NOV 8

NOV 8

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I.S.B,N, THESES CANADIENNESSURMICROFICHE

.+

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,KlA ONi

• ,NOn CE AVIS

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c.C'30,Pleaseread theaUlhorizati onformswhich actompallyt histhesil.

THISDISS ERTATION, HASBEENMICROFILMED

EXACTL Y ASRECEI VED

Larepro duc tion, memepilrtitlle.de cemicr olil""

• est soemise

a

laLoicanadienn esur Iedroitd'a u teur, SftC1970, c.C·30.Ve uillezprendre conn.iu a n cedes formulesd'a u t oriu tion qui.tcompagne n teeue these,

LATHESE A ETE MICR OFILM EETELLEQUE

NOUSL'AVON S'RECUE

?

A'C ASBST UDYOF TH2DEVBLOPHEhAL DIF FBR ENCES IN'

PATTERN PROCES SI NGABILITI ESINYO ~ NGCHILDRE N

by

'---

Edi t.hDianne Mel vin,B.A.(Ed.)

Athe siBsUbmi tted to the·Schoolof Graduate'Stud i es in partial.ful f i l lme n tofthere qui rem~ nt Bfor

thedegreeof Mu t er ofEducati o n

. .

Departmentof Cur ricu l umand'Instruct i on Memoria l Uni ver s it y of Newfou ndl a nd

Nove mber 1984

i

_I

St. John's Newf o u ndla n d

•">.

-,

ABSTRACT

/This~t~dY

:W lIS

undert~kenbec"'ause of the perceiv -

ed 'need for information regarding howyoung children process pstter ns. Thepur~seoft~e ~tudywa l~olook

~~tothe'patternrec ognitl onabilities'of youngchildren . specifically, the abilities of childrenat differentlevels of deveiopment,withinapi a get i a n framewo rk, wer e,~llI~n- '.ed-"." reviewof theliter a t ure re veal e d the variables

whi c h hadbeen shown

t~

be reievent.topat t·eC"n

~recognition

as well as the variousexpl anatio ns foC",howpatternsare processed.

A ceee study res e a rc h design was decided~pon ^and

a'p ur pos iv e

sampl~ :

^{wa s}

cho:s~n~f .9';·~hildr~~

from grades',;

.mein age wa.s 90.• 64 months.

The samplewas first administered several stan - dardPiaqetilln -typetaskswhi ch.differe ntiatedconservers from :on-conae C"vers. Seve ralobservations were Mde re ga rding

th~\role

pl ayed by age lIB II variablein le vel.of devel~pment,and the rol eplay~d by schoolexp ee t eneeas II variable in level of development. SpecificsUb-3 ~ o u p sof the oriq ina! sllmplewere defined allPr e-Ope r llt i onal and

~' ^{Concre te}Opera t i.onlll bas ed ' on the finding8 fro m the , Piag eti a n instrument .

Finally,thesetwo8U~grOUpsee r e givenseyer- a l',.

pat ter ningtasksl~wh i chthe ywe re re q ut red to ext e nd a

,, I' , "

11

pat t ern , even in an erro neous response.

g~venpattern. The re s ul t.s from thisinlltru~entwere examined to compare

~he

two qroupa

:on /~te

of succ:tSS, the t.endencyto receee a patt.ernin'a'ne r rcnecuareapeneeand the type of .e rr ors commit.?ed.

The data wall"~~alyzed^uaLnqnon-param~tric'

. .

. ~

statist ics, aM res,~~ts.we re not,g ~e ra~;~rdbeyond this sample. •.,,' :.• •, " "~';".~.~:'.,', ...., .•

)' ~eftndinqll ee e eea to sho.-"!.,thft:~hi1e:qe did not s~em.im·po rta~t ~s'a.·Vb d ab .le:i,n:}et,erDli rlin~PiJ'g-etian level, gra.~,~·VYel.:.~'id'.lIeem'to Sh~WI·,i~~rt~nce^al!Iavar i - 'a ble. ,Ab o ,'developmen talleveldid'se/ m to differentiate .

th~

mor-esu c c es s f ul patte r n

sOlver~~

^from

~.~.e

les s success-

ful." Error.t ypes seemed to vary for the two le vel s,

hO~ev~ r b~th ~roups

^seemed

pre.dispose~

^{'to imposinga}

",':'0

The the~lll^{concluded.wit h aset of}reconwenda-~:^. tio'ns forre sea rche ~sand educators.·

I i

- ,

^-

- - --- ---- --- - - -- - - -- -- - - - - -

--~~~~.

, f

ill

I '

- - - - .•~..•.•~-...-.-lr~" .;..-~---

.vr

IICP;NOKL!OG~MBNTS

Thereare many',people

.

whosetlille"'and^~

. ,

^,ef fo r t have

.

,madethisp'ro j e c t poasible. "

11 sincere 1;h llnkyou isex.te nde d,to Dr.Al~r;

Brac e,whosekindn~ssand e"l\co u'rll.gemen twerea constant support tothe wri.ter• .Also,Il\lI.ny,tha~ks,t~the ex.u l ning cOllllf1i1;tee, Dr.FrankRig9s and Dr. Frank Mar shfor their

.

^'

, .

time and patience,lncriti qui ngthiS thesis . ' , -' Muchgratitude·isextended tothe'principal of

. . I . . .

St.Col lJlllb a' 8 Primar ySchoolII.Swell a8 the four,cooperat- :

. . .

. , ing primary teacherswho.willing re-ad j ustedtheir"

's c hedul e s

t~ all ~w:,the~r

st ude nts to

parti~ipllte

^{in this}

atudy. Alaothankyouto,the children'whounk no~ i nglY^made thisproje cteeeeeeareality.I

pinally,many thanks to the'writer'sfamily who ,support edt~iseffo r t inever y way·pos s i b le.

...

^-~.,

,

'1

, ,I,

...: i

! !

.. _ J..

.r, _{•TABL EOf'CONTENTS}

"::::::::::::: .

ABS'l'RACT:•• : ii

"ACItNOWL!DGE/IIENTS•••• •••••••••••••••"•••• •• •• ••••~^{•••••••} tv

C8~PT~~t;od~etr~~ . ~~~~~. : ~:: : :

^{::"::: ::::: :::::}::: : : : ::

The Need,•••••••••• ••••

<... •...

The Pur polle /4.•••• •••••••~•••••••• ••••••• ••••••• ••

Definiti o notTer ms ••• ••~\~••••••• ••• •••••••••••• .Ques tio ns•••• ••••••.••••• •:-... ... ••••••• •••••.•••• •• 11

ScopeandLillli t a ti ona••••• •~'i'o•••• •• ••• •• •••• • •• ••l 12

CHA.PTERII REVI EWOFRELATED LITERATURE •••• ••• •••v- 14 Abilities Relatedto Patt.e1:" nPr ocen inq•••••• •• •• 14 The proc e s singof Patterns ••• ••••• • •••••••••~..•• 17 Varia bl es ASlloci atedwith PatternProce s sing •••• •..22 The Prereq uisit ell to Pattern proc e8.si nq•••.••••••• 28

CHAP'I'BRIII "DES I GNOFTHESTUDy •••• • •••• • ••••• • •••••• 35 I

The pilot Study ••••~•• •••• • ••••••• ••••••••••••• • • 36 The Samp le•••••,•••••••••• • •••••••••• •••• ••-•• ••'" 36

. "The Inst rliments 37

. ThePiaqet ia nIna tr ume nt,••••,••••••••••••.•','!...!....'"--_37_

" --'1'hePat t ern..lns tr Ullle rit·-:::•• •••••••••• ••••••••• 3' Adlllini ater inq theTests••_•••••:••••••••••••••• • •39 Ana l ys iaottheData •• ••• ••• •••••••••••••• ••,•••• • 40 Questi o n'1•• ••• •••••••• • • •••••••••••••••• •• •• 41

Questio n'2 41

Questio n'3•••• • •• ••••••• ••••• ••• ••• • •• • ••••• • 42 Question'4••••• ••••• •.•• •••• ••••.• •••••••••••• • 42 Que st i on15••••• ••.• •••••• ••••'•••••••••••••••• • 43

g:::~~:~ :~ :::::: ::: :::'::: :: : : : :: : :::: :: :::: : ::: -', . '~"

~-,-~---,CHAPT~.I~__J:V_ _ANALYS,I S_OFJ fllLD""TA.• •••••^{AAA "}A'~"AAA..,._.46~·--~-~

Question 11••• ••••• ••• • ••• •• • • ••••••• ••••• •A••••• 46 Questi on 12 •••• , ,•••••••••••• •• ••••••••• 50 Quest i o n'3•••••;•••••• • ••• •• ••A,•••••• ••••• •••• • 52 Que stion 14•••••••••• ••• •••••••• •• • • •••••• ••A••• • 55 Question '5•••••••••••••••"•••••••••••• ••• •• •••• •• 57 Q.ue atio n '6•• •• •• •••A• •••AA• •• ••••• ••••• ••••••••••59 Que s tio n

.7

^{A••• •A" ••••• •• • •••••••} 61 Summa ry •••• •• •• •• ••.••• •••••• ••• •A•••••••••••• • ••• 65

TABLE OFCqN'l'ENTS(co nt'd.)

SCM"AR~.

COliCtoSIONSANDRECOOBNOATIONS ••67

!ffig;H~;U~;

Recommendations fo r geeeercnere •

: ~~~~;~~~ : : : : _{~ ~} ::: : _~

• ••

_{~ :} :

•• •

.: _{~ ~}

• ••

_{~ ~ :::)}

•••••••

i!

86

'

ReCOU\IlIe nda ti ona for Educators•••••••••••••• •••••81 Co ncl us io n••••• •• •••••••••••••••••••.••••••••••••••• •88

REPERENCES••••••••• •••••~•••••••• •••••• •,~;••••••• •• •••••89

~./". APPENDIX

A. Plag e t la n In.tr~nt;... ... ... . .. .•.•••••• • 94 B. Piagetla n InstrUlllent·Re eponae Record·She e t.•••• 104 C. Pat te rns Instr ume nt ••••••••.•••••••••• •••••• ••• 106 0-. Pa t te rns Instrument Response Recor dShee t •••• •108. E. lI:ey'toPatte rns.Ins; rument.-••••••••• • ••••••• ••• 111

.'. '-, ._-- -- -

'[

I

,I

I

^vi

^{I I!}

Table1

Table 2

T~b~e

³

~able

^'..

Table5

,Ta b le;6

'i

1

!

Ta bl e 7

,

iTable 8

Table9

LISTOP TABLES

Distrib utionof Sample'b y Age,

Sex and Grade Level •••••••••• •••••••••• •37 Distribution of GradeLevels by, PiagetianStage~••••• • ••• ••• ••• •• •-;,. ....47 Distri butionof Plagetian St ag e by"

Grade"Level - " 4f!

Mean Agea for PiagetianStages ••••••••••51 Me a n'S;; o res on PatternTest'f or

TwoPiagetian Groups 53

Patter-n Impo-s-tt-km Tendenciesin ErroneousRespons es for TwoPiagetian Groups ••• • • •••••••• •• •••• •• ••••••• ••••.•56 Perseveration Tendencies"i n Erroneo us Responses for TwoPiagetian Groups •••••• Sf!

Alter nation Te nde nc i e s i;Erroneous Responses fbr

Two

Piaget ill.n Groups••• • •• 60 pe rcent~geof Errors on'Pa~ternIt ems'

for TwoPi a g e tian Groups 64

Tab!e- -1O--- -0rderof OifflcUlty

l '

~iPattern Itellls ,~

. ' for Pro;-Operationtll aM Concrete, '----,-.

. Operll.t1.onal Groups ••••••• • • ••• ••/'•••• • •64

_-I

vii

__ _ I

Fi g ure1

Fi g ure2

LISTOF FIGUR ES

~~6~~n~~;~;~~r~~u~~~~e~e i:::~

^{fo r}

Pre-Oper a ti on al andConcre te

Oper ational Childr

.

e n •• ••••• •• • •• •••^{" '}• • •• •54 Freque nc yof Error s onEac h Fat t e rn ItemforTwo Piageti a nGr o u ps ;.62

I

»,

•

vii i

,

I

,

^{CRAPTER I.}

I

THEPROBLEM

.

Introdpctlon

Pa,tterns areeverywh ere•. l;)UrlivesIr e eu r ro un ded and,of t en •

·governed bype eterns, Dai l y.out lines

·lead us toant i cipate abou t when the

·morni ngpaper will''arri ve, whenthe

.bu s w~11beat thecorner , orwhen

'l u n chl<Ii.11 be se rv ed_ Innatur e,

··,fl o wers andle av esform symmetrical

. ~~~:~nr~ ~:t:~~~ l e:~~ht~~ds:~~ns'.

foLlow.p at ter n s (Bar ~ ett•.1982.p,st,

our'"abil i tyto functi o ni~ the enviro n mentis

l:argelyduetothe fact-thatthereareso

maL

na tura l l y occur ri ngpat ter ns. Thesegive onea

sens~constanCYT

they pro vi de abas i sfor predi c ting fu t ure events and the re b y allow '18thest r uctu ri n g ofl ivesintorou tines . RlaheandWalla ce (1910) stat e that:

the .ab il i tyto det ect enviro nment al

~ii~l~~;t;;~:~i:a~. co:~~t~:= :k;;~p:~:i~i

toseek andacapacitytofind se rial pa t t ern s insuc hdiverse areasas music, economics andthewe athe rIp.24 3 ) . Our desir e for regul ari t yandpat ternareec

-,-:-~.---i~tens~- that-we-Oft-enccan:ilOe-de~l"""it~-e~e·n€' &ii:rcn' ,''',e;-.!.--~-­

chaot i c. It·aeeas to be an innateinclinati on"'toattempt toO; ga'n ize

.ev~~ the .ll'IOst~ha2ar~

^Of:-

~veo.ts .: . "EV~~; ~hen

notr ue p.4~te r n e~ist9 ,humansattelllPt't o,construct·~l\e.

thatwi l l ena b le the m topredict the

.

^{., /}6eque nc~^.' IIf future.^,.

. r

" ,

-

^"

ev e nt e" (Klahr ," Wa ll a c e , 1970,e, 243). ."The r e i.s.

doubtthatwe feel somedeep need for orde randpattern"

(M~cjo ram: . 1974 ,'p ,'~6 )'

Nowhere"is paeeern.e c r e ~videnethanin mathemllt- it s . The structure_of

m athematics. -~9 ba~ed

^u;on

th7~~~'9U­

'1ari ties andint r i ca t e paterns'of.re l at i onsh i psbetw~en th'7'vari o u s' e l eme nts. se'iera1'authorshave taken the.

.

^.

';lib~rtf'to define mat::helllllticsinterms ofpat t e r ns . ·.Ma:~-··

ene eIce istheC~llS8ificllt io~and.~tUdYof,aU possible . pat~ern's,..-:a cc ord i ngtoSllwye"r(1955;p, 1'21. Mar'jo r am.

·('19 7 41

ge~s lIlathe~llt~c9

^{as "an}

aC'tiv~ty .conce,~~!!d

Prima ; +l yJ

~ithargument, ....itl).sPotti~9^{patterns-and,}p~si~g^{,pr e}.mis e s,"

\.P o 3)'. One of the

~'est

^deflniHonsof

'm~them~tlcs ;

^for

D~es'^{1977 ) "Le-that itis the recognit ionan'dthe study.

of patterns:-

The~e"'patterns

^{ref.eito any}

req~lar.ity

^_that

our minds'can recognize" (p.1). Similar ly ,Sueltz.'( 1976 )

... ..

,.

definesmathematicsas "t he study ofeeructureand.rete-

tion8~ips

^a:nd'thedi s c o ve ry

o~

^principles

and. 'p~t.ter~s".

lp ,

n ,

_{The t~}.seems to~agreeme n t in.th e litera:ll re on

.the fact that."mathematicsis a disc iplIne90ve~nedby

~atte.rns. Indeed,to have a grasp of the struc tu re of • _: _.__,_~tE.emat i c.!-!!! ~-.!'!..e_~e p~terEs_Which_arfLc.s ystali.M...d~,_ _- : '

- iJ

^~

O' w~thi n .

j ⁱ

Inthe field of mathematics educatio n',it is.t he job of teachers to provide,the i r students with exper iences which will-le adthemin deveLc pa ent; towar dlinundersta ndi ng of th e aUbject ar ea . I tis noteno ughto'prov i d e,~i :j oint ,/

,

ex·per i en ce s -ttJat aimfor shallow learn i ng. Rathe r the lonq te,rmaimshould~eec-q!Side childrento a visionof the str uc tu r e of mathematics . "neee er c be r a and cur r i c ulum dev;loper s ori ente dto wa r d conceptual epor cechea seem to agree on the importanceoffosterin~inch ild r ena·s tro ng i~ itiveunderstandi ng Ofthe under l,,:in gstruc turesof mathematic~.~ l~e s n i c k'and Ford, 1981 ,P. 10 1 ). At the· famous WoodsHole"co nf ere nce in'1959 ,whi c hbrou g ht toget-

~ J: "

he r promi ne nt mathematiciansand-e dueat.crs , it,.wa samajor- -.agreement thatthe te'ach ingof"mathema ticsmustbe influen'"

ced by this qoal•.

The cu~r Him"ofa subjec t ShQ.!:l l d be.

determ ed by the most fund ametWalunde r-

• sta ndng th a t~anbe achievedof the , unde rl yin gp r Lnct pLee that e lve et rue - . ture to thateubject; , Teach ingspecifil::

to pi cs or skillswithout mak i ng clear .theirconte xt inthe broaderfundamental

structu re of a fieldofknowl edge is"

uneconomical inse vera l"se ns e s . Inthe fi rs t place , suchtea c h in gmake s ,

~~ ;:~:~:i~~;Yf~~~f~~~~th;o~a;h~e:;~:,~n~o ~

^7-"

whathewill encounterla t er. In the secon dpi ace , lear n i ng_tha t has falle n shor t of a grasp ofgeneralpr i nc iples ha s littl e re ward intermsof int"ellectua l exc i t ement •• •Thi r d,knowledg e one has acq ui red,w i t~ o utsuf fi cient str uct ureto

"ti e it togeth erisknowked qe that is

like l y to be for go tten(Bru ner , 19 60, p,31)•

.I fthenth e coe I is toteach ma tJ;lema t i c sfor struc t u r e we"canno t'be 'jus tified

i f

we do nothel p our childre n't o see the Dat te r nswhich,by definitiona;; the basi s of the "!athe mat i cs. Thus,-in,th iBqlo ba l se ns e, there isa soun dra ti on al e forexperi ences,in patterntobe

part of thema t he ma t i c al curric ulumin our schoo ls. At II.

,mo r e.inl/lle d i a t e level,the inc'lusionof.pattern,experiences

in~he"cu r ri c ul um can beratio nalized in terms of their

ba sis inproblemsolving•

.Prob"lemsolvinghas been siten ast~e ~nderlyinq goal of all educat.I'on, Heathers in Mendoza (1977) suaaests tha't··pro bl e m solvinath in kinq or inqu i r y is aenera lly consideredto'be the cor eof.the educatio~alprocess and the chief mark of the.e e ueeee e nerson" Ip, 135).

'Pr oh l em solving is one,the,·mostba.sicaspe ctsof any mathemat icsprogra m. The Priorities inSchool Mat he - .e ae t e e (P.R.LS.M.) 'r e po r t of 1981, cited,a s one 'of its

i

rec ommend a t i ons that problemsalvina be a ee ter!orga n izinq element in the mathematicscurriculum(Wor th,Cathart, Kieren, Wo r t h and Porth, 19811. AnAge nd a for Action(The NationalCounc!"lof Teachers of Mathematics, 1980)also 8u9ge~tedtha tprob lemsolvinq be the focus of school • ma themat i cs in the1980"' s.

Whe nsolv in g problema,oftenclues to the

seru-

.tionar e presentin the'fo r m of patterns.in the data or inf o r ma t i on.'Seek in gout these patte rnsenables·one ~o organ ize,t he qIven info·rmatio n int oII.moreunderst a ndable•..

us e a ble picture IWhimbe yand.Loc hhead, 19811. Among.the akills wh i c h'we r e deemed crucialto problem eetv t neby elementa ry andse co ndar y t'eacherssurveyed for the

~re por t, the ab.ilitytoseekout pa t t erns.in data rank e d highly (Worthetal.·, 1981) . r e

lit~rature

^seems'

s

to conc ur tha t pAtterndetection'is one of the more funda -:

mental'problemsolv i ngskill s .

Discover lnqpatterns is a very impor t ~ ant strateg yin prob lemsolving; In mathematics,_we refer toeumininqa variety of cases,discoveri ngpatterns , andformingconclusions based onthese patter ns as inductive reasoning {BiUstein , J.ibeskind andtott, 1981,p.21".

It

'i s'un f o"ct una t e l y quite commonin ,mathematics in SChOOl\"that,problem

801Vi~q' acti~itY

^isnot em".ha.sized• i~ p~ima'ryand.ele me nf a r.vgrades. And equallyunf/)rtunate isthebelief that manyhigh school studentsdonot so lve

~rOblemsverywel l. Especially,d i f fi c u l t are~,novel problems whIchstray fro mthewe ll- wo rn path"of simple com·putatio~. Such~r~blem9as detectinqp~t,t~rnsi~heren~

,

li n a ser iesof numbersforexample 1, 3, ~, 10•••,-cs- de t e ct i ng patterns ingeomet~ic ~esigns, for examp le the numbe~^{?f sq ua res on a}che c ke r boardpos e roadblockS:tomany high.schoolstudents. The heroic effor tsput forth

by

high ,school,ma t h e mat i c s teachers,t oteach eeeeeeeteefor solvi ng ,prob lelllsdo not seem to be enough. Perha p s thisis far,too

la t e't o beqinpr~parbl.gstudentsto solve pr oblems.

J~romeBruner once said th a t -a ny SUbjectcan'be taug hte~feCtivelYin some int:ellectuallyhonest formto any childat,a ny staqeof development- (a r une r, 1960, '0.

]41i~'

^AS'

'~ontr~~er'S1aI , a8

^th is statementhas,he,;",it

.c e n be appliedqu l".t er~ad ilyto the,area of problemsoh"

Ing; .Pro ble m solving has bee ndefi'ne.das lIeekfnq"ee answeraquestionforwhi c htha~ ind iv id u~lhall,no rea d ily

avail a b les~rategy^for l3eter ml ni ng theans we r- (DeVault, 1981,p,40). There are manysuch questionswh i c h'csn be"

pcaed at an earlychill3hool3 level. "Th'e National,Co unc il of 'l'e ~ c he r sof~at hematics sawfit to dedLcattean"e nt ire chapter of th~ir^{1975""yearbook,}Mathematics Lear ning in BarlyChill3hool3to the SUbject ofpr~b lemsolvingin early ch1ll3hool3•..Itis,no t l3Ifficultto findev i denc e of agree - mentthat -mathematics-p r og r a ms"o f the 1980'sshou l d

invo lve studentsfnp'roblemsolvingby presenti ngapplica- -:

"ti o ns at ailgral3e level;- (pa'yne, 197 5",p , 4). "Brune r 's·

Idee oi<:h e spi r alcurriculum (19 601is adl3itiona levidence

"t hat pro bl e m"solving , like,otherskillsand co nc e pts,

should be g i n at a basic levelin earlychildhood,'and' shou,lddeve lopandexpa nd-th r ou g h~hechild 'sschooling. I f,as it was statedearlier,patte rn rec og n i ti o n is thou ght to be a major problemsolvingskill; then'it se:,ms appa re ntthat it shouldIreinc luded as part of the primary sch ool mathematics.

The Need

Inthe provinceof Newfound landatthe time of wri t in g, theIma t he ma tic a te xtb ook seriesus ed.rn primary anl3 ele me'nt a ry sc hool s18

Inves;i9:~'lnq

^{Sc hoo l M}a t h e mat i c s IBicholz, O'Dafhr andFleenor , 19131. Beca use the~ serie s is suppose dl y modelle d onSr uner'sspi ral cur ricJL ' Lure., one woul d assume thatpattern recognitionSki lls/lee a pa rtof thepr i ma r yte xtbook s . In fact, thisserie s /;wlIs

examf ned by the writ e r to seewhat , if anyexposu~e to pa tt erns'the chUdren wo uld have ob tai ned ,from kin d erga r- .tentothe end of.grade th ree. I~thet~ a c he r sdidnot use

z.:.esourcesoutside of the,te'~tbookS;'the chUd ren wo u l dhave completedone page of completion of patterns

iJ~

^klndergar-

ten (Eicholz et 11.1.,1973 ,p. 16) ari.d.o nepll.ge·o~colori ng of pat te rnsin grade two(Eicholz et

"~1~ ,

1973, p,-10f yello w)•

Even.p ri ma r yte ach e rs in easter nNewfound la nd whC!

rec og n i ze II.ne e dfor more wor kon patte r ns will.f a cedif f i- CUltyinfindingappropriatesupplement arymaterial. At the time of ,..riting, the Cu rric ulum Ma t erial s Cent reof the Fa,c ul t y of Education IMemorial University of Newfoun d l a nd l hadno materialsu i t a bl e for the tea'chingof p~tt~ rnsin primarygrades., Likewise, theRe s o ur c e s Clearni ng ho use (Memorial Unive rsityof Newf o und l a nd ) and t~e Instructio na l Mate ri a l s,Divisiono~the Department of.Ed ucatlo~ (Govern- mentof Newfoundland andLabrador) were found to be voi d of

, ,

.

^~

any suchma t e rial. ,Typic a l primaryschoolsI especia ll y kinderga r tenc l aae r ocrae, inNewfo undla cd,a re us uallyequip- ,pe dwith, a t least one set'ofcolo redbeads forstri nqing ,

however.anysuggestio ns for games or ecc t v tt tee tO,u s eth is mat er i.a l "to tea chpatterns i~ vir~uallynon-existan t. In summary, eeecoere arelarg ely left to the i r owningenu ity', .when atte mpti ngto teachpa tte r n s in the primar ygrades .

Ster nbe rg (~9751 has noted thegene ra lityof thisdeficit.

,

•

. Not only is th,.ere a nota~l eabsenceof instruc- tional ma t e ri a l availablefor theteac hi nq'of

pat'terns ,

but there isa realla c k'of knowl~d"leabou t chUdren'sabilit y to pr ocess pa t t ern s. Thelitees t'urehal'!littleto'o ffer In exp l a n a ti on

of

what Jdnds ofpatt ernschild r enca neeoc eaa, how theydevelopthe- abi lityto pro c e aa patte~n8andwhat the pr e re q u is i t ebe lla v i o ursfor this ability are. The pr·o blemlies in thef~ct,t h a t ac ti vi ties's uitab leto help childrendevelopthes e pa t t e r n i.nCl abilities cannotbe ._.designed"1.!nlesllmorekn owledqeIeqlellned regarding the

above questions. This type of need is'II.basic purpose for mucheducationalres earch .

''!.'he bll.sicpr oble misto proYi de-l nBtruc.,.

tianthat is appropriat e for ind"iv id ual students' le ve l of coqnlti ve"de velop- lI'Ient •••Theproblemtor re s earch isto' . identifythespecif ic limits fo rea ch staClf!'of developmentand to desc ri be how inst ru ction"tha t isco ns iste nt with these limits can be,desiqned (Ca rpe nt e r , 1980,p; 187)-.

The Purpose

It was the purpose.ofth i s stud.y to look into the pattern recognition'ab iliti e s of yo unqch ild re n. Specifi- cally, the abilitiesof children at diff erentlev elso~ d.~velopmentwere to be lookedat. To.accom~li .ll hthb, ch ild r e n'were examined onavariety of conservation-typ e eeexe to determinetheirPiag et1anstaqeof.de velo pment.

Withinth is. framework, the va ria ble .llof age and-gr a de level were examin ed todeterminewhetheror not theyplayed an

' . .

important.If a c t o r In diatinquishing between thedevelopment- al levels .

The.ra'tes of auc c e e a onseve r al pattern items of twodevelopmentallydifferentgroup~were examined in an eff o r t to decidewhether ornot·developmentwas a key

·f a c t o r in patt"e rn pr o c es si n g •.To91e e n further insight lnt? how the youngmind processes a pat.tern, theer r or sin thepa.~tern tll~k8of childrenat the two dis1tinct·l eve l s of dev~lopment were examined._Thisexami nat i on:of,er r o rs was performed in an,at t e mpt to see how the child processed the

's t i mul us

infOr~lll:ion

even when he'er she could not compre-

hend the9iv ~npattern •..The childrens' errors were coded on theexi s t e n c e cif some structure or repetitive pattern, albeit not the stimulus pstt.ern. as well1515on the exhibi".• tion of ~erta1n t~ndencieswith respect to .identifiable error t.ypes.

The information sought. was later formalized into a see of specific questions.

Definition of Terms

\

Pattern

Period

- any linear sequence of object.s"i n which repetition of a definedpe.X:i~

isv'l.a ua lly obvious.

- any linearBe~uenceof objectll in defined"o"r d e r whichis capable.of.'. bein<;l' repeated.'

10

Pets e ve ratl on^lll- thetend.e ncy to continueIi.stringof one

=:.t-

eolor.For·exa mpl e , in the patternBLO~

YELLOWY~.LOW BLUEYi tLOW,YELLOW,II, subjectwould sh~.... perseverationi f'he or IIh e'continuedthe pattern with YELLOW YELLOW YELLOW•••• whfl e ignorinq the BLUE.

Al t er na t i on. - the tendencyto continue II stringof alternationoftwocators. For eX~Ple,'. in th e patte r nBLUE YELLOWYEL LOWBLUE YELLOW YELLOW,asubjectwo ul d show alt e r nat i on if he or she cont i nue d the patter nwithBL UE YELLOW BLUE YEL LOW•••

Pre-Operationa l -fo r thepurpose of this study, child ren will hecl a u ifiedas,Pre - Ope r a t i o nali f tlley giveseveror more "I nco r rece"

re s po ns e s onth~Pillgetillninstrument.

Trlln sit i o'hlll - fqrthe purpose of thb study,childr e n wi ll beclllBIIlfied'a s Transitionali f they 9ivefou r, fiv e orEli .."Incor rect e re s pons e a on,th e Piagetian inst~ument .

. .

Co nc r et e Opera-

.i

^{tiona l _.for.the}purpose of this8tudy.,chil~ren wi llbeclassifiedas ConcreteOperation~

al

"~f

^they

~ive

^se+normote "eoerect;

unassisted-responseson the Piagetian

~r;;:',uTt:

,,'

• It isnoted that"t.hesete rmsha vea broad , r:de fi nit ionin psych olog y',howe ve r, forthe pur posesof

t~i~'

^{study ,'they}

willbe limite d -eethe i r applicat io ntothesi t uati onof

pat t er ns .

-. ~ !

QueslUo ns

11; Is th ere

any

differen cebe tw e e n thedi~tdbutionof chil'd re nat:t.he Pre-Operation al,the Tra ns itional and thecenereeeOpe r!lt~on!llstll.o;:res~t^thegradeonelev~l and thia.distr ibu tionat the grade twole vel ?

.2. Ist'he r e anydiffer e nce betweenthe mea nage sof't he Pre-Ope r at i on al , theTr ane i t i onal and theConcrete Operational qroups?

, .

'3. Isth erellnydlf f eren ce inthe

rat~

^ofsuc cess : J .h e .pa t t erns tasksbetweenthe

Pre-Operlltiona~

^qrou :;:'::d.

the ConcreteOpe r ationa l gro up? '

.... . Doe s the Pre-Ope r ati on al qrou pdiffe r fromthe

,

^'

Con ? re te Op er ati on al gr ou p in thepro por tionof SUb jects who, in. an er roneoue res po nse , impo sed a

pattern?

. J

"

'5 .

re ther e any differ en ce betw e en the Pre- Ope ra tion a l qr o up andtheConcreteope~ationalgroupinthe

12

I

• , j 4 \ ;

proportion.of~rBeveration-typeerrorsthat they

lIlllke?'" t> . I .

16. I~_~~ereany differencebetwee n

t re

^pr e -:-Ope ratio na l.

group and the ConcreteoperatiOnll.~group'inthe • proportio.nofalte r na ti o n-t yp e errorsth.Atth~y make?

17. Doesthe pre-operatio!!al .g r o updiffec,fromthe concrete Operationalgroupinth~-itein^onthep·~tt.ern8 'instru~nton,which thela'cgest'nud>er of err,ors,were

made?

,

scope and Li m!tations

Th.iss,tudywi ll be conducted,'a sacase studyof ~ 811\o!l11groupof child re nina rura l New'fo'un (lla nd'community.

Casestudies have recentlycomeinto focusas a credi ble f.orm_of educationa l re s e a r c h methodology especial lyin lightofthe factthat it is a frequentlyused formatin the noted Soviet Studies in the psycholog yof Learnin gand Teaching Mat he mat i c s (Kilpatrick'a nd Wirzup,1970).

Nevertheless ,thereareadmittedlysome serious limitationsin,thistype of study. T~ egrea t e s t limitation of any casestudy h itsgener all z11bility. Whe n no popul ation haa beenidenti~iedandthesamp~eisnot

.r a ndo m,one can no tstatewith certa inty tha twhat holds

t~ueforthe sub jectsun~erconside rationina partic ular studyis truefor any largergro up. However, it i.s fair to

'I

13

say that'wh ile childrenwho have had"s pe ci fi c k ind s of bll.cxgroundexpe r ie ncewi ll be u~nique,^{in ecee}a8~ct8. ^the ba si c developmentalprocess accordingto Piaget has been

. . .

proven to be generally consistentins4Auenceand in it's characteris ticsin children.throughout theworld'.

Th~reforeanytrendfoundprevelent!nthisqroup of ch ildrenmight lead to speculation~ha t~hiaor similae.

tr ends-ex is t in gene ra l.

Inthisstudy,''two qroupe.,o f children wh i c hwill be-i d e n tiU -ed as Pre-Ope ratio nala~dConc reteOperatio na l

~ythespecifie dCT~teria.will_be..compa red on pa t t e.r n {n g tasks. ToE;nsurethat reasonab lesiz eqroupawer e found it WlIlIdeci d e d to test allof ,th~grade..one andqr ade two child re n. Grade~wochildrenwill have had more experien- ces wit h mathematicswhi chmayormay not'i n f l ue nce 'ra t e of·

•success.onth:e'pjlt~e,:ntasks. As statedin -TheProble~·, the curren~mathematics oroq ramforNe~found landcon.ta~ns v~ryminimalwo r k on patterns. Thus the exeeeeee influe n-

.

.

"cea of instructiononpa t t erns is very slight , if-atall.

~' Bowever, othe~

experiencesin'ma thematicsmaybe infl ue n- tial and it is acknowledgedthat this too willaffect any qeneralhabllityof this study.

'Hav i ngdefinedthe prob l emtobe'

resol~ed, .~

re vl e w of the releve nt'literatureinthe ar ea'~f m~thema- tics education,'and mo.re specificallypatternproce'!lsing wasunde rtake~.· The informa t io nqather~d^{was organhed} int ofO~~.,.eeeeIcn e andillrontai,nedin t.he fOll.OW.i~9

chap te r.";:;" . '. " ' .

I

CHAPTER II . ' ..,

~

REV;EW OF RELATED

LITERATD~'

^{,"..' . ",-'.}

The

~eView~l\eii~~rAture

^{on'thepattern \'}

abilltiesof 'young chi-ldeenwhic& follows will bedivided int o four "eeeeteee • Thefirst sec t i o n willincludethe literature~oncernin9thekindsof,patt~rning'be~aviou rs

·fou n d in young chi;l.dre ri. Thesec~ndsection looksatIIihat.., .

·

re~~arch Offer~ by~way 'ot>e~plan~tion'

^ofhow

~hild~~-~

^".:..

2<oc...p.tt",n"..

~~<~

^eeeetenwiii

involv~

^wh.tare

·"se en as thep.rerequieitebehavioursfo r-8UCC~89ful^pattern

processing. Pinali ; .a discus.sion,of.t he lllajo rvariables which have beenId~nt-ifi~dasreaeveee to patternpro~e9~- in91

r~gell[(::h~ c~mpr~se

^the

f~urth;. 8ection~.

^.

.~"

Abilities RelatedtoPa t t e r n Proce ss ing

Youngch ild r e n~how'e~'idenceof agr'eatlI'lany m~t.~maticalbeh~viours. Thi s'i a.e vi dent. from st.udies

j- , '• •

which'h llv ebeendone on children fr om infllncy.. t.o eacree- cence•

Ind_ee~,

^i'n

t.~rms .~f ~Il.t.tern relat.·~d

abilit.'ies, th i S... assert.ions~emsha r d t.o dispute-.

At. aver~basiclevel,o fpllttern~ngskill" se;--er-' aI,studie'!, have t.est.edyou ng children's abilit.y,t.o match a givensequenceby direct. copying of it.. One suC?h st.udy,

°conduct.e'dby Puhll and Fu r th (1966), tested'subje ct.sOf

· ,

ages lour, five and lIiil.on various copying t.asks. :The sUbject.sinvolved in-t.h i s st.udy, ~t.^{all.t.hreeage revels,}

/

14

.15

i i

;

,

,. /

. . _. /~ ^.

~

.

.could~.~par~iC:Ularlinear

"""?"

gi~en,:,ith," ','hiqh,'..

de cted,of suc c ess . ,Th i sre s u l t wassubstantiated by Brown:'-

j ---- . \ ' . .

;,;---andMur ph y'(1915) in a re p lic a t i on

of.

Piaq,et'sclothesline

. .

task. Stibjectswe r e 'presented'wi tha minll.tu re clothe~1ine·. from wh i c h hung.a paeeteut.ar arrangeme nt'o f paper cut~out clothing. Thesubject!" we re thengivenarie~pty^ci.cthea-

.

' .

"

,

line of,their

.own,

with a pile of thecut-o~t clothes~an~

wereinst ru ctedto-produceanidenticalarrangement.;The

~ubject9, ra ng i ng inagefrom tihree yee re,one month to,_

fiveyelln~, ^ninemo~th9^{(meanage.fouryears,eightmonths)} exhlbi ted a highdegree-of 9UCC~9S,contraryto Pla9,et' s

\ ownf~nd in9BthatSUbjectsyoungerthan f

1ve

^{~earsof aga}

.wereq uiteuns~ccessfu1(Brown.ami Murphy,1975, p.•'311). : However,when dealing with non-linear or matrix stimuli, Chap and Ross·(19 79 1 foundth·at their,five and six-yearold subjects made a -substantial riumber of·,pereept.uaj copying er rors ~ (p •.203).

Researchby Frith(1970)concent-rated on er rcra ,madein patter ncompletion tasks,by normalchf Ldren of ages

,r ang ing from five years, two months to six years,

three~

months and

aut'is:i~

^{childre n·in}

~he

chrOno;ogicalaqe

~,:qe

^..

of seven years, threemont hs to fifteen years, one mont,

'... . t

but witha mean mentalage of threeyears,t~omonths. -c ne ve r y prominent discove,rymade·wa s th a t evenwh e n the normal child rendidnot complete thegi~enpattern co:.reC:lY,most of the ~imesome patter n wa s imposed._

'. ^. ~-: /

' .

. /

Furthermoreeven the autisticch ildF e n see medto have a real prop~nsity,to'imposeapatte rn,even W'h~.n--it~asn~t the stimuiuspatte rn. In a second study, Fr"ith's,s ubj ec t s we r e're q uir e d to p,redict·th ene xt color in a twocolo r ar'r angement wtle n the only ClUll,s given_. were acknowl~dgement

.

9£.the correctness of theirguesses.

r-

^thoughthe

st i mulusar r a ng eme nt"wa sra nd om:-t h echild re~'s^guesses showed~highlypredictabl~paceern""(p. 1311 .'"Ath i r d

. ' I • ,_ , •

expe~im~ntinthis'studybyFt;ith..concer nedagroup.of normal, Bub-normal and

a6t iatlc

subjectsin alsitua ti on ";}

..whe r e theywere enccureqed to make their'--own'pa tt erns. The;

successrat eforimposingp.a t t erns wasa_highin genera l,bl;lt (._

perha~sa very au rpr Le Lnqfindingwas th atwhile ,85%'

of_

the

"'ormalchildrenproduced irregula rpatterns"75\of the '.sub -normalandauti:sticchildrenproduced "strictlyreg~lar

.p att e rns. The s en~rmal'child'renwereof chrOn~log i cd·ages.:., thre eyea rs.a'nd five yearsas

'c~mpa red wi~h ~he ,sub-n,or~al

andautisticchildrenwho s e ment al'ages eeee th ree 70four

/ ./ , . .

'" /

,/ .

.

y.ears.

Inapat te rn recognition te et condu ctedon '.pre-kindergarte!1 'k_inderg a; tenend"grade one'children-of

'lows'o_~i'o-eco1mic-status,Stem be.rg.an'dLarson(1n~)', ^-'p

~ound ~hat

^-t he\ ,SiiCCe s s'

r~t~

^.ofthJ'

~oung

^childre?

·(pre~k~~-··

derg:arten) ee s.ctcee to ;~ance•.'_'~'his.re s:ult-wa sS.ubs~~n--

::::~:h:Y~::::::::~a'::i:::e:f(

^{:: ': : )}

y::: : ::' :::~j::t:-~:::

.... -

-.

:- " ,.

17

to dis cover theeffec ts of selected learn i ng experLe nceson the~aljlilities. W~ th anoriginalsuc ce a a rateof.soli ght l y ,less th an 50\,th.etre atme nt causedapositiv e changein; .succeaa. At amoread vanc ed level, Blacka H (1975) stud ie d

thesuccess of grade thr eechildre nto ec tveen extensiv e ar rayof pat tems bothlinear andmatrix, invo l v i ng.qe eee- .tric shape and number. She fO'{fldthat"!n genera l ,grade

thr eechildrencan'solveIl.~~ i devariety of pat te rns.

Cro mie(197~1ej.sc testedpattern process ingabilit iesin pre- k i ndec,\srte n, ki nder gart e nand gra de one child re n end foundthat the ywereon thewhol e su ccessful,wi t hmean grade le vel s

.

cores ca ng in g from 59\to 92 \•

ThePro c e s sing of Patterns

TJ;1e~iteratu("eon patter-n proc e s sing abilitiesin ch,ild renin,g e nera l'i s meagre , howe v e r it ispart~c u larlY so in the area of anal ysisof howch i1dre~process pat t e r ns. scenau re (19 7 1)id entified,~th~ability to

.detectmat hematica·l reg~lIIrities" Ip , 61as'one of si x

~ . t

basicintell ectua l pro cessi ng skills. -Howe ver" heno'te d the ne a r abse nce of re s e a r c h regard ing thetech niq uesfor det ect i:ngpa tterns :

Althou g h suchtech n iq ues are noto ri ousl y ha rd to pindownindeta il, they are clea r l y impo rt a nt t9 l,arnandus e.

The yhav e be e nshown tobe help fulin a wideva r i et yof si t uati o ns,and mor e atte nti onshou fdbegi ve n to the m in

~-··math eJ.1laticseduc a t ionIp, '·6 ).

18

Bartlett- (1958)agrees that~on.one has adequate- lyexplai!'ed hl?'" humans extractrules·{p , 43).

The,processesinvolvedin pattern ing neve been.

explained via an informationpro cess ing model by Simonand I':O,tovskY()963)who attempted to~i m\Jlatehuman,pat t erning processeswith acomput erprogram. T~eydisco,:,ered thatto

"rec o g n iz ea pattern,thecomputerhad to translatethe

pattern sequence i,n t oa '3~neral ~u.leor patterndescrip- tion. To dothis thecomputer firs t had to discover the

~edodicity

ⁱⁿ

th~ ~equence,

^or:he

len~th of th~

'o ri g i na l set to be

repeat~d. 1

^It

acco.~plished

^{th i s} by -looH,ng for a relati:~nthatrep~aesat requ lar'inter.v~ls•.•Oncethe...basic .' - - ' periodicityha~been discovered, thedetails01'."the patte r n

are supplied in almostthe same way-by detectin9and 'reco r d ingt~e rel~tions ~of equa l and next -thathold. betwee nsucceae Ive sYmbolswithina periodor bet....een s~bols,i_n cor reepend friqpas itions of su c ce ea I ve pe riods~, Ip,540) . Thes e prcceeses , then,are ee e ce ea to qene ral.La e tohu man SUbjects Ip, 5411.

Anothe r pair ofresearcherswhohave at t emptedto explain pat ternprocessinqv La information processing are Klahr and'Wallace (1970). Like'theirpredecessors, Kla hr andW'a nace also'Wl'llltto generalize human.proc e s ses in pstterningfromtheprocesses,us ed byaCompJ1ter. 'F r om theirrese a c c h.. t'hey'haveatte mpt ed to .explll1n st ra t e gi es

·which are li kel y used by humans.

19

The'first'of't:~e!le ^{is,templatecons}t r uct io n. -The evidencesug g es ts,that somesUbjects sol~'ethese pr oble msbyconstr ucti n gtemplate s of inc reasi ng.size unt i l t~ey finda reeuer i n!]

.

pa tter n"'-lltlah r

.

and walla c e ,197 0.^.p, 2_5).. 'This procedureinvolv e sthe subj ecttryi ng,~ach .segmentasthepe riodbe ginningwiththe sinqle first item,

then moving't o thefirs tplus secon ditems,onto tilefirst plus second pl ue

,

th i rd it ems. etc^. •• until theee e ureancyis foun,d. Eac h tr ialperi o?is te st e d 81"on9 the seri es , and when ard sma t ch is discovered,·thi s period Is~bando nedand thene xt on e trie d.

An~ther ^{stra t_}egy whi ch,may.e xpl ai n th e pat ternJnq proce s s 15."backwardscanninginwhi c ha temp l~teof ttle.

last fe....objectsinthe seriesismat ched o1S9'a~ns t,th e

.

,

prob lem" (K14hr and Wall ace..~19 70 . p.24 7)" T~ iB p.~ffers fromtemplate construction in that itworks fro mthe\r iqht si~e of.the eeque pc ebackwards.a~opposed.towor k lnq:from lef t-toright.

Th einformati on pr o ce,ssin gllIOde1sdes cribed above maybe thought of as present inga behavi or ist orient e d model forpattern solvi n g. Whilethe y mayoff e r som.eplall- ,sible explanati ons ofhow child ren process patter ns , Restle (19 7 0~cont e nds that"noneof thefiveco ~venti on\lstbu - Ius-r e s ponse,theor ies,of se ria l,l earn i ?9.caanhan d ; eev en the,SimPle';dataof selia l.pattern le arnin g.

~.SUCh,

^{the o,ries'}

take noprop'~rac co unt ofthe intrlns).c or g a nlzi nq

"

possib iliti e s in thesequ ence"(p, 48 21. :Acognitive model of processingabil.ity wo'ul dli~elYaS,Bert thatchUdren heve somein nat epredlsposlt l on:th atthey brin g some. neeu rej.II\sthematicalor logicalreasoning skillstothe pattern task. . Suchabi li ti e s aredi f ficultto st udy. hOIi- ever researchersha vefound th a t muchinsigh tcanbe obtained fro man~nalys'is^of theer ro ra committedby child- renin'a pa t ternta sk•

• Bartl et t11958)stu died the pat ternta skof' extrap olat ionand found that themostcommon.mistakes

.

.

invol v e "discoveri ngeomesin q leruleand thenneql ectl nq

~the r s forwhi chthereiseV~dence " and-missing.,ou: steps of applica t i o n" (p.47 ) .

I . .

. 1 .

Fr ith(1970)analyzed the err ors madebyhi~ nor mal Bndautisti c sub j e c ts in ter msof their re la t i o nship wi t hth epat t ern gi ven. He"id e nt i f iedtwo types"ofdomi n- antfeatures inhi s patterns . Oneofthe sehecalled perae ve rati on. The s e arethe typewblch eeee.ec encourage repet i tionofone yar ticu lar par t of the period whlle not theperiod asa-whole: Por exampl e ,ina color pat tern in which the pe riod isBLUE YBLLOWYEL LOW, the ten d e ncy mi ght be,to~ont inue....ith all YBLLOW. Theot her dami na ntfeatu re identi fi edbyFr ithwas alte r natIon. Al te rnationpat tern, ar eth osewhich seemto encou ragec:ontinua tIan inth e farlll of alternation of.t he el ements. Fo r exampl ein,a color pattern in,:,hl ch.tihepe,riodisBLUE YELLOWBLUE. the

.~.

21

t~ndencymi~htbe to,co nti nue ....ith a Btl'ingofYELLOWBLUB Y£LLO~BLU.E•••lnate ad of BLUE YELLOWBLUEBLUE YELLOW BLUB.

Fi nd.ln Cil s in Fr-it h'sreseaE"~hcan be surrunirizedliS follo ws:

Mo st-~r ror8ma deby norma 1child renwe r e inacco rdance wlt hthedom i na nt feature ofthe patter ns. Mo s t er ro ramad e by autist i c child re nwereduetothe impos - i tion of simp1eperseverationor alter - na d on stringsinde p e nde n t of th egiven pa t t e rn •••It isconc luded that autisti c child r e n are insensi t iv e todifference s inthe structu res pre sent and ten dto impose th e i r ownsimplestereo ty pe d patterns ,whi1enor malcliildre n impose such pa t t ern s inabsenceof structure d inputonlyLp, 120 ). . Whet her or not\the re spon s e s of th e

autistl~

..child ren ,'whose.mea~men talagewas three yeers, two

lIIonths ,can be compared in any wayto normalchildren of the same men tal,ageis uncle a r,90generali %~t1o nsregard- ingde vel dpm e nt al differen ces i~terms of pro~e s s ing tendencies'cannot bemade.nere, However, Gerjuoya.oo- --_Wlnter~'(19681 have givencredit to thenotion·that'~oung

chlld["en,genera l l yunderBveyears of age showperaever- eeton tendenci eswh i ch d!ffe[" froirt ·chlid r en.~folder tha n etve yeats whoeeeereeshow alterna t ion't endenc i e s. Th ef claimthat aimpl~ ^responseprefere ncesin YOU~9^children, take into··account only one previo us stim ul us ,which may shed someli 9 ht on theerrorsmade,bynormalchi l dren in Fdt,h'sstUdy.

'n

:1 •

V..ri ll.bl es ASioc ia ted withPath rn Proc es sing'

Stu di eson pat ter n rec ogn i ti on whi c hwe re re vi ewed.s~ell^{to poin t}

t o

thefa~t ^{that ther eexiltsever al} lII&jor vari ,!,bl~!l.wh ic hseem to.have sOIIleimpact'o n child- • rre n ' s suc c ess on patt:rnrecog nitiontasks. The firstof

\the s e var iable sisIge. In a stud y whichtested'subjeCtl '

abilityto"n:at ch ordereoisequ e ncee, Dass 11975).found that lIgewall.an illportan t facto r. Tbesub je cts ' ag e.rllnqe WI!

appr oxiNtelyfiveyears~oap p rod mat~lyeightyear8. and :'Bau "found~hil.t^01",rchi i dren were wce succes s fu l than

young erones. In allIat he matic al uniton PAtter n i ng~

Mclt.q~_i p(1 9101.f.ound.thatfor copyingpatter ns, auce eee variedaccordi ng to~ge. Sternberg (1973) concur red "t~lt' exeee isan improve ment with age in"t heabilityto re~o9nize~pedfi cpatternse~uences-(p. 611. ~,I.lIckal,l 's stud y 11915 ) of,a variety of..p'a tt e r ninq tas kswascont'l"n ed telchi.ldten atthe third l:Jrade level . Wi t h in thisllmi ttd

l" . "=

ageranl:Je, lll:Jewa~~o undnot tobea facto r"in pa t tern i nlj succe s s . ForBr a gman andHa'r d y" deaf subjects , -theage

of"the

:~ubj ect~

^{affect e d onl y'the}

"~r forJnance

^{on thesame'}

patter n recognit ionbut not on tiletoUl patt ern onrev erse patter"n -(1919,p."·aDJ .' . "

The variableC!fdeveloprne n ta l"s/tageinPla(]l'!tian eeeee ,

Wh~'Ch

^{might 'be}-li n k ed to"age , hn

t

als obeen

id~ntl-

. . , ,\ I

tied.i"t\the s.tudyof B;ackall (197S). She tested her'9uc1e enree subje ct s on P!aqe tianty~tasksfor conserv a tion of.

2l

number~ conservationof ar eaandclassifi cation . The Pe a rs on Prod uct -MomentCorrelat ionCoefficient foc area c enaerwat.Ion and patte rni n gsuccesswa s judgedsignifica nt .fo r mostof.th e patterntasks,-but no t signi fi can t for a ,g e omet ri c':' li near : compl.etion tas k. ccneervet.tcn of .number WAS notlI.~gnifican twhen c?rrelated with success on

any of the,p att e r nta s ks . BllI.ckall suggestedthat this ,re s ul t mi ght imply that conservationwasII.prerequ isite f,or

,,;, ; all of thepatt ern tas ks Lp,~4 'I. A8ignific~tl Y positive correlationwas found'be t ween one of the" ..

olll.s ai f i c lI.ti o n tasksandsueees s on one of th epatt"ern tasks.

Previous.exper iencehas be enmelll'!uredby school backgro u ndin term~of qr ade levels. Sternberg and Larson (19 76 ) found\that variabilityin pattern re cog ni t i o n cor re- \ lated signiffcantly wtth grade level andabilityin combin- atio~. 'MCKi l li p(1970)alsonoted,thatsuccess varied accord ingto.a ge and pre viousex perience. TO,support thi s.

Croml e (197!) fou~d thatgra de onea ubjects wer emore successful

on

patter n' ta sk s than were kinderga rterie ra. wh o were in turn mor e successful than pr e -k inde rgart e ne rs.

Sternbe r~(1973) fou nd that both ofhi.s pre- kinderg a rten groupssco re d low onpattern pr'ocessingtasksas compared

\wi t h ki ndergar tene rsand firat' graders. Con s i de r ing that I

th e abilitylevelsof the pre-k i nde rgartene rsseemed·'notto showany81gn ifica ntdifference in score ,Sternbe r,g hypothesized that- th is mayindi cate th at you ngste rsat

. I 1

²⁴

thi s gracelevel cannothandle patte rntasks of thisnature

w i thout~in9truCti~n~·-

^{(197 3. p, 66)..}

Another interesti ngvariab lewhich has been st udiedis mathematical achievement. Blackall (1975)found th a tal l c~rrehtlonsbetweenmatheV\atical ac h i e v eme nt and eecqtask onher pattern,test were significant. She noted in particularthat on the taskcalled geometr i c: linear:

continuethe correlationwas strongerwith problemsolv i ng

achi~vement th~~ Wit~- achie~ement

^on

m~the1atiCal

concepts",' Ste rnbe rg (1973)also fou nd~hatachievement asa variable did show131g n ifi c an tdifferences be t we en groups on vari ou s

<.. "

patterntasks. Bragman"il.OdHa'rdy(1982)f&,/Jod that there

";IlS nosi q nif ica nt rela t i o ns h i p·betwee.n ar i t hme t ic

.

.

achievement and identical pattern recog niti onin subjects of meanag e six years, ele ve nmonth s, but thattherewas'a significantrelatio ns hi pbetween. arithmeticach i e v e men t and re ve r s e pattern recog ni t ion.

Relatedtomathemati c alachievementisin~lli ­ gence and /or~athematicala~rlity which·have aleo been studiedby Bl a c ka ll(; 975) and Sternbergand Larson (19761. · Blackanstudiedintelli ge nc e andde cided that,in general, intelligence correlatedhighly with success on each of her patter ntasks. She also noted that,successon the geometri c: lineart contin.uetask sh o wed ast.ronge r pos i tive correlationwith verbal intell~gencethan ,,!.ith non-verbalintelligence . Sternberg~n dLarson found that

25

pattern re cognitionability onlyCorr elatedst rong ly with abil ity lev e l incombinationwithgr a de level.

- t

Variabl e s rela t e d to theactua l pat te r n giv en hav ebeen ex_in ed. Puhlland Fu rth (19 66)fou nd that

. -" I .

con cretesequence sseemedeeeteefor thei r fo u r to 81:1yelJ(

old SUbjects thandidpicto r lll.~ e qIU!ncel. ~iB8u b s t an t- iate~Piaget'sand Bruner 's cla i mfor thene c e ll.lity of concre teuperienceaat~islevel(Co pe land.1974l a,runer , 1960). This contrastsCromie~5 (1911) find i ng s th:athi s su b je c tsperfo rmedbette r onicon~e(pictor.allta sksthan enactive (concrete) ones.

Black.a (".'5) createda hie rarchyof-pattern taskswh ich invol v edII~Ombinli.tion'of Urendin~.the len9.th I.of thepe~i Od , va ryi ng the~unt.of infor mationgi ven_and varying thenu. ber ofattributes tobeconsi de r e d. Several ofthe s e.upect l variedsiIDulta n eous l y, and it isthere f ore difficul ttolIIake·anyauulllpt i on sabo u twhi ch aspe ct in par t iCUlareedethe di ff ere nce in difficul ty.

Frith (19 70) lllai n t alne d thatpatter n.whose dOllina n t featureh pers ev e rat i o n wereles s ~ficu ltfo.r normal childrenthan patternsWhor edominant fea ture is al t:rnat.ion:.

l'i'ithi~

^the

petBeverh~on doraL~ant

^{patte rns:}

nhc ae wi t h the repeatedelem ent at therightend of the period, for ~xampl:,GREBNY~LLOWYELLOWYBLLOWwer efound tobemor e difficultthantho s e withtherepeatedeleme n t at the left, foreJlaniple,-GRE~NGREEN-GREEN YELLOW-.Within

.alter nati~ndOllinantpa tte rns , thOl e wi th th e alter nating

2.

eleJ ents. as opposedto any repeating elements.at the rig h t end 0'£the pedod',forexample, GREEN GRBEN YBLLOW GREENwe r J moredifficultthan thosewi t h the lliternati nq ete e en ue Jt the left ,seee xe mple , 'GRE. . VELLOWGR" ; . GREEN. Cromie (19 7 1)also found that an alternationtype .of patter nIABAABAlwa s most difficult (or the gradeone

subjects butsu rprisin~lYeno ug h wasle ast ilfficultfor thekinderg ar t e ne r s .

Simon andKOtOV8ky~s info~mation.proces~in~!fIOde\l (196.31wa sused

tq

makein ferenc~9'about pat te rn difficu l ty and itwa s decided that the

fa~tors

^{Whi 'Ch'}

he~~d r.a~~

patte rnsae more or les s,difficul twere't he length of.t;h~' patte r ndeacr Lpt Ienorrule,and the number.of~99ition8 ._

the'pattern filledInimmediateme mor y •..Itwas foundthat -t h e prog ra mwas inca pllble of organiz inqth~ 'partsof the.

patter nintoan overa llstructurewhen twoib-ed i ate memo ry positions we r e involved - (~.544)'; AgainC.rom~esupports

·t h i !i..o cla im in that his younqestsubjectsfoundmost diffi -

cultthosepatterns wi t h four eleme ntsas ,opposed totwo or three (197 1).

Seve raldiffe renttasks have been-used to te st .patterni nqabi lityand these taskshave,inthemselves been

found,to be a varia blein dete r min inq success. Brownand- Murp hy(1 975)stud iedyoung chil dren ina copyinqtask and.

they fo und tha t'therewas a diffe r,encein child ren's ab ili ty tocop y aline ar modelwh i chwasdire ct l y opposite, or paral le l to thei rown as opposed tothemodelbeIna

(

,

.(

.~

21

displaced or off to one side,'the latter'bei n q ses-ediffi- cu l t. Th i s distincti onhasalso beenfound byCo p e la nd 1.1974). 8lackall (197S)identifiedseve ra l ta sks whic h rela t ed'to pat t e rn ing lind ranked these,as followa. The

ta~,

^of

interpolati~n .

which invo lvedthesu b je c t filling' in missingelements of,giv enpattern ofcolo redshap es. WllS found to be re lative ly,easy. Mor e difficultthan int e r pol a te WllS-t he taskof cont i n ue ,.whi ch involvedthe

• I . . ,

sUbj ect'viewing IIgive n segmentof IIpatternand then ,pla c i ng theapp r opri a t eco l ored shapes soas toextend the,

pat t,ernaccording't o'thegivenruj.e, Evenmore-di fficult tpan con tin uewa sthe task of rev erse, wh:;re theSUbject wa.s shown

a"segment .Of :.~ ~pattern

^and

tOl~

^{to giv e a}

. se~ment

^'

,wh i c h reversed the pattern. Bragm a nandlIa rdy (19 72 ) too,

n,o ted that re versepattern reco gnition....as moredifficul t for thei r sUb j~cts^{of mea n age'six} years and el evenmon"ths, th a nide rtt i c a l patternrecoqnlticn,,Cromie (1971) cencrud- ed-t hat theont o ge ny for patter n pr oce ss ingwa srep ro duc e. th e n-id en t ify followedbyexte nd . Relate d to-task diffi - ' cu l t y , Blackall (197 S) alao found that lin~ac ~~tternBwere gene~ally lessdifficultthan matrix pa t .ee r ne, Sternberg (19 73 )fo u n d that,hispatternta s k s differ ed in di,fficulty.

in c r e a s i n g in,the'f o l l owing order: ori g i nal learning,

"r e v ers e shift ,intradi mensiona lshift,extradimensio nal

Bhift~,(cOl?rand category ), extradime nsional sh if t (name). partialintradimensionalshift and extradimensiona1shift (latiet). Anint rad i me nsi o"!alsh i ft u8 e~the,same patt ern

\

, I

2B

but varyillg the elemen tswithin the eene stimul.lHIdimen-

,. .

sion. For example,a ce8po~ setoGR EEN YELLOWGREEN YELLOW

might be'RE DBLU~^{REOBLUB. An}extadimensional shift uses t,hesame'p a ttern but va ries ele me n t s outside thesti mu l us dimension. For example,a response toRBDRED.BLUEREO':RED BLUE might be a se que n ceof picturesof Tur t l e :rur,tle Bike TurtleTurtleBike .

Other vari ables wh i c h havebeen stUd~dare so,ci0reeonomiCstatusas foundlby Bass(19.75)'to be i~flU~!ntialand sex as found by Blackall (1975I to be only o~minorimpact.

,

The Prerequieites to Patt:e r nproces~ing

The related literature attempts toO.ffer .~everll.l skillsor aspects of behaviourwhich have been deemed as prereq uisitefor the llbil1ty to solvepatterns . Sinc e a larg e portionof thes e refer to Piagetianclassification~,

I

a briefoverviewof p.i.aget'srelevant workwill be--giveh ,"

here.

i

The basis of P!aget' e theoryis the id e nti fl c a- ". ti an of four majo rphases of intellectual g rovththrough

.J

w:hich childre~pa s s in a necessarily sequential order. It hasbeen stressed, howe v e r that wh i l eall chlldren follow the same general pa t t e rn of transition fromone stage to, the next, the y do soat an individua l rate in terms of ch ro nologica l age.

29

Fromthetimea c;::h!idis bornuntil.heIs roughly two year s _.old(the child'sthinkinqisdependent'up o n tne.

I : '

action;he per forms on Me environment.' At firstmany of his

ac~ions

^are reflexive andunc o o r di n a t e d ,

bU~,

^dUrinq'

~hisperi o dthe y beqi'n

to

becomecoord inated. This pedod

is

·k n~wnas~he Sensori-Moto c'at.aqe, Fromthi S- Sensorl-Hoto rstage, the child be ginstra ns i t io n.~n t oII pre-Ope r b o nal stag e. Thisperiod , lasting fromapproxi -

~t elyage twountil age seven,includes the acquis i t i onof .' lanquage. Wi t h'this mediumthe ch ild is able to represent his~orldsymbol ically wit h words. Aswe ll, hereoften glv,e n to representation th r'o ugh action, asca n beseen when children play house, orpr e t en d't o besomebo d y el se. The cllild' slo g icis, at this poi nt;unidirectional. ThechUd can realizecause and effect relationships ,but cannot reversethis'pr oces s tosee the conver sereLa t. LonahLp e,

Transiti onfor the child begins at appr oximately seven ;into the'p h a s e of intelle.ctualgrowth kn own as Co ncr et e Operat ions. This phase, whichtypicall y la s t s fou r to five years ,is characterizedby thebeginnings of logico-mathematicalthought. The ch,ild cannowrev e r s e his thinking intermsof re~ationships . The cla ssic ma r k of ha v i ng arrived at the ConcreteOpe r a ti o n a l stac;leof developmentisfacility with theconc ept ofco ns e r vation.

Thepre-operatIonel,ch i l d willwat c h wat e r poured fromastout'glassintoII.tall,thincy lind er andwi ll th i n k the amoun t hall.changed,eve nth ough he saw none

30

add ed,srm~lybecauseitlooks'bigger'. However, the ce n e eaee Oper'ationa i-c h ild isawa r e that;eve n thoU9h'it .appears to be,more, th e process can bere vers e dto. return

to it's original state,therefore , thewa t e r.rnu st;no t·have ch a nged in quantity.

TheConcreteOpe r ati o ~ a l childmanipulateswhat he perceives, through direct actio nupon it. Thushis think,lngat.the begin ningof this stagedep e nd s on experi-

enceWi~h 'phYSiCal

^objectsand material. Howeve r':.a s

h 1

deveIopa through thisstage"he bqgi ns togenerali zean1, thu s'becomes lessdependenton the physicalmateri a l.

Finally,at.app r ox imat ely agetwelve,the.child will,acqudre the ability to rea s on loqi cally and abstcact- Iy, He canuse his thoug h t prp cesses wi t hou t physical cbjec te orconcre~ee xe ep te s, Thi nkingcan operate hypotheticall,yandde d uct i v el y, andwil l deve lop inth is mode throughadulthood. Thisfina l stageof developmentis kno wnas Formaloperations (Copeland; 19 7 4 )•

.A majorstr uctu re of Piaget'sby whichthin ki ng at theva r i o us

st~ges

^{is definedis'that}

of~n

^{operation. .,.}

Fla~ell clad~ies i

^Piaget''s terminology: "any represe nta - tional act which is anlnteg ralpa rtof an organized netwo~kof rei.aeed.eceete an operation" (1963,p, 166 ) . Piaget'sope rationof cognitive 'functioningis verymuch like themathema tica l structu reof a group. THe mathemat - leal group isa setof elementswh ich possess the prop e rtie sof closure .commutatlvi ty;associa tivity, r~ver-

31

sibilitylI.~d,anidentityel e me nt. Similarly thePiaqeti~n

•oper~tionmustco nt ai n re versi b ilit y and an identity .~ (Copeland, 19 74)•.An operation"isthusthe essence of',

knowled ge l',it is an inte ri o ri sed actionwh i c h -mod i fi e s the Object ofknowfedge {Pi aqe t ,:19 ~4. p,Ill. For Piagetv the operationisce ntra i to thlnkl[lg:

Operational at ruceures are what seem to

~~et~a~~~:ii~~~~h~~~9~~:~s r:;1 ~;~~ l~~~e,

terms ofwh i c j1we mustunde r s t a ndthe· developme nt of knowledge . And the ce n tra l 'pro b l e m of development.te tound e r s t and the formation,.e l abo r at i on,orga nization and functioning'of thesestructures (Piaget. 1964.p ,9) .

Operationalt.hinkinq"isamajor distingulshi'ng fa~orin,determiningthe,ch ili'l',s.tra M i t i onfro m pre.-Operati onal-chc uqht, to ConcreteOperational thought.

ourinq all this se c o nd periodof Pre-Operationa l representat ions, there are'asyet no operations••• Inth e abs e nce of operationalre versibi l i t y, there is no cons er va tion ofquant ity••• In a thirdstaqethe firs toperations .appear; but I call these co nc r e t e

operations because theyoperateon l-.objects,and not yet on verba lly

exp r e s s e d'hypo~hesis(Piaqet, '96 4 ,

p,91. . .

Amonq the opera tions wh i c h-pi a ge t irlentif1es are conservationand classification .

Several of these.ope r a t i o ns have beenhypothe- •

.sized as being prerequisite fortheabilityto process

. t'

/"'

patterns . Blackall (19 75) hypothesizedthat conse rvat ion

'o f number mi g ht beprerequisitefor all pat te r ntasks"

based on a siqnifi can t correla t io ncoefficient forconse r-

32

va ctcn

a·n~

^{pe t t.e rnSUCC:5S. Beagman}

lna

'Ha r d y (1982) Cited.

that"o ne.l:lr~ requisit~see nfor tr ue pat t e rn recogn i ti onis the.'abilityto performone-to-oneccr re epcndence" Ip,45). One-to-one cor r e s pond en c e is largelybased on.conse rv ati on of number.'Sternber g {19751sawthathi g h e rord er classi - ficationskills we'r ene c e s s ar y to solve patterns whic h r involvedthe sequenci ngof classes of o~ects. One ~tq-one

'"

corresponde nce , describedby'Mc Kil li p {19.70J as bl ock- t o- blo c k comparisons,,seemedessential to perfo rm sin g le.copying.of pat ter ns.

In additio n

to

^{the above}mentioned pr erequ fsIt.e a, severalot he rbehaviou rs ne c e s s a r yfor'patte rn pro cessing havebeen found . S~lvia(19 7 7 1 sawthatth e ab~lity·to

.so lv e pat terns whi chvaried oneattribute was prerequ-isite

tothe,abilityto,solvepat terns-whichvarie d twoor th ree attribu tes. 'Simon and Kot~vsky.(19 63 )decidedtha t a. concept of sameor eq ua l was neceaservto solv e'pa tte r n pro ble ms. JUa h r and Wa l l a c e ·!1970) substantiated this eIemen t, andaddedano.thee: "the abilityto re c o gn i z e 's ame s' whenthey oc c ur andthe abilitytoke ep trac ko~

p~sition·wi t h in two lists:,the pattern and th e prcbIee"

(p , 24 5). Vbual dis crimina ti onha s been se e nby,St ernbe r g (1975 )as pre r equ isi teto .mostpat te r n i ngbehaviou rs,and, fo r higher order classifica t ion patt er ns,kno wled<je of lan gu a gela be l s isne c es sar y. Aga i nth eab ilityto see. samenessor diffe r e nc e s wa s sai d to benec e ee eevfor pat t e rnco pying by Hc"illip(1970 ) , al\d he notedthat the