Cognitive St1rategy instruction Math Problem Solving of Middle School

hrn-1lti1111rupubA1gtJt1

With Learning Disabilities fJSAGE

Abstract

The purpoae of tleu was to improVan1athemaxccai for midclk schooi studtmbull wltil a lnstnlttionmi -program In ndusfve- ~ducation math ctassesA total of 41 rnkidle

chJJ1ols fn a middotkmiddotHzu0 urban zmcl 1ocroee-onomk Sttttts One -srihocent1 from

performing) tcr the middottntetvt1Btio1l tcmclician ind artrc) ~ghth

bull4U1 ecarie of nttrftian It theDllJStlt 24 _sr5hools co111vleteurotl rhlt Iv

f1raregy middot11n1rtutionnl -progritm wns monltcntrrg was condutterlA-dusrnr~middotrandorntzed was usedand the

datxi Yite consistBW- vllh a threeiev11 modfil -tn Which regtlte1mltl rneaures werex1este-d middotMthfrac14n st11frac143tents and $tt1chplusmnnts were nest2d-wfthf-n tchoolsTh12 irrciicatedthatstu-dents whomiddot racBiv-atl thr mterv1r1tion J shOyented sgntknti)gfttlaquoSH2r

in math nrnbl$frr over thri schoot year than swdents in tv ccip--isan group (n who rect1tveurotd das-sttgtotn fnstrtJctlon M-oretjfot~ the intervenriori effect did nnt rHffer for sttrttents WJih earnim iHssbiitifuS

sttHiem1 11nltl lMRJl[t1thilt1viin~ StUdurrts Thus the vieftl postttv0 and su11xwt thlt of thoe rnerventior when by education muth ttrruhers n fndu1lw1 dassrnorns

ttBcmch 111 fhe- eflfosw of Soive Ji an munrs11)plusmnjtJ11

tn 1m~n1yent tb13 n1lttTl1elr1aticaJ uf mlddk mshotl stmlcm~ with dhmbihfreamp

fU)L hi ther1evicmsirtt0rvemiort sruz1 1992 amp

swcients with LD vrere tntglH ttitlter in-dlvirlu~ in sn1i11l gnYU$)-f the rtcScanhe1middot or a

dem tJ-ut7lde the daampsrnotL hi the pr-ette11t cciuw1froo mnfh teruthcn Voefn micronrvcdcd wiill

siunal kvclu11JXlaquo1ct pnpMe t1Jcrn to interventinn in c02rsmn1ms tfoH inclttltled stttditrts- +vjtb Il)

zs1d amptu-d011ts f-11 thtH tvc we-re r+ble m

fo-rtnhzd eJlet1s of lnsrnutfon DH stuik11tv ofyenarvirtn

tnlt-lusiVY venrrrm math cases in recent rep-un

NscJrcn 1J fr~irthe 1gtfarcinnaJ (tJllnci-i of T1sad10rn nf vfothernatics focmmdnn 10 crifieal qn0RJ011S thm

mc1flltruim if n~feardtcrn nml pr1ctitionors aTe tn be sucCsJul m rnalh educiuinn ttBG-ktrch ttnd

ei ul 2009)fhe

teachers ~ach stndtJttLs rmtre11lll)ica

2fJl3 Thtampgt

l well that h2ve diffiruhies ht mlttlhtrnatk thJ-t cialiietl t11t1rurmi1m ruidrtfrac34SeB 011e ur1u1 of tnltlthJmsttici+ middot-middotmnthen-mtitd

ptasus for studettIB 1vfth

LD as iveU ilS thcJr t1xfmiddotl1ers arid au irrttrvc-ntion

cJrilvtfrac34sity d Miami C-011 Gil0r FL U$A

Arirona Siattmiddot UnmiddotivenJt TewqmAZ USA

Co~middotpondfllAuthor

ncunfrvc (og~ prlti-ce+gti-ttN And

Mnrnlic MrJl1tUg1Jfi Univqrity cfM-0l-Nti D~ afl0ttrhlt1g lhid I itf1ing Phimdlt Btdg 3215-202 Unlvtrstty Or Gidlctfl 3J 4pound ampmAil rnrnorttrgw1110Anm

0f thoK microro0-s4es prnhlem reprc~cmathrn and probl-rn txecmion (Mayer I 99K Polyrt J 945il 9S6J Prohems rnay be repnsenrctl w1tJ1 phyicn ohjccts or mani11ul11tives writshyten symbolic rcprt-1entatinn~ 1 mcn1aJ images or ti comhishynatimi (hmvier 9RTl Pmhiem mproF11~nti1tion engage- pn1cesses that faciHrut-e pmtitom compteh-onfioJt hy inttgt grating p-rt~blcrn i11furrn1tf(lr11 meirrttf1tlt1gaieAtaJ -imttge1 af ptoblem in wmtin~ nwm0ry i1rrd d-evel~tng viahle stilmlon pampthamp lt)tl111 hy Intling all0mnrive ruii umsuil 111bull~bull lo ht problem 4Silar 7) Anudi probshylem tcpresa11tation 1m+nhreg tmulating arul Armampiiumittg Unguhrtic and r1mnericaJ infi)lmiddotmetioll trlro vciibttlgrapbic tymbofie arnf qaantitative 1cpniet1tn1 iniis l1uH Si1omiddotw the tel~tbullmbullh-ips amOrtg the prtihlem parls-primmiddot 10 generatshying iipp11Jpri~11 rnathe1n-11tk11I eruatinm nr algo1ithnu1 for ptclil001 siulution (Meyer Jt Mmucgu1~ amp ApplcgairL 993 Vfr1l Gtdcren amp Mom1guc zou-n The stmiddotomd phdjt pn1hi-ini exeJution middotqnlT~s problem snlv-en t1

ev1km-te- the sgth1tkm patl1 pedont1 thi awropfiaIc talo1~ )tition~ imd check for ~1liCHrncy

SttMi~is widi LOmiddot olrnLl~~torisi~cally t1re poo-r _prohlctn gn_Jvetlii Timy typically lac-k knowledge- of pnblcm-holvir1g prtrGcmses parric1d-erly those uec-e-ssar_y ft1I middotroprcsenti11g probiln- and tltlmfwn lft1d tn he tallght th1Jj( pnce_cs XJtbcidy and- sbcnAJ-11 hmv tn app-1 y tbi11 middotwhen middotlt(1lvint math word probrn~ (MorttaguI~ IL AppkgfttC 1993 c To du thls efficctively tealtlt1~ n1ed 10 ttnderstmrrl the pn-ihleitH01ivitPJ prooess and prtrvide apprnrrTa~ irurtn1c1Jon within the con hx1 0f n v1rt-t1y nf pi-ohlembullbulltoving activities fKrol1 amp filler 993i S-ove ti the ir1tcrv12ntrori i1rv-e1ti~111ted fnthh schooi-haicd cfficsc)- snliy htip~ tcachens UTHkrsta11dthe 1yyes of pnnes1es nn-d )ltrategie~ profidcm pnbiero lvutr-s use why mMy smdenTfrac12 are i~ctive pcot~Jcm el-en w1d hn--v Ibey tgtiln tench snJdtnts to he St-tccossfut- _prnbl~u 10Ivotb (Morullle 2003 j

Salve It and Students Wittt LO

The Solve Ji instructkmaJ Jld~Qduloty cognitivc atmttgy irwrtt11ctirm 1s h+1amp111d on ~vejo~t infonxiatlfln p-rnceBRmiddotmiddot fng and snci-Jctrnxrnl theories at well tt11middotdorttifiettH)bull ltkrm ons-trated instmcri-011iJl principks tHt pmcc~uret 11oc- GnmltVS 1991 SvarrsutL Hm1is amp Gralrnrt1 2005) (~1initibullie stratshy~g_y ini1tttuc-1iomiddotn focusltis 011 till()fii1g y1Hmgstcrs -tr range of cognitive Md mctac()ga1tivce prneowtpound~ fi11itcgi-es und-men- trd se1ivities to fa-ullitine learnmg nmi iru-rrovo middotporftmt1anc-~ Thtre pncesG-tes and stlftteg_iti may bt refotitiy silnplc m c-ompIex lll a fun-c-1fon ofU1)- tak di-ffhm4ty anr1 the contexshytuaJ cnnltlit-inn0 Cugnilive nmiddot1tegy inu11T1ctinT1 has bctn pHrshydcobirly cffccttve frJr improvi11g Ne1dzmic perfrn111ance nf stLH1tmiddot1ns 1v1th LD vbo typ-1tlly have ntH acquirod etmlrgJes that fi-Hiiitak prohlern soiving or hsvv dJfficulty stde-crint~shyiho~c appH1ririurt to ti1c ta-sk orchestTfftinpound the-fr Ht and

follo9lng through wi-th their executitm ((iruhtn amp Hards 20fl ~ Montague amp IAett 200bull SwtrrHmn 2no2t Thc~middotst s-tuderrts iufrcque1nly abarnfon aud ravl11r~ i11t~ffcctivUc stmte-_gfo1 rm]y adapl preYiot1sly earned l-tntqiobull tU1d typica[ly dn nm gcneralize ~trateg-y use acn)rs dnnuiins (Rw-antton~ 1993) fo_ contraimiddotH~ su-1~i-ic le----rrners hive a rep~ crtoirc- middotof Hkltegia_it-aild middotuBt fuito1diectively and -effititiltly They middotnre-sctfbulldfrected s~tfbulllegidmiaamp and n10tivated probbull 1-rnn middotstrJvers kl1z1can alSo gonrrn1Jte-bulltmcgy QlemiddotPrNampley Jlwlmwampkiamp iclmgtider l 9t7)

5irilreuro tJ Jt1cnrp01~middot-thtllo~irivt p1tlC-frBSZamp essentia-1

m prnllem solvmg enrJ delllJlbull i11 llliliDfrac14lt tile thiJit w apply thnse -ptoccsi-es 1Afh1m 8olvin~1uat11 -iwrdmiddotp()hlm11s S1ve ft ~Jarc parrfoular emplia JD ~chi~ mudBllls tht pr-oceamp8C t_tn] strMtegitiB neethvl tD 11JJfefrac12AC+H 111-athcew 111ml10J-i probienu S1ud4Ttts karn tn J)Ulphritae pr-obtom by putiini the problem fntn thiir ryvn words and v1tm1izt ploblc11~bull hy d(jveloping i1chon1atic rcprel(ntbullfrons P-rohlcm rtlp11s(Otbull1tion Jends t-o pmblerr ex-Ltmiddotutiozi bullvherein sue~ Cehrilr probtn1-slv(rlt middottnonitorti1emeives as tbeydo~kpshya11d carry om a -logical roJnt1o1u1 pl~m-Gjfen thatntetMJogni-M tion-l-T ~elf-regulmiddotation pia~1 1 a ccntraJ toleinprobttm Stih10

i1-g Solvc 1 t 1 intorportl~middot itffiinstnC-ti-ltm 9ltrlfq1~middottiit-ing 1ml l-liiirnongtitorjng~ 111 sum St1ve lt -L a-ocmtprcllet1$ltr -stutcgit n1tHinectrtt~itting o-f SLven ccrguicive prtJc-esstiimiddot (read JllntPhrase1 vieualize bull hypotht~ize1 etimott_ tombullmiddot pute and t-hcc1(t ftttd t-mrespond1ngmiddothdf-regulation 1nn11cshy

gi-ei ( s 11 Jf frtstrnc tic n seJf-qJJeitimsin~ bull1u eeifm on it or1 tlg) in ihe l~mn nf u SAY~ ASR~ -CHfiCK pmaod1m~ 17H~ nltinmk gual of h1stntclm11 is ro have simlentf 1JKHttli1H~ the cognt~ 1ivt pn1Cf-s1~e0 a11d it~Jf rcguluinn strlltegiemiddotll o t111ll tht~middoty are llttt autarribulltl~iJJ during pmhlcm fliving Vigal-t l priplusmnrieHs ihc Soyenve lti rourfoe

An expiidt it1Strucii1Jn mndz is thi hrbit JtnlQ(l(middothinlf ~1fHltltch fOr telobin-J tudints fFvv 1n degu~c ~ivamp Jtl ExpJicit insmt-ctiou W1o(raquoJ(1Qfrei1middoti_1dida1ed tc-ahilJf -~bulltqtie~ poundntch as ctaing~ moatitingrehear-ai ~mtHC0dhacentk Thl frac14 ~1 ppreacli durac-tfizedmiddot bf strucrtEmd~ rn-ganitedmiddot le~~cui 1pi1mriatt -cues -ud pttbullrpl---_ guid~d- rmd dtstrUiuttid pJactli~t~ middoti1m11~shy

dinte 011dttc111~ ive foeiUlaek on kfrac34rrm-ew 1Jedb1middotrn11ncemiddot poMshyitive rcitrfOt-Genrent )Vedcirnisr ind n1J1~tc10 is rno-rc flexihlemiddotthlt1n atl1erbullitHgtYw1Jont11 rncrdekw (tsectt cllni middot mst-rti-tgt ii-oni becauxc it is interactive and aHows tttiDhers to 1ip1 tile teaiJting routine and tttilor in$iructfon 10 accn1-tmio-da1 1he filu1gthi-tdlti 111~~irewscbullmiddotbullfrtudenttMont-bull~ne lOfJJ Mnntagne Werga-~ amp Morgan 2000)

h1 the p-esern Rtndy~ f)vc Jkf miginnlly dcviojt-d irt

oificafly to in11JNll- m11themahe-al probt~m tolvtl~middot 1br $tu dents with LO (~fooLagui l 991 Montague amp Bns l lf6 Montagur~- ct tL I 991) was inve9t~gi1tltxl in the con1txs of genen1l etJuutiltm tndttsivt rrwJh drrnses thB1 1udud1td LA and AA STIJdtrrts as 1veH M srudcrrrs with LD rhrce rescrplusmnnh qneitmiddotiflfi gu-11ied the pntTl titttdy-

S-11 Rwtwl the-f)r(81tc411 1f dont umirfrac14ttrntL ro1d it 0gio

A-Sir Hrivit i n09 rind uncterstiod Httc microrobi1ndi

Check for uncte-rttsnding at 1 smiddototve tm pmbiemiddotm

Say Underifrlt tht imm_irtim i-nforrnation Put tile prob1em in mv ovm word

Ask M+ve i underfoied the rnportmi htorrnation Whirl tc tl1t quzsqzui Vir1at ilffl I

kJGklngmiddotfot

How d(Yls rnv 01SW(H C~)1f1rBn wlth rny rrctirnate Oz11 rnv tnlPNBt HUtkC

the ctecimiis or monJf)Signs ilt ttie right pc0s

Say

Hi111 l c1w-rKttd evrry stepmiddot Htivt 1 crw-ckgtS(J the cltm10utmkn ~ mv Cimdc ThGt 0v0rvthit1-g right lf nUC fi) biJfk Atk fop tHtj) ff I N10 l1

t Math p-t1gtble-11Molving nnd 5t1bull1nizgie SourceMG-ztfague 2(Hl3)- omnhmiddotbv Ext-01)1)ot131 innovirionigt vitt microtrTnt1noN 10 mprinL

interv0ntfon (rrt progbullshymiddotstudents to smdcnls recrn v~

inxtrn--ion n- rneasured urTi umr1bull-briscd rn1asurtts 1CffNt1

265

m matched 1 af mtclltlle schonts 40 wtft- tttrnited fi)tn a poss1bic 59 tuidtlk Bcho(1ls ln the tvfiamiJ)ade rntv Public Scbml~ the fourth EtchnnJ dl-s1ric1 in fhe m1tiotL pounddumts Vtrr-eTt1Htchetl rm the

k~1 SES Wi$

FCPr irc1bullf01mmz

Fl btiscd un CAT n1bulldnmiddotrrrsn1bull2

love and BPcioeoonomic slams Sdrnol tevd gtVt1s

Flridn nfEdt1catinn s

Vlhf

bafa1netI atttYgtBJt the smicro-etrum of tigtw tY 11t1ltl SrS ttgt thc tJcumt pcssih1i One gchou1 fnrn tnch

from e11ch sctl-ooJ was The critlltia foe

n1atd1e~1 rnrnlm111y assiJntl to the rnath rcacher ttrlmjnistratttf

that-the certified in 1n11tht1n$ttit1sS ed11cae

limL tc1cl1mQ ax lea-st tlwrt-e fas rcrnms tbM included LA sTuJen1amp ampfJd sttUlenB wilh LcJantL fur the tntervemJo11 reru~h-

tn attend ti Tht irtrkt wa ai thc middotof tht ltGGfwo-l yeitr

1r1ftny tez1c-hers schudfo s11-d dn$middotSts ckis-i to the smtt of schooL At1rhion the first 2 n10-nths- of

Becat18-e the for the 1ilalfC(Jf)f

Three tead1r-rs cinitrnstunces intervtmtiun anu two naehe1middot were (rorn the culdmiddotitional three intervention txrreht~rn

Two new nrimcinals chnNe t1ot to JrnvIT their One tencher waamp Ltssitmrd Gt~1dz

middot~middotmiddot 1bullmiddot bull-bull-- 7 dasBefrac34- rmd Dtie

nor SIJIJ the GOllStHil tiD-rffL l0101robulle1-i1t ofthJ-ampc ntv

mu afler the inte17Jt)ttt1r1y1 wnt initittUd redtscttd pnrticiJlfiing schnolS to 8 111tetmiddotveritttm plusmn1ch0ols and l6 c-0m1Jlt+1nanscJmlt1lr No ftJrther atTriti-on middotmxJ+lJnd for the nmaindcr the ye0r hovrevcr tttl rnmrn-ier te-1chcn whr tdJ their s-ehnoJs consenttgtd to tcacherg Vbo and the

37 arc nn vnhvl in Tahk middot1 The 1hzu ranltlnrnint1lou fai1uro ntmhcd fhxn attriiion

r111Stfrac12lt Tt61tftL

Frum the

a cltrnc2n v0hanv of thlt-

----------------------~middot-middotmiddotmiddot

Dam

lt1tfilN-ention

fl lamp

Gltnder 11-ae Parnae

~

r

lS 65

5 15

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6 35 10 51)

J IS 7 sectlt

8 47 3 rs

3 2 p 2 O +middot9 5 29 30 O or more 4 2 45

dnta a 3 ifi

$fl 17 brr 20

lnrerventicxn middoteffmcL 1Ve diNcusi -tl1t nsui1s in dmuii ltJter hJ hut it

group mum aifecatltl a lnvver pttien unumsmc pntrftest mean than (ll(li$

2and As r21ro2i with the

It is es

effJtt i-lws fn1YJ thfa (fatrt cn1fobullr-0d m the first

amp 2)09)

AH students frm11 thz teurth-ers inc-hw1o-n math frrttnfrve OJath ru1xI

to rnirti1oirotlt in U1t

dents in the f1ltcrv-ention scJ-mols nnw ided instrrxtfiuri but i1pound1m Ven c11Uetgttetd iinnt stwdt~11t lvho nlttuutc-0 cottiietJ frrrrns ( 11 Jl iJate were c0Hz~n1ed 011 01m

tnned fi1l1fiems in the ccu11parison ampthtHJl-B u1 410

the 11clw+inn rnath efoMse-s 8ttJcient0 vfflh LD wtre wot J1l10clm1ill from trtmU

1ncluded fl pcrngtcntctge of mrnknis with LD fnnensivc n12th 0lassz1s- cnxnllt41 preclm1in111olv LA r1ittkmt-

dfatrict ide-ntifrcltl i BCmiddotC fiyr LJ) district crittffa md trad FCAT math tevc-h oJ 1 OT

01i ti-raquo ~ amptrt fteyh amphit -Apr MWyen k1n

MWfflm

L M()Oliltmp1od groNtil ClNV$pound

irnerverrticrn JJ1-d comptti-s-on conditions

t)et- a- $Mor hffi ~ MgtW kpt ~ hill

Mlt1r1tb$

tfla irtt2tVet11ion afld mmnvi1on for studcttts Ztrd

5 2rultlcntr iitho wete F()T tTntth scott foveJ of nt 2 iJUt of ztudint c11imtJm1cii ns Airhad FCiT mailtsccre levels tgtf

CBMs of mrtth LfltiJUC uc~H itemamp

were- calibtllttnJ itern responst i 3 the Rrwth n10dcl Ost0rJ-i-nzL

level

thti CBtvis were finrt ltllSltrfocd in Mltnilngne aL CWJ

Tabk 2- SttHient Dari

irmrVtntion

w ariab-l-e ~ n

j~(~

ll iO 4pound m f7amp 56 66 3li lll9 J4 248 54

Grnlideg Male Pi 54 ma 41 Ferrw11~ f4B 46 212 59

Wh-ttc- 11 4 43 li8 61 2yen9

Black G-0 33 107 Asfltn ltI 7 Othcr 2 lt I 4

FlWgt GJ r reducB-4 hmch Ye$ l98 65 165 No 162 35 54

ampD frac34Pi bn4-SO

a laquohnrdanliced meTric that resrmJb-le1~ 11 tl irrttrJ1ret1liiiiiy ltYftlit parameter t-rill1Nfbnned -rhe problcrn~iolvhlg mul-

lt1ci1 middotstturc ft- -L41rnztf1m of 1) The i-nrent of this tnitmfiinTiiltioi1 was ttr JX-ptrIamp the C~B0lt1 semes 1gtn R rsctfm-Hkr rnetrie and it hnrl besnn 011

67 io RO Each of the revcn rnttampures t1lnBWplusmn11ed of l0 nnc- two- and ihJtesJeJJ re1book-1vuc pml11le111s as iHu0~ rrm-terl lnfov The proble111amp did n-01

nmthum41ti0a J KmiddotlUd~nls

whole rntfn-htrs or clcltimttltL

93 Bhi1-t-B Th-is lVNf mnn~ tfHHJ had s-ulrl ltm km much did 1lte stre fiT aH tfu iihfliG FHlld

)fl h(t1h

Tb rts-i st-Ht1em tt1 qnve Ftff1Vk trnc Du tht 1vi lndudc-d -1 ciccb

Ro-dvel tgtttrns $ 12SH Her GmTtf)liTiY deduets 17 of her pay vvetk ftr Ctifrac12tgtS Rt1c-hc-l th-2 hlfluv1111g fbrrntda L fR3 (1 ro 0orrrpunmiddot hfrac34lr

u-fier fitpound lHYlJflt ( Ii i

267

Vhat vrrn be Rachels after nn-es if she wnrkB 4D hnurn

FCAf

Solve Irf imhities a dctailtd instri+ctionfil

dah14 sets leSS(hltL class A J inttrvention n1aterl1 Ls

were frrr the sc-1100 yeac The lesszgtns inhtrucrionnJ p11ced1rres

for ~trnt~Ytil Hf0111 rll and microenen1J~ ize and kiJJs (see

in _-()ct11hz-r and

1-eu dJMl ttm lJe di11ricl mnm1abt The teachCtrs were ems as wttll a tmmiddotekctnrn1Je fih crl1rubllt1rts

cion The- rrrs1 rHHhnT ITJ(H1i5ie-d iJ CTf3Xrice intervention 1c1chcrs n cJSt oncc Smdems in illc compansnn group rcceivzltl ciaJsroom instnuLinn which folh1wed the difrtrfot numdated

that lmkcd the 111xthook to theI-tforirla State Sunshine Swmiards All students Vci1 allowed k1 Uht cal~-cuiarors pr1rtiee ancl sesslonw

CBMB were adrnini1i1ered to ~h iuteFvernion teachers cfa~CS six

irrtervtmtion (hagtltli11e) and then the remaimGr of frtt scbuol year mcaampuns Vere altlr11lnistered four times to the group cLasscs amp11r1t1eru1v to fue interventio1l and 1hcn at the thmL fifth and sixth t1Jln11nistratiorrpound Cmnnrnnn group t~achen wen ubServed faH and sprmg narrative remiddotn1rJ11npound1

Pdrnfois1ra1on of the s-con dtna Ne-re tt1tpoundtCli inw the datnh$$e and ind-ividtw1 cmtstmted sto-den-M in the intcrve-n1io11 group WfTC

T1u1se lfbulltrv1ds1d foedbttck to t1n-ckers and over tfrnc hrtd six d11t1

Ohicrvatwn cheddisrs for the fnitial three lssons of the iruervcntiun anJ the prc0e11cc sr2l1ons rdlecied teacher bthaviors sssociated 1th 1mcpcaticn for eaih lesshyson 11nd 1mp1memm11n of the iess011 The ellampGldists for the three kEt11J01fS czi-nmirterd t l-6 -and 15 it4mh_

eitht1-r Wns demmrntrate-d or vva mt rtYview the chart vith TVro tmined rescmeh

per for the 3

i11tervenri-0n tlass for -each of themiddot inttventiJn

igtCsampiom~ vcr-t 12~) nfthe prac

assis1an1s Levef middotof treat~middot 1nern wore acm~s ihe ObsefVtttiom sepmmtoly for the inith1-l thrfrac34emiddot lti~1+011s ssid the nntciebull t-Hils+ions Pe1rc111tagc were tiih-utntlfrac34i II Hcv1lt1-

the rnm1ber of agreements by tthreemcnts

~

rn1ll1nli0d by lOD Y-r t-he obSlNirkTns of the Ttlitlal of treatrnem avernged 90

ill-0ltigt1Jtem 1 Vere u~s1od wHfdn Level 2) and s1udents were HtSfed tvithfo sdiriols

we uned multi level for aJJ nnm1sc Because tl1c

ruDdltrrni~~0d wlHrre achonh Wttfe

cnnditiimE the fbcal -ris a Level 3 dumrnv vnri-abit-- thm demited in the iutervzmiiDn (U

Tt iNLlAl-nf

irucr-et tn determine wblttther tht~ two- c0mlidn11s dlfii$ren

tfmlp in detaiI lzHttr We tampied fbJ1 lnt1rn111tkm likelimiddot uod estimatfon in i1e SAS aHMLM

A brief of the ranted The MIXED pnc11rlt in SAS ttpoundes n nrnxirnum

11HzHNS frtt

Thilaquo pn

routine tbt1

mcBsuros vmxtfthks amp

a s-o-cnJcd

thaL after

vtfttJ varia-bte$ m the MAR

fot CflrHrimtces and the (Jbserved CBfv1r fro-rn e-urHer waves an 111rlivkhml pni

for missing dllit oil tht hfrac1211 tfrac14 un10 fll~ or her ttndmmiddotly1ngpn1blem-B1ivmgskms

1pound1blc tJ-u obsxrv12d trics b nt11vmioTJ

condititrft and dttts col-lettiun wivc Notice thm the CfJmshy

scl1ooh were rmt agsesGetl Ipound1 the-secotiltl u1tl middotfonnh datH coUecrinTl waves These otl11ervatinns arc iut1nior-ud

dnla -tlurr are turns-istJnt -vith tm lv1J-R 1rHschau1Sn1

268

lzlhie l Ohmuryen13d Smiddotmpie Sizes by tnterverrtJon Colrlithm aM Vmve

Data corl-eiJcn wave

Ccmdltkw1 1

157 f8S 174 7-4 178

NIA 358 NIA 3il

lWJ ~ 4amp h1$ 1lilt Jiltmiddot MWf Ml

NbiRilM

RbullltilI 4~ lk1daJi111pti4id JI~ trJvDS ~ibullmiddotbull timple irQpei) for tlr1t -ahlJty 31-ouri amp-frar c-ontrollillttiw ttu-rit- a1Ts schoolshyftive covarfa1kt

by diplusmnfi11itirm The fltu1wrtioT1 in th unplo fiizi5 fCtosfrac12 the LfatJ io Hcctf un r-efl_1-L1s-uninten tiona l mi- i ug dtta AJ thnugb thtn~ i0 nc middottiyaupir-ic-aUymiddotto verity that unimcrxtiuntJl nriss~ Ingrni-y llc(nisistcnt vith-an ~-fAR tnad1bull11ii1n 1 tiH TC$eacrd1 teai11 ke11 exwn5ive remrds 0n-tfiLtTtiflSOHS flir attritfom_ and the-1- tyfh nu cevirltHte tn ~_per bu mi -acitrgnoas wa1~- ampYtt tcmttpoundally rd1tod t01- 11middotsiudeuts middotJWmiddotvhi~~-mi(11plusmnn1 skilfL Rafh-eY H11t mus1 tiE)rn1r1tJn rensons Lr 1t1ll-ing data wese thai Btt1tkn1t~ ctaSSmiddotfrac34cheduJa yenVere- bongo-ti or they left 1he schtlGL

Tl idernmiddotify pmontiaJ cmrelt1t-zt-s uf-miiiillllieS-_ we 0till

fm1r10d ii smcf oflogsrtcmiddotregr~s11l(HJ armlyes that 11-cdicird thi pro-pltnxity 1hr mt~itll darn (D CJ1 s-can afal]fVt at a ptwticular H41t1e 1 --middot CBivf tltOYC m_-11g at rhtll VtttzFe)

amprlnHhefoUowing 0e1tefmiddot-RtudmJ-lev-cl predictors tdu1ie-i1y (r~priRen1ed by tlnmiddott~t dmxnriy Vilrfab1est ge-111kr tree flt

reduced lrt11ch iitlll1 Et1gEsh 1-rofoh~ncy htvel FCAT -randa1ii2xd matb trBI sttJtes~ and FCAJ st1nd1Irdiccd readitif tcR ~curu Thse 3mtlycts is1dica1middotui thul free or red11lt1ed hwc-h B1EilYcl and VCAT t4+i-11ricor-eb middotvfcr12 -prCQlative of 01iBQilmer at later dtrf11 cnilec-tion aYt s11ch that irushydCllt8 who received hit+ch as-ista11Cc v-c-re n1on likely tc htivc n1h-1 Ji fi111tL fiefrac14 were- s--t11d-e1Jts wirh hrJt~r FCT temes H dcs-crihtzd lattlf in th mich~ tlKmiddot- final ff12v1 indu-ltil21l th2 prcvioux sci of Rmiddotntde-mbull-kve prelictoo a-s c1warfate1L so rht 1 i R ~btitd 1m~m~- dn1-B 11iindho~ prnq~d111e -tmld

alltofnatirally cmlcCt for any nzimtsponse b-iRS that mi[Jil1 result from the-St v-niablts hr effect the covariates rK-rve as auxiHiry variables tlmt co-mcl for at1y nzmresporrse b-iat that might rcmh front theic varfab-k F-Qr the MAR 1trt-zha1ism to be lfot-1ed an ifldfvidunFi pn1pcnH-iy fJr rnissin~ darn would htrvt-~ tu be rdaied tn pro-bkm-tolvin~ abiHt_Y ecn after oolro1li11g for he covarltltcs Ahlmugb there iB no 1iflY ru $RpidtiifJY vmiddote1ify thtu this is tnJC we l1t1licve thar MiR 1s a vtry rltemonabk aistin1rrtltiR _pardoularty J11 the fl11al 1node-l- middotthi1~ aqjulltrmiddot (]iM- lscttRti for tiudttU- and sdfain-1-l evtd cm Jlri mt-eit T fr ir11-bxicrrt tr3at -0ur belief lraquo truemiddot ftle only rrepniv-e -impt1ct of the m1bull111pound datE Lb a kbulliii of J)TU(1

Au rwted prc-vfoHlo-ly thc 11tudy utWzc-d n ruinted dbulldn strngt tltrc such hat 11tf)Clt11-it rn~ux-cs tv-Cot 11-esLt-d within stushy

dM~ Bti1denrtL 1011 nc~khdJhffl olnllitfQmtlraquo ttt1ddaai101ns

Vt1C ncsteltl within hdtno (it- a fo-ur-bv-el da-111 amptmcturc) 1)11or to cdimatQ1g the gnrwtli ti1nd-cts frac14( t8timnttd ti serer 1fm1cunditwn4] nroltlds lt modd-u 111-tb no prodi~tora-)-1bii pariitivued 1l-11- middot1carc vuri111ln11 hm fi-nr- orthoiotta1 szn1rces 11mlfc rrg1d0ls fi1ilod to tom-trge1 prC61ltnaMy htianse middottl1ere was n-m imficicrt-f v0u-ianbt1 in the tfahi to 311ppm11-ruch a tllOlple L4rvar1BT1CC wtnrcnttc Tlrese i1titi1l ilatlyioJ proshyvidcd strrmg_ evidcn(~ thai it poundi111rtgt-vd mcHie-l vas LtrmccrsshygaJ ~- all tubseqaetJl ~u1ly~g wmiddotere conamp1frac34hJ1f with u threi-kvtl nmltlel Il1 t-1hichr0~1ctwd measurer (LtirJ ) Vere nestid within students fLcv-erl 2) a1+11 strnJcntlt IWC-tt nt-St-cd w1-ii1ln -s-clruols- (L-ltn-el middot1) The U-111Sc-foviJ tmcnrultti-oru1l MLM indkrttx furn iridi-vidnn1-diftbritJtCefmiddotmiddotberweiin students (ic Levd 2) ruixYm1ted -fo-r 2ti 7r of fflt varUi~ilhy 0tnd n1-0an ditlttrenct7B l1tween sclloolii (ici LtiVltti J t10Clt1-Ulted for l 9 81h 6f the prob etl--illYIif va1i21ti-OJL The remit]J)v ing 51 3frac34 nf tJfrac34tmiddot variability r0flc~4- v11fon-pemiddotctll -ampeurv cH ffCretueE

lhtvlng e+omiddottatllisLted tht 111eii~1cc o-f varia1tnn at all t1m-t ievel7s nf th-t- drn-a l1-i61nrcb-y wmiddot~ adritl the L--rt-1 l terripotal pizdicttJr tb8t q1rnrnlfied t-tic rfrmnpound of the r~-p~ecl rrttiLStires varlllblltfrac12v Tffr_ Vlillit1hk middotng e-prta-ed amp0 the numiH1r of nrrmthB -si11ce- zdt-c firsct cUy o-f (ktnhec CeJ1t111middottn a1snrrrntnem tin1t- l-11 thiy rruumor exmicro-rtiVeited the intpoundrtcq1i1 01 rhe MLMai- th-e Ot-tse-fo-1c rriJb4rn-tlJ~bullbulllnu frac14Cf)Hv Next VTt

perfmbullu1cd n series of 1tm1-lye~ to deteanin1 wltYfhs0-r the gtoth nuc-s vHrltd a-crftfrac12gt ind+vfrluplusmni1pound rr Level 2 a-nc acruzs -ti1ol1t~ st Level L Atrer aHcnbulltnQ the- averngeshy~rowOJ rntt12 to vnry a-crni+A frac14chn1_1Ts themiddot he1 eeH-txirmr v-ariimrc in gn)Wth r~1tc v_-r1s nonli~J1lficrn1 ( middot1mB1tquently we rctrnweri rti rnnd-nrn ffl~middotcl anil prnce-eckmiddotd qrffb i

mnflc-1 tJun allowed for hitHtJme icn-n~ difl~rtmcc- amtmg rnditidualk yenif1hin ti schooL huellnc rnesm difitren1e beiwzn ~thoob am4 varimfon ir1 th-lt mmiddotcrntrc mouthli-

Montague et aL

~wlh rntcs b0lwellJJ schools FiHllf note tlll1 we xpfored ij1c fll of a qm1dn11it giilW aiodel bUi il likeibull hfHXl ratio bi-iiqum--e statistic indicatedmiddot that thfa n1oticl did Ol iotpmle model iiL

Iffling ~4Ihlished the coY11rim1Cpoundt stmtture 0fihf initial nodcl we roclej ll bios-y Leven vtabs lbst ltJlllmrtiltl merit proup llOmiRnbip (0 ~ lt011yamo11 scUJlt1L l ~ int0

vercrion schooh Thefirud MlMfrtim the ini1ia 1itmiddotof lt1Wytea wm~ performed to de~ine if the mtervernion efflfrac14irs 1Nete n11xlerated hY ahrn~ group (ie~ BtHLkn1s ith LI) LA htUshy

cliliHts AA smrk11Mt A1 bofort we reprc1cmd teilhy as 1w0 dumnty v21-iaNti that crn11n1sted Multlenb middotvrith LD and LA sttidentgt to AA 11tndenttt Because thlt sLlbst11nmiddotlilve gnaj wt10 to assotS a crc~15deglltelinteractin11 the Level 2 abiHty vnrinbes V3rZ- bnth gTTRiJJ n1x3J1 centered at ilieir resftlWe scJmnl rrteRTI ( FJ~n- middotIi T at~hi1 a 107)middot TLJe set of ctivarfatts fmrn tLur pre111JJN CWyttti- vttTe ~rmid n1rm cen1t1middotc-d bcxat1se li wits- -nf fffteresr 4Xgt trltITTlfn l f(ff theiStY liXtria hks F1 micromemiddot 4 middot-slm-irtl thre ~irnp-it~-ilripCl- (Jet tn(nkilmplted middotJToYith 1arva frw tfrac14Leh itbin1y grourgt ~ em-ffl iht middot5gcm 1h1 studentsmiddot with ID irad prohtcrn-so l vinmicro eorc-t- Utrif w01e lower rltamph those ti 1middot the A A studenrs by 111po-t_Jfnas-ly five poinmiddott~ The LAmiddotmudentt had sc-oms that wtse sp~imandy onr- poim krtv~middot tticm The AA smdenEL on average From a pmcmiddotticfll pef1l[)active the mtJdef con1p1riKIM inih~~iiitid Lfrac12ut althtJtigh fhe pounditi1derrt~ with LP

had lower pmiddotroblan1olving scows the ink-rventior1 hadmiddotn unishyform lmpact llCN)le 1bility revtJs

The asslttcimion bctiveen ability grnup and FCAT prohshyie-rn petfonJianc~ vas soo1ewhi1t amb1ge-oui beeusz h VirM dcp~11deut cm whethcr the ctwariat-efl Jetemiddot ittclttltltRd fo the 1110ltie in 111i)lJeh with nn GJVttri2te1 the LA srudoots hruJ a

iiignifoantly lower prrb1btiiry of u cornct resjnJttsC thmi tfo AA -nrlt1ems The stutforit0 1vith LD aIRo hnd N frffl caHlv hgtwer probabillry but uniy at tbe Tnitial und the final asstJsn1ltmv1 ffoweveL af~ addirig 2tudtni- and 1c1l001-ieved covarimes tn the multHevef r-nlt1det lUt~e grnup differ nces wetcent no longer Higniiicmt Tht only eompari~on that remfined ftmiddotignifiaurt after Mkli~ th -covariatcamps vvflB themiddot dif erefrac34llt~ hm11een stmlenrn with Ll) Rllrl AA srudcnts ~1 the tH1ampe1ine t1JSse~11X0nL 1t middot Ls impott111t fh111 fue lrtterimtitrns hetllieieu expdtftcrrtid OOJtditUm and 1bmty-gtoop middot-weremiddot D01-

sig11itioam1 r~-=gRrdlM~ of whether tbe eovariateti-llfllOarcd in the rnndel This rmgge2ts that aJttiough ahiHty gtitup may a-Fft1c1 JJtrihnttancc un the PCAT~tyle pfoblems the h11ershyvcnrior1 had a unifonn Jmpeict aer11amps 11bUi1y liveb RecaH thnt 1hu growth mndd l11tlylls productd the same snhiim-1ive cunch1ion

Discussion Prtirrcamps nwnilortn as tleltrmimrd hy pcIfurman~ oo the CHtvis over schoz11 year shm-ved tbar CJgh1h graltfc SL11ctenJEi

whc neei-vcd the i111t~tvtntinn rnitdc ~i~nificauHJ grcnter gnnrth in n1111th-e1nati~)li middotpmh~m ~olvitg thnn thr- ri-f)n1pari1f)O

269

group sttule11t-s who received typical dassrocm1 inmtructi-on Tomiddot~ tl1e findings -ttere po1ntilC 1J11ltl uppon the efficlCf of Stgtw It as an interrventkm to improve ma-th problem ~oh~ ing fnr-midcHe sltlmol sn1dcntfk Sp~cifieally the resuILs ind 1 cuted that sti1dcnts middotwho rectiv~ Samplve 1t inmtuction acrtn11R ebility tJciUJX including 4tuxlerrts wITJ LD~ shtY1i1eltJ iranermiddotgrowfh ilunath pmbloro 5afviJJi crvffl the gt1chool year than stndcntfrac34 in-the compa1iBtHI 4Toup Thnt iii the interVtJn~ tirn grmip petfonned staforticeiJly igflificmtfy better tbnr1 the lt~ompadon group fflJ the CHffvis acnSs time aurl tht differcrice lfts afao praeticbullUy signlfictttt with a dHicrshyence hettveen groupti of neariy cure SiUndtid oNiittlnn a ltgt effect size furthermore the isuerver1Lion ppiilred ngt have tlltgt sanic iir1lci for 11rnd-m1-- oomsz -ahility grou~ as tl1c~ improve-d at the Kllhe n1te0i~rtirn~ bulllthough a0 mtamp vnnild etpamp4 tAsmdpoundIDIB pefi1t~11ed btrtlxr lllitiaiiv 2nd GIJt1tf11ned thr1 adlbullnllyene tn OOTInlSt llUdltJut will LI) crusrn1en1ly atxred Jo-wetthan both LARnd -rsludtmts Ht~cr a middottnnra c11Cl)urigin-~ fi1uli11g wfilgt thraquoigtriixllit11tfr xyen4fh IJ) out~rl-m-f aB eH-ity groupi in -ie 001npmiaon griRtp~middot-evexi tltc AA 1w01~ dtntJ hy 1he end ofl1e Sillmtll yea

Tbefrac34t findiag arc [1lrticul1rly irnpurtani with 1tbullSpeGt tf1

imnructixn1 for fndrms with Li) as the trend hi RehrhJh is trJvard fun inclusiltH1 in grnerll educar1Dn dnsstm (US Dopertman1 ilf ti-dueniion N1titn1n1 Ctnier fUr Edn-c$ttion StatistilcS 2fnoi Fcrrtbese st1uteittamp to achi-tvt 0ucc0ss in incluiv1 ~bullbullbullmiddot Yell and W~llrnt (O lll I mcmmmdiil ft12tt frac34thoctlt lilo Yeadingmiddotrouf t11llll-ten141itw prt1J~linnnlng llllt nrearch has shown 1fJ be eflbcrl rz in the g~llfral 1tlueatinn tJCttin(~ j) i 35) trod nLs-f 0

ad0fn enltl tHlC reserrrcfl-based ttngre middot n-mnitoring wylti31ns tn coHect dctffl on lt+tndent fer fom1aooemiddot~ (Jt 13-5) ihtimiddotpltbullmnt study inmiddotestigated thi efitcri of Solve 111 0 resyent1rchb0sci t inFiT1JCtfon3J prngntnJ to impr(Wt 1nath probfcrn ~Hviflg fDr 1tJdertts Vith lJ) in the euntoxi of gtnertl tducation clE2-18-eS mid demtm11tra1ed itfrac34 efftutdvcntiiffi for thxlSe students in that ietti-ng_

T11-ere Wrre stvemJ 2uidhioJ1al finding~ uf merest FJTampt we exper~td thai the inhio1 1l-ttlramp of AA sTvrhnts wnuM ht relathmiddotelr lligh at haseHne curr111ared to the LA studetits and the 0il1dttnt~ with LD HITtd that they wGuld maintain thai rebitiyrJfy high pcrfunnance Level o-ver time l-fowever 1Jw

AA poundrll1d1Jm1+ ifrd nrrt appear thnt dlfirent from LA rtndents in both gruups al 1 he 01rtsh vvht-Tcas lh1 stmlct1fs with LD scntett on 11veran five points lntvmiddoter rban itc ltA smdem initially ami rrndrm1ined rht~ iower pcrform1mce ovc-r tmio H1lwtvcL an ability pnnrps lrnpromiddotvcci irt the mm rntc Th1H 1s thfy sWtiCd m llppro-xt 111stebullty the ~uni level its tb(fr comp11tiWJl group peess and irnprov-d 5iprdfi~anty 1Vtr

time- In contra1-1 the petforrm~netbull of thci1 comprri~nn gnJ1Jp peers on dn CBMs ren1aiTmd virtuafly LHJ(rnngcd rcross rhe schnoi y~ar

Mth lCSfHCtTo the ~in~le FCi--style pmhler1s ntlffl1mi-iishyrercd ai CHMamp l 3 5 aud 6 thtomiddotcompnrison sectfiOUpmiddotwas iiig~ nificantly ti)ifrtt ltiely tr get ffn- pmble-rn cotli)Ct 111 CBM 1

I

IYliJJV[lEL Stu~

prac1HJC n11l1lrms Afan Tl1lrnymiddotenr the sutdcnt0 flfrac14lou1rl

the )0amp students 01l(n1hi be 2hfa 0 nom1l0lr

rmd TTNgtdel the endof

f-VOmiddot

an-d 5 Hcwvr the illll1l CBM 6) rit the end nf tixe school tlon group yenC7C lHa11tlymnre- ti correct thJ1D the c-e)middottnpansm1 group stucl01xrs Tltltgt mrmcr f1LtltTil of the groupc LA i A on the F(AT pnrn1c11 XVpoundis s11tiihrr to thegt pattern on tbc C-BWht

rh intervenJiltm haJ lesi of abi111 poundlfn11p rncmes11n Overall rlmt wilt LD cortsLltnttv

schonl year h Is 1mncmm tu remember that Solve

vvas dehvered erlutation mt-lib ren-chen 11t tKit1ca1ion clast-tJnms 11ttfe Jeacl1eTh ilid uot

tn meemiddot1 the 1re0tfo Hft1tc ~m1iepoundrth rdth ln hovv tt)

atidrcRB the tldUtatiomtl mmiddotcltlf of tltQamp~ stnde111t I nwever th1t hJmiddot

ottd ihemiddoth10111-1igtmiddot

0ith nnvtledaamp ftx-dhllik un nhwicCnn~

fbr tciiChern and stmlents the tcacm10 risuBJ middotinforntatiou nhmn the

1unnoc-0findividnat students whnrmrcurs

resh i enst11t1al to dete1rninin11 w hich stucltt11s netd more iudlvidualiJti1 middotfccdhack and ninfornernem ()ver tirnt the tewhcrn blcarni 1 rnon at visrbaf rctmarsal rn st1ltlt11Tt itxtcrmifrztgt thr-Solvc lti rcrtttine aho a+tnnciel-

alnud as mtndt5ntt beearne the Hmilne Thtwe are tgtrlfiffl

dmnems of i115truftim1 and are as pitff of the Instructi iJmtl prtreeu11 crfrhe inner~

fOlV~bull

a11ltl middotamomHtic i11 then middotre2dmrs nf2Bd In keep in n1ind J1nwve1 that Rtudemrs witb LD and

vryvmrd caveatfrac14JbBtBhmild be t1EnHoi1ed tn JJCmiddotmiddot nlh11k1m nscarch tn p-actitte

reamp ffch~based irnnn1crionl1

lrsehm SHlshy

uhi J

and tl10m ro HowttVCL imcnshy

dass timt~middot for

currictiJum n1inn ru1der 11ressure tt1 prepare sttulents for the FCAT Gntdn 8 is cnnsldernd a t1tidi~stulbullJCsmiddotmiddot year as stndeats mnst pass 1hr FCJ(r 10 erHer Sd1iml TheRe- CHfl(ti)rrJfl nr(

hecmse teiehtrs Vill rn1r 11npJtrr1ert a pr0gram w the- curriculum ivhen fr-el

have time u nreet the Gtuthnlas ~~rmretle1middotls

prepare for llm h11itbbullst111~ stme as$ltSSt1tC11l F or thfa reaBori we erntbtdiitSd S1yive Jtf htto the cnrrfouJtun to the cxcD poshy

tYf lTIBtnrction initiilv ttnl timn

The tca-chtrf C(YJdcl use chher rm JV4rittad

SmaTH30ard

from t1-e dist1ic1 curtictihun for 1he CiJt1htc ivt

of11us inteJ-vontit1t1 wen 1ehm11eli iinkcd NtHtC sr~mitrrrcl ff[UJ VlSU-

a ls t0icher- tarhcr thmi rnem the intervention

Auot11er n~ the pws of imztrucT1or1 Ar tbe orusct ts mpcnim lo slaw csn~1n that students uwicrstand how

ead1 pT0C(SS is u1iJized nniblem und how directs the

solvt~L h rnay take us a l5 n15nutcs to solve lGrn mctially Over timt hovvevcr the w1rnh0r model mit1i1m evrdt1vrtfon at1d fiefrac34ibk mimmii 1n ntlrcr

the te11d1cr 1mideh huV w plusmnrize 11t11blcm vith tliSptlt1 rn lt-0

Lhr cie-mR stumltl b0

tbiee or 1hur

and 9 01 Hi

Ctm(i1uforgsd1011IJr1Cc1Cl flitfrac14lnJb is n 11li1JOJ ern1Cfrac141vnr 1101 frtr t0Stltthcrs LnIl uJso thx 0dminfstnncm snd ttmiddotach

ers fbe +orisilics of

Ttn ]Yt2rpoy nJ the rtresent rriaI in

impi1m10ntir1g riEtimu amJ 1nttTViNf1lfm

can cm1trihme tc uur emiddoti-deA1cc~h4frac12-CHi rnsirurtict1

StnJirL corniu-cr a rauGnmfzed clirrictl rnntb cJasst~gt to m1s111ate The

fH1d ~ore vvitflin thpoundlt Jne witifrn a cinss

( 1987 Prrxbhmrs ofrttprrsenitW)II

FrnntJS0 Ci fteeiTJftl1

et aL 27

tluu Jmd been validrtted with students with LD ~1JL~1u the restJJts wo11 ge111iliy oost1111e several caveats were med thzt should he atldreSBed in fiiture studies math the 1lf11rrir1v rerrrains an -campwutial neeltl111

smdents math better overail in 11Ytrhc-

wl1ich shouJd have a Sltr C-C-6sS in

OU1iC(Jl1W-$_

in

the

or

prtK(-S-tS

11c-ampk1n1 11chi V0men1

e-ciuc-atiouul -aiteimfTve-s in nr11ntmu the students t~dncatioual needs

Thr nutl1orn nn g-raxefu1 the s-mdenti as teH the teHchcrs adnsinistrriiom and othe1 seohno per-iJirr1d in the Miruni middot Dtldf Onmty Public Scho-ols for t11eir c1Jzrp1tatiu1J amJ support

Oedaraitlor- ef

Tw amlure(- l declared n-0

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