'~- The Effects of Short-Term Memory Training on, Children WhoExhlbln Mathematics Learning,Disabilities and Short-Teem Memory Retention Probleins ·

. j

'~- The Effects of Short-Term Memory Training on, Children WhoExhlbln Mathematics Learning,Disabilities and Short-Teem Memory Retention Probleins ·

. .~ ~

CD StePj,ani~~. Mic~ael.

^B.A.

~Hon

^•.)

. ~~<

~

^"

'A Thesis Submitted tothe SchoolorGr~ul1t~^Studies

in PartialFulfilment or Requirements roi'theDegree or

~as.terorSeieDce

Department01Psychology MemorialUniversityorNewfoundland

March,Ul86 .-" .

Stjohn's

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New(oun,dlaDd

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Perritission1laSbeen granted to..the National tibrat"y'o f Canada to microfilm this

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de vendre.des-exemplaires du

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L'auteur teteu iatee du drc te d'.auteur) sa: eeee-ev e les autresdroi ts de',publicati on I n; 1a th ~ s e ni

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lon gs extraits d!-__celle-ci ne 'd ctven e @tre Imprim~s au

"a ut r e nie nt .rep"rodu.Lt:s sans 'Son.

.eutorfeetIon acriee, f

\ ISBN- "-315";31938_3

Abstract

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Chiidrenwh~performpoorly ODmathematic~b!1u alsot~Ddto"do poorly onbOth auditory and"i!:u~short-t ermmemo~y ~a.sks.Thepurposeor thi.i study wastocompare therelative

erreeti~eDess

or an

inte"~DtioD pac.ka~e co~isting

or short-term'memory'stratea,instr uctionand'standard math practicewith an '.

·inttrVe~ion.·.~lc:kage consisti~g

^or

st~dard l!!~~h ~r~tice alon~.·,~Childre~' ~hO ')

^.

.rec'eived,thecombined math,'andmemdry'instruction...ere'~redittiedto'perrorm

, ,.'. ;. '~~" ." " ,." ' .

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^,.,

bette ron subsequentmathtesks-tb enthose whoreceivedonly mathiDstruction,~ -...

~'~~rtee~

^cbildren..

{mea'~·

^age,=:'lO,ga

y~ars)

^or,average,

~~telligence:'

^{wh'o .:}

<~--

. . ' . ': 1 .. ," ; . -.

pe~rorm~ he!ow'average onseveral-rtthh andmemory..teste-wererandomly assjgned'to~neortwo conditions.

A

contro lgroup received mathinstr uct ion', consisting_or.

~r~~~I.~~,_i~plication.

^or

th~ : r~~r h&Si~ mat~

operatio ns.

Th :.: .~~-:_

experimebtalgroup received shorto- termme~ry instr uct ionaDd'training,in

... " , . "

additil?ntothe mathpraeti ce,,;T reatment.rorbothgroups,consist~o~sixo~e-, .hour sessions"spreadoyer thecours~"or^twoweeks.'AII'~hildre,n~ere ~~ed

pre-and post--ireatm ent.Ass~mentin"voiv.edbothv~u~ ~ndauditorym~thand, memorytesting. Th~.expertmeatel groupimprove~significa ntlyfrompre-..to

.p~as~essmen~'on bot h mathandme~orytasks.!hemetb onlygroup did

ei t.·

..For-children perrorming pccrlyon'math.and memory tasks, these results strongly, derncnstrate.th e errecti,:enessora~omb.inedma~h~.ndmemory_t rainingpro~am:,

.Ac.kDOwl~dgeme~ts

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ywo~ld like toexpresssincerethanks to themembersof mythesu

co~nftttee. C~;istiDe

^.

.:vle~t

.(my"supervisor;,•Rita Anderson,.:n;. Bar bara

H~pki~8.

for:their praise,their

. criticis~. .

,-.^and, ^their\. ^consutentcoop1!ration ." Maay: •

"--"

th~D~

^alsogoto

Mic~;el S~~r~iek,

^ror.

answ;ri?g

my

~Dtinuous st~e~m

^of

8tatisti~at'qU;'UODSu"dto

J ack:: -

Strawbridge,

^.

who^:.

o neo.

helped

^.

me

^.

when my'

',knowle~geoftb!!computer'sYs.~em·~ailed;Ia~'gratelt~^toGrad~at~^Stud

A.

forlb

·providin~."me with financi~1'support through i.Memorial University'of

,Newfoundl~nd'fellowsh ip. •

Thanks are due to t6e Diagnostic andRemedia lUnit at Memorial Unive~ity.fOf.providing an··acces:'ible subjectpopulatioD,mater ials,~IMl.~rkiDg space.--Also,l-cert3inlyappreeiate--tb~parenls-of·th e-ehildr ei:ritr mrmattrgroupi .

B"~d" '''l"~'''~:JP rOZ:~I~-<iill~".i ^{. • h oi. mad. ,,- ,'}

^'ib.t

^{'h :: - ,,07' . -.-; d} <d--.--.,.---:

every-s~ioa." . 1' .

.F:inally

~

^C;rry,

thaD~

^youfor

al i

those hours)IOUlistened,-waited,and :~-.- provided-eocours gemeni.

Introduction••..'.. .• . ' , , ,, • ,pag e,1

N.thO:~~;:~~:: :: ::' : -: : ::: : ::: : : : .: :: :':: : . :: • • : ~:: ::

~ater~ai"&J1~ ~cl.lIliD.btrat.i·o·n

procedure.,) ,..page . , List' of Tabi .."•

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LiBi~t'

Figure.,, ,, ,,

Table of ConieoUi

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p.roc~d~re ,^.•,,

fle~uit.,~•...1,'.".,'."

Discussion.' . '"'"., "

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:AppendiX A:Math Sheet., ,.•.,,

Appn,dtxB:Matli'.Pr~elU..

AppendixC:Gam. ..nd~ctivlt1'1IIf

• Gl .

AppelJdix D:Rl.1J scciru_, '.' . , ,Appendix E:St~dard^sc'ore,.'""

'\':'iJ." '.. ,.pag e 18 :pag.. 24

"pag e 38

_..-P...·~

,:,':.',pa ge 47

:pag,e 81 :pag e84 ..'..,..p~ge 6~

,...,pag:e 87'

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Appendiz F:Analjei,lI"ofaaw

'~ata .

^'. .""" ..

-:-',-:--Pag~ _ ,

App'indix G,:

a~~ Sco~u

^--

:'"~i&!l:.·

^&J1d,s.0,'s

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AppendiX"1f':.St&!lda~~~~oru... Mi&D, &Ild S.D:.~" , ,pa~^{.. 11}

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t'

iv List

or

Tables

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^{T..b~~1: Pr ogramOutline}

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^{... . . . :page 20,}

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Table 2: Th!.Di g i t. Span Subt u t - Allalya18 of

VarlaDe,OD Standard Scor page25

Tabh '3:

n.

nlaalAttntloDSpanforL.~t~rs SlIbtut-ADalrail ofVarianceon

S~d&rdScor. .: , " ~."-' ..page2~

T~ble

^4:The }lentlll

>C~lDput&ti~1I.8 Subt;.·~t·- ~&11.·1s

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.~Of V~rl&1lc,ODStU.d~Scorls pag.'2?

Ta bl e ' 6:.Tbi IrlttuCrll1Jl1it.~lonl^Slibtest-An~~YdB of.Variucl011St~~~rdsc cree, ~...pag. 29 Table6:Wean seere efor Gr oup. at Pre and

pOlt-rutingforallSubt. .

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page,.37

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Figure'1:

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DigitSpan'Tu t - U, u. Scor~ ,at .Pn-'uclpo~ t-t..tb.g.~ .:: : ..~&£~iO Figur, 2:Th.'!'lIualA,t.t U ti ODSpanforLlttn .

o •ru t7"WI&Jl:"Scor n atPre:-"&Del •

c- Po.t. tf.t1~g:'., ':, : - pag.32.1.

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The generic term,iearningdisabili~i~.rerentoahete.rogen~us~upof disorders'm~iresud^bysignifi~~t·difficultiesintheacq\lisition.arid.use01 "

I~t.~;n~,

sp..k",! ,

·~" d;~g, .~,i'lng, ,.;"ning

^cr

.mUh.m.t;~al

ebiflriee. These di80r'den ar~!Dtrin~ietotheindividual.and'ar e~resumtdto bedeeto cent ra l nervous syste m dysfunction..Even"tbou~h ^a l'uDinl_;.disabili~y ^{mar oeeur .}

(Qnc~mmitaDtI~

^w.ith

o~her ,!I&!l:diC~P~lDg ~o.dit~bD.~ironmen~ai\n~uence:s, :

it"isootthe dir,ee"tres~U.^J)(

th O:se

conditionso~influences.D"ependi!lgOD.the

definitio nused,esti~atesof thepercentage01schoolagedchild~eDwit h learning

"disabilities,lvary

rroy%

_~,30%.with boys outnumbering girls

by

aract~r⁰¹⁴

tollKirk-~DdKirk,1983). - I

WordeO"(1983) outlinedtwo pop ular models thatareusedto ex plain the . \-...

,.

bulS orlearningdISabIlities.Fro~ ~~eperepee ur e orthe Developm ent alLag Model,chiidren~itblearningdisabilitiesexhibit "slow ra.te or deve,Jopmenti~

pa.rt icula!are u andthereror ! resemb leyoungernorma lchildren.Underthis modei.eognltive

de~ek>pment.

^isseen

o~IY

^{as slower}

tba~ ~orm·al.~

^not

ditrer~nt

ⁱⁿ

,1.0;

Iuedarneut alway...Learnin K.disabled

~hildi'en w ill ' p~iress

^throughthe

sa~e

deve,lopment~l.sta~as norm alchildre n,butat1Lslowern,te: !his~iewimplies.

that withmat urB;tion,-lea rning disabled'childfenwill'catch up toth~irpeen.In"

eoni rasr,Ircmthe

.

perspective^{' ,} orthePeemsaeat Deficit

' .

Model,childrenwith lear ning disabilitiesshowmildversions orsymptoms'typically observedinvictims

. "

.

^'.-~

.crbrni ndamng'e.Thesedeficitsarepertnent'onc~i..'"earning.d~nbledebildre n

\VfI1contin~e'to showthe samecop itive prQfile~edoleeeeeteandasadults:--- '•

.

.

Mathemati " LearningDis"biliti~. Alt bough learning dillabilitie-!,('an be'

thefirst.TheInt ellectual St1llsApproa chstresses,deficits incognit ivea.bilitie.s:Lt observediDmanyschoolrelatedereee,therocusintbis studyiso~ma.themlLti".

Englehardt (1983) describes severaldirrerent approa.chesthat areusedtouplain

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tbeunderlyingproblem(~) asspeiat~witbamathematicslearningdisability.The

·Intellectual Skills!'-ppro&Cb presum'estb~tthelurner',~roblemss~,?,from..

·defici' in

som~.

^{cognitive'abilftJ}

~r process. s~('b

^u sequential·

mem~;y

^or

~

·

'vis~ospatial

alliIities.Under

·t_h'~ P~oc~llral ' Approa~·h. learner di(ficlllti~'

^are

· . ..' . i . f .. ' . '_

. . 'attributedtoabsentor '!1iso1eredstepsin mathematicalprl?Ced ~res.!'his, mny be

• seen'whenone:doesnot)fave all"themathem~ticil.1 prerequleuesnecessaryto

~co mplete

^rtproblem

T~c~Ptual

^{Approa ch}assumes that difficultiesInmath renect thefailure toJll1derstand variousmathemati calconcep~.: SlnClPII'S or

procedures

,I

I ~

.Twootherpotentialsourcesordl(fit'ulty inaddllloDtothoseIdentledby

Engl~~I escribed.The Ma.lhema.tit'31B~kAP.proat'hassumesthat

somechildren may exhibita blockto IQatbematics,result inr; in a lackof

:' . '1/ ' . . . . . _

motivati?D.and.~oDsequ.eDtlypoormat h performant'.e.Under.t~efinalappron.t'h,

,

^,

theLanguage,Appro3,t'b,ehildrea's problemf-mayrenH'ldiffi~uIHes_inreadillJ

' ! ' ,

andcomprehending thewording of a problem.

'Eat'hofthese?-pproachescoul~refleet eithero-rthemodelsdisCU"ed'-b~

Worden(IQ83).These approachesprese~a broadspect rumastothe nat ur eof :__le~i:~gdisabilities:They arenot exclusive,ItS.achildcouldhavedifficultiesin 11.11 .or~~ombinationoflI.rea.s.Whereasnilor the ll.yproll.c!lescanbe appliedto Childre:whoexhibit mathema tica.ldtrneulu ee,the

~ocus

^ort-;:, study

~ ill

^{be on}

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theunderl ying problem.SpeCifically,thisst udywill,focus00deficits in theuse of shor t term

me~.(STMj

^strategies

jo

mathematicsdis:bledchildren'"

Sbort. T ermMemory, Short.teem memory(STM),.or working!Demoryas it iscommonlycalled, referstoahy pothetical burrel'inthe.informa tio nprocessing system wheres'timuli~areheld moment arily torfurther processing.Hence,ST~

has~ee_n hYr)ot~esized -topl~yacent ral_,rolein a.rangeof.important.co~itte. skills,'~rom.sp,eecheompeeheesionto.arith~etic~nll(rom.Iearning to complex reeece leg.Instead'of. 8 singleuDi't~rySTM system,Baddeley~lgg21arguesthat work ingmemory shouldbe regarded ~a set ofinterrelatedsU.bs~stems.'Inhis

Imodel,working memoryisdivi~dintotbreeeubsystems:a centralexecutive' systemand two.sleve systems,the articulatory)~pand thevisuo-spetial scratch pad.

The centralexecutiveformstb~^controlcen~reor the system andis,~ura.ed to selectand operate varihuscontrol processes.It,is'also assumgdto:have.'a limited amountotprocessingcapadty. someatwlrich-couldbe devoted to the,

.... . '~ h

^{sb·ort-termstorage}

~t

information.The

ce~t~al

exeeutlve'Is able

to ?t~o~d

^some

:i

the storagedemandstot~etwo subsidaryslavesystems,

The articulatory loop. consists of twosu~system~,ap~ooemic,store end !on

~~rticulll.toryrehearse! process.Thephonemic storeisassumedtoberespcesibie tor'pho:nemic similarityeffects00

8TM:

'That is,s~rialrecall is better for

seq~ences.

^at

Ph~nem~caIlY

^{dissimilaritems}

tha~

^for

se~~'~o~e~

^at

··Pho~em'iea.lIY

^,

similllr items, According to Beddeley'emodel,accessto,th!! phonemic storeis'~:

llSSum~d

^tobe

au~mnti~

^torspoken verbal

mat~rial.

^{'b!it tort'quire}

a~tic.~lati~o,

'.

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when.'t he verbal materialis⁷presented visually.Theartieulatory

',1

'rebe~rs;l'process

~

^>-_':is

~ume:d t~ e~h~DC~

^memorY .!lpanb;.

'r~rr~~i~g

^the

rading·.m~mory ' trac~

^of

itemsregister~d'withinthepboaemlcsto~e.Withoutrebea~sa!.the lirespan ofan ite~'in'^{storageisshort.The more}rapidly a sequence'erteeme-cen bearti~ulated,

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thelnore rr.equ~~tlyc&n.its,m,emory,~ra~ebe:refreshed(Badd.eley~n4·.Wilson,·

1085). ",. 0;

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. ~. ^The' v.~.~~.spathLI

^scrat.ch

~_arn' ~~g:rded '~ ~ t~7~r~~ ~~IL~al

rr;e:n,orysystem and has been'shown'to bl;'involvedin~a!lipul8ting ~~~uo-splltill.l ". II

information..Becausethis~studylooks_a~basicmeth operations ··thatdonot•

• . • ? .

involve~h~vlsuo-spetialscratch pad, thel!ba~acterlstirof this'system willno~be, elaboratedfur ther.

,.

Developmen tal

S~udies

^{ofST M,'},Memory sl udl es COiiqucted,in ttle

mid~le

" . ,, ~

and thelate'J'9609have revealedth at by'8 or 9.yearsorage,children.use

I · . .. ' ' .

ou.merous etre tegies as aids-Intb~irerforts toremember.Theyrehearsethe,nlLmes; of.

s~imu~i

^{(by saying}

the"n~mes ~p;~tbJ.IY)

^and

~rgan!ze'"~fini.Uli.

^'in

~er~s

^of

seman tic

pr~perties'

^(by

groupi~g). Y~unger

^children

.nu

to u.-:ethese

p~teriH~'IIY '

.helpful.mnemonics.Strategies-are firstuse.~with~omeconsistency,inthe_.early

:~::::::e'" : ;::1 s :::' _{t: j':~} a ~:~:LI~::;,ll::'m":ti::h::.r:~:n ~P':~: .' .

errecti~fn~ss

and nexibilit y.itbwhich

stra~egies

^{are, imJ:};"lemeotedIKliil',lLnd Hagen,~9~2).Theacquisit ion~rstrll.t~use occursw~th,POrmil.1~evelopmilD.t. ,

, Developmental studies haveJoundthatwhenyoung"children!a il touse'~'.

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^{' . .}

particu lar!Itrll.te~,.they can oftenbe t,rnined.to_do so,Upon instructio'n they

,"

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.Individuals (Robinso'o'and Robinson,HI76). Muchofthe evidence shews that

r~~?rdc~ i~di~idu~1s 'ca~','m 8;~tain

^mnemonic

;t.;~t~es

^·for

~oo5id'erabl~

^periods

.\

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,

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!hO~".'ri!t/i~prov~~eDts

in utilizing,theIt r.leg)'.In'these stud ies,failur e to useaparticUla\ st rate gydoesDotseemtoreneetaIimitationinthememory s)'stt m itselr.Instead,it.ppe'ante.bea failure0!1thepartoftheindividualto employ

tb~ appr~p;~ate .tra~egy.

^{Errort!!toinst ruct}

ele~entarr

school children.

whodoDot

!IpoDta~eousiY

^{usestrategjeihave been}

s~ccessrul.

Norm&!childre n ea nbe

,

taughttouse rebeanal str ategies.&Dd^.

.

.when they' do, their performance.

o n

,:ST Mtuk.~improYes'ac:cordingly(Waters

and

Andreassen,1083).",

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'. rll.~ti~~!argr9u~s

;r

c:~d.r~Ddo not .ponta neollsly employ STMstrate gies.

nppr.opriate

to

theirdevelop~tallevel,Theseincluderetarded,individu~and

~ 'ehll~ren"e~~iPiUng atteDt.i~~ der~t

disorder,..

As'outllne~ be~, r,~earcb ~vjde~ce

.suggeststhat both~fthese'groupscan.improve.ODST M tasks once theyreeejve instructi on onS~Mstrategies.:

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Ret~rdedpessc s arepart icularly inefficient at usingmnemonicstrate gies , tha trequirerehearsal, rgui lotion.andelaboration.These individuals·do not

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tend

l?

spo~taneously re~earuinsituat ions ,;"lMchcallforrehearsal,and thereby

b!

a grea t deal-of.information.-Asthenumb; rof items iiia to-be-remen;bered lis:oritems lnereeses,t~e pe~for~ance'~r"tetardedind ividualsdeterioratesmere

·th"an.it

d~ f~r

^normal

jnaivid~als: Trai~iltg-~etarded

^{person.s to};ehearse leads

to

.i.mprovedpe:for!,;a.nce on ST Mtasks.Inthesam,tmanner,

pr~enting

^normal

•~nd,i~i~uaI5from,rcheaningresultsin a perrorma-.ee.similartountr~ined retard~d

, .

...

,t.:l.n~i~g

^jrom

~~ we~ks

^to

o~e

^year.Altbough evidencefor the general!zation of

sut.h"st~ategieswiththispdpulaUon is span e,.whatisavailablesuggests thaithe

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ef!ectsof train ingare usuallylimitedtothepart iculartraining context (Haywood,

•MeY,ers'and Switzky,HI82).

Attention deficit disord erchildrenhavebeen observed to have poorschool

"Performa nce;despit etheract that theygenerally achieve average scoreson intelligencetests.Atten~iondetidt disorder childrenseemto~B.venop~rticulllr difficulty storing latcrmeti on ,as long as it bas been adequa.tely processed.The processing skills and' eUort required to estab lish dear, well cegaeiaed representati ons,o~newlearnin ginthis groupofchildre n frequently-appearto be, Inadequete. Th'ey'a.ppe~rto .have less masteryof mnemonicdevicesuhennorm~1 children. In ·par ticular ,atten~ion^deticitdisord~r childre~^donot seem totakethe. t~ouble

.

tomentallyrehearse

.

mat erialth~t is

.

)toberemembered(Douglas;, Hl8.1'j.

Attent ion-de ficit disordercbil~rendo-no"I'0r:sethannormal childreno.n memory -tesks that provide a built-in str~tegy for remembering . However,Jb.-ir perf?rmanceis'nota bly worsewhentasksrequirethemtogener:4.t.,their own strategies(Kendaland BraswellHISS).

STM nnd Learn ingDisabilities. Much or the work-on mathem atics\- - d~abilitiesandST~~erici tShas()l.lowed from earlierstudies that ex: mined the rela tionshipbetween'reading disabilities-andcodingeWeienc)" in

~T~~:

Conrad's research(lQ64,.lQ72)onphonetic coding hassiown.thl1t it is~oredirticultlorII. 1_'- subject·to repeat a st ring 0(" phcnemicelly i1imiliar consonants (Ilg.

B,C ,D,G,P,T ,V,Z)·thana sequenceofconson4 s- t ha t differ rromeachot her in sound,or articulation(H,K,L,Q,R,S,W,Y)." Conradinterpret edthis ea evidence that STMu.ses aspeech basedcoding~ystem.Aclearndva-Dt nge tothedi~similar

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set emergesby age8.

Sbeekwe tler,Liberm"an,'~ark,Fowlerand Fischer (l ( 70),found thatpoor readerswere less arrectedbythephonemic sim'llarit yof theite ms·than good readers.This-wastor-bothvisual and auditorypresentations. Sbankweiler·et al concludedthat poor.readers weredeficientin the use ofa

pbonemi~

^code:Theygo

.

^~

.on tosuggest tbatindividua lvariation,in coding efficiencymay be arelevant factor inlearningtoread.

._SiegelandLinde~(1.084) elsqcomparedthe recal(ofpho,nemicallysimilar

~D d dissimilar.lett erstrings in groupsofchildre nwho differed in reading achievement.The~ormally·~cbievi!lgchiidrenrecalledsignificantlymore?fthe .

pho~emicallY dissi~illlr

^{let ter}

~trin'ss

^thanthe phonemically similar ones.The poorreaders did not .LikeShankweileret el,Siegel and Linder concludedthat normallyachievingchildrenshow sensitivityto the phonemicaspectsofstimuli during amemory task,hut children with

a.

readingdisability do not.Furtherm ore;

Siegeland Linderpostulated£bat~el'1cits'inS~area generalcharacteristicorr lear ning disabilities, and are pot justlimit ed to reading.

\

Overthe last severa lyears, resear chershave examined the relationship

I . betweenSTMskills and mathematical performance.Webster (1070, 1080),Siegel andFeldman(108 3 ),andSiegel and~inder(1084)foundthat poorperjorma aee"

'on STM tasks is associated with mathematicslearni~gdisabilities. When asked to

,

^.-

recalllists of items,metbemetlcsdisabledchildrenperformedsignificantly poorer thannormally achievingchildren.hi thesestudies,lists consisted or lett er strings similn.rtcthose devisedbyShnnkweil~r;Webster used digit strings as well.The.

lists were prcsen.tedeithe~.nuditorallyor~isuallY.Allchildrenin, thesc studieshad .r

"

average I.Q.'s.

,

Webster.(1079,_12BOlfouno significantdirreren~e9ⁱⁿSTM cnpllcityamong three grOIl?'of ~athematksachievers. Hisgro u pswer emad eupof mildly' matbemat~disab led children, severely mathematicsdisabled childre n, and JDath ematic5 proficient c.hildreo , ranging in agetrom11-12 years. Hecon~lu~ed. thatthemathem at icsdisabledlearnersrailedtouse thesameeodingmechan ism asetricientl yas theadequa telearners~

.Thesubjects int~e..sie.gelnod 1..inde!-U{)S 4)studyhad"either11..ma th disabilityorwereachiev;ingavera~lyinffilll,bin~~hool::th~i'.ranged

in

agefrom 7 -13 years. Fortheyouni ee math em aticsdisable?child ren (7-8 years],no .-differeuceewerefound betweenthe recallof phonemi cnllysimil.a tanddissimila r

, . .

lette rs.Thenorm al'grou patthis:age'd id demo.nstrate,a. ditrrrence.'rh,.older mathe,!u~~icsdisab ledch ildren (9 •13,yeera], like the,normalgrou ps~ttbis age;

had a sign'ilicantlypoorerrecallof similar.es compared.k,phonemica ily'dissimi;a';

lett ers. Overallor the ages,perform ance of themathd~abl~dg~oupwas signirican tly lowe r t.hant~atofthe normalgroup.The younger lear ningdisll~leJ childrenin the Siegel and'Linderstud y werecha racteri zed byadeficiency in phonemiccoding. The older lea rning disabledchildrenappearedtobeusing a phonemiccode, but

...

bada moregeneral deficit inSTM,SiegelandLinder(1084)

suggest tha t suchdatasupports'IL~evelopmental,~Ilgmod el in whichdis!1bilit ies repr esent arnnhir ati onal Jagra t her thana dericit.

Baddeley's (1082)rri~delofworking memoryassumesthat~h ~llrticulato ry loop canstore any infor matio n,either 5p~kcnverbal materia!, orthro ugbthe articul~tionofvisuallypresente dverbal material. In hisresearch,webster(1080)

'.'

round·asigoificant mainerred usoeiatedwith modality orpresen~ation.VISUal iDput.wassuperiorto oraliDpuL

Si~el :lp.d

^Linder(i984)reported deficitswith'

( " .' '.'

.

bothoralandvisual stimuli.However,whilenodirect,romparisonsweremade, the deficits.were'less obvious wit h luditory'stimuli. Although'complete comparisons orthe modalityditrerencesarenot available'inthesest~dies,the .observeddiCl'eren~es~U ggesttheimport anceortestinginboth modes..

.; M3t~~nd'STM Proce'S5es. At\&stiwodirferent theoret~ca~.app!oaehes. "

havee~amiDedthe relationbe,tween.mathandST~processes.Brainerd(1083) i.~eribed aworkin~-m~ory.model (or meo-talarithm~tic'in which problem i~ro;mation^{isfirstencodedinto}the short-tertrl'~tore^{andthenretrievedand} lI.p·propriate!yprecessed.Hence,thissequence canbedisplayedu: uumerieal encoding -

,-

short-termnumerical

.

store- retrievalCromshort-termstore - ari~h~e~ical proc"essing - ~esp'olllIe decoding.Suc~

a:

model allowsone to determine where in workin, memory theerrol'S'a.recceuelng.Brainerd'sresearch hILS~emonstratedthat theestimated proportionoCerrorsattr~butabletoSTM

Cl1i!~.

^is

c ai

grea terthan the

~timated

propor.tionor

erro~.

attributableto p~essingIailure.ThemapitudeoCthis dillerence,however,issubjectto the qUllliryinginfluencesoCencodingrormat,typeoCmathemati caloperationand age level.

Baddeley's(1\)82) modelor working.memory,as previously'described, consists'oCthe executivesystem, the'articulatory lo.op,and the'visuo-epetlal scrll.tch pad..When examiningmathdisabilitit'l!l inretD.tio~

to

^{Baddeley'smodel,}

oneisablJtoassign elements,oC math'tothe

c~mpon.en~

^oCthe

m~el.

^The

(

.,

10

articulatory loopmay storethearit hmetic signandJhe numbers of a problem, whereas the.executive syst em mayretrievetheelgcritb mueeessarytosolvethe problem(Siegeland Linder, 19S4).Inother_words, thearticulat:'ry loopis

'responsiblefor immedia tememorydemands, suchasremembeneg thenumbers

o r

theprob~mand thefunctiontoheperformed(e~.a.dditionor subtraction) .The executivesystemc~mesintoplay when incornipginformatio n(anewproblem)is integrated with past knowledge,or what to do with.it.'~math andmemory processeshav~been,shownto be'related,itseems_th~tjnerriCieot'use_o(~be .

ar~iculatory'

^-lcopis

resp~nsib?e' r~r

^{the'problems'}

witne~ed

^{inchildren who}

performpoor~y

on _

both STM'and matht~s.It is.thisloopthat controls the retention or informationthroughrehearsal.Thosewho makeinadequate useorthe loop are likelytobe poor .a.t.math"(Baddeley,lQ1Qj.

Anassortment or mernaI"}'.strategies can be usedto aid rememberingor to improve memory span perform ance.Rehearsal,forexample,ean beas.simpleas

- .

spontaneousovert verbalization s.Rehearsalisnot a common cognitive activit.y priorto 8or 9'years orage,andmaynot.be evidentin olderchild-;tnwho exhib;t pool' pe; rormance on STM tasks. Another memory"strategy

" jl~olves

^aiding

~etention

^by.deliber atelY

~rganiz'ing

^stimuliin," ": o.r

their l!inembe;~hiP

^in'

conceptualcategories. Similarto cate gorizationisthe proced~'ewhereby om.' clustersinfcrmat loninto

gr~ups; 'For

^{example,,10dlgltspan.}

t7r~s

^Ithelps-itone euemptstc remembertwo 3digitnumbers,ratherthan on 6digit number.

Memoryis cne eimprovedwhen childrenare madeawnret htheymust employ .' t, . ,.:gies

~o

aid th'i;-:ee.IlIK.Hand

H,~,n.

^{1082).M,n '•.'r h,. ;,.ihash:,nthe}

mainteaching,strategyin:workdone withmentallyrete ded.attentiondefieit

. -

, /

11

disorder,and learning-disabled children.

ProposedHypotheses.-la summa"ry,researc~hasshown that children'fha

.exhibit mathematicaldifficulti esmay aboperforrnpoorly onSTM'tesks.This_.

relationship'has beendiscussed.byS~egelaad-Liader (HI!4). Sucha deficit Calls under theInteUectu al Skills Approach modelifes~ribedby Engleha rdt_(1983).~t _ .the

5~me tim~, w~':k' ~i~b'

^ecrmel,

~~Y

^{retarded,.and attention}

.de~cit

^.

disorder children"has shownthat,in;struction instra tegiessuch as rehears,al'are ertectiveinimp,rovin g their perform anceonSTMtasks.

Torgesen(19~)and Torgeeen and Goldman (1977) suggestedthatitshould be possible

to

lmprovetbe performance

o r

le,arningdisabled

children~o~

^at

le~t

somekindsor readingtasksby teach.ingthemtousemore efficient'medl'ory lear ning strategies-."Expected differencesbetweendisabledand normalchildren onthe basic-bskwouldbe significlll:!t1yreducedif bothgroupsweregiven external

Silpp~rt

^{intheuse or}

verbnliza~ion

as amnemonicstra tegy-

(T01_,e~en

and Goldman.1977 .p.S9).

Thep,e~entresearchfocusesOilchildrenwho areoraverage illt elligellce,.but"

\ • who perro,rmbelow averageon

m~the;atics

^{andST Mtask; .Given}the appar ent relationship betweenmathemat ics'disabilit ies andSTM,instruct ion.deslgned'to improve performanceon 'sT Mtasksshould leadto animprovemen~in their mathematical performan ce.

Childrenwhoreceive beth STM and math instruct ion willbe comparedto ch ildren whoreceiv~.mll.tbinstruction~l(;lDe.ltis_hypot~esizedtha t thosechildren whofI;ceiveS'I'Mf nstuction willsU,bs-;quently improve onST Mtll.'lks', Those~.ho

\

12 do notteeej~ethistrainingwiUnotshowan Imprcvemeut onthe STM task!.

Furtherm ore"itis hypothesizedthat those"children who receivetheco'mb ined

, /

.

t~eatment[memoryplusmetb)will showa signifjcant improvement on mathseeke instr uctedon matlir..~-'{~ST Mstu tegy .-'".

in!ltruc~ionwill be instrumentalIi mprovements seenoverthe test ing sessions....

5t be madewhendevelopin~memorY/mllth

instr~ctioo

^program.

⁶

^By.,ta.'s

i~~:~count

^the

9ugge9'tio~s

^{'o r mlloyauthors,I}

, ., .

^{. . . .}

. .

^~

de,:elQpe~a programth felt beet suitedtheaimsofthis project.

As.suggeste d by atels·"and

Andre~en .(.lg8~),

^{.a researcher 'should\}

manipulatethebasict~k[ie.useofSTMst!.ate~i'es)bypresentingitin a'vnriety

a !

forms ."Theseauthorsalso suggest tha.tto ensuretask familiarization ,practice should be ineorpcret edan~explicit verbal· jst.ructionb.egiven'.ⁱA:!appliedto teaching theuseorstra tegies,these suggestion," imply thata'variety oftypes of-- strateg iesshould be explored.There ar eseveral differe"t wnys,to presentthe conceptofst ra t egic useor STM,"and therebyencouragestrategyuse..The~"e include'rehearsal,chuaking,"andcategorizati,oD, Idecided to~ive p.xtensi~l"

prac ticewith the rehearsaltechnique asthishas'beenthemain teachingstrat egy withethergroupsof memcey-detlclent-cbildrea(Kailand'Hagen,,1082;

Robi~SOfL

andRobinson, Ig76;and Waters and Andreassen,W83l. Practicewiththis technique involved ~oth auditory and visual modali.ties,<The digit strings,

r

present edwe~e l o.fvarying)engths. lnstru et icnswererepeated rpany timesto the children.

, ,Kennedy and MilI,er(1976)suggest ed that persistent.use anduliiityofa newlyncqui..redstrat egy.(rehear~al)m~~ de~end ,·nt least in par.\,on havinga

. ?

13

~'.i~ ^{... .} rationale Cor.engaginginsueh activity.They found thatfeedba ck give..nto childrenob.how wellthey rehearsedhelpedtheirperformance,Bydemonstrating effectivestrategy utilization,l.wasabletogivethe child renknowledge abouthow the'memory system a,perates and its role instrat egy generalization(ie.

metememory}.'Strategy-training must

b~

^{linked with 'use,and·.with an}

understanding

.

of'the'

;yst,e~.

^{TrainingODSTMtasks}

sh~-uld

^{. thereforeinclude}

inCorma.t'oabout the~trategy,^{howitcanhelp,}practice,with'i-b~^{.strategy,and} feedback,allofwhich'wereincorpor atedinth; present st udy.

To test':Cor the specific effectivenessot \{!':emory training, two gfOUPSwere

utili~ed.-; Each gro~'p

. ^:eceived thesame

atte~n

^to'math:'. ~^{Only . ;}

~roup

. - receivedthe memorytraining.. ^@

. ^\

,.:

Me th od

SubJeets_

Subjects wereselectedtromthe Popula(io~,orchildren referr edto the Diagnosticand

Reme~ial

^Un.it

'fit~in

^tb'elast

se'f'e;~:

^years.This Unit , witltint,h"e

Education·"'epartm:~t

_{. .} at Memor\al_I Vniversi (_· :C,

Ne~foundland, is.,

_.^{refer ral}

cent reIor school agedchildrenfrontthe provioce.of Newfcundland who nreeltber"

. ' . I . ' .

experiencing learning problemsorrar erati ng anissueregardingth!!ir academic plac~meotat school.Examinati cuor the350current filesat theDicgncet!cBod Remedial Unityielded a list or 30childrenwhosefilescontained'inCormation meeti~gthefollo~ingfivecriteria:[a] thechildren hadamathe~aticsproblema.,.

defined by below averagemathscores00adia~osticmathtest

.I6r

3.speeifie. requestCor mat~ remediation from the school;(b) the children.h3.d.some .i~dic=ati~nofa memoryproblemas~efinedby belowaverage memory scoresona st.andard testorpoorretention observedbyschoolperSonoel;IcYtbec~.ild rens' inteJligl:nceW&!Iwithin'averagelimits; (d) thecbildreo werebetwee n 9aod12 y.ears orage(inclusive); and,(e)thechildrenlived within::Lreasonabledriving dista nceof.~emorial,University.Theparentsorchildren whome~allcriteria~ere 'contacted by pbcn e,inrorm, dotthe proposedstudy,and asked iftheywouldlike theirch~dto participatein't he group .Fifteen familiesindieuted int er est,with14 ,bild(,naduallyeornpletingthepregr'm:0"child didnotreturnenerthe initinl·wess mellt.

Fourt eenchildren,between, theagesor 9yellrs,2 months,and'12 years , 8

"1;-...

IS

m\uths participatedinth~stud y, (mean-age= 10.03 years].Tl}.gseincluded12 mal~(meanage

==

.i.02yea"),a~da.Jemetes (mean age

=

10.38years).

Subjectswere eseignedtooneoftwo groups, theSTMgroup_or

th~

math group/

Because all 14 childrencould not berunatcnee and holida ys end camps

- ~ I

interferedwithscheduling,two successivesets ofgroups~res,ctu~,one/each.

~ringJulya~dAugust, 1085.?!O~Passi~ment~tookplace inseveralstagt '. Eight'children were;init iallyavai~a.bleto startthe programinJuly.These children weredi~idedaccordingtosex_endpairedon the b"asis ofage,milking4

p~i". Pai~

^were

",at'b'~

^againonlb.

~!§~ ~~

^of2pairs ",

child ren.Onepair from eachset"was'r andomlyassigned.toeacq:group.Each group had twop~irSof children.

The secondsetof childrenwer e'test:d.duri~g^August,Thesecbildr~n^were also paired in the sa me !ashionendassignecf'~a group.'Asthere were6s~bject9 (3pairs) inthisgroup,1 pair was assignedtoeachgroup. The remai nin g~was assigned )totheSTMgroupasa female wasinit.Theonlyother femn.le(r~om -rgrcup1 ~assignedte the_mathgroup. Overalltherewere8 children(1 ales and1 female)in the ST Mgr~UPIand6 ehildtee(5males and1 female)in the math group..

Inaddi tionto thechildren who participa ted throughou t the study,four pilot subjects wereusedto help.develo p thetreatmentproced ures.None of these children hadlearningproblems,

'"'

^\

.,

'6

Spe~IfiOassessmen t techn iqu eswere selecte d for each of the rel evant

~,-,

.

Junction s Ub-pet tan ttothisstudy.'

,>

Generallnt elligenee. Two eubtestsfrom theWechsl~rIntelligenceSealefor Child~en .Revised,{WIS CR)(wesehler,J914.) were !1d mi nillter ed toensu re that

. . .

.

Ior both normativeand compa ris ion purposes,allch ildren wer e0"( average Intelligen ce.The,":"ISe-R isthe .

m~t com~only

^{used test to}

~sess·.

chil dren's

~

intelligence .Itco~^of12subtes tsltwo or^{which are}~tional)^{- 6}verbal, and .!>- non-verbalorperformanc e tasksubteets. The two subtest, usedin this stu dy wer e theVocab u larYand BlockDesign subtesta.TI1isshortfor m of the WISG-R bas bee n-ShO\VDtobe validforscree ning purposes (Silverstein, 1974,H)83).

Mem oryTask s.,Twomem or y tasks wereused, one deal in gwithauditor y ST M,th e other with visualSTM. The au d itorySTMtusk consistedof the Digit .Spa nsubtesr !'tomtb.e_WISe-R.This sub test requiresthatth~individu alrepeat num ber strings read a.lou d by theexamin er, in bot hforwardend backward order.

Thenu mbe rstri ngs increase in lengthfrom 2 to 9digits. Thetestbeginswithth~

presentatio n end forward recallofdigit,st r ings.String leng th is increasedbyone digituntilchildren make'two- consecu ti v eerro rsondigit'~{ringsofth esame length.Whenthis cr,iteriofi.isrea~hed,the stringstobe repeat ed beekwerdsare -...Mesent edin the same way.Fr~~^{this,th eexaminerobta insarawSCOtt'C9nsistmg}

• , !

ofthe totalDumb~rof correct lyrep.en t edstri ngs.Busedon age norms,this

17

Dumbe risconvertedinto a~st4Ddardscorewitha.mean

o r

10anda standard

"

d,eviatio nof3.

.The visual STMtaSkwas theVisua lAttentionSpanfor Letterssubtestfrom

tb'~

Detroit Tests of LearningAptitude (Baker

a~d

^Leland,

196~).

^{The Detroit}

I • ..~

.Tests ofLeer aing.Ap u tudeis a diagnos tictes,t comprisedof 19eubteets, designed to examinechildren'slearning.problems .It basno rm,atiiVe data

r;;;

^children

betweentheagesof3-.end. 10.The,Visual Atte,ntion

Span'

for Lettersaubtest' consistsof'Jetterstring!!th3:.tareprese nted'simultaneously oncards.)Vbenthe '.. cards_• are_• removed,thesubject plUstrecalltheprope rsequence_, of_.",the letters.'_<I Thesest rings vary inI~ngtb

r :om

^{4 to 8}leU" l! ,begi nning wit hthele tt er,strings, with4letters.All ofthese strings mustberepeated in forwa rdorder.Thetestis c04plete wheechildrenmaketoureonseeurlveerrors . Basedon'bow manyletter stringsthe_cbil~renremembercorrectly(raw_sc~re),'a standardscoreis"obtained bycom paringthe rawscoreto normativeage data.

Math PerrormnnceTasks. Aswith tbememorytasks,tweimatb taskswere chosenferadminist rat ion.Bothweretaken'from the KeyMathDiagnosticte~t

- -

(Connolly~Nacbtman ,andPritchet~,,1\)76 ),which is

an

individually administe red test'designed to providea diagnosticassessment or skill in mathematics.KeyMath test items aredividedinto 14sUbt~ts organb~i~to^{3 major}are~:^content, operatio n,!a~deppllcettons..Them~ntal'cdmputatiQn^{sectionfrom the.KeyMath\} lest was usedto.tapaUditot~_^math'perfor mance.This section'is made up~r¹⁰ menta l'ma thqueeticnsdesigned to becom e'increasinglydifficultovertheleggt hof the test.Thementalmathquestionsare presentedor1'l.l\yand bavetobea~swered

;( :/

- t l

^"

^.

18

orally.Thissectionisdisecntinuedalter3ecaseeutlveerrors, Astandar dscore~ o~tainedbycamp_aring theto~Dumber'ofeerreetansw~n(raw secre],wIth the Dornfativ"e da ta..

VISual math perrorm~9co^waseiami~ed^psi!lll:.the"written.comp~ta~iOD .sectiontrom the KeyM&th Test."This section.isdividedinto 4subsection,:e~ch' dealicg with a apecifiuoperation',(additio~, suJ)trae\ ion, multi~lication and.

division]..The re

!'1(

~etweeD ii,J..~prob~etn!l.~Dea~~subsection ;aUpresented'~\

.paper.Children,are.givent~eproblemsheets'a ndaskedto solve

t.he.ni

iuwriting.

Foreach:subsection,

a

st&t\dardscoreisobtained throughthe sa.meproced~r(!' e

usedlorthe mentalmath prob lems.

Othermateria ls used inthi!stu dy includedma.th sheets andmathp;oblems,

~

. . . . .

a.s

desi~ed

bytheexemtner.Bxemptes

6f'~bese

.i repr'i5entedin AppendixA

~nd

,';

APpeD~Brespectively.Ot heractivities and g.:l.mts userj,<hltt ng lh( treat menl

£ ^'Ols

^{anlIs ted.}under Appendll C

~

^{• .}

I .

• rceedur e

Eacbsubject was'"lnd.ivia ually assessed twice dutingt~eprogram:cnee beforetreatm ent began.andag3inlit thecoecl usicaoftreatment.

~ ^"

. .. /

~

•Prf!-onssess ment.Pre- llSs~sSmentconsistedorlin individualsession with..eech child. Duringthissession,the child was screened forintclleetu'afability,usingthe

. .

Vocabul aryand the BlockD~ignsubteats fromtheWISc.~.Then thecbild"wM assessed on the twomemorytest.s~theDigitSPIlD,lubt;' t f{Omtb~^WiseR

- .

- : _{\ "}

.9

r

(audito~ymemory ) and the ':"tSualAttentio~SP~^IorLetters.subtest(romthe Detroit"Te;tsDC LearningAptit ude(visual~emory),followedbythetwomat h .'tests,the-mea t&lcamp~t.tions,ectioDCromtheKeyMl.tb Test(audito ry math) end the'writt ento.mE.~tations^section(romthe'KeYMat hTest(visual math}.A '.childwouidnotbaYe'teen included intb~studyif·he 0"sheb~Botperformed .belo.w averageon atle~t·ODeoreachDCtheSTMandmAth tasb '/ Infact,aU cb"ild'rtDperror~ed'below anra geo~allofthe tests.Atthe completionofallpre-.'

• •: . ' ,, ' :., • " 't:' • _ . . ..

te"ll.~i,;,g:"theparentswerec~lIedandgiventhe,dateand

ti mfor

their'ch ild'sfi~t.

"

!~ter~ention·

^..

'~re~~ment con s~t'ed'''or $tr~tegy

instruct ion and/ o;

~"th.

. • ' ", I· -- .

. -.~ pract ice".~heST~"rou~receivedinstructiononSTMstrategies,pract iceusing

:.' - -.

-·"tb~....;'~~, ~nd ·~atb ·p~act~ce. ·

^{'Tbe math.practice was aimed.a,t}

. inrorPofating

'~b~'

^memory

!ltr~l~~es

^intothe

mat~ pr~hltrns.

^{Themath.only'}

.... ': ' ; ' .

.

grotip nceivedmathpractice identicalto th'e'STM~oupwiththeexception.that .all_mathreferencepr~tic"e,toSTM^the.~hildren

.

or memory

. . " -

we~estrategies^.corrected" was^if

.

eliminat ed.^tbey-mad~

- .

errors "Inboth groups,dlleto improperduring

. ,

'"1.

,

.

^e'

^•

Table 1. Program OJ.tHne·

~ ~

:e~~°to~ry

-neroryexmrples "

"'flI:ItDrY strategi,esam.practice

- gone ./

'~~"sion,i.,(60mins-.) -revres of iremry strategies -- 'practice-

- " " ' ! "

"~Sion'3.

"'fleforypractice(5m1ns.J

-math facts(15mjna ,I -mathsheets'(75m.tns.)

j

'""mllth CJ3l"e(IS',mins.)

,/ session~. .

-m::!fOry practice(5m1ns.) -math facts (15 mins.) -mathsheets(25 mins.). -s tory problems (15mlnsvl

.~~j;~~~~iJool

'~~~cti~-,,(;^miAs.)

-tteth facts115m1.ns.I' -mathsheets(20 mins.1 -story prQPlems(10m1ns.), ,-mathgaJTe (lO min s.)

session6.. ' "

-nerorypractice(5 m1ns.1

-na:th

facts(15m1ns.1. -mathsheets(30mins.) -stoI¥ problems(10. mins.) -m;3.th.ganB(ift!Irei . •

29"-:;,

~ session1.

-math facts (10mins.) -mathsheets(20mins'; ) -acUvity(30mJns~1

sess.1on2.

-math facts(10m1ns.). -math sheets (10mins.) -cicti vi ty (35 mins.1 ,~thqane (5 mins.l

~ss1on3.

-mathfacts(10mins.1.

-mathsheets (10 m1ns.) -mathgane (5 riUns.1 -activity(35 mins.l sess1cn4•. -math facts(10 mins.1 -math sheets (10 mins".1 -sto ryproblems (10mins.I -activi ty (30mins.)

session5.

""1t\'lth facts.U':O mins.l.'-- -mathSheets,(20m1ns.) -s toryproblems(I Smins.) -mathgarre(I Smins.)·

session6.

-eathfacts(10 mins.l -math

ereeee

(30 mins.) -story problems(15mins.) -mathgarre (10m!ns;L~.

21

While the ST,M.n0upreceived memorypractice,the Math Onlyr;roupwere engagedin activities that did notdea\wi~hmath or memory(see Appendix C).

For theSTM group, memorystrategies involved mainlytraining in rehearsal (subvoolly repea tingthin gsto oneself),but also in cbunking (breaking items into

.

---

groups). S!rategy practice also included games designed to concentrate en memory.Ibegan the firstsessionby focusing oa memory.fasked thechildren what memoryisand whatthey do ifthey want toremember something.I asked- them to thinkof.ways to remember things [eg. "Howdo you remember spelling

~ndhistory? What abouta phonenumbert- ].We then dlseussed their ideas.

Next,thechildren were given examples of applyingmemory strategies.The tirst example used Visual Memory'

card:(r~~m Dev~lopmeDtal

^LearningI

Materials).1 gavethe ehildreu 2

s~ts

^orpictures'to remember, one set at

&·t~:.

T'hefirst set

was

s,erambledon the~able.Itincluded pictures ote pipe, dog, key, milk carton,light, line,'andfork.The second set was presentedin an orderly r~hion,the cards were lined uP"inpairs,and each pair had a similar feature.

These included picturJor hammerand scissors,chairandlamp, boy and girl,and

!ree andflower-.Although each set~lI.d8 pictures,everych!l~round the second set easiertoremember.Theywereasked why. We talked about organization, grouping ibings that aresimilar,and.remembering small groups or informationa~..

a time.

The ?ther memoryexample dealt w.ithnu'mberstrings. Ipresentedeach efilld with a numberstring'l(Sdigits) to remember.Onechild in the pair was not givenan opportunitytorehearse [l asked him orher questions).The-ot her child in the pair was helpedbyrne saying the digitsout loudover and,over.Tbisled us

22

toCalking about havingtoconce ntra tein ordertorememb er.•and theadvlLnt ageS' of beingable~say somet hingoverandoverto yourself in order

t?

helpyou rem embe r. i.e.the rehearsal techni que.

The next stage

o f

memory training involvedactua l practicewith reh'carsal.I beganbyplacing indexcar ds thathad Dumb er str ingswritte non them in frontof eachch ildalte rnately. A !ptal o( 150cardswith numberstr ingsvaryingin length (rom3-8digits onthe m wereused.The st rings wer egenerate dfromrand om number tables. We bE;gan~iththe

i

"digitcards (eg. 528).·"Herearesome numbersthat I wantyou toremember. Let'ssay them out loud. 528,528,528, 528, 528, 528. OK,'I'lltake the card away, end let:s seeifyo.~canremembe~, the numbers.s Sta rtingin this manner,thechildr en woul dalwaysgetthest rings correct. Theywere congra tulat edand were show.n the card.

NtertlCewitems'Iwouldstopvoclllizingthestr ing, but encouragethechild to conti n'!..e. Lat er ,Iaskedthem to say itover~ndoverjust insid e their-head- As thechil.dren,beea~epr?Cicient at"thetask,I incr easedthenumber string length , .and shortenedexposuretime..

Wewentthroughthe same.routinewithaudito rynumber stri n!r',sta rting with3digits.and worki ng upwar dstoa maximum018...vter everyexample. the childre n were told whether theywere corre ct or incorr ecta~dwere always shown thecardso that they cou ldseeforthem~elves.

For cardswith~~8 d.!~ih,I alsointr oduced ch unk ing,orbreakingthese longernumberstri~ (I;lIinto smallergroups.For"i'nsi:mce,63·12[,4 becam e 6:1,·12, 54,or634 ,25,1.

At thebeginningof ever y session, time was spen t reviewing andprac ticing

/

',:;.

23

the~ehearsaltech nique.

Math practice Cor both groups eoaseted or written and mental computa tio ns.Thill was dividedintoseveralsections:(a)Mat bCad s , suchuthe timest~b1es;^{(h) math}she~tst^(e)storyproblems, withboth verb alandwr itte n answers,and(d) verbal math quest ions, such!L5·whatis2+4 +8= r-.AU praetieeiovolv~thelour basicoperations.The childrenpractice donaddition

fi;; t,

aod then, sub tractio n, multiplicat ion,anddivision.Thistctlcws^{the standa rd} orgnoiza tio n

or

teachingmath.

Post,;-assessment.·At thecqrn pletionortheprogram,'the childrenwereon~'e

. . .

againseen individu ally.'rhi! assessmenttook placetheda~immedia telyfollowi,pg the rinal session,and the ch ildren wereadministeredtherou~tests ( 2mat h and2

.- I

memory ).FollolwiDg~thecompletionortheprogram,alett er waswritt en to the parents orthe children, giving inform a tion on bow tbeir childperfct med

I ... .•. .

:throughout the program,results Irom pre-and post-t esti ng,and suggestionsror continuedremediation.

. ..

2.

Resu lts -

Theresultsobtai ned through.thisstudy clearlydemonstrateseveral rindiog5.

First,as predicted the children in the STM groupimproved significantly onthe memoryscales.Themath~:)Dlygro~pdidoot. Secondlr.. and more importantto thelocus ofthisstudy, '\hildrenwho receivedbothST M~nstru ctionnod math practice'improvedsignificantlymore over time00math tasks-than.did those

--

childrenwhoreceived the math practice alone. -.

General I.tellim , ' aodAge·Com...;, o",. Atpre-treatmentthere was

'0 .f :

significant dirrereocebetweenthe agesofthechildrenin the two groups ;t(l :!)= .0.35. Tbemeen ageswere 11.02 yearsfor"the STMgroup and10.82to rthe moth group.No significantdifferenceswere foundbetween the"twogroupsofchild re~

o~measures of I.Q.:Voeabulary,t(12)

=

0.75,~ndBlockDesign;t(l 2)

=

0.3~:

On~bularythe meanscoreswere9.5fortheSTM~roupand8;8Cor the math -group.On theBleckDesi~su.btestthe.ST M g...oup had a meanscore of 9.7and'

the math grouphad amean~f9.5.

I

OverviewofAnalysis-."Both theraw and thestandard scores Cor'each measure were analyaed..Becausetheresultswere virtunllr, .ent ica l,only the res~lts"fromthe analysisor standardscores willberepor ted.The standard scores refer toan age or grade level. AJI rawscores are presente dinAppendixD,all

standard .sc~res i~ AP~endix

E..The resultsof thestatisticalanalyses perfotmed .on thest andard scorescen beseen in Tables 2·5.Analysesoftheraw data are

\-'

Table2

'lheDigitSpan_.SUbtest-Analysis of Variance 01 StaOOardscores'

.

..

25

i ·.

.Sourceof variation 55 df es

~SUb1ects

A{gttIUpS},- 2.678 1 2.678 O.7J8

.SUbjectswithinqroJpS 43.500 12 3.625

Within SUbjects

.~ /B lt,ilre l 30.035 1 30.03 5 37.939

AS . 12.964 1, U.964 16.376

BXSubjects'witlUn

'groups 9.499 12 0.791

.:

.

⁾

.

- -

^....

Table3

'Ib!V1Sual Attenticn Spanfor Letters SUbtest-Analysisof Variance an StandaJ:d scores

Source

of variation 55 df

'"

BetweensUbjects

A (gioupsl 6.785 1 6.785 6.462

SUbjects~w1~groops12.60 0 12 1.050 WithinSUbjects

B(ili'el 6.270 1

-

^{6.270 12.658}

AB 3.192 1 3.192 6.444

BXSUbjectswithin

.groups 5.944 12 0.495

7

26

-\

Table 4

...-'Ihe

l€iiw

CaTp.It:atia'1sSubtest -Analysis of veraence on

Standardsccres •

27

Sourceof Variation 55 d£

""

BetweenSUbjects

~~!nth1n

^{groups 31.8517.832 121 7.8322.654 2.950}

Within SUbjects

,

B(t11re) 21.262 1. 21.262 20.164

.AB 7.893 1 7.893 7.485

B XSUbj~swithin

groups 12.653 ,12 1.054

Table5

'lhaWrittenCotpJtationsSUbtest -Analysisof Variance 00 Standardscores

. ^,

sccece

of Variation SS df

'"

aeeeenSUbjects

A _I 33.820 1 33.820 1.012

.SUbjectswithinq.roJpS378.462 12 31.540 WithinSubjects

B (titre) 250.203 1 250.203 97.153

lIB 59.331 .1·' 59.337 23.040

"BX SUbjects.~thin

30.904 12 2..575

<J%OUP'

,.

^.•.

-- - 0

L.-.•.

2 .

preeented.InAppendixF.The means and standard deviationsforeachset ofdata, raw andstandardscores arepresentedi~ ,,~pendixesG and H,resp,ectively.•

Foreach ofthe fourtests, the standatd score for eachchild was submitted to an analysisor"variancewheregroup;·~andMath, and Mitb'"only)was a between subjects fac,tor andtest(pre-and post-]wee a wit hin-subjectsfactor.For

, -

each analysis,whensignificantinteractionswere noted,fou'rmultiple comparisons were performedusing the Seheffemethod. Todeter mineifanydiCfere~ces^existed between the,'STM and ma t h only groups at the start.oftesting,'performa nceon

. .

the pre-testsfor each group was compar ed.To-determinewheth~rthe mathonly group imp rovedover time,a second comparisonex;m inedperformanceat both pre-and pest-testing . Similarly,todeterminewhet herthe STM group improved over time, theirperformance~comparedatp~e-andpost-testing.Finally,to

\ -

determin.eifanydifferencesexistedbetween.theST M grou-pand the math only

'-J--_... .

gro up at the end o(testing, performance on thepost-testsfor eachgroupwas compared.~nlessotherwisenoted,allsignificanteffectswerereliabl eat the .01 .levelorbeyond.

,AuditorySTMTask. Thestandard scores onthe Digit Spansubt~t'ofthe

\ .

WISC.Rwereanalyzed.Ascan beseen inTable 2,asignificant~aineffectof time ofteSUngwas found F(I,12,)=37.Q,4.A!Jshown inFig~re1,thise~fectwas qualiCiedhy anint erectioa between groups andtime of eesessmeat[pre- and- post- testi ng),F{I,12l=16.38.The Digit Span scores onlyimproved at post-testingror subject;whoreceived- memorytraining.Perrdrmanceotthemath only groupdid not ebengefrom pre-to pest-tearing ,howeverthe STMgroup didshow an

..

ao

·- -stm . 'math 0

0),

~ .

o .

. CJ

l/) C

II'

0

0)

~

E

\. _-,

pre post

time

\"

_\

\

Figure1.TheDigitSpanSubtest-·l~^{SCores atPre} and Fost-Testing.

~

\

.,

31

imp rovertient inper fcrmaneeovertime,F(I ,12)=:53.3. A1fi1ough theSTM. grouprecalledmore digits thanthe mat honly group atpost-testing,theeffect railed toteach significa nce.

Visual ST M Task . Visualmemor ywasassessedthrpugh theadministra tion o( the VisualAttention Span for Leit_,

_.

erssubtest Irom_. theDetroit

' .

Tests

o r

LearningAptitude.A3 shownin'Tabl;

3, -

timeoftest ingwas significantas a-mai n

, I " ,

.efrect,F(l,12)'=12.66,.aswas theetre~t.orgr.oup,F(l,12j=6..~~,p<.OS.Figure 2illustrat es thesignificant'intetac t ion betw een groupsandtimeof assessment ,

"F( l ,12)

==

6.44, p< .OS. Onlysubjects whoreceived memorytrainingrecalled

more items atpost-test ing than'at pre-testing onth issubte~t,^{Similar tothe} auditory ST Mtask, tbe ST Mgroup recalledmor eletter stringsat post- sest jng thanatpre-testing, F(l,12)=,18.87.'In addit ion:atpost-testing stude ntsinthe

a

sTMgrouprecal~dmore leu er st rings'than st ude nts in the themath only group,'. F(l,12)=Q.3,p<.05.

Audito ry Ma.thTllSk.

Th~

^{sta.ndardscores00}tbe menta l

co~pu;~ion

sectio nof the.KeyMatbtestpertaioedto

: ~itory'

mat b performan ce.'Onthis

'.

depende nt measu re, as seen in Tabl e 4,a significa nt main erre'ctoftimeoftes,ting. was found,F(I,12)= 20.16.Figu re 3 showstheinteraction betw een gro upsQa t

.

. ,

.

pre- nod post-t esting onaudito ry mathperform an ce,F(I,12)= 7.4Q,p<.05.

Specific~arisonsrevealed th atalt ho ugh themat,h.on lY group did ootImprove. . signil'ic'Dnt~^{over the}cou~~eofJre at mentonmeo~al^mathcomputations:-...~:~T~

.grou pdidimprove,f{l",12)= 27.21. At post-testing the ST M group' correc tly answe red more oft~~auditorymath questi ons'than~idthemathoolygroup.This

(\)

... 12 0 O ·

!IJ

l:

11 Ill '

(\)

E 10

.' . '

- strn ' . math Q - ,

. "

'\

R ^"·~

^{' .}

^·

^{' .}

^·

^..

^··

^.;

^··

¹

^-Y

^.

.

. ' . . " .

^,"

c . • " . •

.. . ^{. .}

0--- - - - --0

pre

time

^"t

post

^{I '}

. "'- .

. .

Figure 2.ThevisualAttent.icrlSpanf9rLetters Subtest -

~ ~s^{at Preand'}Post-Testing. ~

•

_\

< ,

r

_.

;

_i

3~

v

s~m ...

math o .

^"

,Q)

....

'CJ O.

en :

~ :

Q)

.S

^~.,

^..,

pre ,,' ^.

post time '~

, Flaum3'~'nleM:!ntalCarputationsSubt:est~1'MeanSCores atPreandPost-TeS~.

;

dillereneeapprdached significa nt .e but tai,ledto eeeebthe requiredlevels

VisualMath Task.Ther~naldependentme~~reinvolvedananalysison the standard scoresof thewritten,computa tion sectio.D IrcmtheKeyMhth.te'!lt.A5

seen"inTable 5,asignificaDt main er{ectof time ortest ing was round.F(1,12)='

I .

g7.15.Figure4illust ratestheinteractionbetweengroupsand timeorassessment ,

°F(1,12)=-23.04.Thisinteractionreflected thesignificantimprovement

cit H ie

STMgroup" Irompre-

to pos~testing .

^on

writte~ ~h ,

COlllPutiLtions, FII,I;)

" , ~

113.50.

-"..".

. . ... .

Other Anatvses.The wr itte ncomputa t io nsectio n oftheKeyMathtestWM ' c0r,rtp rised of rOUt. sub-sect ions. Performance on the ~dition, subtra ct io n,' multiplicl1tiqn and division sections was examined individually.Inorder to

, -

^.

determine" the1iffe ren c ~ between the two &!OUps .on eac h operation, Ionr individualaaovasandsets of means compa risons usingtheSchejfe method-were per formed.

No~!ic.antinteract ions wereroundbetweenth~twovariables, groups and'"ti"?-lcir assessment,for addition,

~(1,12)

⁼1.34, or forsubtra ction, F(l,12-)

=

1.7~. _"\

^{Foeeecboper ation}_. ^{bow'ever, a}_'significant

-m~itl

errec.t or'.lime

Of~~S

_"^inl

•w~!of nd.For a:ditiOn,~( 1 , 1 21

=

:.00, p<.05,andfor "llubtrtlcti~D,F(I !21

=

36.2~.

^{\. .' , '-}

Asignificantmain erreetoftimeof'testing was,ro~ndin.t~eann.lysi~of the multiplicat~on problemstandard scores,.F(I,12)= '11.64, This analysis also.

revealed~significant interacti onbetweengroups and time of testing,F( 1,12)=

~...

.

^; .".. ;' -~.\ ^'

. .

^{, .} ~

~

..

^,

', -

35'

.st rn ...

math 0

'4)

... ^,

"> 'lJ)

r 0

C

lU 4)

E

-

-- .

pre time

Fi~"

^TheWritten

~+ons

SUbtest - ."." SCorep

atPre st-Testinq: _ . '

.

^,.

--

,

. ^.

, \,

36

")

,

16.80 .OnlytheSTMgroup improvedover time on multiplication problems, F(1,12)~58.07.

The final analysis examined the standard.scorestrom the divisionproblems.

Asignificantmain c'rrect ortimeor testingwasrou nd, F( I,12)= 51.40. An interact ionwasfound between groups .and time orassessment,.F(1,12)=30.42.

Aith ougb the matbonly

gi''oup

did notimprovetrompretopost-testing,~heSTM groupdid,F(l ,12}=BO.78.

Pre- to Post- Ageand Grade D,irrerences.All subjectswho tookpurt inlhi!

study wereperto~mingbelow avera geon'bot q math and memoryt~ks.Overthe treatmentprogram lrom.pre-to pest-treatment,children in the STMgroup reached the normative scores,whereaschildren in themat h only groupdidnot.

Th e gains.madein,all task areas aredisplayedin Table6.

.. /'

")

,

Table 6

Meanscoresfor Groopsat PreandPost-TestJng enallSUbtests

) '

Digi t V1sual Attention _tal ---Written Span Spanfor.Letters CCltQrt:at.ia'lsCcrtp1taticns

'10.00 10.82

' .S ' .S

"'th pre 7.50 9.05 3.' 4.4,

"""'"

^{post 8.00 9.08 '.2 5.0}

rorm 10. 00 11.02 5.1 5.1

SIM pre, 6.75 9.67 3.' 4.2

"""'"

^{post 10.00 11. 34' 6.3 6.3}

~

•

.'

. ^.:...-