiplefundsofknowledgethatareactivatedandtiedwithmathematicscurricula(see,forexample,AustralianCurriculumandReportingAuthority2009;DepartmentofEducationandTraining,Queensland2010;DepartmentofEducation,TrainingandtheArts,Queensland2008).

Attheheartofthisprojectafundsofknowledgeapproachisadoptedbecauseitprovidesapowerfulandrichwaytolearnaboutcommunitiesintermsoftheirresources,theirmathematical

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competencerelatedtosotmaute (sorting)andsermaute (partitioning)throughthegivingoffishandthewaytheyutilisetheseprocessestosupporttheeducationoftheirchildren.Throughfamilialandsocialnetworks,TorresStraitIslanderparentsbuildcapacityamongstoneanotherandwiththeirchildren(Makuwira2007).Suchnetworksvalidatetheparents’owndefinitionsofmathsastheyexistintheircommunities—‘fundsofknowledges’thatareappliedindailylife(Moll1992:133).Theideaoffundsofknowledgeviewsthatpeoplearecompetentandhaveknowledgethathasbeengrownanddevelopedthroughtheirlifeexperiencesthathavegiventhemthatknowledge.

Ifoneacceptsthepremiseofthisarticle,thatfundsofknowledgeofmathematicsarethosethatreflecttheuniquehistoriesandcultureofcommunitiesandwhicharehistoricallyandculturallyaccumulated,thenthequestionarises:Howaretheseknowledgesandthelearningofthemconnectedwithandsituatedincommunitiesandthevoicesofthepeople?Here,IdrawontheworkofLahn(2006)whodescribesthepracticeofgivingfish.Givingasermaute (share)offishisasignificantpracticeforTorresStraitIslanderwomen.Whilethechoiceoffishingcompanionscanillustratearangeofrelationships,forexample,familyandfriendships,the‘distributionoffishisnotasflexible’(p.301).Withthedivisionofcaughtfishcometheexpectationstogiveasharetorelativesaswellaselderlyneighbours.Distributingthefishisgenerallytowards‘ascendingmembersoftheirownfamilyandthatoftheirhusband’(p.304).Thisemphasisreciprocates

theearlierphysicalandsocialnurturancereceivedbytheindividualsinthisgeneration(inparticular,parents,aunties,mother’sbrothers).Theseindividualsareviewedashavingnurturedthemtoadulthood,anideacommunicatedlocallythroughexpressionslikelugaut(lookafter)andgromape(raised)....Thisethicinfactextendstoalloldermembersofthecommunity,whoareseenasresponsibleinamoregeneralsense


forcreating(nurturing)thephysicalandsocialcommunitytowhichtheyoungergenerationsnowbelong.(p.304)

Womenareexpectedtoprovidetheirrelationswithfishofreasonablesizeandtypeinrelationtotheiroverallcatch.Throughthisprocess,theideaistomakeindividualbuckets‘lessunequal’bycomparisonwithothersthatarenotnecessarilyequal(p.301).Thepreferredwaytocontrolfishdistributionafterreturninghomeistochoosethefishtodistributetospecific‘householdsandindividualsfreeofscrutinyorpressure’(p.301).Butthedistributionoffishoccursamonganumberofhousesthatfunctionas‘multi-housenetworks’(p.303).Itisthroughsuchnetworksthatfundsofknowledgearelearned,sharedandpractised.

Where is the community, and what did I do?

Theprojectadoptedacommunity-basedapproachbecauseit‘conveysamuchmoreintimate,humanandself-definedspace’(Smith1999:127).Itreliesuponandvalidatesthecommunity’sowndefinitions.Iestablishedarelationshipwithcommunitymembersovertimeasaconsequenceofanotherprojectthatwasbasedattheprimaryschool,butchosetoembarkonapreliminaryprocessincollaborationwiththecommunityfollowingculturalprotocols,respectforthecommunityandbecausethisprojectwasbasedwithinthecommunityandnotschool.Whereisthecommunity?

TheTorresStraitIslandsconsistofeighteenislandsandtwoNorthernPeninsulaAreacommunities(TorresStraitRegionalAuthority2010).TheyaregeographicallysituatedfromthetipofCapeYorknorthtothebordersofPapuaNewGuineaandIndonesiaandscatteredoveranareaof48,000squarekilometres.TherearefivetraditionalislandclustersintheTorresStrait:topwestern,western,central,easternandinnerislands(seeFigure1,TorresStraitRegionalAuthorityMap2011).

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Figure 1: Torres Strait Regional Authority Map

AlthoughIhadvisitedtheislandonpreviousoccasions,Icomefromabackgroundofspeakingonlyonelanguage,English,whichwasoneofthreelanguagesspokenontheislandoroneoffourspokenintheTorresStraits.SpecificlanguagesarespokeninTorresStraitIslandercommunitiesincludingStandardAustralianEnglish,Yumplatok(Creole),KalaLagawYa(Mabuyag)andMeriamMir(Osborne,2009;Shnukal,2004).KalaKawawYa(KKY)isunderstoodtobeadialectofKalaLagawYa(Osborne2009).Thetraditionallanguagesofthetopwesternandwesternislands,KalaLagawYa(KKYandMabuyag)areunderstoodtocomefromthemainlandofAustralia,withtheeasternislandlanguage,MeriamMir,emergingfromPapuaNewGuinea.Yumplatok,identifiedasamodernlanguageandstemmingfrom


colonisation,isderivedfrom‘meshing’bothtraditionallanguagesandEnglish,thuscreatingalanguageinitsownright(Osborne2009;Shnukal2004).Thislanguageisidentifiedasunifying,thatis,itistheonethateveryoneintheTorresStraitscanspeak,whereasthewestern,traditionallanguagespeakerscannotspeakandunderstandtheeasternlanguagespeakers(Osborne2009;Shnukal2004).

Who are the community?

Communitymemberswhohadavoluntarydesiretoparticipatewereincluded.Thereislittlebenefitderivedfromcommandingthatpeopleshouldattend.Whenthereisasincereinterestinreciprocallearninginacommunity,relationshipsandtrustcangrow.Twentyadultsandeightchildrentookpartinthecommunityconsultationmeeting.Allresideinthecommunitywherethemeetingwasheld.FouradultstookpartintheworkshopwhichwasheldinanIndigenousKnowledgeCentrethatiscentrallylocatedinthecommunity.Allparticipantsliveinthatcommunity.Theiridentitiesareprotectedinthispaperusingpseudonyms.

How did the meeting and workshopcome to be and what were the methods for doing this?

Recentinvolvementwithcommunitiestaughtmeabouttheimportanceofmeetingwithcommunity.Ihavelearnt,andcontinuetolearn,aboutwhatworksandwhatdoesnot.Whatworksispredicatedontheassumptionthat,ifcommunitycanengageandidentifywithwhatisdiscussed,themoreinterestandenthusiasmisshown.Individualmeetingswereheldwithseveralpeople,forexample,theschoolcampusleaderandtheIslandCouncillorandtoseekpermissiontomeetunderthe‘OmeiTree’—TreeofWisdom—whichwassuggestedbyDenise,aseniorcommunitywoman.AmeetingwasalsoheldwiththelocalradioannouncerfortheIslandradiowhichthenresultedinaradiointerviewthatwasbroadcasttotheIslandcommunity.WithsupportfromDenise,andaparent

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fromthecommunity,apaper-basedflyerwasdeliveredface-to-facetothehomesofIslandparentstoletthemknowaboutaproposedcommunitymeetingandaworkshopgathering.Thecontentoftheflyerwasbriefandaimedtoprovidesuccinctinformationforeaseofreadingandclarity.Aspertheflyerschedule,themeetingwasheldforonehourundertheOmeiTreewithanumberofcommunitymembersinattendance.Accordingtoonecommunitymember,thefigtreeisbelievedtobeoveronehundredyearsoldandhasbeenasignificantmeetingplacefortheIslandcommunity.DuringthemeetingIexplainedtheprojectandhowparticipantsmightbeinvolved.Gainingconsentwasrespectfulofthecommunity’splaceandenvironmentasalsowasthat,asavisitor,Ineededtobemindfulofmyactionsandpresenceandconductinthecommunity.

What kinds of questions did I ask?

ThekindsofquestionsIaskedemergedasaconversationratherthanaresearchinterviewformat.Icarefullyexplainedthatconfidentialitywouldbemaintainedandthatpseudonymsarealwaysusedtoprotectthecommunity’sidentities.AtthemeetingIaskedthegroupwheretheyusedmathematicsintheirdailylives.Theresponsesincluded:buyingfoodatthesupermarket,cookingandcountingfishandshells,indicatingthatitemergesthroughdailyactivities.Asthediscussionprogressed,Iexplainedsomeoftheearlynumberideassuchassorting/classificationusingshells,sticks,leaves,andPoincianapodsthatIhadgatheredfromthecommunity.TheseitemswerecollectedafterseekingpermissionfromJulia,aSeniorcommunitymember.AtthesubsequentworkshopIaskedaboutsharingandwhereitwasusedindailylife.

Data collection techniques

Forthepurposesofthispaper,thedatacollectiontechniquesincluded:digitalphotography,fieldnotesandaudio-recordingofaworkshop.Digitalphotographyasanon-writtensourceofdata


allowedforthecapturingofvisualimagesthatwerecentraltothepreliminaryprocessandwhichservedasareminderforme(Stringer2004).Fieldnotesprovideddescriptionsofplacesandeventsastheyoccurred.Theyprovidedongoingrecordsofimportantelementsofthesettingandassistedwithreportingandreflectingbackoverevents.Audio-recordingservedasadetailedreminder,capturingparticipants’knowledgeandunderstandingsverbatim(Stringer2004).Italsoprovidedongoingrecordsofimportantelementsofthesetting.Eachtechniqueaffordedthevalueofinsightintotheimportantpreliminaryplanningoftheproject(Stringer2004).

What happened at the community meeting?

Inrecentyears,buildingonwhatcommunitiesbringtoparticularcontextsandontheirstrengthshasbeenshowntobeeffectiveinengagingwithcommunities(Gonzalez&Moll2002).Howdoesthisoccur?Awaytoengagecommunitywastodrawtheminwithknowledgethatwasalreadyfamiliartothem,andwhichthenservedasabasisforfurtherdiscussionandlearning(Gonzalezetal.2002).However,withthisprocesstherewasachallengeanddilemma.HowdidIknowabouttheknowledgethattheybroughttothemeetingwithoutfallingintostereotypingtheirculturalpractices?HowdidIaddressthedynamicprocessofthelivedexperiencesofthecommunity?Smith(1999)hasarguedthattheresponsestothesequestionshaveemergedfromcommunity-basedresearchthatreliesonthecommunity’sdefinitionsanddiscussions.

Inthemeeting,IintroducedmyselfandexplainedwhoIwasandwhereIwasfrom.Ialsoexplainedsomeofmybackgroundandexperiencesasamatterofprotocolandrespect.Byintroducingmyselftothecommunity,Iprovidedinformationaboutmyculturallocation‘sothatconnectioncanbemadeonpolitical,culturalandsocialgroundsandrelationsestablished’(Moreton-Robinson2000:xv).Thisprocessthenallowedthecommunitytolocatemeinthecontext

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ofancestry,whereIwasfromandmyfamilyrelations.Asthemeetingprogressed,Iaskedacoupleofopen-endedquestionstoinvitestoriesaboutwheremathematicsmightbeusedindailylifeontheisland.Thisledtoconversationsamongstthegroupaboutwheretheyusedmaths.Theirresponseshelpedtoconceptualisethemathstheyused,forexample,sorting.

Whenaskedhowtheymightsortshells,Denisevolunteeredtosortarangeofdifferentshellsintogroups.Wethenhadtoidentifywhatcriteriawereusedforthegrouping.Sortingactivitiesassistwiththepromotionofunderstandingsofgrouping.Childrenlearntosortobjectsintogroupsfromtheirdailyexperiences.Theylearntoidentifysamenessthatdefinesthecharacteristicsofgroupings(Sousa2008).Theideaofcreatingandnaminggroupscontinuesthroughoutlifeandisawayofcreatingandorganisinginformationandmakingconnectionswithpeople’sexperiences.Beforeyoungchildrencanlearntocountgroups,theybegintheprocessofdefiningacollectionusingtheobjectsintheirdailylives(Baroody&Benson2001;Sousa2008).Hence,theyneedexperiencesthathavearichvarietyoftwo-andthree-dimensionalobjects.Noticinglikenessesanddifferencesamongobjects,childrenbecomeawareofthefeaturesthatdifferentobjectshave.Theyalsobecomeawareofgroupingobjects.Suchanunderstandingpavesthewayforlearningaboutpartitioning.Deniseestablishedthefeaturesofeachofthesetsofshells.Ifthecriteriaformembershiptoagrouparevague,itismorechallengingtodecidewhethertheshellsbelongtoaparticulargroup.Wetalkedfurtheramongstourselves,withDeniseallowingustimetoidentifythefeaturesofeachgroup.

Frommyexperience,Icouldnotidentifythecriteriathatdefinedthegroups;however,therewasconsensusamongstcommunitythatcriteriahadbeenestablished—edibleandnon-edibleshellcreatures.Inthisexample,thecommunityusedtheirdailylivesandactivitiesasanopportunitytotalkaboutsortingusingtheirhome


language—YumplatokandEnglish.WhenIaskedwhenchildrenlearnaboutedibleandnon-edibleshells,therewasconsensusthatthisoccursataveryyoungage,forexample,onetotwoyears,andduringtimeswhenfamilieswalkalongtheshoresoftheIslandandwhenfishingorplayinginthewater.ThisexamplereinforcesMoll’s(2002)statementthatlearningcanberichandpurposefulwhenitissituatedwithinthatwhichalreadyexists—theculture,communityandhome-languageofthegroup.Gonzalez(2005)explainsthisfurtherbystatingthatmathsisembeddedinsocialknowledgeandmediatedthroughlanguageandtheactivitiesofthecommunity.Itisnotlearnednorisitdisembodiedfromitssocialmeaningandcontextashappenswithinformalschoolingandbecomesalinearprocessofdialogue.Thelearningaboutsortingedibleandnon-edibleshellcreatureswasdistributedamongthegroup.Itwasashared,collectiveconstructionofmathematicalknowledge.Ifoundthatthisexperienceofsharedknowledge,richinitsowncomplexity,evincedknowledgethathadbeenhistoricallyandculturallyaccumulatedandsharedthroughdailyliving.Thecommunityvalidatedtheirdefinitionsofknowledge,sortingusingshellsfromtheirenvironment.Indoingso,thisprocessprovidedarichwaytorepresenttheirknowledgeandcompetencetosupporttheirchildren.

Asthemeetingcametoanend,memberswereaskediftheywouldlikefurthermathsworkshopstobeorganisedfor,andwith,theparentsandchildren.OfimportancewasthatthecommunityneededtimetonetworkanddiscusswhethertheywantedmetoreturnandworkwithparentsandchildrenontheIslandandiftheyidentifiedthattherewerebenefitsfortheircommunity.Thenextsectiontalksaboutoneworkshopandwhathappened.

What happened at the workshop?

Buildingonwhatcommunitiesbringtoparticularcontextsandontheirstrengthshasbeenshowntobeeffectiveinengagingwith

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communities(Gonzalez&Moll2002).Thiswasevidentfromthecommunitymeetingandfirstworkshopconductedthatfocusedonearlyalgebra.Asecondworkshopwasheld,withparentsinvitedtoidentifyitsfocus.Itwasduringthatworkshopthatsharingandpartitioningemergedasmathematicalprocessesthatparentsusedintheirdailylives.Usingasemi-structured,informaldiscussionandusingitemspreviouslycollected,allowedforunderstandingsofhowthisknowledgemightbeusedtosupporttheirchildren’slearning.IwasinvitedtodotheworkshopintheIndigenousKnowledgeCentreontheIsland,aplaceofagencythatpermitsandpromotesengagementinarangeofactivitiesforthecommunity(Taylor2004).

Partitioningexperiencesareimportantforbuildingrationalnumberunderstandings(see,forexample,Piaget,Inhelder&Szeminska1960).Theabilitytodivideanobjectoragroupofobjectsintoequalpartsisidentifiedascriticaltounderstandingthelogicaldevelopmentofpart-partandpart-wholerelationshipsandnotionsofequalityandinequality(Lamon1996).Thisabilitymayalsoinfluencechildren’sunderstandingsofmathematicaltopicssuchasmeasurementandgeometry.Partitioningisaprocessthatgeneratesquantityand,indoingso,buildsunderstandingsofrationalnumbers(Lamon1996;Pothier&Sawada1983).Itisanactivitythatisintuitiveandexperienced-based;indeed,thisprocessconnectstheprocessofconstructingrationalnumberswithchildren’sinformalknowledgeaboutfairsharing(Pothier&Sawada1983).Unitising,however,isacognitiveprocessforcomingtoknowandunderstandtheamountofagivenitemorsharebefore,duringandafterthesharingprocess.InthefollowingexcerptstheprocessofpartitioningisdescribedbyAilia,oneofthreewomenwhoattendedtheworkshop.Ailiaeexplainstheprocessofgivingfish.ThisexplanationcameaboutasaconsequenceofaquestionIaskedaboutwheremathsisusedinthewomen’sdailylives.Ailiadrawsonlanguagethatisassociatedwithpartitioning—division.Ofsignificanceinthefollowingexcerptisthatsheexplainshow‘we’involve‘ourkids’ingivingfish.


Ailia:Likeyouaskedmewhatwedoherelike,nowwhenwecomeinwiththefishandtheshareforthecommunity[unclear]wedowithourkidsandtheywatch.

Inthisexcerpttwoaspectsaresignificant.Thefirstistheuseoftheterm‘share’andthesecondisthat,afterthewomenhavegonefishing,that‘share’isforthecommunityandtheirchildrenareengagedintheactivity.Throughtheprocessofwatching,thechildrenlearnedthesubstanceofsharingexperiencesthatcanthenbeusedasopportunitiesforexperimentinginothercontextsand,indoingso,buildingtheirknowledgeoffairsharingviafamilyactivitiesandrelations.ThisprocessisinlinewithwhatLahn(2006)identifiedinherworkoffishgivingpracticesintheTorresStraitIslands.Thereciprocal,nurturingrelationshipoccursacrossgenerationswiththewomennurturingandmodellingtothechildrenhow‘oldermembers’arecaredforinthecommunity.

Here,thespecificcharacteristicsofcommunityrelationshipsandactivitiesseemtoconvergeonverysimilarlyorganisednetworksofrelationsbasedon‘denseexchange’(Velez-Ibanez&Greenberg2005:53).Foreachfamilyfromwhichthewomenandchildrencome,thefundsofknowledgeaccumulatedandthatformthebasisofdailylifecontainmuchofthepreviousgeneration’srepertoireofinformationandskillsforliving.Thesefundsofknowledgeareembeddedineitherhistoricalorcontemporaryexperiencesoffamilies.Thefundsandexperiencesarea‘currencyofexchange’(p.54)betweengenerationsandfamiliesthatformthe‘culturalglue’(p.54)thatmaintainsculturalrelations.Thisexchangeandtheideaofsharingareembeddedinthesocialknowledgeofthewomen.Itismediatedthroughthesharingexperiencesthatthewomenperformanddistributeamongthegroupincludingthechildren.Inthenextexcerpt,Ailiadescribessharingasapracticewhichismediatedanddistributedamongstthefamilies,activitiesandcontexts.

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Ailia:Whenwedividethefishamongthefamilies,likeifI’vegotmythreesistersandtwobrothersthatIneedtocatchfish[unclear],withthefish,itdoesn’t,wedon’tall[get]thebiggeronesinthisfamilyandthentheothersistergetthesmallones,wedivideitquiteevenly,likeallthebigfishinthebasket,wegetoneeach.Andthenwegodowntothesecondsize,evenitup.

Bron:Sotheneveryonecangohomeandfeellikeithasbeenafairsharingout?

Ailia:Yes.

Bron:Andthat’stheprocessmostofthetime?

Ailia:Yeah.

Bron:Andthechildrenlearnthat?

Ailia:Yes.

Bron:Theygrowupknowingthat?

Ailia’sexplanationprovidedcriticalinsightsintohowdivisionwasdeeplyembeddedinfishgivingpractices.Itisthesesamepracticesthathavethepotentialtobeinvisiblethroughthetrainedeyesofformaleducation(Gonzalez,Andrade,Civil&Moll2005).Themathsinvolvedinsuchpractices,go‘beyondfacileconstructsofsocialcontextandmusttakeintoaccountthedeeplyfeltrelationshipsofco-participants,thesocialrelationshipsinvolvedinundertakingthepracticesaswellasthedeepengagementofconnectionwithaproduct,andnotjustaprocess’(p.264).Ailiawasinterestedinexplainingthefish-givingprocessbut,indoing,sowasalsointerestedinuncoveringthemathsinasystematisedway.Forexample,sheexplainedthatshehadthreesistersandtwobrothersthatsheneededtocatchfishforanddistributeevenly.Thefishwerefirstsortedintodifferentsizes.Thegroupswerecreatedbasedonsameness,thatis,fishweresortedbyweightthroughtheactionofhefting,andmeasuringlengthandgirthbysight(seeFigure1below).


Figure 1: A fair share

Thisprocessaffordsyoungchildrenwithopportunitiestolearnaboutsorting,sharingandpartitioning.Howmanyparentsandchildrenareawarethatthisknowledgeasitrelatestodivisionresidesintheirdailypractices?Intheaboveexample,thefishweredistributedandthencheckedtoseehowmanyeachbucketreceived.Whenpartitioning,thenumberofgroupsisalreadyknown,buthowmanyobjectsmustbeplacedineachgroupisnotknown.Inthenextexcerpt,Ailiaexplainsthesharingprocessfurther:

Ailia:Ifweonlyhavefourbuckets,evenifweonlyhavethreebigfishthatneedstogointoandthenwetaketwosmalleronesthatwillmakeitlikeabigBron:Oh,okay.Ailia:Andthenthere’s[one]forthat,andthesethreebucketswillbethisbig[one]andthisone,twointhere.Bron:Youknowfeelintermsofweightorbysight?Ailia:Justby[movesarmstoindicateheftingaction].Bron:Sight?Ailia:Yeah.

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InFigure1,thesizeofthesetisunknownandiscalledfair-sharingorapartitionproblem.InAilia’sexcerptabove,thewhole(fivefish)issharedamongaknownnumberofbuckets(four)todeterminethenumberoffishineachbucketandequality.Equalitywasrepresentedastwosmallerfishequallingthesizeofonelargerfish.Whenaskedabouthowthesizeoffishweredetermined,Ailiarespondedbyheftingandgesturingtowardshereyetoindicatebysight.

InthisexamplepartitioningwasfoundtonotbeapossessionthatresidedinAilia’sheadasafixedattributeorskillonlyknowntoher.Rather,partitioningwasapractice,andgivingfishcreatedacontextforthedevelopmentandteachingofthatpractice.Gonzalezetal.(2005)arguethatunderstandingmathsisnotsimplyaboutthepossessionoffundsofknowledgeinmathematicaldomains.Thekeypointhereisthatsuchdomainsmustbesociallymediatedinto‘productiveknowledgeinordertobemeaningful’(p.266),asdemonstratedinthefollowingexcerptfromAilia:

Ailia:Whenwedothat,kidswillstandthereandsay,whydon’tyouput[indistinct]thequestion,sothenweexplainittothem.

Bron:Yep.

Ailia:Sowewantiteven.

WhatisevidentintheaboveseriesofexcerptsisthatAiliaandthewomenshereferredtowhowereinvolvedinthefish-givingpracticehavetheskills,connectionsandunderstandingswithhowtheprocessworks.Itisuptothewomentopassonthisknowledgeandsupporttotheirchildrenbecausetheyarebroughtupthiswayandthereforeitiswhatisexpected(Lahn2006).Thereciprocityamongfamilywasevidentintheexcerpt.Eachstepintheprocessrevealedanetworkoffamilywhogaveorreceivedfishandadvisedthechildrenoreachother,thusmaintainingsecondgenerationandorthirdgenerationrelationsandpractices.Suchactivitiesdemonstratehowtheprocessestablishedenduring,socialrelationshipsandinterdependenceas


wellasthepartitioningprocess,wherethefocuswasonequalityandsameness.

Theknowledgeofgivingfishhadnotbeentaughtsystemicallytothechildren.Butsuchknowledgebecomesusefulwithinthemathscurriculuminschoolsasameansofstimulatingandengagingstudents’curiosityabouttheirenvironmentandtheirculturalpracticesinacontextthatisrelevanttotheirlives.Whenchildrenbeginschool,andwherethereisanunequaldistributionoffundsofknowledgeandwherematerialsandtextbooksmaybelimited,theuseofapedagogythatdrawsonthechildren’sculturalknowledgeandtheresourcesavailabletothemmakesgoodsense(Browning-Aiken2005).Whenchildrenareprovidedwithactivitiessuchastheexamplesaboveintheirdailylivespriortoschooling,astrongargumentcouldbemadethattheyshouldbemuchmorecloselylinkedwhenchildrencommenceformallearningofpartitioning—division.

Conclusion

Inevaluatingthemeetingandworkshopasstrategiesforengagingwithparentsandtheirculturalpracticesandthemathsthatispartofsuchpractices,theexperiencehasrevealedseveralthemesthatdirectlyaffectthenatureofhome-communityrelations-earlyyears’schoolingandhavethepotentialforimprovingeducationalachievementsonthebasisofmoreknowledgeofpedagogicalpractices.Forone,Ailiaplacedhighvalueonfairsharing—partitioningwhichwasindicatedinthedailypracticesusedtosharethisskillaswellasexhibitingrespectforfamilymemberswhowerealsoteachers.Learningwassomethingthatoccurredinthecommunityandathomeinaformofincreasinghouseholdresponsibilitiesandinthebusinessofpeopleintheirfamilynetworks.Together,thethemeshaveimplicationsforthenatureoftheteachingthatparentsengageinandforthepedagogywithinclassroomswhen

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childrenbeginschool.Thus,teachersneedopportunitieswheretheycanengagewithparentstolearnwhatfundsofknowledgeexistamongtheirstudentsbecausetheyprovideanimportantpartoftheteachingandlearningprocesswhenmaterialsandresourcesarelimited.Conversely,fundsofknowledgecanbeconsideredasenrichingasthecurriculumwheresuchresourcesareavailable.

Acknowledgment

Theauthorrespectfullyacknowledgesthesupport,enthusiasmandengagementoftheIslandcommunity.Withouttheirconsent,theprojectwouldnothavetakenplace.

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About the author

Dr Bronwyn Ewing is a mathematics education researcher at Queensland University of Technology, specialising in the pedagogy of mathematics classrooms from the early years to VET contexts. She has a special interest in the teaching and learning of mathematics to Aboriginal and Torres Strait Islander students and the role of Torres Strait Islander women in their children’s prior-to-school mathematics education.

Contact details

Senior Lecturer, Yumi Deadly Centre School of Maths, Science and Technology, Faculty of Education, Queensland University of Technology, Kelvin Grove Campus, GPO 2434, Brisbane, Queensland 4001Tel: +61 7 3138 3718 Fax: +61 7 3138 3985Email: [email protected]

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