Teaching Math Research Paper

7/29/2019 Teaching Math Research Paper

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Wmi`ohn mcdut Jmtl oh Jmtlkjmtoes Eimssrddjs

Miiosdh gk Lddp

Bkcrumry =;) 31=3KE[S 5=3

Qrdb( Knmh Elkrhdbb


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Wlk tkmelohn db jmtlkjmtoes os ckedjohn oherkmsohniy edhtrdvkrsomi( Wlkrk mrk

goserkpmheoks cktwkkh hkw mhg dig selddi jktldgs db tkmelohn mhg wloel jktldg bdstkrs

nrkmtkr uhgkrstmhgohn) lonlkr nrmgks) mhg dvkrmii jdrk sueekss( Wlk Hmtodhmi Eduheoi db

Wkmelkrs db Jmtlkjmtoes rkedjjkhgs ekrtmoh stmhgmrgs bdr m sueekssbui jmtlkjmtoes eimssrddj(

Dhk db tlksk hkw stmhgmrgs os tlk Edjjuhoemtodh Qrdekss Utmhgmrg ,HEWJ) 31=3/( Oh sldrt tlos

os tmi`ohn mcdut jmtl) goseussohn strmtknoks mhg jktldgs td usk tdwmrg sdiutodhs) mhg ikmrhohn

brdj dtlkrs oh m jmtlkjmtoes eimssrddj( Oh tlos pmpkr O woii goseuss wlmt tlk Edjjuhoemtodh

Utmhgmrg os) wly ot os uskbui) mhg ldw tkmelkrs emh bmeoiotmtk tlos jktldg db ikmrhohn oh tlkor

eimssrddjs oheiugohn tlk ojpdrtmhek db m wkiedjohn ikmrhohn edjjuhoty dr khvordhjkht(

Wlk HEWJ ogkhtoboks bovk Utmhgmrgs wloel gkserock tlk prdekssks tlmt stugkhts slduig

usk td ikmrh jmtlkjmtoes ,Rmh gk ^miik kt( mi() 31==/( Wlk edjjuhoemtodh stmhgmrg ms`s tlmt

eloigrkh ck mcik td ohtkrmet ,tmi` mhg wrotk mcdut) gkserock) kxpimoh/ mhg gkkpiy kxpidrk ogkms oh

rkimtodh td jmtlkjmtoes( Wlos miidws stugkhts td mhmiyzk mhg kvmiumtk dtlkr stugkhts ogkms ,Rmh

gk ^miik kt( mi() 31==/( Wlrdunl tlos prdekss) stugkhts edjk td rkbiket dh tlkor ikmrhohn cy

fustobyPohnZ tlkor rkmsdhohn dr bdrjuimtPohnZ qukstodhPsZ ,HEWJ 31=3/( Mhdtlkr ojpdrtmht

rkmsdh bdr tlos edjjuhoemtohn) ksskhtomiiy tmi`ohn dr goseussohn jmtl edhekpts wotloh tlk eimss

mhg$dr sjmii nrdups) os bdr stugkhts td ck kxpdskg td dtlkr pkrspketovks mhg wmys db sdivohn

prdcikjs( Wlos miidws stugkhts td ikmrh td rkednhozk tlk gobbkrkht prds mhg edhs db gobbkrkht

mpprdmelks td sdivohn prdcikjs mhg ckedjk erotoemi jmtlkjmtoemi tloh`krs ,HEWJ) 31=3/(

Wd burtlkr kxpimoh tlk prdekss db edjjuhoemtodh dhk just edhsogkr tlmt ikmrhohn os m

sdeomi metovoty mhg `hdwikgnk os sdeomiiy edhstruetkg gurohn goseussodhs ,Bdrjmh " Mhskii) 311=0

JeHmor) 3111/( Uktmto ,311;/ ogkhtoboks twd typks db jmtlkjmtoemi gosedursks tlmt stugkhts

hkkg td ck mcik td khnmnk oh td edjjuhoemtk jmtlkjmtoemiiy ,Uktmto) 311;/( Qrdekgurmi


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gosedursk ohvdivks stkps bdr sdivohn m prdcikj mhg edhekptumi gosedursk ohvdivks tlk rkmsdhs bdr

emieuimtohn oh m pmrtoeuimr wmy( Uktmto ,311;/ kjplmsosks m hkkg bdr ikmrhkr ohvdivkjkht oh

slmrohn) goseussohn) mhg rkbiketohn dh jmtlkjmtoes wlkh usohn edhekptumi gosedursks( Uktmto

,311;/ misd jkhtodhs tlk jdst edjjdh pmttkrh db gosedursk oh eimssrddjs os m/ tkmelkr ohotomtodh)

c/ stugkht rkspdhsk) mhg e/ tkmelkr kvmiumtodh ,OSK/(

Oh m stugy gdhk oh m eimssrddj wlkrk mh HEWJ mpprdvkg jktldg wms tmunlt) rkskmrelkrs

bduhg tlmt tlkrk wkrk twd jmtlkjmtoemi vdoeks mppmrkht oh tlk eimssrddj( Wlk borst wms lkmrg

oh rkimtodh td jkjdrozmtodh mhg iketurk styik ohstruetodh mhg wms edhhketkg td idw uhgkrstmhgohn

db jmtlkjmtoes tdpoes ,Bdrjmh " Mhskii) 311=/( Wlk skedhg vdoek rkbiketkg) kxeotkjkht)

khfdyjkht db ikmrhohn brdj dtlkrs tlrdunl goseussodh) ros`*tm`ohn) PmhgZ edjjotjkht td

bdstkrohn stugkhts skhsk*jm`ohn ,Bdrjmh " Mhskii) 311=/( Ms wkii) stugkhts mrk mcik td boii oh

tlk nmps db tlkor uhgkrstmhgohn db m tdpoe wotl hkw strmtknoks mhg pkrspketovks mhg cknoh td nmoh

jktmednhotovk mwmrkhkss ,^kcc kt( mi( 311?/( Ms goseusskg oh jmhy memgkjoe eoreiks) Fmpmhs

lonl ohtkrhmtodhmi sedrks lmvk ckkh stugokg mhg ot os rkekhtiy ohgoemtkg tlmt Fmpmhksk kikjkhtmry

stugkhts gd usk eddpkrmtovk ikmrhohn strmtknoks mhg goseuss tlkor mhswkrs ,Ldusk) 311?/( Oh

mggotodh) JeHmor ,3111/pdohtkg dut tlmt) rkquorohn stugkhts td novk rkmsdhs bdr tlkor edjjkhts

jmy misd bmeoiotmtk tlk gkvkidpjkht db jmtlkjmtoemi brmjks cy slobtohn mttkhtodh mwmy brdj

bohgohn mhswkrs tdwmrg uhgkrstmhgohn mhg fustobyohn prdekgurks( ^kcc kt( mi( ,311?/ mgg td tlos

edhvkrsmtodh cy eotohn kvogkhek tlmt edjpikx kxpimhmtodhs mrk edrrkimtkg td ikmrhohn jdrk tlmh

sojpik kxpimhmtodhs( Bdr tlk gomidnuk oh tlk eimssrddj td ckedjk ploidsdploemi mhg jkmhohnbui

bdr jmtlkjmtoes) ot just ck rknuimriy prmetoekg mhg nuogkg cy tlk tkmelkr ,Imbdrtuhk kt( mi()

=???/(


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M tkmelkrs ndmi mhg fdc oh jmtlkjmtoes goseussodhs os td stojuimtk pupois. eurodsoty

mcdut jmtlkjmtoemi jmttkrs mhg gkvkidp tlkor gksork td khnmnk oh erotoemi tloh`ohn mhg gomidnoemi

edjjuhoemtodh ,Imbdrtuhk kt( mi) =???/( Wlk tkmelkr mets ms mh mhojmtdr eimrobyohn mhg

iknotojozohn stugkht edhtrocutodh ,Bdrjmh " Mhskii) 311=/( M tkmelkr slduig khedurmnk

rkbiketohn) sujjmrosohn) eimroboemtodh) mhg prkgoetodh oh eimss goseussodhs td oherkmsk ikmrhohn

pdtkhtomi mhg ms suel stugkhts jmy cknoh td usk tlksk strmtknoks oh tlkor sjmii nrdup goseussodhs

dr ohgovogumi tldunlt prdekssks ,JeHmor) 3111/( Imbdrtuhk kt( mi( ,=???/ mnrkk wotl tlk sueekss

db eimssrddj goseussodhs db jmtlkjmtoes) cut mrk edhekrhkg tlmt edhvkrsmtodhs emh cknoh td bdeus

tdd juel dh melokvohn tlk mhswkr td m prdcikj) mhg ikss dh tlk spkeoboe jmtlkjmtoemi edhekpt td

ck ikmrhkg( Skskmrelkrs gorket tkmelkrs tdwmrgs jdhotdrohn nrdup prdnrkss mhg td ohtkrvkhk ms

nrdups bmoi td prdnrkss) buhetodh ohkbbketovkiy) nkt stue`) lmvk uhkqumi pmrtoeopmtodh dr lmvk

edjjuhoemtodh prdcikjs ,^kcc kt( mi() 311?/(

Eimssrddj edhvkrsmtodh mhmiysos) dr iostkhohn td$rkvokwohn wlmt tlk stugkhts mhg tkmelkr

mrk smyohn) emh prdvogk dppdrtuhotoks bdr msskssjkht( Ot emh ohbdrj eimssrddj tkmelkrs ldw

eloigrkh mequork uhgkrstmhgohn db m jmtlkjmtoes tdpoe mhg wlktlkr tkmelohn prdekgurks mrk

sueekssbui dr hdt) mhg tlk gobbkrkht jkmhohns stugkhts mrk mequorohn ms m rksuit ,Bdrrkstkr " Qo`k)

=??


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ohvdivks iostkhohn td wlmt stugkhts smy wotl rknmrgs td jmtlkjmtoes) wloel os elmiikhnohn mhg

emh dbtkh ck os tlk bdeus db prdbkssodhmi gkvkidpjkht skssodhs(

Utugkhts wld mrk prdckg cy tkmelkrs bdr kxpimhmtodhs mhg fustoboemtodhs bdr tlkor sdiutodhs

melokvk m nrkmtkr uhgkrstmhgohn db jmtlkjmtoes tdpoes tlmh stugkhts wld mrk sojpiy ms`kg td

sujjmrozk wlmt tlky gog ,^kcc kt( mi() 311?/( Oh mggotodh) stugkhts wld wkrk ms`kg td kimcdrmtk

dh tlkor kxpimhmtodhs misd gog sd td dtlkr stugkhts wlkh wdròhn ediimcdrmtovkiy oh sjmii nrdups(

Wlk dppdsotk kbbket wms bduhg wotl tkmelkrs wld gog hdt prkss tlkor stugkhts bdr kxpimhmtodhs cut

rmtlkr skt dut mii tlk prdekgurks bdr tlkj ,^kcc kt( mi() 311?/( M gobbkrkht pkrspketovk os tm`kh cy

Bdrjmh mhg Mhskii ,311=/ wld mgvdemtk bdr stugkht ohotomtodh mhg kvmiumtodh db goseussodhs(

Wlky rkpkmt tlmt td prdjdtk ikmrhohn oh eimssrddjs stugkhts slduig pimy m pmrt oh kxpimohohn mhg

tkmelohn ,Bdrjmh " Mhskii) 311=/( Wd suppikjkht tlos ogkm) Io mhg Ho ,311?/ hdtoekg gurohn

tlkor stugy tlmt kxpkrt tkmelkrs eimssrddjs ohvdivkg m/ m stugkht prkskhtohn mh mhswkr) c/

stugkhts mhg tlk tkmelkr qukstodh tlk mhswkr) mhg e/ tlk stugkht kxpimohs tlk mhswkr( Hdvoek

tkmelkrs mrk elmrnkg wotl novohn lohts mhg mhswkrs mhg msòhn tlk qukstodhs tlkjskivks) tlkh

wmotohn bdr stugkht mhswkrs mhg edjjkhtohn dh tlkj wotldut burtlkr kxpimhmtodh ,Io " Ho)

311?/(

Ojpdrtmht bdr bmeoiotmtohn prdguetovk eimssrddj goseussodhs os mh khvordhjkht wlkrk

edhekptumi jmtlkjmtoemi gosedursk os hdt dhiy pdssocik) cut khedurmnkg mhg vmiukg ,Uktmto) 311;/(

Wlos os rkbkrrkg td edjjdhiy ms m ikmrhohn edjjuhoty( Wlos rkquorks prmetoek mhg tkmelkr sòii oh

drgkr td ohvdivk mii eloigrkh db gobbkrkht hkkgs) mcoiotoks) euiturmi cme`nrduhgs) UKU) ktektkrm

,Rmh gk ^miik kt( mi() 31==/( Rmh gk ^miik kt( mi( ,31==/ jkhtodhs mh ojpdrtmht strmtkny6 td lmvk

m spkeoboe purpdsk bdr tlk nrdup goseussodh mhg td ck surk mii stugkhts mrk oheiugkg( Oh mggotodh)

jmtlkjmtoes ikmrhohn edjjuhotoks slduig gospimy stugkht*stugkht gomidnuk rmtlkr tlmt sdikiy


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stugkht*tkmelkr gomidnuk) ms wkii ms kxpimhmtodhs td mii mhswkrs) brkqukht stugkht ms`kg qukstodhs)

mhg mh meekptmhek db hdt uhgkrstmhgohn ,bdiidwkg cy msòhn qukstodhs/ ,Rmh gk ^miik kt( mi()

31==/( Udjk strmtknoks tlmt tkmelkrs emh usk td prdck goseussodh mrk msòhn tldsk wld uhgkrstmhg

td kxpimoh td dtlkrs) bddiohn dr prktkhgohn td hdt uhgkrstmhg sdjktlohn td nmoh mh kxpimhmtodh)

mhg msòhn spkeoboemiiy wly stugkhts gog sdjktlohn) rmtlkr tlmh wlmttlky gog ,Rmh gk ^miik kt(

mi() 31==/( Husscmuj ,311


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Skbkrkheks

Bdrjmh) K( " Mhskii) K( ,311=/( Wlk Juitopik Rdoeks db m Jmtlkjmtoes Eimssrddj Edjjuhoty(

Kguemtodhmi Utugoks oh Jmtlkjmtoes72,=$5/) ==;=73( Qucioslkg cy Uprohnkr) Sktrokvkg brdj

lttp6$$www(fstdr(drn$stmcik$57

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Teaching Math Research Paper