Patterns of choice and visions of future: What role does ... · Patterns of choice and visions of future: What role does socioeconomic status; gender and culture play in students

CharlesDaviauDraftReport 1

Patternsofchoiceandvisionsoffuture:Whatroledoessocioeconomicstatus;genderandcultureplayinstudents'choicesaboutmathematicseducationin

NorthernOntariosecondaryschools.

Charles Daviau

Draft Paper Prepared for: Rainbow District School Board

2010


FocusofStudy:

Whatfactorsaffectagradeninestudent’s‘choice’1intakingappliedoracademic

mathematicsclasseswithinNorthernOntarioschools,andinwhatwaysdothese

factorsinfluencethemathematicscoursessuccessfullycompletedbystudents?

Background:

MyworkasamathematicstutorandinstructorinthelocalFirstNations

communitiesofSagamokAnishnawbekandAtikamekshengAnishnawbeksparked

myinterestintryingtounderstandtheroleofsocioeconomicstatus,genderand

cultureinstudents'choicesaboutmathematicseducationinNorthernOntario

secondaryschools.Iquestionedwhystudentswerenottakingacademiclevel

mathematics;sincenottakingthislevelofmathematicsseverelylimitedtheirfuture

careeroptionsandearnings(RoseandBetts2004;RoseandBetts2001;Levineand

Zimmerman1995;Spence1973;Altonji1995;JoensenandNielsen2006).AsMason

andMcFeetors(2007)putit,“mathematicsisviewedasthecriticalfilterthat

distinguishesstudents’readinessforfurtherlearning”(p.293).Mathematics,touse

Bourdieu’s(1998)concept,constitutesasymboliccapital,andasallcapitalitis

sociallyandculturallydistributed.Someyearslater,ItaughtonManitoulinIslandat

aschoolthathadahighpercentageoflowsocioeconomicfamiliesintheareaand

over50%FirstNationsstudents.Again,theacademicstreamwasnotthestudents’

firstchoice,notwithstandingthefactthattheirpost‐secondaryandemployment

1 It is important to note that the word ‘choice’ in this paper implies that the student’s ‘choice’ is influenced by parents, guardians, teachers, councilors, and community members. It is the student who takes the final step into the classroom; however, it might be the parents telling him/her to go. It might also be the case that the student is a passive participant in the process, completely influenced by others.


opportunitieswouldbeaffectedbythischoice.Iunderstoodtheproblemas

complex,asWaldrop(1992)defines“complex,inthesensethatagreatmany

independentagentsareinteractingwitheachotherinagreatmanyways”(p.11).

Further,InoticedthatthestudentsItaughtgainedgreaterunderstanding

whenIusedanalogiesandexamplesthatweresituatedwithintheirownframeof

reference.LakoffandNúñez(2000)andBarton(2009)arguethatmathematicsis

bestunderstoodwithintheembodiedmind,whichmeansthatmathematicsis

understoodthroughhumanexperience,storiesandmetaphors.Sincemanyofthe

peoplelivingonFirstNationscommunitieshavedifferenthistoriesandexperiences,

itfollowsthatbyteachingthemthroughanalogiesandstoriesthatarefamiliarto

themwillhelpintheirunderstandingofmathematics.

Variousstudies(FinnieandFrenette2003;Jamesetal1989;Arcidiacono

2004)haveshownthatdisciplines,whichhavehighermathematicalrequirements

suchasHealth,EngineeringandComputerScience,Commerce,and

Mathematics/Physicshavethehighestearningpotential.Yetlittleisknownabout

thereasonsthatleadNorthernOntarioAboriginal,Francophone,andAnglophone

studentsfromlowincomesocioeconomicfamiliestonotembracetheacademic

streamintheschool.AsMichelFoucault(1980)contended,societiescreate,through

theirpractices,websofpowerandknowledgedistributionandinducecultural

valuesthatnonethelessmaymakesomeknowledgeinaccessibleforsectorsofthe

population.Itmightalsobethecasethatthosesectorsfailtorecognizethe


empoweringopportunitiesthatcouldfollow,hadthosevaluesbecomepartoftheir

horizonoflife.Ifdisciplinarytrainingcorrelateswithearnings,howought

researchersandpolicymakerstothinkabouttheunequaldifferentialthatexists

betweensocioeconomicclassesasthisinequalitymanifestsindisciplinarychoices?

Iaminterestedinresearchingthesocioeconomicstatus,cultural,gender,classand

therural/urbaneffectsonmathematicselectionsmadeinhighschool,particularly

inthetransitionfromgradeeighttogradenineforNorthernOntarioyouth.

FinnieandFrenette(2003)showthatprofessionalfieldsrequiring

Mathematicshaveahigherreturnoneducationalinvestment;i.e.studentswith

degreesinfieldsthatrequiremathematicsmakemoremoney.Therefore,the

mathematicsselectioninhighschooldirectlyimpactstherangeofoptionsthata

studenthaslaterintheircareerchoices.Withinthecontextofsocialandcultural

distributionofwealthandknowledgeitisimportanttoconsider‘choice’notasa

meresubjectiveact,butasasocial,cultural,economicphenomenon.Thefactors,

whichcouldinfluencethe‘choice’inanonlinearway,includehowachildenvisions

her/hisfuture,theparents’educationlevels,thesocioeconomicstatusofthefamily,

communityvalues,andschoolconstraintsandaffordances.Theobjectiveofthe

thesisistheinvestigationoftheinterrelationsofthesefactorsleadingtoastudent’s

‘choice’ingradenineregardingappliedversusacademicmathematicsclasses.Some

students‘choose’nottotakeacademiclevelcoursesinmathematicsduringhigh

school,perhapsbecauseofcultural,socioeconomic,orotherinfluences;andnot

takingacademicmathematicscoursescanlimittheirchoiceswhentheygettopost‐

secondaryinstitutions.Studentswithoutthesequalificationscannotgetinto


programsatthepost‐secondarylevelthatrequiremathematicssuchastheSciences,

Commerce,andmanyHealthFields.Myfocus,therefore,isasfollows:Considering

theconceptoffactorinaholisticway2,myresearchquestionis:whatfactorsaffecta

gradeninestudent’s‘choice’intakingappliedoracademicmathematicsclasses

withinNorthernOntarioschools,andinwhatwaysdothesefactorsinfluencethe

mathematicscoursessuccessfullycompletedbystudents?

Perhapsthedegreeofparentalsupportorthestudent’scultureaffectsthe

placementbyeitherinfluencingstudents’perceptionoftheirownabilities,orit

mightbethecasethatthepedagogyisnotculturallysensitive.Forexample,a

studentfromaworkingclassfamilymightbeencouragedtotaketheeasiestpathin

highschoolinordertogetajobatthelocalfactory.Theculturalaspectof

mathematicsplacementmightbeinfluencedbythelinkbetweencultureand

cognition.AccordingtoLuisRadford(2008),aSemioticSystemofCultural

Significations(SSCS),meansthatthereareculturallyrelevantsymbolsandmethods

forlearningandunderstandingmathematics,andthereisaneedtotakean

anthropologicalviewpointtoseehowsomeculturesseemathematicsdifferently.

AnexampleofthiscomesfromtheknowledgeIgainedfromworkinginFirst

NationscommunitiesasaninstructorfortheGeneralEducationDiploma(GED),and

teachingmathematicsforCambrianCollege’s(ACE)program.Inoticedthatmanyof

theaboriginalstudentshaddifficultieswiththeGreeksymboliclogicandImadean

efforttousesymbolsandstoriesthattheycouldrelateto,andthismadeadifference

2 By holistic way, I mean that I will take into consideration the complex ways that factors affect students’ choices. Holistic also implies a complex and non-linear relationship.


intheircomprehensionofmathematicalconcepts.Ibegantointroducetraditional

symbolsinmylessons,whilestillfocusingonanarrativethatrelatedtotheirmilieu.

AccordingtoRadford(2008),SSCSinfluencesfourmainareasofmathematical

knowledge,firstitinfluencesthe“waysofconceivingknowledge…[andthewaysin

which]oneseeksknowledgeprimarilyasanendinitself,whiletheotherpursuesit

asameanstoanend”(p.459),thisimpliesthattherearedifferentwaysoflookingat

knowledgeitself.Ononehand,acultureinfluencedbycapitalismmightsee

knowledgeasameanstoanend,awayofmakingmoneyorincreasingproduction.

Ontheotherhand,acommunalculturemightseeknowledgeasanendinitself,a

wayofgivingbacktothecommunityaroundthem.Thesecondisinfluencedby

howacultureperceiveswhatisimportant;apersonisaffectedby“whatisrelevant

andhowtodealwithrelevance”(p.459).Thethirdwayacultureseesitselfin

relationtomathematicalknowledgeisthrough“theculturalkindsofrelationships

betweensubjectandknowledge(e.g.attitudestowardsmathematics)”,thisimplies

thatcertainculturesmighthavedifferentattitudestowardseducation.Thefourth

waySSCSinfluencesmainareaofmathematicalknowledgeisthroughthe“formsof

knowledgerepresentationthatmayvaryfromoneculturetoanother…West’s

emphasisontherelevanceofwriting,mathematicsisoftenreducedtothewritten

dimension”(p.459).Radfordproposestheneedforan“anthropologyof

mathematicalthinking”(p.459).Thisimpliesthatthereisaneedforfurther

researchinthewaysinwhichculturesrespondtothetraditionalWesternviewsof

mathematicalthinkingandplacement.


Onewayofunderstandingtherelationshipbetween‘choices’thatstudents

makeaboutmathematicscoursesinhighschoolistouseethnographicresearch

methodstogainagreaterunderstandingoftherelationshipsandpowerdynamics

withintheclassroom.Holt(2004)usedethnographicmethodswhenshewas

examiningdifferentlyabledchildreninordertoseehowtherelationshipswithin

theclassroomcanaffectastudent’sidentity.Holt’sresearchwaswithinoneschool,

weresheconductedtwentysemi‐structuredinterviewswithchildren.Formy

thesis,Iamplanningtoinvestigatesomeofthereasonsforparticularmathematics

choiceswithinhighschool.IfIfindthatFirstNation’sstudentsdisproportionately

chooseappliedmathematics,Imightbeabletoconductsimilarethnographic

researchinordertoinvestigatethereasonsforthesechoices.Perhapsthe

classroommanagementpracticesusedbyteachersintheclassroomindealingwith

certainstudentsaffectmanyofthestudent’sattitudestowardsmathematics.The

observationmadewhentheteacherisnotlookingmightshedsomelightonthe

students’realfeelingsaboutmathematics.TheobservationsmadebyHolt

illuminatedhow“childrenconstructedchild‐cultures”(p.230).Child‐constructed

culturesmeansthatstudentscancreateandtransformexpectationsfromteachers

andinfluenceattitudestowardssubjects.Forexample,ifastudentisstruggling

withamathematicalconcept,thatstudentcouldinfluenceothersintodismissingthe

importanceofthesubjectentirely.Thesetypesofobservationsmightshedsome

lightonthedynamicswithintheclassroomduringmathematicslessons.Ibelieve

thatHolt’spaperisusefulformythesisbecauseofherclassroomresearchmethod.I

amplanningtostudychildrenindifferentmathematicsclassesandIwillbemore


awareofthechildren’sown“child‐spaceswithintheclassroomsinwhichto

performtheirowncultures”(p.232).Thisimpliesthatstudentsarenotpassive

recipients,butactiveparticipants,overtlyandcovertly,creatingpowerrelations

withintheclassroomthatcouldaffecttheirattitudestowardsmathematics.

AnotherexampleofthesocialissuessurroundingmathematicswithinFirst

NationscommunitiesisthetensionwithinthecommunityagainstWesternculture.

ManyofthestudentswhoItutoredoftenfeltexcludedfromothercommunity

memberswhentheysucceededinschool.Thisisalsoevidencedbythederogatory

commentsmadebystudentsinthecommunity.OneofthetermsusedbySagamok

Anishnawbekchildrenistheword‘apple’;studentswhosucceededacademically,

werecalled‘apples’byotherstudentsbecausetheymaylookredontheoutside,but

theyarewhiteontheinside.Thistypeoflanguageandexclusionofstudentswithin

aboriginalcommunitiesshedssomelightonthetensionandpeerpressurethatthe

youthfromthecommunitiesfacefromwhatHelin(2000)describesas‘lateral

violence’.

Methodology:

InordertogetarepresentativesampleofthestudentswithinNorthern

Ontariowhoaremakingthedecisionaboutwhatmathematicscoursestheyare

takinginhighschool,Iamthereforeproposingtousearepresentativesampleof

gradeninestudentsacrossNortheasternOntarioschools.Ideally,Iwouldliketo

sendoutquestionnairesandthensurveystudentsfromavarietyofschoolboards,


includingtheRainbowDistrictSchoolBoard,theSudburyCatholicDistrictSchool

Board,AlgomaDistrictSchoolBoard,Huron‐SuperiorCatholicDistrictSchoolBoard,

theNearNorthDistrictSchoolBoard,Conseilscolairededistrictcatholiquedu

Nouvel‐Ontario,ConseilscolairededistrictduNord‐Estdel'Ontario,DistrictSchool

BoardOntarioNorthEast,NortheasternCatholicDistrictSchoolBoard.The

questionnaireswouldenablemetogainanunderstandingofavarietyofschools

acrossNortheasternOntario.Iwouldalsoliketosampleavarietyofschoolsfrom

variousFirstNations,includingbutnotlimitedtoSagamokAnishnawbek,

M'ChigeengFirstNation,WikwemikongUnceededIndianReserve,DokisFirst

Nation,NipissingFirstNation,andAundeckOmniKaning.Thequestionnaires

wouldberathersimpletocompletewithminimalcost.However,theinterviews

wouldrequiresubstantialresourcesdependingonhowmanystudentsarechosen

fromeachboard,andFirstNationschools.Iwouldliketoconductenough

interviewswithstudentsfromavarietyofculturalandsocioeconomicbackground

toprovidearepresentationofthestudentpopulation.GiventhatIamcurrently

workingonManagingInformationforStudentAchievement(MISA)aprojectwith

LaurentianUniversity,theOntariogovernmentandmanyoftheschoolboards

mentionedabove,Idonotbelievethatgettingtheschoolboardstoagreetosucha

studywouldbedifficult.Thedifficultydoesnotarisefromgettingtheschoolboards

andcommunitiestoagreetosuchastudy,butratherthedifficultycomesfrom

gettingtheappropriatefundingtopayresearcherstospeedupthetaskof

interviewinganumberofstudentsfromthevarioustownsandcitiesfrom

NortheasternOntario.


Arepresentativesamplemightbeachievablebysendingoutquestionnairesand

samplingstudentsfromtheRainbowDistrictSchoolBoard,theConseilscolairede

districtcatholiqueduNouvel‐Ontario,M'ChigeengFirstNation,Wikwemikong

UncededIndianReserve,andSagamokAnishnawbek.Thegeographicalareawould

covertheareasofatleast14,537km²includingManitoulinIsland,Massey,andthe

DistrictofSudbury.Theseschoolboardsandcommunitieswouldencompass50

elementaryschoolsand15highschoolswithinthesamplearea.Thediffering

socioeconomicstatusesandculturesfoundwithinthisareaareindicativeofmany

ruralandurbanareaswithinNorthernOntario.

Iplantodevelopdescriptivestatisticsofthepopulationofstudentswithin

thestudy.ItisimportanttogetasenseofthestudentpopulationinNorthern

Ontario,whatpercentagehasFirstNationAncestry,whatistheaverageEQAOscore

forthestudentpopulation,andwhatisthesocioeconomicstatusforthevarious

regionswithinNorthernOntario.ShapkaandKeating(2003)alsoexamined

descriptivestatisticsonthestudents’“parentaleducation,perceivedparental

expectations,perceivedteachereffectiveness,school,andpre‐highschoolmath

achievement”(p.937).Thisinformationwillenablemegetagoodsenseofsomeof

thechallengesfacedbythestudentpopulationbeingstudied.Themeasureof

centraltendencysuchasthemean,ofcertainpopulationgroups,couldprovidesome

insightintosomeofthedifferencesbetweentheruralandurbanpopulationgroups,

differencesinmalesandfemales,differencesinNorthernOntarioAboriginal,

Francophone,andAnglophonestudentsfromlowincomesocioeconomicfamilies.

Anycategoricaldatacouldbeanalyzedthroughthemedian,inordertogetapicture


oftheresponsesfromthevariousgroups.Thedispersionofthedatameasured

throughstandarddeviationwouldalsobeusefulingaininginsightintothe

differencesbetweenpopulationgroups.Itisimportanttonotethatassociationdoes

notimplycausation,descriptivestatisticscouldprovideinsightandunderstanding

intothevariousgroupswithinthesample,however,itisimportanttonotethatit

doesnotimplycausation.

Inordertofind‘choice’patterns,Iwillusestatisticalanalysis.I

proposetousequantitativedatafromtheschoolboards,regionaleconomicdata,

andtheEQAO(EducationQualityandAccountabilityOffice)generalizedprovincial

test.Becauseofthenestedstructureofthedata(student,school,community),I

proposetouseahierarchicalmethodmodel(RaudenbushandBryk,2002)inorder

toexaminehowcharacteristicssuchas:socioeconomicstatus,class,culture,

languageofinstruction,gender,andtherural/urbandifferencesaffectastudent’s

‘choice’inhighschoolmathematicsclasses.Ihypothesizethatonefactorthatcan

influenceastudent’s‘choice’istheirfamilyhouseholdlevelofincome.Mighton

(2007)arguesthat‘intellectualpoverty’isoneofthedeepestsourcesofpoverty,

andthateverymathematicalconceptisaccessibletoeveryone.Theaccessibilityof

mathematicalconceptsimpliesthatanyonecanlearnmath,andthegiventhe

correctinstructionanyconceptcanbelearned.InanalyzingtheEQAOscores,socio‐

economicdatarelatedtospecificschools,Iamhopingtobeabletoshowa

correlationbetweenmathematics‘choice’,income,andotherfactors,suchas

socioeconomicstatus,cultural,gender,classandtherural/urbaneffects.


Iwoulduseahierarchicalmodeltoanalyzewhatrelevantfactorsaffecta

student’s‘choice’inhighschoolmathematicsclass.Themodelwouldbesimilarto

theOrdinaryLeastSquares(OLS)approachusedbyeconomiststoseeifthereisa

correlationbetweenthedependentvariable,astudent’s‘choice’inhighschool

mathematicsclass(Mp),andtheindependentvariablesnamely,Income(I),

Population(P),EducationQualityAssessmentOfficetest(EQAO)3,EQAO6,First

Nation(F),Sex(S),SchoolFrench(SF),SchoolEnglish(SE),SchoolAboriginal(SA),

Immigrant(I),Parentallevelofeducation(PL),SouthernOntario(OS),andNorthern

Ontario(ON).Thehierarchicalmodelwillbeusefulbecausemanyofthesevariables

arenestedwithineachother.Forexample,astudentcomingfromalow‐income

family,withalowlevelofeducationinaNorthernruralcommunitymighthave

morebarrierstotakingacademiclevelmathematicscourses;thiscouldhave

compoundingeffectsthatatraditionallinearmodelcouldnotanalyze.

Inordertounderstandtherootcausesofstudent’schoicesIproposetouse

qualitativesurveyquestionsandinterviewsinordertoanalyzethereasonsforthe

students’selection.Inordertofurtherthestudy,surveyswillbecompletedby

students,parentsandteachersregardingthemathematicscoursestaken,and

followedupwithasetofinterviewsbasedonthesurveyresults.Iamproposingto

usesurveysandinterviewsinordertogainagreaterunderstandingofhowthe

factorscontributetoastudent’s‘choice’.Perhapsthedegreeofparentalsupportor

theculturalbackgroundofthestudentaffectsthe‘choice’byeitherinfluencingthe

student’sperceptionoftheirownabilities,orthatthepedagogyisnotculturally

sensitive.Forexample,astudentfromaworkingclassfamilymightbeencouraged


bytheirparentsandfriendstotaketheeasiestpathinhighschoolinordertogeta

jobatthelocalfactory.

MasonandMcFeetors(2007)surveyquestionsincluded“Wewouldliketo

learnaboutthereasonswhyyouchoseyourmathcourse(s).Often,students

describemaydifferentfactors.Listthetopthreefactorsthataffectedyourchoiceof

amathcourseforSenior2”(p.296).Thefollowupinterviewincludedquestions

suchas:

• Describe,briefly,yourexperienceinpreviousmathclasses.Howdidthose

experiencesaffectyourchoiceofmathcoursesforthisyear?Yourapproach

tomathclassthisyear?

• Howdidyoumakeadecisionaboutyourmathcourse(process)?

• Whatstrengthsasastudentdoyouthinkwillmattermosttoyoursuccessin

maththissemester(p.296).?

Thesequestionswouldneedtobedevelopedfrommyownonlinesurvey,however,I

canusesomeoftheideasfromMasonandMcFeetors(2007)studytohelpguidemy

research.Currently,Iamnotinterestedinhowstudentsplantosucceedwithinhigh

schoolmathematicscourse,nevertheless,thisissuecouldbecomeimportantin

followupstudies.Myconcernisaboutwhystudents‘choose’themathematics

coursestheydo;therefore,mysurveyswillquestionthestudents,parents,and

teachersabouttheirroleandreasonswhystudentsenduptakingthecoursesthey

do.


LengthoftheStudy:

ThusfarIhavebeenworkingwithvariousFirstNationgroupswithin

NorthernOntario.WhenIbeganmyresearchinSagamokAnishnawbekIwantedto

examinehowFirstNationsstudentslearnmathematics,Istartedbywriting

researchernotesweeklybasedonwhatIobservedinclass.Thescopeofmy

teachingincludedteachingtwobasicmathematicscoursesforCambrianCollege,as

partoftheirAcademicandCareerEntranceprogram(ACE).Someoftheteaching

methodsthatIwantedtoevaluateweretheeffectsoffrequenttesting,theuseof

culturalsymbolswithintheclassroom,andtheuseofstoriesandanalogiestohelp

thestudentsunderstandmathematicalconcepts.

InJanuary2010,IbeganteachinginasmallportableinSagamok

Anishnawbekthathadlaptopcomputers,blackboards,andawhiteboard.Theonly

reallimitationwithintheportablewasthelackofInternet.Althoughtherewas

Internetwithinthecommunity,itwastooslowtobeeffective.Mostofthestudents

atthebeginningoftheyeardiscussedtheiranxietytowardsmathematics,andhow

theydidn’treallyenjoymath.

ItaughtMondaysandFridays,whichpresentedachallengeduringholidays

orfestivals.Thelossofonedaywouldoftenmeanoneweekwithoutmath,and

consequentlythestudentswouldhavesomedifficultyre‐engagingthematerial.

Attendancewasanissuethroughoutthecourses,anditposedconsiderable


problemstodealwith.Thestudentsmissedclassforavarietyofreasonsincluding:

familycommitments,funerals,personaldays,andappointments,infact,theaverage

attendanceforthestudentswas60%.Thestudentshaddifficultiesre‐enteringand

re‐engagingthematerial;therefore,Isetupanindividualizedmathprogramfor

eachstudent.Studentswereabletoworkthroughpracticetestsandmaterialat

theirownpace,however,anyquestionsormini‐lessonsweredoneforthewhole

class.Ifoundthatmanystudentspaidattentiontothemini‐lessonsinorderto

furthertheirunderstanding.Manyofthestudentswereveryquietduringtheclass,

anditwasdifficulttoseeiftheyunderstoodthematerial.Shirvani(2009),Wolf

(2007)discussedthebenefitsofregularassessmenttohelpinformtheteacherand

studentsabouttheirlearning.Subsequently,Iinitiatedasystemofmylessons,pre‐

tests,andtests,withtheabilitytoredoatestwhenthestudent’spersonalgoals

wherenotmet.

ThestudentswerealsotakingComputers,Science,andanEnglishclass

throughCambrian.Thestudentsseemtorespondwelltotheworkload,andit

increasedtheirconfidencewithintheclassroom.Theabilitytoredoatestgavethem

confidenceandallowedthemtotakesomerisks.Thestudentsbegantobuild

confidenceintheirmathabilitiesandstartedhelpingeachotheroutmoreinclass.I

encouragedthestudentstoworktogetherandtocometotheboardtoworkontheir

problems.Althoughtherewassomeresistancetocomingtotheboard,itseemedto

helpthemtoverbalizethemathproblems.


Inoticedthatsomeofthestudentswouldgetanxiouswhennewtopics

whereintroduced,andsomestudentswouldevenhaveoutburstsinclasswhenthey

encounteredproblemsthattheycouldnotunderstand.Itriedtointroducenew

topicsbyrelatingthemtopreviousideas,orsymbolsfromwithinthecommunity.In

oneparticulartutoringsession,IusedtraditionalAnishnawbeksymbolstosolvean

algebraproblem.Theuseoffamiliarsymbolsseemedtolessentheiranxietyand

oncetheGreeksymbolswereintroducedIcouldeasilyinterchangeavarietyof

symbolsbecausetheyunderstoodthatitrepresentedanunknown.Ialsouseda

varietyofstoriesandexamplesthatrelatedtotheircommunity.Idiscussed

wheelchairramps,andSagamokRoadtointroducetheconceptofslope.Iusedthe

ideasofafeast,walkingtofamiliarplaces,andsharingfoodtohelpthemunderstand

conceptssuchasmixednumbers,wordproblems,andfractions.Iencouragedthem

tojournaltheirthoughtsonmathematicsandcreatealistofnewmathematical

ideas.Thishelpedthemtowritewhattheywerelearninginordertobuilduptheir

confidence.

Theproblemsontheblackboardweredonewithattentiontodetailwitha

step‐by‐stepprocess,whichwasmeticulouslyexplained,andthereasonsforeach

stepweregiven.Thestudentsseemedtoliketheattentiontodetail,andattheend

ofthecoursewhenIwouldaccidentlyskipasteptheywouldquestionhowIgot

fromonesteptoanother.Themathdiscussionswouldengageallthestudentsand

participationincreasedasthecourseprogressed.


Intheend,thestudentsrespondedwelltothefrequenttests,andpre‐tests.It

seemedtobuilduptheirconfidenceandtheywereabletotakeownershipovertheir

learning.Theuseofculturalsymbolsseemedtolessonthestressofnewtopicsby

givingthemsomefamiliarity.Theuseofstoriesandanalogiesfromtheirown

experienceshelpscaffoldtheirlearningandhelpedthemtounderstandnew

mathematicalconceptsandideas.Ibelievethatthetruesuccesscamewhenthe

studentsactivelyparticipatedwithintheclassroom,andintheend,eachstudent

discussedhowtheyweremoreconfidentinmath.Thestudentsallfeltthatthey

wereabletotackleanymathproblemthroughhardworkandperseverance.The

abilitytotakerisks,combinedwithhardwork,andconfidencewillsurelyallow

thesestudentstosucceedinanyfuturemathcourse.

ActionsandStrategies:

Inordertoteachmathematicseffectively,Ibelievethatassessmentis

important.ByusingtheWesternandNorthernCanadianCollaborationinEducation

(2006)publicationRethinkingClassroomAssessmentwithPurposeinMind,Ifocused

on:

• Emphasizingprogressandachievementratherthanfailure

• Providingfeedbacktomovelearningforward

• Reinforcingtheideathatstudentshavecontrolover,andresponsibilityfor,

theirownlearning

• Buildingconfidenceinstudentssotheycanandneedtotakerisks


• Beingrelevant,andappealingtostudents’imaginations

• Providingthescaffoldingthatstudentsneedtogenuinelysucceedp.7.

Thefocusonassessmentforlearningprovidedtheframeworkthatenabled

metohelpthestudentsandencouragethemthroughtesting.

Conclusions(includingnextsteps):

Thisresearchwillprovideanin‐depthstudyofstudents’choiceinapplied

andacademicmathematicsclassesinNorthernOntario,andsomeofthereasonsfor

theirchoices.Thestudycouldprovidefurtherresearchregardingthecomplexlinks

betweenculture,povertyandknowledgeinruralcommunities:giventhelarge

aboriginalpopulation,theruralcommunitieswithlowsocioeconomicstatus,the

lowpercentageofpeoplewithinthecommunitieswithuniversitydegrees,andthe

lackofemploymentthatrequirepostsecondaryeducation.

Inessence,thisstudycouldprofoundlyaffecteducationalpoliciesdealing

withFirstNations,Francophone,andgenderissues.Forexample,ifitisfoundthat

studentsfromruralareasarenottakingacademicmathematicsclassesbecausethey

donotseeparticularjobswithintheirrealmofpossibilities,thenperhapseducators,

theprovince,anduniversitiesmightneedtochangethewaythattheyrelatetoand

promotedifferenteducationandemploymentoptions.Iwillcontinuemyresearch

overthenextfewyearscollectingdata,preparingmysurvey,andinterviewingfocus

groups.


KeyLearnings:

Ihavelearnedalotaboutteachingwhilereflectingonthestudents’

discussions,assessments,andachievements.Ibelievethatusingculturalsymbols,

storiesandnarrativeshelpslessentheanxietyofnewmathematicalconceptsand

therebyallowsstudentstobetterunderstandnewideas.Studentsalsoseemto

respondfavorablytofrequenttesting,andassessment.Ibelievethatmathteachers

couldusefrequentassessmentsasawaytobuildastudent’sconfidencein

mathematicsandprovideexcellentfeedbacktowhatthestudentsactuallyknow;in

sodoingthisinformsinstruction.


References:

Altonji, J. G. (1995). The effects of high school curriculum on education and labor market outcomes. Journal of Human Resources, 30(3), 409-438.

Arcidiacono, P. (2004). Ability sorting and the returns to college major. Journal of Econometrics, 121(1-2), 343-375.

Barton, B. (2009). The language of mathematics: Telling mathematical tales. New York: Springer.

Bourdieu, P. (1998). Practical reason: On the theory of action [Raisons pratiques.English]. Stanford, CA: Stanford University Press.

Finnie, Ross, and Marc Frenette. 2003. Earning differences by major field of study: evidence from three cohorts of recent Canadian graduates. Economics of Education Review 22, no. 2:179.

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Patterns of choice and visions of future: What role does ... · Patterns of choice and visions of future: What role does socioeconomic status; gender and culture play in students