ED185794.Pdf

DOCOMENT PESUME

ED 165 794 EC 124 110.

_ AUVOR Goldstein, Kerbe,4: Gol4stein,..Marj6rie T. TITLE Peasonina Abil4+y of,Mildly Retarded Learner.s.What *esearch and Flueyience Say tb theTeacher of Exceptional Children. INSTITUTION Council fcr Exceptional Childre.n,'Reston, , Va. Information Services and Puglications., SPONS AGENCY National Inst. of,Education (DHEW), Washington, D.C. PUB DATE BO CONTRACT .400-76-01,19 MI6 NOTE 76p.

. AVAILABLE FROM.nhe Cotincil for Exceptional Children, Publication - Sales Anit, 1920. Associtition Dr., Reston, VA 22091 ($5.75) , . I

. EDRS PIIICE .. MF61/PC04 Plus Postage. DESCRIPTORS Cognitive ProcesFes: Elementary Secondary Education; Eideptional*Child Research: Guidelines: *Induction; 4 /nformatiqn Utilization: *Logical'Thinking; *Mild , Mental Retardation: Problem Sclving; *Teaching --- / Methods ,-- .

ABSTRACT The bogklet focuses an the use cf the lcgical inductive strate'gy .to teach troblem splving skills to mildlyretarded learners. An iptroducor 5eCti9n examines three research studieson Interventionsi,n the hrei of croblem solving withltheretarded learner,and conc1u4s, among other things, that mairstreaminghas. unders6ored the need for this poptlation to hatecompetent'problem soltacg.skills. The second secticn explortes 'strate/gies and tact4.cs, such' hs role strategies. Divery type inductivestrategies, especially the guided disc y strategY..in which the learner is provided some structure for the experience,are reviewed. Ihe tourth section, deseribes th logical inductive strategy, iith emphasison the three stages--mass, differentiation, and integratiob:and the fivp steps that comprise the stiAtegy--labeling, inferring, prédiCting/verifyinaj !and generalising. The firalsection discusses iethods of implementl_rulth6 stragegy andpresents two siiulated lessons and .Ch'art -Illustrating the inductiveproblem solving sequence. (Author/PHR)

tip 4

Reproductions supplted by fDRS are the best thatcan be made 'frcm he original. docuient. * *****************1****************************************************' U olliallyTMINTOONIALTN. IDUCATIONISWILFAUI NATIONALI NSTITUT!OP IQUCATION HIS DOCUMENTHAS SEEN UCED EXAMy AS RECEIVEDREPRO HE PERSON OR FROM TING IT POINTSORGANIZATION ORIGIN OT VIEW OROPINIONS KAOONING ATED 00 NOT NT DEPKIAL Ntql-SSARIL Y REPRE NATIONAL INSTITuTE UCA.TioN post TION OR ,^01 ICY AIYMTQr. OILDLY a&TARDGD 11PRKRO Nerbett Goldstein Matjoile T Goldstein

What Research and Experience Say to the Teacher of Exceptional Children

The CoUncil for Exceptional Children 4

144

N11%111111(1 Ail n11. P111"):) )0303V (101110: 'tttqs..m 1.010t.11A 07,. I

. . , . p0 v iiiouI tp 11H,i 110) J osimtliitu.n!,11:) potItht:uptutI putt pow!) 110.uppti:)

.1.11'11111 ) 03S.I.ltIO .10111111IN (Out.;9-01?

: 1 hI0I SUN% 110111?:111(11H1 1o.1.11U1'.1.1d LOVA N(111)1111 tuo,Ij fitp ptuttunN -Jo oinuistit 0101pruip...1 1 SI 'tpptaii pUlt .1.111.1AA 131%11110E0 '011 0:41L-00t, I '61 .1 tuovntapi Hupitti,t0putt trItts ot .topun 0.1.1tutt.htAttli (IlipiAttsttotItt paliumuntio titiomixa A100.11 atom itr.ttuttpu pttuutiliopt.ul putt Itrilltl.t.).11 JlHtu JOI.Iti -11:41(111(1 01.13SSItotto St!M 11.11111tOlOti .10.111:1t1110) lt10003V:1 I1 110.11)1It1) .101 tILIO IP A.1.1 II 111, pttv uttuututuJolop .10 y0101.8,4;40,1(1 '03u0k(1t1ng) ttowtltpitul 1.utf taut tont; 'sp.mputtis SIOIN 'JO 'MOO '.10A0M011 Op Wu -80301.1 Apithi ittas.tatlat ptrujw,.np rti3OA to :mum ulo Jittipopt p111110;) Juj -t1oax:4 .(1.1.11)1O1:) 1111 .1111118O1 JO 110101:1111).:1 illti JO I .1111111!!11111:1 I)(IP 'imoJI,IAA 0.101111.110.1(1 S

11.100,1(1 (11 .1111 11.111Oil 11:)1.1.1111V r 24,

Coiltents 4

.411.bout the Authors 6 1441

1 Introduction

2 SiriliVgil!S and Tactics

3 Discovery-Type Inductive Strategies a.

,t1 The Logical Inductive 'Strategy

5 IrUpIernen-Ung the I,ogicaI Inductive Strategy

'References

r..

iii ) ,

*/1 What Research and Experience Sayto the Teacher of Exteptional Children

Series Editor:{one B. jordan 11

Series Editorial Committee:Carolyn M. Callahan, Ilerhat T. flo Goldstein, Alice 11. llayden. Merle 11. Karnes, ThomasC. Emit!, josepli S. Renzulli .

Other published titles io.the Series:'

Managing Inappropriate Behaviors in the Classroom Thomas C. Lovin

Developing Creativity iefi the Gifted and Talented Cayo lyn M. Callahan

Early Childhood Merh? fi. Karnes drid Richard C. Lee

Social Environment of the Schools Mitynord C, Reynolds; Editor

Affective Ethination for Special Children and YOntli William C. Marse, AhlizzoLre, Cathleen Macdonald, and. Pat 'Halo Pasick

v./

. iv II

About the AuthOrs

I. Herbert Goldstein, Ed.D., is Professor of Special Education in the Department of Educational Psychology at New York University.Dr, Coldstein's major imemstsare ltinthe preparalion id professional education wrsonnel and in curriaklum for special educalkmstudents. Ilestiwied hiscareer in special eilucation as a leacher of educiible mentally retardot clfildren. He IN*a member of thi/Institute for Research on I:txceptional Children the University irf, Illinois: After chairing the Department of SpeciiilTducationat Yeshiva University, lie directed the Curriculum Researtand Development Center' in Mental R.etara'at ion, which moved to NwYork University in- 1977; Dr. ;oldstem's interest- in curriculum deve pment includesboth the contentof instruction and the relationship hiween teaching strategies and tuctics and learners' problem solving abi 'ties,

'Marjorie T. Goldstein, PhD., recently.comp'led herdegree in educational leiulership at Yeshiva University. Heraim interests' include the study of innovation and change. andsu eivisory practices in / special education: Dr. Goldstein has knight coptional students; servedilf; edttaional specialistat the Bureau bEducation. for the Handicapped, and was coordinator of field opert(tionsat theCur- riculum Research and Development Center. in Menta Retardationfor 10 years. Most recently, she wasthe sukrvisor ofspKial education for the East Ramapo Centrid School District inNew Y9rk. 'No

G ,

Preface

fr Mildly retarded limrners are notas Competent problem solvers a.s, their nonhancleapped peers. IPurther, themore complex orebstract the problen{,Ae greaterthe distinction t;eenv; to be. We need only-cm- ./ pare the results of intelligence tests, tests of school achievement, and the social historiet; of retarded. and nonhandicappedindividuals to draw these conclusions. . Research and experience with retayded children and adultscon- tributes a great deal to our understanding .of why suchmarked differences in problem -solving abiliiies-occur. We have learned that there are many reasons why retardedpersons kraAv less than thdr nophandicapped counterparts.. Somesay that they )(now less becouse some condition or set of conditions interferes with their -ability to remember what they have learned. 'I'hus, retarded individuals charac-

teristically bring less information.to bear on a problem.,As a -r6sirlt, they often fail partiallir or totally to match their nonhandicappedpeers in arriving at an acceptable solution to gip prOlem. I lappily, there is considerable research underway in identifying conditionw that itterfere with learning and remembering what has been learned. Some ret;earchas speculate that thi' conditionsare inter- nal to the individual: that the chemistry and central nervoussystem physiology oftherNiviilual have bearingon his-or her problem sOlv- ing ability. Others theorize that the conditionsare external to the in dividual; that the way in which teachers and others organize and present conter4 16 mildly .retarded learners influelices. their ability to retain inftirmMlon and, thns, to)selve problipts, Thereare signs that research along both of these lines is.prodeicttyv,. . 11. vii ).. U( P Ad -1.P11WP 'Fli'01 ;)/N 1! ippaads. sio'lPanp;) lam] ol ',xi pail...loamy). gum Jogiotpvi OM on liu!qa,poi Allyn' paddpa,!pupq siouiPol 01 ))%los SW01110,1(1 111101:11.1.10 plIP .Aiongaoip j, om suogsonb znIJO:), 01 .pmul

0.1P OM 1 Iti.1.1e1 `iimtlaPoi )1):1444 $.11n1.1P01 ipqm Amp "poou oi mowt u! Joplo oi qi!m....$105 .APp 01 Ail) i,stuoNo.u1 oloq,I, am oums oqm lumpy.) pun 0.101.0 s! p uo!p!pplitio..) tlimmimi iptim otli &mono] %?!pnis lpu! olpa pootirlihx1yopiP)01 .01 moul pup atil unipmpana ilitil poJatio,s! tu,nli ;lump :mull lomps .s,1Poif sail tio!lamovp $.0(goa4q gono oJou! sp,sno!Aqo papilla.] sluopnis :LIP pa./00/%u! oiipluu puirvinumpusupgu, . . 81!!!!!tu (Iwo aguopPap 11014:maispi . t 0111, Il1lo:105 1101001th :til ;1.1V OM *Imp Weinogo oi clioq pop.miol .-nis sluop unspoi ,;,Alluargua .)Jv am ',IurtiaPoi 51(1)111115 051:10.1d 1fF101).1011lIll SAPM 01 ssoao.ui gogigu.k0Ju! imp si ipluotunpunJ oi `.-igpvios (1,sum1Ojo.id st .3Adq.1, ou .3:moplAa oi isoliXus 1p91 8g!gospo,t, A11,101P. $! Alinaqogo`et poslui oams XinuosPoi Agluip up.s! poimb:w omipls o.lp pougsnl 'llt 1-it1111111titil! imp ..fiuluosp..).1 su p 'ssoao.u1 upa oq .itfitnpi OM OM) 1)S111 po!pon! (II Xupiu!til Imp so!lialp..us pup sa!rmi oi i'molduli 8muosPoi . Amu!!! UP!) ail 11011!1 . S1S18(110U101tildil--S,1011(10S011l1(1 pUP SIS18010gaiiti(1 U1 olp,11111:111.11)d sluopnis Jo mug supumq ubsPo.1 Jo moq oldood )1tIttlossp pup ssaaoid uogPuLloiut os Imp /coy upa Tulqslopun gulcixo pup p1)lop0 -anpoid tilot0I gom :mull sigotguoi!Auo mil, Apnis Jo 8milospoi sari till 1.110.1.1 ',comoo Jounig;Opid puP 'saoqu? lapq 01 pup puthioq sognaos am iip.a.lp .1Pq!Mpi qiIm mil a!ipiaos potilom JOJ a/01:mpg! 8mg0spoJ zmws sJoilaP,ii osn sity potoop u!. oqi osinoa Jo gown.gsu! put? alum; -igs Nump u.ipal M0l1 01 Otil) 11 till P U101(10.1d *unios .ssoao.ui .. so130.0H. Jo 'fimuosua.I aim's omi ;s:ms!.torwitup Ao9,1, am! ipa0101 puR :mmualsAs u! .gotil ...go!Ipz!up810 itgLI, s! ot ON u! ).138muosPoi sogiolp.lis luosoldod p luols!stma pup prupold op :wound /Coy z)/mq u imuulP3 oLd!ipaguipio.! :humps:co pm! /foto mono.; p iPguonbos .iap.ut Xml.nulou tuOJJ sup ipuo!puodo mop% JO .(11l101i1)0.1 OM 0)11?1 Ot11 -1SOd 11,K1I g! 11011 oqi soagaJomp .sovicmd ti!gosuoi 'sampqn WI) u Jonpui Jo mutt ifiltegawo Aoqi imp imp! 01 ssoao.ui uo!i4Lu.I0Ju! llv s8u!qi Hulaq IP111)o .10J 'olducipxo iumnup Jo go!imusoJg! lung-tau:lo(i 'sagquin -.lad ti Ol; 111.10.1 A1111!U0 plIP /149l1S.SIll111/1Alpl11 Silalli1J:4111) 411 1.3111UOSPOJ $P I? lligiatini Jo y sssompowo pup ssougloriuma JO J!oqi qapg.uldp 01 ukopload .81!)%los iv ouo ouguixo ihni osoqi mon onnq log pamgbau ri oppuloasIp Mioituis .11).1 ulimumi .8uvtios Jpitt orsiduump uostma qlinoiqi P tuolquld Jpochin umplum pm! Ailu.mhoJJ.Aoqi qapoJdde oqr mum; spupi Jo $movio.ut ut rfiqq.mum.1 igaJoinp 'tofum iv lnil .10410 -XO 0U10.11 OA? ;mull oqm ;mint poldopp P MiolOis os _Liam pompg.q$ AI j! $1 laop!ko 01 up ..10AJosqo ui .nuos '$osua oqi ssoamd 11 0$ mop uppip Jon:tamp) pgma ismur la!po.ui lnii ti,.10A10S11101(10Jd yam 'dais rcippiN 01 ) pop.wial $11mpp0pu! A111m$11 mod& aq umplo.ui sio/00$ JO oqi

tutu go!imulqnd 110.sosna0j OU0 1UP1,10dUJ,1 /010111.11ti 01 liallin wamoJd 8(0/00s svpi 0i Aiplug 11011,11110J :S.10U.11l01 P 11t30101 lvqpninq 18011331S , . . . . i f !!!A

,C)) 0

The 'logical inductive strategy, likeThiost other 'reasoningsystems, eVolve%after empirical testingin practical ettisngs. In this. case; the strategy was, refilled oyer, nwny. years -of uise in classes for mildly 'rebirded stmlents. andisa key component.of the Social Le-iirnipg (C,O(dstein, 4%9), which twas'field tCsted and evaluated for- matively in hundreds of special education classhanns throughout tfie II-lilted. States. Tlw mductiye strabNy'has also bec.!n tht! subject of resean:h, reported bere, in which certain key assumptions underlying the- strategy were tested.

We windd like to ex.prvss appreciation to Dr. I. Leon Smith andDr. 11. Sandra Creimberg for the researchon the logical inductive strategy. 1)r. Smith, in par.ticular. plovided the data am! data analyses used in this publiation. The Test- ,of Hierarchies of INductiveKnowledge (THINK) was dosigned Drs, Smith and (:rcenberg; the initial use of the test to ascertain the systematic iind logical,,ia trihutes trf the logical inductive strategy became the. instrumentation for Dr, (1.reenberg's doctoral dissertation.

1_/ 5..

Introdudion

, -The I 970's is commonly va!wedas the decade wheik the civil rights of handicapped cit'vens gained nationalprominence. The litigation.and legislation of the 1970sare often looked upon as the lt1I-of rights of the handicapped and are seenas having evolved from the civil rights movement of the1960's. liowevery the tadvocacymovement on behalf of handicapped individualsdiffers in important ways from other civil and human rightsmovements. For example, in the civil rights movementwas the notion that if attitudinal and economic barriers were removed, hithert4 discriminatedagainst people would be able to capitalize on socialand economic, opportunities. This asumption applies only toi limited. segment of thp handicapped populat am under a lialited set of conditions. Removing architectural barriers, for example,can broaden the social and physical world of physicallyhandicapped persons insofar as they avail themselves of ;teals& By contrast,access to the least restrictive entironment in the sch.00ls, commonlyaectipted asmem- bership in a regular class, doesnot necessarily hold a similar prdb- ability asuccess for educationally handicappedstudents. Access, by itself, does not guarantee successfulparticipation. The critical facto,r is the student'scompetence to become a functioning member of the regular class. gomestudents will be sufficiently competent tofitinto the class quickly, while others will needac- commbdations if theyare to be able to tapitalize on their competence. arge majority of eduCationally handicapped students,however, 'Will req Ore intksive intervention in order to function, productivelyin a. regar class. 0 Often, comfuetence in educationaketlings is equated with academic proficiency. However, successful adjustment lo'a regular class rarely hinges exclusively on academic competence, although this rmiy be the criterion that guides litany decisions made by teachers, administrittors, and supportiv(staff ( Mercer, 1973), TV social-psychological nature of the classroom nquirs students to demonstrate' açademic, social, and- fiersonal competencies. Inmost cases, success or failure in the

classroomdepends on how well academic competence can be used as,, it means to solve personal and social' Problems. The way handicapped studerits get along with nonhandicapped classmates often determines the quidity of their-adjustment to.a regulier class. There is .ii sizabl1 '. group of students who, while mindally literate, are remarkably competent in regular classes. 1,/Vhile this may appear to a coat radichun, it is not. Even though these students do not read al or near:grade level, they cot tinue to learn and to use iinportant con- ciii.s and facts..Succes:i these students is often based on their abirey to recognize the existence ofa problem, to identify its parts. iilil to reason through to a solution that is consistent with the expectatiglis . and values of their teacher and classmates. While the message of the civil and-human rights mowementswas, in effect, "Renuive tire obstacles and we can make it lin our oWn," handicapped individuals are, in large part, saying "Give us an education that is appropriate to our needs aim.1 more of us will demonstratecom- petence awn you would ever believe." In ihe final analysis. then, the value of the legislatim of the 1970's will be measured by the, extent to which hatidu'Apped students. are prepared to bmoine cOmpetent partici- pants' insociety; by the extentto which they are schooled for the .. skills they Will need as adults. Comprehensive individualized edwca- 46 hon plans and administrative decisions based ono complitnice with mai7.1ates are important. By themselvethey-cualsibute little to e rhimcing ti_ ie competence of hamlicappe41 learners. The chissroom

teacher, who . tpiu'lures tire content and methods of instruction, has the greatest rolbe in contributing to the success of handicapped learners as ot competent Problem solvers.-

AVOIMNGSTEREPtiTYPES

Some educators ma'Y consider it a contradicOon in.lerms to assochlte the ileVelopment of reasoning abilities with certain handicapPed Ou- dents such as the mtntally retArded, To them the perceivedpurpose of, special.education -is ..to improve students' academic skills to enable them to moy'e into regular classes. By concen L aling on correcting learners' disabilities rather than focusingcmthe'abilities, there is a ten- dency to deemphasize the 'development Of reasOning skills. In the education of hearing impaired students for example, great effort is

directed at ameliorating the disability through iri,tenNim instruction in . communication and literacy skills. Euless effort is spent developing the kmds of masoning abilities neuded_do maideuse or theseskills in day to day siMations. T1W position iispousednthis book is that the developinentof acadenin: skills and freasonirig abilities-are .not mutually oxclusivivnterpreinw. teachers. can pronuite academic': and related skills while at thesame time enhancing, students yeasoning

ALcording to Masland. Sarason, and Vdadwin(1958), educators engage in much stereotyped thinking about the abilities-of mildly retardeadiersons. One pervasive stereotype is thal mirdlyretarded individuals have particular difficulty 10mpiyhen4ingconcepts and abstractions. They claim, that this view of 'retarded learnms.reduce.s teachers' expectations about yhat such students.cacIlieve. Fukttler, thetsuggest ihat this reads leachers 10-relyon leetures,,,,nemorization, and drill as their teaching taclics. Inso doing, 'teiu:hers oftegn fai teach reasoning skills thus. do not offer the 'kinds of education the students require for successas adults in a soeiety,that rewards in,' illative and mdvpundence. 441 individuals who have achieved the deAree ofindependence necessary to soci:ei'.(I may be characterized by their abilities (a) to drawupon km.hyledge in some systematicway, an(l (1)) to apply that knowledge to, solving problems,-The hrs1presupposes that these individuals haVe been involved in learning experiences that will leadto the acquisition' of Mevant concepts and facts, The seCondpresupposes that Iliey.have the dbility to think througha problem, reach a conclusivn or dedsion evaluate the solution. mid adiost their behavioraccordingly,with little or no help from others.

STUDIS ON IMPROVING REASONING ABILITIES

Research oil problem serving and reasoning skills is increasing, bothin the number of studiOs conducted and in their diversity.One problem with 'Such studies is that researchers rarelyuse the same lermS to define ,their area); of inquiry. Some speak of.reasoning, others ofpro- ductive thinking. and stilt others use behavioral terms such as-problem solving. It is not surprising, therefore, that Wolman(1973) found this to he one of the most chaotic researchareas in piychology,. In education,' less.attent ion has been.giyeo to "reSearchon problem solving, but what

has been accomplished is enlightenin.gihe work of such . ,r) resenechers as Parnes. Toriandlikatul (Milford hii3,014*(euuell teachers and administrators-in elementary. and secondarjschools. In sPecial edtica- thin, researchers have borrowed frorn, or elaboratedon, research done . in the regular griule-s. Tisdall (1962)studied mildlyrvtarded children who participated in an experiment to congtare the effectiventiss of spocial and regular classes Woldsteim Moss & Jordan, 1965). Ile noted th'at teachOrsin the special clas,kes taught in,a structured, iminctive style whilethose in the regular classes used more ecliletic teaching methods, Drawingon Tor-

1A .4 UM. \ .. . 6 ' . ' i, 6 .-_..,...... 6 . 11;a:luiLi 'Isom. ii;isodo-jdifnpst.i. pup Alpitut pap.notaJ uaJpioti:t otin.) -.nod . , [111110111:0 110111A11:111.11100.11110114;111 W11171$1111(1114) -U0S11a\l,J0.111aU1d01LIALII) .(01 084111 8111/13 i.iii4onglOi.u! iiur 8.1.npo.0441 Si)111111111.19(1a0 VallaiMil :molts ,60)111o.1.101.1;.1111;: 8 mpg); ittittpi.0 i.140111 s,1Inpst,i, . t OnOtpdati.. lit4iqt14itiolunii . 110.1Pogii,i 5 N. , , )1.I4Kidll -; . ..uhtiltp;01 .asnoN ((Am) /in, plooi!jjop gonood(in sditisuottillo.1eti!unutoxo.th

tioonntoti : 001, titti:ntol 1 .spotoatV Inn'? Xuttioi;no.J* .soptlitin 'JO Alpitto Jai 4.nomo 1..,:infoppIr4 110111ti0) iviii,sirm uaipliV;Os01.0 pillok; illvai s:ni:noi loptom osnarrat 8111l11111l ii atii Notuosnirsi.. , Jo ;?Atmnpoad , sotnInly`iiiiPitiNI oils !mondani shdysoilt ot oA18 sittopnis tiom0:fl1od ot iittratootgratuti N10.411018 otu.sulorgood sitifstio! Ottipt.4!)norrolilo f' . p.hitino tutuj 8100160661) $1'.n.lat;(10 1101 .8119ts 91 80114)44p sidwum jd Votiottisting (0 J0I,Si)$111,Mall .1111I1(1111I LOV141 8ras!no.Ritra 'Nikki() illIANI 8:04:o41 atom imp, pit ay! ati init.] Vinootp 01: 'slIttsoi WUUUJOIN41 -Jfio !sow .14....1ot otpin. tit'poin.id .swAsol . sOotpuoi ;Ativtagti,xo tio sosgtop p;Nit r : ow AiltoraatiS polniop suosso! pun ()6)811.1110pm til CM, 01 tisi)idxi) e . . -lnuttitoo 8001101p lratt ;strati:no v !tuition sfilk1im.18 3 pouotimanu,t 4 * ut .10Ni sassiou) 81014)! Solnpatood, # nint,4,..,Ateitolipi p.41.00(14114 JatI tiottuottraf) Imp tallyput pop tei navy p1no3 011 034:nt! 041 pino4 olotp..annotitto XratiOsnoo s;iitoinito iv teti otp traopplp tit utitsnruoT jit 'Apulyoati ;up poipoolitpotixo (11)0.18 ,p011!02 .- Aputo:nittIWIs ut rung) jo otp pantstootu snail! jo antrmipmd :81.11/UNI Aft Tsit.Iplioil 6,11$ thoolattr) to flit looltum (1110;18 /claim! play oi may$ IntitSt.to . 0 . . ,nuntuJoi.rad ..sIallo! T6 omi 'soopois ?oral] ssoN -.6 11T to!"Iimaillos poinFiJ On (C,L6i..) ItiWntoi iciplout popontoo. n 0.1114? 'itmoolitp inti IMS 1111101111i1AUIT.), IL18 JO 81.11UOSUL1.1 um! sit parni:moii%Oragn .suosso! Ili .m11 Nu 'ApItts otp inivatul.tatixo ) if pp 0.1%1M 01 do.] pihittontmuit satitittin.otogranoodun traisitioi ot puto -un cepAteiso,ip tuolvad 01 .1.1111101U Illiatill SIULIUILIILI 111 tePtitttnids 'tuoitioad iton44.40 pup 'autos suloititiod ;mug atom tonmi atm. 'uotinios put? oi . Jim; oratil dold.A.10 *3001,040w U.! tuoitiomi WutAlos .sotiljnin atm, , tio.ippto....., poinooltum gum to jo s:ttiani Joj Jrayi 4. ,jakt. Amonn Suinotyp pita! ptitt- tut ti,l -untos 86:11::t1s'sinoW '8lo8sto.8utipti111lip,'Stit 8titpojjo soliu po:ntotootixo ounos-...011 ussolia tu suolitputm oti.r...600*.. . tin,p.014;looltio:t * It 4-11.4xo In InItem. littolos"tuoitiood sti!iipli sym TamiLlo IV alll VW) JO -.: , 111111 Itl();) 10.1 i),ILIAA L/1:J.::j40)11111.11111-.* 1111114411.10XL) 8d110.18 Km !mom Hutsti 11 laIAL1.1(1 ' AI isol jo naoppqn . paralsoratupP knolipiod 1.1toinjos- atuiiim(111 lit 6)4i wilidulpini our:of 0.16)AA Alitinufjopi Jotootins 111 ilall iiiiptin oi . e . .tanoltiood'anicts ui mil 'Apitts ititton, !Lwow Into:Nis e sdnopi 10 51pIttu. fnipalwa, . 'tioappti:;` inno.ssoN fosoH posh:raj 00 otp iutraidolonop jo $40,ourold ...-.811Ploo no-apport on. otp - otc, Initritutiodxo tittoaii inn, 8uouitoli tit .10.80-tuutt1d pawn inpoSittmot! unopptia lunp 48110,101 sAtom 01 ilAtati 11 4191403d IQ- P. oriknrio.1(1 'uoti:oti 1;3;1(1010AI .jo OM 11.11Y.) 10,1 (110).18 pu,11 alp 0190s ItoJouoll osoull ;np sinolo9onixa Woo. to poitratutiotixo dimaH.. Ida:1XL) -1111,11. A0111 IlaALLIthil on litItutttal tit liutdoltutop 41.110 Micid Hult 'SHIT; NV tu ...u0to Jinfito Awls ssoN pun foram punoj'6 into alp tlimputi3 tn ;nil Initionipadxa

. .:II ..1.1 ' .-,...... , ,-, 1 ( , .r

punnotis di1m8 urstoeli 81111111pp-I swls oq.;Jul juir inqi JO 0E11 10.111103 .(11101.114 I 4 if' suoymptioD .4 .4 alb am, oo,uri popi 0A0(111! O solinus 0,11111111%).1(10,1 4.10A1 ;mop litusil surnjuoNJ.um thuM pop.mo,i Jo sJon.ly?ol von'otii tuoicio.ni Elm atnos osaty 'Sownis pdtp sispqrlino uo Xnuormiis inn suown!Jolut tyonniou samptial pue sinoinqs alp .15.10o3 Jo 01100.ISSP131/i00ii.tilA.) lioWAtun1 1;otu,uni so ot Awl) itwAds .stiotsnpnol sotimis 1:mi OS Polutod nun suit noi 110119 .10J I/011111.18 .11011 A1:13P.1 SIOX 001111014P saatuualpa LI aJhunuJoiJad 11011221)i1J SillnplAjp(11. () iUI) JaiiIMU JO aatilap pl11) )011 1)11111 .1tilr) JO JO '8InnosuoJ soquus i)odioq 01 Au! oi l'soi *nil nu:, Jo ouou sttoll:nuisip noompri *i;Jou.woi Amu, pommy; pup 1aimpo.1 mu) UJorq pupil paddna!pooquou ualpp .uJoal 1011 Amu Sulu ti.il sv tpmn tiow dq tunholutiob JO sidaano;) puu in:nq elo noArfii :)!(1Ol Inn &ctn./cow uniot inq Amp 4110 .u,ivoi ./i1Julinos oto .sonmis 01a1100;) letp+A lupods nowinpo s.linrwol niolj 'Xiintiun pun wilum %duo& JO podritr'np subynis .)Jogi mu innueisqns somioloipp til o:muttiJopod oomil smogs ponNotis imp owns Jo oto. popauloa naapptp pOSINUllif .110111 SIIIIIOSINH SO1111191! Il $l)J !nap opqm Jump() -xo po:ni000d oluJ.4poui .10 11101 soon sou nuow imp oulos Tumph3 1011111!:1 Una' intim saatillN i,una Jonnsuu ii gum soic: Xwsn flIt Uir.ippqa -,10.1 MIMI .10j IMP ,tip0I00111 til!AA injosn topit alp ....sJount8 Jpauosom IJI till imp utepo3 111111 1101.1.10.1d .)/k03(11.11l.1)Ull? MO 11010110W JO 1.10111M11,1001 a,101.1.1 on!poijo Milos niLiputp ump o.ni /Nolo .s.unno IIl 8tiinJosqo moti UoVUtfa -1.1! ailuodaol 00,11 ()MAWS tili00,111.110141 .1,0,11110:10.10, r 8,1014MOI iIl I)I upodtod inidioq,uv:pitii JO.' (pea cntil.pplts) stiaaRld una o8 tug APM. ILWOOI 8w1niJXdo ogi inoulon)urni Jo o.wun.un .'ssup 1111 31.J4nows Ii unpnJwoa ;NI /flown ppni (union imp Awn hp..11I10.1 110.111411lp *iunual s1out:T.1min pUIT itild001.109 ..IdASMOI AMU hp oinno.ul imopoo o ifunputm- Paz!unitio polio opotu o) pool Wutoosmu 'stwis /Cantu Awpw pap.mial inuppqn 003 iLuntym Nirlivnioa poo loop IIHAN ion.J)stp) sow.) puo "saidpupd hm Jpool polunioJ nomup lii alp owns siinAN Jo fig mil mulls spogioni sn poddmninuutuou Iumplltp magi suoloundoJ gnu1 Inop'ioad %Jo/Nips 1pAN motioati oftitnaj no mil viv) .putni OM 0(11.13figlifi 01 MO AAOIA into Innpv4Inn 1o;m0Joinp ant ImilJodtw pun loll opooml liu!gionios ptilonds tunimmisilnpads Joi popiniaJ IJonattoi, /imp tun nano .111J :MOW until sett utwsn nocni joilwairdxn . ,

r,) (.1 v polpia.! ounitili!sul JIJI ll!uost5.).1, Amity! Jo satu Haip!!!1:). Si pull Alpulu papimai 1/035..tatimal tit.t0a1 uosnal Ill alp A.I0upi asnma JO 11100,ISS013, H)110/10 41 .hain soauapadxa aTh Annpuna 1.0) '50011 ./10)0J)uolow 1)110 )1,40A0fal 0) Mg) A0pAJana 'San!! III sjiji 'osifot; 1tP smpnis am! ovp!)}.0unai .101 'AlTrif.lottofumil -mummy) ,1511)S !IrW0,1d(11' di0tif 0,1,1N1 OIl 's:mmoti .S00111111111:)111 011!.10(11711 1011! amsumIxa 40 511115)1 jo rap!!:)mis xunipisI10:)

1 DNINOSV311 NI 3AILLINOO9 UM" NO.LOIN DNINIIV31

ai(I!:)!!!.u1 Jo 11111111s1)11! sa:maJain) salvidp 01 alotu !null Jthi -qaual .1!) ;in! 5101.110(y) 'saln.1 pm! .%)1(11)u1.101 UI atil 5,0961 ) .101010;),( put! I -Jai 1111m11 ) 1110:) p0.1151 din a:)111!I11.10J.Iod Jo poci(I!!;)!pumitunI put! pap.11!13.1 uoippti..) i! aiduus .1010t1I filitunal lta!I hIf alp p0impo1(1 'anal dip padolympumplau pau.!!!or.uo.ipptia 01 uuojiad 15h!j aptim 5.impuotu inn pappilal (100).qi 1011 imal5u1 .10 .I111!1 itl!l!!!nul.lal Npnis pun 011.001 .10u110),() 1)1111 JIll papivia.) ua.11)101:) anu101(:) .1!atn .51.10jja laijv a.101!! 'aa!im!,1(1 pap.1111,1,1 ua.ippif.) 110Imi .moths. st18!S jo 'itl!t1,1!!!)! Onothilv AJIII 1)o.unl).),1 aim!! I1P111 saum tr.n!!!) amim!.u1 oi o;m0 Ph avls stm 'patiapai ajt!.1 j0 110014 pa51'o.r.)111 imp J0 mil triii411-01 1h)01011!:)1101M111011 .(111011-{ IV17' 1110(lp 0111 .IIIVZti .01101 .(7,901).%.0,111:) opp,1.1!!!neL ssaamis itl!!1:)!!ai .1:0111!.! vivt100;) .1010111 sipls 01 Alopuopoill 1).)1).ula.! .siin pa.1111:0uls Ilan!) daili 1)111! paaalp! -03(1 01 50.1111),r) ouvuutuo:):)!! 010.10jj!!) 5:)!Is!.101;m1!!!1;) jo a.thi -s.tau.mai !!! 1,10I15 .1.)1).1() ;Nato 1-)1(10)(1 datv% 8!1!)1.101 paJoilatis s8u!lias pun iv H901 .!!!.1 *How x.plui!):, !will mil itmso a(1olanui) Shopul0:) put! 7{00441 Hltal II sym 0L1 immitiu 01 u.lolua lituuu!.11.1091as ;.).1111!):) ur 101!!!8!IA pu!! 1)101 pop.miaa swipe slool !mu 8u!p1am pm! Z4u!,),)1)105 .mm11(1101)0 pun `iii1101.101.10(1 alum.1111! Alquloss!! 'tolta!I u! tioqi pau.n!a! asmil $1100 i).10u1 Almois -dlimphnuituul 111111! .1301h1 0.I0AA (J11111,111A 111 :lthl pad 'timis.I.)(1 1)0430111 tilt 0111?.1 1)UP 41111111) 0111 ,4-01014.10ti 1.10M .11411110; ,1.1014 .fi1111,rhEl 1,10M S1111 0009 auOp 1111M AlaJOA01; V41,11310.1 -10

911h111)1/111) p10!) 111111 ) (zaji 1)01! ti.lilth10 OMR) IIMOIIH AIM) A10.10A0S 110p.11310.1 stilIt0A 1)111! pi! 11 1 si Tr) 11.1!!!)! 1!9!1(1)11 poi iimulassit $15111 iu.0)1/0!!1!)11 51501010p/ft-A 0A1111 A11111iNS0:1:)11ti 10019 It 1nt0.1(i atilloi JO .110S ,),It!;) 511115 pin! winos Apal0!Aa.u1 paaap!sima ')pustimitu) 01 iiia.ionas put! Aipun0.10.1(1 pop.1111a.1 .tams.laci laX0,1, 'Jag asaiii is $own pup samiapadx!) !pi HO imp tfuipuanD O -tr! - puip!"!1) saatIalaillp I)! an!witiO:) 1)110 10)(I141 sawn)) (Ina diati toalia0a) ajn):10.10; Wuruwal Naduapatha LII RAN,An 10111. wAi act, Isom 0) .11)el ftlIdipti vitiapflifi 'opluinxi) mop)! am Aim pull Imptol 10181119 11.!!!,)! aati .imputu1..a110II)14)1 otatuaaq atis 1,011r) .111(111101111).1 0110,11.110.1j /Op 01 ,11,11 1X411 011/I 01111800 0110111DM 1110IM 0A,;IM (100(1 '8(1)01) I 0AIII a/VI 1100(1 4041 111)11i ILI 1! 01 81011".11111 (11 10(1110) 011III1 /W1V. aM 11181101 0# pop 'Xl11 inroi 'o .0p.tir) ipop,hr.r.ms.App!oh p1(1 .1A1 JApi 10quiN ,1.10111 011115 0.10111 01,)111,0,.olo:mJ.J.Imi! I ,i,w1 po!JI 01 PHU p onrd.)111011109111 plow iicionil:1/4)55J.Jso I JApl 'JAN ';(iutl.hmi um 011E0 0.111111 111. 110011111.mi 111'111 .015 1)1110.) 10(IP1NII).1 i:011)11101 0(1 on% \.1 01,1.)11 11.1pdi IllS pod 10110110,211111's P1 looluo:) 51'111 ,1M 110(11.1:M0d In] ;,..s.10.i0101.1.011.).1..1011 5.1001,1N Ailpy,!!! .im5ltiatuo.1.05 Amu J(1 yyno p 100111101 io .051 otis SI ,1PAN 1.111Ing nini, P ,11101(1'atics 11 SI 1111,5.ind11ll ,)m 0111111.10pp 010 0.10.10(1.m111.10.5 nAA , 1(1.).) .1,110,1 to, 1, wi I in 0111 11ni5s111411) :111111.1!,01 tnipi.vt Jill ixol110..2 :111!tios1'ai s! 1011 sr, timou m,,tints.toNti) 51 Aim! -woos ditqm it SI A.1101105sdr) 035 Mali% 15:).11,0s0.i imp sipdp .1151.v .1050111 Xn!!!.!pal pup otoiluNo..) sp p.51Js (II .111,.14(1,. .511015.31, oprip.).1 0.1p .loapuJdopaalto JO, lap.; s! ipti4 1, 1op5.!0:) 'Lwow!, Jo :juitiospo.i op!! N!!!!!,IpJI,Jip. Jo .1050111 .spidonis ',)1(1t1IP\,) 1)100:1 wit Ilmol (15 ilqutossy -Atm sp \.)111111(y, sp P 01:).#61(1 J10.10 inotpIAA XoluiuJI moll 0 -s!p 1JAII,H1 .1115 olur)ossp 11:)111A1 isiiiiti 11,t '55.1141 Sotpplip 01 .11.01IM ,r7.IIIfo:0.1 11,01M p Al(011.)sspqns spiv% .81101m poi! .ImpoJtual mil -.15 slud,\J 1110.1.1 don 0.monl) ¶0 Spp 05 mil 5x,01 IIV .15d115 0.11! 0A111 smi.% 11111, dip 1-1111.1o(1101 si11,011,110 .(10110sPo.C111. 40/0 1,a11 111,) poi)11.)(1 .1010111 III '0:011!111.10.1.10(1 sV IIIIM sotpilis PU tooppLul Xiultios 's!ppi JS,051 5011)111,5 10 Joiono ,r1nq1Iio5.10(1 ..10111.111.1 tio;) oho] imp sipop!iopti! JoJJ!1! ow ),Leg-iop !imp dip poll Jo 0:w1!io.loJ.101 Jo tiopinit Amp J.IU imp sipop!mpoi Aip. .tilopm III sinjw(lu(h!:),;00111-, mo..i Jo 5,10!) -His sloop 0.1,m 111 I1'(1.1.)A Itiornio.id /c01011! o lii X10/t1os 1P1105.10(101.ao5 sP In solo1(l0.u1 ,ti,011 X!!!tuJoJiod 1op1.1.1..) HJAA ILIII1I aolow 'Sri!!! iv Jill J.IJ115 o.11! ',noo.II)Ct.!4.1J10O siunp!A!pti! !Him th! XLI!ptiulsino LII (11 JA1o,A xavittIoli sulamo.1(1 lug ()him 'J.It! Julus.ati 'Itt!!! AJ11.5.'111J10(11no:11i z!tort !IX!)!).!!ii J11l si)110,1, 11.10MSso.c) dprrup--nr,.;.1(1 .11,4111 otoolul sox!!! AIJIp.oriou pin! 110 'am!! op HP 553m: )POIPII (01 SoApSttylii ptiP .11,011 liultoilus i1 UI aqi OS.1009 JO , III1lP1l P

1991. glialliniV

I in10 pihni Aim! ortiosilo Mil 'Si11.1111:) '.10111110,61/101,) 1011 S.10q10 ti! -MI iloo os puli imp ;no ol !atil /0.4 Nuppolipiissirrins JO 1;11;111.100'w s! ti! oill Aim Imp toisui',Itp ,up potiturid pm! pompuJis lsili, s!sAilluu s! my isa!J up .,I H mii.smoipt Jol1:m.)5 ol mom' sutim lIaltj us aq 'alloy 111 -OS .0111.00h 000 (1)11i 11! II 'atoll SOatiiiiihas Jo S1110A0 0.111 pug' pimuuld u! u p lui!tioi 1 AIIII:0010pAsd pasug 'who; 1tij, oatiump uoomol !Map; pun atp pinount Jo itioplo;) () aq poJoisuui lu pm! doss am pimp!!! os J.til ti:1114,11.1a110.mtia JO ..lati.1001. 1:1t1IS 1n11 Vila 41111111; alit! 'allpX01J. 111 Jatiavol Amu aim!! Lump J! is.tu sninumso Jo ii s,plopuis sompipl ;mu u! 'J03.10 'slum J! alp !Homo!! ol aq !mum!f in Two (toss soAo.u1 oi aci o(n!! (rum! .toi u pialmils oi 'Aiptpsiy.r.uts ay Junouni tti Apia1ub .,14tiutt!

/ '"r 1)0)111)0.1 pot! it)ton M A111)198!Jo 'N1111119(1 SY? i1A1.1 11!11U011DOS I "Ul . . S(1)1S 1.1i1SP:1.1:1 01 11.1AOS '.10 1 1 1101 .S(101S 311SOlit10 S1 1 011.1 1.1011M P satopop) . sitt0pnis. amoi 110i)(1 '11011111111S0.1i)plin 04a 7f 4 spiumaN

09,1, SI-41:MS 'S.101:111 .1111 191 811111:1Por 'S111?1(1 0.11! Annia,ty:) is PO319:flu 19 091 itionitisqdtoorrn! Jo .4 Joloto ..sIst9 1091001m Aqty 0.11! pot1Ii0 'sp.o,m0.1 . . 'sa!attalitoltoo:) *s.10!Js!lys Aatli 0.113 purl Jo th 1.11)(1 81119:m9'091 .0s!JoiJokts) 091 IPLI 0.11) Jo at') pmov)03 , mpg] moll tpoto itiplitidun i!,`,-it9t1Poto .1 1 t pot ..10oina1 muos A1!11I'S.1A.11?11 0(1 IcflflJ poqs!ms lig 09) 0.1 s11 Jo .1!091 :spun!) op too paau Amp 0111 lummicit) ttowttoatium Jo .saatpo .109I0 si0u.o)01 Sow IOU anotto.t Xtoti 0.10001' Imp atp pooli 8otioal Amp 108 tiatim -autos 0110) ol lump smogs Jo) J!atil p)itomlift) .S1.10110 1111S S.101/10 APy1 P .1(1 .1010.1(1 .)8011A1.1(i ...MISS:1:111(n Juni ol 081)8uo ut apitunsnoid ../9!'n!) s30910 Apo) 09 possoidtto Aq ',moos pup' Jo plaoplut 'pipovt0.1 tumt; 1! §? '1.1.WtS 1! '11101:1 .10 1! 14111111i1Illi 1 30901 ) (6(Thi 1)119 um) Jo solitoili p0lut901 suos.tod /1.11?.1 LIP AP.1.11! JO soz!.tot 8t9p.to:):n) 0 9:)!qm pm) I/W.1010M ISOM 01 'ISM)! q1011 S(1.1)0.1.8 0,10N1 11,1AI8 .1111 allIPS .10101111 )1SP1 01 111.10,1,10(1 ill1( (11)038 slliVI pas!woJol 091 Isom Sotp poP.p0.1.10J0.of 091 ati oft! d swot .9a91 ispol pl)slu10.1d p;),IJOJO.101 .07!Jo1 asoqi oym 0.10m 'Al0111109)0J('1 )aspuoad 091 074.1(1 A. 1)033.9L1d Isom polaom 0.10u1 of119(11).1 twit) usotp paspoom1 070It1 panp)A Aatil ists)i oatim suompoo0 'posJon0a 091 IssJ saalaom Amp poatipol 011).1 JO liom aptim ttI 11.t1)ttiJOJ mop) dooi8 polyods oln .App).10p!stior) lopliothoontj, 1319 09 al u! pu!to s! imp auto') saatps,01 Ailui 100J motoi iptimt s! sag I JoJ Aotil sinapnis pun pinotis W0.103010 UL11111.101011 1PlIM Sp.IPM0:1 .1.1P s! Imp% 091 middy '!9!)!,10 pmpv9im! mapnis 0111111 spoon Isom Imp net t 09 alp Isom Inpamod 'pantvta.! IV tuoy. 10.ippy oltuu S!til OXPSSOU1 J11011 11111! aippnJog .9091 spiond m p3s:)141,1) UP Sato 0A!suoolx0 /Sol pm) 1cii1d 1)t)0I1u! 1.111M 0111 X0(1 OU1119 iwqm S1110tu.litoiduli Joloof i13111411.1op0d 0413 isJ 0.101tu alys!A onto u! splatuonomiut! 0/9)!Oloa 'irnontuoJJ0d t991 saop IOU moyt .0)91 .101091 pus Orono/Ma %99.11101 Oil optandas 's3slad30190 timst tipm sp ow) 010.1.0s!p las Jo sollttiells pule tr.mi Imaltati los.; 'pup /foto 0.1t) u0uo polupwapp wappu(Ltu, Huvtlos slitoXlins into tooth UP3 poo.otai oi0JJ s09)nis u! Joloto 11.9)01 Hu! ploy! s:)!psi pitii U103 09 o JL1l Jo poqd Hooppol. aft!ipIXO:) 'snois

Asymns .10 HD/II/BUS NO ONINOSV311

tumatiam puu 039;)!A0o1xt) itiolitim 091 tititmonoj siu!od inowt littiumniaa sotilwin Jo w Awn polutriim apqm oimplop pop Nitwit aioni falliNpf popoou ato twoahm U opio imps Aupbann Inuolgoid s!til Paoli Nog

9 1 I been dramaticallNi underscored by changesin schpol and ()m. munity situations brongh-t. On by litigation and legislation. Sui:cessful mainstreaming, for example, does got dependexclus,ively -on acaetrmlic skills andproficiencies. Mildly retarded students in[egu- lar classes 'need to participate ina lwoad range of activities requil'- mg Gollaboration and choperat(ion with their classluates.Their ability to do so succei:sfully often depemlsOn how well they can

enter into problem riving 'situations and classroomactivities that. require mor( than the ability I() read.and reckon.. .2 Wine it isomportant that these studomts learn academicskill, to the , best of their Addles, itis equally iniportant that they learn tactics to help(Them capitalize on their reasoning 'ability.Studies show that : wil4 retarded studentsare responsiye to instruction in tactics that imprvve.reasoning ability if instruction is coasistiint, onlerly.and mateked to individual students'learning styles. 3. Reasoning ability is not confined to cognitive activities.Motor learning tequires reasoning ability, and the procedures thatteachers use to pi ()mote nmior learning are often aupropriate inteachiong reaSOn- , Mg :kills. A inoug these.itrAask analysis. prescriptionof the amount , of li.arning at each step, constant assessment of studentprogress alll10.111810IIof the-stein; as needed, and appropriate reinfqrcetment . usi ig ,Ailndev er has value for the leather.. ., 4. Mildly retard(41 children. like all children, have acquired whatiwer .reaSoning ability they possess, What oftensets them apart froin n . other children ,are the,ir limitations andnot their inability to per- lo'rin.nuli, having.. acquired or learned whatever redsoning 'abilities they exhibit, they should be ableto improve them if they are taught how to employ the necessary strategies and tacticsto do so, 1, .

01.

. el

2 Sttategies andTactics

To some degree everyone thinks andeveryone reasons. Since reasoning is an acquired skill, it follows that,peoplecan be taught to improve their reasoning abilities. Research,hasshown that most vtarded students improve' their reasoning skillsiftheseskillsare taught in systematic and logical ways, and if the strategiNi and taticsused are consistentwith sound principlesoflearning. Since the terms "strategies" and "tactics" are prominent in theeduCational lexicon, it is important to distinguish between them. Strategies are formulas for reironing thatare generalizable across broad categories of problem solving behaviors.Without intending to oversimplify the extremely compleAnature of Aategies, the position taken in this monograph is that all problem solvingcan be subsumed under three types of strategies. rote inductive, anddeductive. Tactics, by contrast:are viewedas individual proceditres that are used to meet specific teaching objectives. The majorattribute common to strategms and tacticsisthat they :both contribute to problem .solving.The difference between them isseen in the scope of their application.' 4 SIRATEGIES

Rote Strategies

Using rote strategies, problemsare solved by way of remembered in- fo mat ion, This type of problem solvingappears to be almotit mechani- cal: Hawing learnod certain 'facts,we are able to apply them with4ut obvious thought. For example, thecommuter, asked the cost of travel. 1 9 11 - . .- .,t4 . .. by a stranger; quickly Inates, thecorrect amount. The history' student I0, names the thirteen original colmlies at his teacher'srequilst, ann the woodwovketv having inserted thescrew, twists the screwdriver in a clockwise directionin oilier to set it finally. . The keys to applying rotestrategies are (a)- III scopeor n'umber of facts.learned and their relevance to day to-Thiyproblem solving., (b) the quality of learnn g and retention of thefacts.: and (c) the'accuracy of the problem solvers perception ofthe problem, iond h ispr her ability to draw on relev4nt informaion.

Inductive Strategies

Inductive 1trategies makeuse of both facts and concepts. As reasoning procednyesinductive strategies proceed fromthe gpecific to the general. In practical terms, theprocess begins with thei acquisition of 'facts and concepls; proceedsto the assembly of facts and conceptsto arrive at.a generillizotion (ruleor princiPle), and terminates with the applicutiop of the generalizationto a broader set of problem:1!

To illustrate, let us assume thatwe havv to get from one end of Manhattan to the other, butwe are strangers visiting New York City for the first time. We couldpot be expected to know much about traffic or distance.or how these relate to travel time. Allwe start with' is the knowledge that we may choose eitherwalking, or taking a bus, sub- waY, or taxi. We also know tlintwe do not have an infinite amount of either time or.,pioney,so we put walking and tax's asickas options. Now we loin( at busesas an alternative; among others facts,we know that buses are surface vehicles. As such,they could gd'in olved in aft kinds of traffic slowdowns. Even if that didn'thappen, they must contvid with traffic liPhts and controls. Subways,by virtue of their site oftransport, are not prey to 4uch delays. We don't know if theCost of a subway and bus ride is thesame so we ask a passing NeW Yorker, Ile informsus that the fare. is thesame. We infer fkom the informationwe have col- !vete() that the subway isour best bet, and we decide to take it. When we. reach our destination, we verify 'withour friends that our choice was the better one since the bus, weare informed, would have taken considerably more tims. This illustration of indative thinkingfollow* a logicalsequence in which the individual collects theinformation needed to solve the problem, acts on a decision, and thenverifies that the deyision wagap- propriate. hif Chapter V.an inductive teaching strategy is appliedto this same problem- 'Me success or Whirl:, of indattivestrategies is determined by two intiVrelated conditions. First, theproblem apd its elements-=facts and concept---must he within the learner'srange of knowledge; they must he in the learner's tormwledge bank.The individual must be ableto recognize st problem, and must have thelanguase. and priorex- perhmcns that.conatituteproblem solving tools. Second,thcksteps in (-7 1244 ;nu ttiopptid 8tomos sso:toJt1 11000 oi oft podolonop us fivtp pinq podn imp!) u! e 111:e;i1 :datIonhAle:)!go! 'Tem poppy iv. ppimis .flp lu!tivof pupd S..1:403pai )1(-{pairkn0ul luvg inu, two Jo e tuointe.! uottNo.cSoad unl-ta1011; ptoitip oto saA!polgt) uldiyhut liu!Ajos otti, .royuldoldnop tuessal*ml im!l:elput sa!`eforils s! !Hayti Jaqie.! Until .Jnoup )Nt diP Spotonuptiol *Alumna! Mau sionj pun din 'si(Ioluo;) 'fipunitillo:t !iiuppy Juo 5lup(1.08polm0to1 050113, filmoti Jh.tlJI1$ soil pup sidaatiol sit oi dAIJJP IP matt,. Salm pun sv onit osporme -styli:mud 1o,a,001J0(10.1 sopm '501(1p11141 OM usp, .pa?0,1:I0J otp -am ipm Ap)IgiSsud ;y0?.)(4 0/qu's SUI0100.1d p dAlvelp s.0:11p31.5

anuanpaa 8at8ap.ns

aAliallp00 dmp SpuJinpo:nud dLII )I!!d)(1ti() Jo antionpur trmus Amp pooao.td utoJJ otit puotto8 dql 'ttp:tot1t; tt.tlutsfi ototonimp 'OtoteJn.; alp pm din o aqi Wapiuld SI 'poOlsJopue otp Jouattoi stmos tooJj oatopodaa'n sapu pun soptputgt )titt J(I) (o.nnu imp onlos alp purt.t.totpitin *Juopiold Soei 'oldwexo -nog 8t1I potuttoi otil sow.' pue Sp/to:mini! sav11)t!!.e1 811!fla8,;..10,1 81.101!? tipAet ut otp 'wow-tont dql ittopots un:t tudtp"fiptdy pnititoi otp Iwo uo .punOJXfield JO ln P tuotusstp tit Ioatps Jo le v. limn; Jogioun litutootu ArtoN 1JoA Sin ionnJI apittnnot tato act post) -p ote.osui tittp tutod 81u/tell pou.ntoi otp fittAntins ifpuJoutt8 n pun 'tIpirlIttJ Atsuoth(aut lonnal Ji ttnn punoj samositth ti! uns olt.olumi..1 pun polunNt t JoArtoi tovitIN totuts 01 mil tio!ssuti '1:nitsto onn tu I tftit b -Npi:!!!! pap .aa ipt ptAet 1;43 sn ;until Joisuj :nu .stui 'fil.inon anti:wimp litpitosnoa s! !.! iumu imIletu Jo!netiaq UPtil -10 y)1.0f; II Upa ifplo powidp Jaw? Up1.10;) SOI0J [Jell sophoutJd uthni fippitnuotp potuttoi limy-Apo uno ifogi og unfeup uodn Apspo ,tApts stutipputt UI intim sittocidy og Mfl is011ir :nptutoput Annot

9NISPOH3 0,NV DNIS11 311.1. SaI93.LVILLS atu, aa si)!Waviis iertiew poivia!A seinuiJoj Joj 81pAps suiamoJd UI lle :)!tuopeal 'my) u! puotuad Pun leuotuadJaiu! seam! se 'Ham Amu, Sew aq pose ssavettai Jo ay luoium imp stwoj aq s!seg Jo .waigoad 'tipAtt tillp Le 'pupil JO0 A31100Up UH SeaU0A930110 fie ULIDICI0Jd NJ0A10fi 0JP polcuwiap lig alp iuoixo tp!qm pi/oxide UI H ulomwd 1110101 pun wenaistis- 'Alb% ups 'Awl! nyi mem 01 am,qattinn Anal paddlii)!puey smapn u0sea4 le:001 pug aquwaistis !Mem !pm 'imutuolop u! )4u' lijed Anoti russoaaes Amp Om, tip 0.101(10.0 .SJOAIOS atu, pa:m.uf Wu! u018101:elp pOSSUJIS Anoti sa!Hapuis ()letup.' itieuosee.i. sr! u wavoad $u!Alos aoliwyaq inotium liu!Apaup 010.1 Jo saaveui s!to .1sa9oad 0,N JOHeill moti tiujipeal Haipa OJe pautjap .10 pimp:nap ", . . .0 X . . SI Ittikpini) Imp litng:)Pal ipso SI p m01010,001 liutnios ..00)!Aptjaq siatpeal , . . Isitul los sompalqo Joj .tquapnis litqui1s1 /fay" isntu ap!pap 01tirvt Amp . III.A1 .11Apoi ol 1.iota 'son! pol.! impvt spq.laillul "Pm asn 01 ' ...! Oalgo)q! 'Amp ()sr Anoti 1 dinitIOLIO1 1-iiiiiI.Ino1 sioti:wo.1. ping! opv.h)i) apnIs sit IPA ,....11!el 4,4 III ollia1:111 ' inn Ntliii.Witi '0:W0140(1)(0' 'AIII;l1!,I. S.1011)yi VA SSaSSI! 1,0.111011AI Jo Intl dill so:Air).11q() Adill ,Ittliti loS pAI!li 1100(1 'ILI)lia!5:1it OS011.1, .1,11! 11:)o,I NULL! sAdS I4r Stumm:fa!) ipto 1811111 q apPtti Aq '8.1aq:)pal lo aqi isPiq -Jo suots!:!, 8! 1.1olop asatf! litqtqt TAN/in 4tit61:)Pal Alialp.118 HIM aqtql.quo:! tow 0 itl!t!!!!!!!! p .tp111:)q3INI 'aitnanko si atm! 4- s.,Iatupol amoolqo !pin dip sillopnis ipm ii.ipoi isattlini.Jorm, .Appar) I? .INkil!:)!Nnil s000 ;no .1011:wol mem otp sinapnis alai!'" .ixdipusiiiiippili s..1 ()...44, avqpnido:mo:, mil old!:)tn.101 jo a:m101 aninA sp p A.mtqulq.)301 da4s 01 . liti!iLly.ii ..XlitA.1.11!:).. ,..ìit1!m0).1.10)(1.. am, pmm aztiOniclaation --IIIIII0 Soleil imill!,I;ipistIo;) Jo ItIlsii I! opLI 'AIIMI!,lis SI I! MOII 11(II:)111.1(1 01 )(1 ,;.1all.11811 si mil (ti JIB tquapnis flii J1 08 t !VON .,1,11!li 4...1.qpiat1oli b)101!..)tqat1 LH! dAII:Mptll `fling:Th.)1 AN;)ii!lis IpM ilttliES ASi)(1 I S Mil I ..1{ni:WO rqop)S OA! . 0! ottPti .11!)to 0190111 , II ;n11 smapiqs pttp010 aìipoutlotni aptil .1iqu1tu1ttio..) litlipup(1x.).ntlis .stIpatu lit!!Nalqa.) (10 Appall! patulral sain.t itql! --!:)upd 1! a.m. " - 'said pupal) ìititti:)Pol Is ASa!!!.1 pvt AlqpqR101 aq Isom .aittpajJa S.Mtpl!.),I, ,.III! poil,hr)00:) 0.10111.1k4fAn twill Aiditipi `flupannap -anaisn! -noli Ainti, dm! ()sr d.1111StMs oi VHS SI9S.101:)1!I ,Iti)Lji .SIll;)1109S -IIAIIOUI (1011.1 01 'IL1Poi jidS 'Itio:rnol pill! Mil '0111 Mil 1109S0111) SOSI.IP O M011 - .1m.'Wlio(i S)naJj1, ;)SZ)111 :S.10111!J oi SJOIMITA fr illIttl:Mol 8u1!),I03:iy NOW pill! .8.1.)1110 S1,)11:Woi Q.It, ANNO).1(1 ).1()llf.lta 1I11.10M0(1 WIMIII 0.1 .1 --MS .solop 30tArtiool tluto 'aZlit?o,p.riotli S!Iiii, `fillIMI 11ji .i1SIla 11 SI 10l1 AlMnitlil .1?111 Ip11.8.1011:Wal ,r)1101 .8111411.11S Siilllij 8l1p1.11l)1010(ill .1.1LIP )110(iP s.0,)10.111,11 atii a111a.1 slualqq8.0)1 tq ;nil asJno;) sp.s.)Alostilfitqu. Aq * Aervt Aaqi r .twirm.listI! 1 1%10)1 Adill oplim l $ 1ppild3 m0.111(1(11! u! flii Sio!Mniaq -, Iv:n(1AI Jo Irma NtIqpiNq -Altql!.lis u! aq).! litoturnal .10.1 'avittIPica my aatjapol sappop illtim s! 01 aq Ahruilli sual smapr1$8,,aq! letolt s! 01 aq 'ItatIJeal sam.r.)saJci 'afmolud Nil:H.10 a:)u.)1)1Ao jo litiqupal Pau sip! sluopnis uatim 'foto an laa.1.10);) ,to ..r)o.I.IontI! 8,q()H am! %way) .)tp aatjaval $! aqi Jor)n pup tquapiqs ).111 :ana.t '8,101 ivatii, $! .11101 AquinJoddo .101 is !qualm oi Jo 0$ luttli -u! !iitl(Ir.)!!Jild . -iiptiaptIada t -\-) . attqaapt pap :);q1:)111).)p tlo imp() .. Hattialla! 'Ho!tiaq!dis my Tutu' -aid L. ItIoaajiy las JO sa10,0 Joj tpoq .layaltal pun ltittapnIs 'Ltakk.) mil tIl:)..taganal os aHtle.i.nl saanapadxa imp tquapnot ISUOS !NI uta0oicl inotypvt port Jat1.)0Cal .011.)q intaIstq Jo tiquial tquainqs intim !I);)!)u oi aq "pou.ntal\ 1 a Joirmai sir.)!F) s!iii tio!imuJojil! Jo 1;;III1Oppild twAn 4.11 -ow 'quo!) LI! IA 'Xu!iiiii) 0 u!. Jap.u) 01 anios ay AnovioJd sivapnis WON -cIA $a!puni3od 11 MoU10.1d Matil IlMo NtIll1.11lai pUll 01 ailidpIpltd, in &MAO ci)ili Li! inii d tu)l(p. Hu!niot; '1i8alo.1(1 Amu Am, 'mitt apldpIpod ul ?tutiltiqpita ato ) Amin) Jo .1.4my suounlas prof ti! Hur7.quou0H sairu .1() said!au!al posuir tIo intim Amp amtti Tounh)1 ui -tato° lipium mil 01111101 sias my ?is a pull salona )111 sitiapnis Jatptu ., 81)f3U0d104 tiumj uttql titimai Lump An itt 01 01) isitopnis 'Lnr.) j! Amp 'tispm puodsb.1 Ito itaitiq 09 aqi 1)StIOdSaa JO ,Iptil Aatil.NaiiiMSHI11:1 'Anti Li! *aum tuna!

(.4 1'01 that responding yields dual rewards;One fin responding and par- ticipating, and another accordingto the apprOpriateness of the response. Even if sludents.respond incorrectly, theyreceive approba- tion for having Irked. Shy, .withdrawn, or avoiding, studentsare only inthe limelihrwhen tjiv teacher\feefs theyare ready. In the meantime, thOy are observing-I e inle'ractunis between the teacher andmore respon- sive,classmates and are in the midst (if li!arnijigsituations rather Aan heal); ilohned. as is, thecase in mos.t.te'acher ilirected transactams. Do(7s this, nwan that rote teachingis "biar'..and induct.i.ve and deduc Iivvteitehing are "good-? N/otal all. As noted earlier,. rote telicbing is most elltictive when the learning andretention lifacts are due objectives. Inductive-and deductive teachingare tnosteffective when learning. retention, tranSfer. and gwieralizationale the objectives. Wbat is good,- then, is selecting teachingstrategies that are consistent with the instructional- tibjectivesto be mastered and that, Will get .the job' done efficiently mid erfectWely. Of the three teaching strategiesdiscussed, the focus here will beon inductiyelteaching forthe folkwing reasons: (a) teachersare already well versed in rote teachingstrategies, arid (1)). studies on the reasoning abilities of Mildly retarded stialeatsindicate that these studeutsare at a "Tule and principle accumulating stage- for-most of their school years. Thns. experiences with inductive teaching and learningqre needed from schwl enteringage forward. -I lowever, before the discussion of inductiveteaching strategies pro- ceeds, thet tse of tacticsas teachnig and thinking tools will be discussed briefl; .1

TACTICS

Teachemand re!searchers have hadmore experience with tnaching and problem solving tactic,s than withstrategies; Recent publications 'reporting on st'udies of teaching:effectiveness(Peterson an(I Walberg, 1979) and on teaching styles ((;'age, 1978) dealmore with tacticii used in teaching than with any other aspect.of theNlucational prdeess. While the .literature describesa broad 'tango of tacticg including classroom management, psychosocial development,arid problem solving tactics, this discussion, will be limitedto ,problem solving laclics used 'n prior resparch because of theirdemonstrated influenceon ming, Only a publiclit ion devoted to the rich andproductive array of tactics available to teachers could beginto do justic'e to thiS topic. Earlier, strategies were disiinguished fromtactics by the statement that strategies are fornlulas for appii-oachingproblems whose results yield rules or principles thatmay then be applied -tp a whple classiof similar problems.It was also noted that strategiesare situation free and i:ontoUt free: theymay be used in every area of intittiry. The- t ics are wore situation ti'pecific. Thus,- the teachermust select the tactic 15 9 . y)!111,1 oci p0s0 811q)30.v3P 01 ;)11) oamtut J0 og) .spiapois sigullopt put! ;up tuol(loJd og do! .pattios slotpeo.l, tuu dO InJaitt:) sJon.tosolo) Jo alp tualgoud 811Alo8 ;s:)!ptg pa,so Ag .sittapnis so!pigs at" pmogs ptql otuos -nu; S10011 OAK' S(L1,)1(10.1d litilplIp111) 1)111 1111IA.MS010 OttIOS Atti(1s!!) papuul so!ppopt 01. Apssiqo pun avrJollama optikt s,tagio ;mg Janalf pl1.11!01 AVM ol 'oluolsgris 'optul Jo )1illot1oxa sliu91 pup /foto ;mg .10J intp oqi ItInm s! oviviap.suo:) q:).1pwi0,1 lioddns uo!pm IPI1I osagi s:1!i.oni two aq 'pou.ntol 01 autos 'oo,18a1) Isom papogoi .s.1011.1nol doll( :)!Snol s:)!1:)ni oat! 'pouvol J.Ja IUJj)I15 tun .ipna.) oii ulna! olotti xopit000 s:)ooni pun oqi suo,upuoo .101 ,00qI plIP 011!1111!.10 Juno .ssatioAtpaJja SOldllIPXA 0.1001.J0 XJ1d010:1 ti:111:11q 01)111MI lilllIt11.101S1111!.1q pUl? sttm postl A(1 sso)4 pun sSOM (CL61) 01 -old ,gout Htuttosna.! so!ppoin jo Alpptu papalgoa .uimplup sty 9,1ani s! oftwojja uogm dq a.,uumfolo, s! Jamus!!) mou snap! Jo mail sAnm ol Am) uct.tipm antis! Jo 'utolgoad A1att1o3nJed Limon p s!" Jnolo imp -WM 1P0011110,1 tii1111)111p0i ! 0.1( 0Afr,10110(11 '0111.1d0Jd0ittu! 'Jo Joj autos 'tiostta,t -apitysainto V Agnagjti) 8u!sit unigstueJ(i Nu! S311:)11 JOJ st LII sosuosuoo Ito p101(10.111 8I11.110ti litulpPO.1 go!tim JO alp Auttw g4aJJ snap! !pm aq .paidopn "Jogiatti HuunJoistuttati s! ou R1 rap! 3gotti :suotiunps Su!mouN. iloym uljoisuntJoi .s! 'wawa .S!tu, :)!Iatti pinom 100 do! Ikaltr)!!)11! Jog 'oldutexo anios sulalgoad.sts!Ja -JuthaJ 8u! alpopattitu! pun PaJ!!) 'trou:)1! U s! ItntiJodtu! 'Limp lou Att() 01 tiattol utoploJd Xu!Alos luouf 'Altpitumotil mg. og IUII aq own o agi -dn oinudo.td suo!optun Jog sp .asn (I 'Auttl)gagua.).tud XtutuJoisuutaq st utt Agepodso Ipi3tiltp Autupe JOJ autos popiew .thupptio autos sJagoattosoi poi uq stgi s! astittoaq' papalqw tp MUM! %UP AJon angna,u) 'Janamojj smeps!,!, 1) (Z96 Apols pomogs popattioJ sploptus patpiew alp tyouttuwijitad Jo Junp paddn:)!puntluou sJood u! anunon u!gi 01..Sup1 pJaaJs!!) sup OdAl J0 1101IIMIJOJUI LII JAU JO Sull.11P103 sadAloatals Jo papattiaJ suosJad 01 um, lsp Jo) SuituulsaJopun J!agi samptitt pUt! J0 SUpivtA01 -sioadxa A suog Jog Juno .ountuJOJJad Xtuttuotid s! Jogrup ittelJodw! atpul pup saingt.gum 01 walq0Jd Stuttios !iv Suunntid saJ!nbaJ innpvtipu! 01 mini agi 'Oulu aiojag 'ftu!sly Itutli y800.1111 P 'wolgo)Jd 8uppil 01111 IU11099P Intim -dntoglittu uod /WA.) 'dais putt 01 in(!:)!Iutt agi sautoolno Jo luoJamp SI)N JO -311 .suo!I Stuttunid Amu aq patidde 811101(103d anng Jagiut otjpads pialtiall 1111%13 utt Amin jo alquidtme .sattlintuage sa1duwx3 jo JatuJOJ apopu! Suutunid ,10.1 u our.4 Jo mog oi asuu spunj JOJ ) WM( said jo agi apniout JOJ U 11(mo3Uit 'JO .)Joul 'Agno!intueJp Jog jcluatua,giaJ ag JoApinnh tumid Su! -aiJoa.uau() spuods ij i ic1 gum alp Apinntr jo alp linsai &gum)] 'moil "'film pun uatim unid spool, 01 KJ pOMOIA AptumgaJd dais 01 uo!lott j! 01 0(1 0,1011I Ulit utt -JaNa.inniaaliapul 'asp alua!Jadvil smogs pup Aidugs Rugmo 'nowt ilutuunid gtm 'nog! putg 01 Jana(' tuamoJd 'fituttios awisa siuuuuld fun &mum

91 - those who die rntestat& the-InternalReyenue >ervice offieb has its., share of tax specialists. anxiously milling around its officesos April . 15, and lafge numbers of intelligent peoplemay 1.ie fO-und in line at the vehicle Apection staticalon expiratimi day. . . the key.. t/oi .using planningtactics I,A.cith. tonicityhahdicapped yoringsters is to t ych them toTake1he timeio thtnk through a probleny-d- IIIdll orderly way before.they act. I lowever, if lessons.onplanning are to be effective the.Y.muSt prociideopportunities for st944ents to acton tbeir plans.to evaluate their effectiveness. and 'todiscuss what changes. if any. might iMpr.ove thein7Carefuland realistic planning by the teacher is needed to itmomplishthis type 91 activity. Teachers also need to develop Viohlem situations . that gradually in- crease the demands made on students This. too; requires careful and realistic planning. Equally important,tache,rs need to devotea regular portion of classroom time to teaching4uniusin A. problem solving tactics. Rouse (1965). for example, used dailylessons of 30 minutes 'each and the Rosscs prescribedinstruction fur four 15 minote lessons each week:The fact that both studies showedthat retarded students gained significantly in a period of pnly6 weeks should emphasize the impor- tance of building problem solviug activities,into the normal routine of the class. From this brief discassion, it,should beclear that problem `,..i'olving tactics that are useful for mildly handicappedlearners are neither ex- otic nor special, theyare everyday commonsense procedures. For tho retarded student. however, it.isnecessary to teach the tactics directly and intensively. Further, the tacticsmust be applied to the ty.pes of problems that have meaning andimportance to.the students. o'

17 t- -

Discoverg-TypeInOuctive Strategies

1. ts

The review (If researchon problem solving strategies in th`b floodbooic ofGerierol Psychology (Wo)man, 1973) hoges.from strategies thatare Peculiar to an individual to highly organited, logical systenisthat 'can Jpe used by anyime wholearitshow to apply theni,

INDIVWUAL STRATEGIES.

While.indiYidually'devised,strategiesare provocative and interesting, they generallywork bestfor the individual Whoconceives then', Some ,are so esoteric tharthey defy'explanation.Others are so complex that they are costly 1n4-both time and effort. Sometimes the'yaro so in- geniotr that only the originatOran fathom the convolutedretiSoning that results in problem solving.'- -Thee:are, however,important drawbacks in relyingon most mildly retahled learneis' devisingtheir ownlvoblemsolving strategies, For one thing, the teAcher is placed in.fhertie oqeactotsince the student must show some. evidence of apcoblem solving style. beforethe teacher catiebegill te act. For another;the teacher needstobe apl e. to discern the stylemid ascertain whetheror'.not the student is using it a systematic in or,rabdenn manner. Multiplythe demands madeon the teacher bythe number of studentsin the class andyou cangeethat this iippreach le teaching problem solving is both timeconsuming and in. - efficient. Nenethehms, iridivid trallydevisedStrategies may be valued forwhat they reveal about.the student with uses them. Theyare signals to the thiacher that, in somi%way, thumb modeling,trial nd error,,or airected instructionAtOt stulient has workedout a system tbcapewith

.prablems, . , .9c

, * l'; V__ I

;IVII3N19 S3193,INILLS 4 , . t .. s.li*Jau0,1., p001.1 lot1 uum sumpol8i0J of oJeJ181101110p t? tio,u1 tu; liwitio8 is opi 0JoJaq Aotn '13P 1$3.IP0SOM smogs pup 8utuose0.1 s! m igurnb:m 'n!ls 'SA4611011.1. 11041 ,111111 .8,10tpuoi um Uri atil ntiPtitut 01 dolottop . .triTrinau*....1 Stortios.0,10100.u1 uti,sim vow 0111, mum; Atm pup.. A0111 dolottop 811!11 fri 0111 0).4 '$,m 11 8! itm,lodat! Joi 0(11 latjauol 01 ISO INVIP P 0IPU1I13. rnin womssur) ley soluarilq .81uopols 81iumai - 10111 li1lpitil1'11(1 1110J0SP0.I 'tillIlli (it OA0N3Il 'titql 01$) J011aIl0I 8yoau oi 0101104as wolq0.1d .81,11.1108' soottolou no. t? JuinH0.1 Pull 0Ill1?p!po.id- u! atil '$!fll(1 0) 1114IMP)S0 I1lI1)11111 180.11 put? (180.1 rf. TagoJs8up von. 01 .17quodu;) tto mil S1%0.10)111 IMP' 0300I,10(1X0 JO 'S)1I0p1118 U. 10011(101 .101 1110p$0,1d XIIIAIOS IltAlp11 fi. AMU MI LIMU..11) 1110,1J aqi Aiwa! '810eJ 00 '$ido. '80111,1 put? &mud mg ,IP inn suotIppupJ JOJ . punos 11010sJod pin putoSJod.kilut t? Inm0.l $o Nam 811 wo,li ,a!tuilmtw ..itlogim Au 810811. luolu00 ply sett 011hutt010,1 Jo) 0111 8itiopro8 III .110111 A1!111) ti0/111 8.1Ifitiill,10(1(10 ilL.IP S,APM1P 011111V/111 ,I0J way oi ao!r1l,u1 Somosuai slms ;put Aotp OAPL1 uomi p;n1Juai 011,1, 0311ITIOdUll Jo .8111811 SOplAil3p )Plf) 0:IP )1(P/101.1.I 0) 011I gp0011 p1IIVSISO.I0p11 *Imo! :atuntia sllistml Jo hipput paddr!:)tpinq sJotuvai loutwa 'popuuttswaptprog 11 .si 'sdnIpod dun ago() isoliuoJts. sJoulioloto Jou 84uJu11 Our Joi -uptia,t 80! Ititim spu mot! 'pattJual O 'Aisttolitoid ow itietuaisiis s0!ki0iu.0s 110J 811!008e0,1 0.10M :pOsial3S11) onillopto put! ziAti:mpop .so!801e.lis 11 SPAA um pup tie .0n!popu! palutod . . Mia1U.os s! Isom qm,i1AJ110.1.10 u. 0m q Om? (11) tl umitioJd pun (q) M3,3.01111? JO 11M0111 ti)3PJ 11111) 01u10.1 1 moos Aum oi ;NI uotinio8 J0 otu 'tualgo.ui poi (a) 1:1tq aipoinnot0i Jo 011 0ld!atu.u1 Jo 010,1 into 80yopun atil adAi in tuiliquA 11)!M 113IIIM 0 0,111. -v9)90.1.'1100 a/01001)0a liu!UOSINLI rig 911,0110a 1 sum iroup:)80p su n101(1(41(1 letpluvtios 1piltd01) WOJJ li umotni oidtaupd .10 4)10.1 imp 8(11011 so (t?) oi oi(ituasst? mil siauJ ointtputoi 1) ( 01 '07!sotoodit1i J.! 'AJUSSOaoU 100u11 Stuss!tu '$1311.1 )1T. (3) 01 0/11.1.1P IP ll los in 1191 l'iu!moHOA osaqi 'sown! Om 0,111 u! t? 1Ioil!s(H1 01 AJ!Joit sogiotim Jo .lott om &sop aqi 0111,00.0dt? ovi!aupd Jo 010.1 0) )311 110(111

OH, 1110p10.0 JO 1 8utione. 100.1.1 ouo Pula Jo tumuquitlisi 01 atp jullio 81 uu) ovitutixo Jo 80 89 IIP 0A93111)111 "AtIoR118 OM 0,10M 01(1li 01 011111(UJII0 1)011 pOl) 08nua0ti mouvam anti Om :Liam OWRJOJ pun P111111PM.. possoad .Aouotu Sumnd Jogia$ intim ;IA pinm oonpu! inoqu NI suuloutirlfi pun puo4oJJ!!) ti! 011 i3)OAJ JO 130dfill1:003Ippld 0101(11491AP 'sn pun atli suotitpuo:t J9 Juijnood'iptomi 01 liana Om poppop Imp !my-Is:alp A Joilaq 01 Om u? nom *pi mi. 0111 'cum lonuJi 03110 ptimaJu ano uo!immoop am potipatt Imil ano uo!tuaiip sum alp alendouidu 'auo in s(111 'Aum am J00 put? pouJuol u 1 lano. u! pimps:- Ja11igo.10 aldfou!Jd HtuuJOAO8., soup 0.01 11p0p 0.1;upw JIIIIILI11; ti0A91111331111 ilpillp11/01. 8111811 I! `1ami ItIaluJis oM pomoys any mil oldtatuJd pauJuat u! Jno utinuqueiN spawn sum Ind oi oso om.00qm ImauJ u Juutius tualgoJd u! ups 4 '0a8puo4 4 attlrwitan Wimuost?0,1 's! oJotu limo tiegi, 'ipu t1 Jalauit? pun WOW. 011111J 'AS41111,118 ',IaA0M011 I! tpia au pami Ala/mount) Apo JI mil tualgo,u1 .. .10A1Oti fill 0111 AJUSH09011 soopipmi P. 60pu 1)0,1011i u! s!ti Jo 4011 i>.: 081)01m0111 Itin( tin 0111(41.101: tillintstt pi1on:H:81m Linn% 0q1 intti-inin now:nth:In Jo ;Jana:loth,: !Win '110141 0.mpopt11 'Ii1.11:1i;) 8011-011t,118 il.lit WOW 0.In !Ii.Inntottiala mu alp 18.134 08118 II! los an 8111(1010A0p ,sittapills sawycin oi 8111aloo.u1 a ,u1018As : am,:mpul .siii;An satli.nn.118 ai0no.1(1 -Ills :quip tioni 'itunti:31,01 atiaLlocha :; 1110.34 tialtpvt oin $oin.1 V. 1 pUJI11114,1 304 ..Sal(iplipti .wia.14,0 0Atianpop 1-0111101W4i oli iiillii than ' 4).11 :nu, st ion ol ?ins intil ,3\11:n1pop t 811111osn.0 1811111 aq porillop plun ,S0111,1 11111'. Alli!ili' .S.)1dIAtiT.Ici ..).11,14 ilaaq p1(4p011.1,01 !Inn II Ipm pun Appnio.1(1 011t1 ottol Wunto s!,:a1:01.10(k.: In otp onuanptil 0pOtt: 030.40(4 0Atianpap -t11osIt0.1 *it sottormq I, 8it:op:118 8.11Pon.:(1 timppi.:(1 'ef1:1..1108 is 014,1. Jo 'AI-I011:.: aaptImul.:i tioll tianfetotiou: wm 00:31110a1ura uo ,antranput tu0.1.1 Atli $.0,),p.il8 ill(H),INNu(.) Itoodm.11. Jo) Hti!tplii), imp -00.111.1. :implIptil 1pm mi .811!II.11101 s.)1holv.iii; logy:my tipm sna0-.4 no 0Ati:mptn i! awainis 111.1ploSt1 litil'Alos Miinn,lis intil smog oso .mplah3m1 asopold .10,4 torm Sipptil s101,1,tual illti0-i lathipatpunti iltolili,lild lin,WilsO.I illli Sp 8$1o111,:l1phini IIIJ IitIN:Wil) IMP `AltIll,Wili $1.101.1:WHLIC.11 lit MO 111003SSIV 0 !pm aq, possil..1814) 0.10t4.1. am, 10 003 In3.)11.0I Jo sottiain.lis anti:mini! itotiattiti pun -tuna$ :811! flo .A.1.)NE)s,(1.. (co poinn!) *If.mnoasto pun (a) 1: Inatlicri tililin.08 optiAtt 0.1041 .1.11, onnanpul 81:0301111111 8u0tit031m .40 asotn inn inn11m3.00.1141. :in 'siOinit318 puipap 811ianiii8 30.1 8tItyan01 pun lit1tt1.1I?01 itioN -tiioll I .A1(1 mil 0:4 8011100%118 .iP1II pownStnIstp kti :40403...n41 pop3olan I " .1.)14:woi imp °I '111.4)111s situ. 301(letr) sosse;Ny put? odAvklimontill) NZ)Iiit!,118 0141 0,..fil .foltIpto Ithrgi":) sole.1 no mil Iv:witty, im!oliptil . otim polvimil.liq _pup ,Axolt"Iti pornio.id atIAI-A3at0oa8tp anwmput sa1801n.:18 pip 08 tom poddir.npuntinon puu ninjo toipptia ut . pinut dito0.1oIN otp poutli '3 speinturt 1110.1.4 tiattlm 080t4) 80!Sont.118 ..1.1anet 030111 oar until paSaatna i 'ion sanumatosto pun 0141 .soattoms stioti op 080341 -0A3asqo lou papa,: iclaminnat: no ixt/iviidamnsq) :S100)1Lli8 .111100411! Ainli moliS, Oil .mnii ,),\M4 sotHoilM.v, 1124K4 pawn!! II! 3tat4l AI011 )It14mil1110.8 -1:0!4(icht

AW3AMSIO. A93.LVHIS

atm; 1.10,10.381(4 tiSanuis st .t: atkplosoptid plit! ;)18010lpift;(1 i9IN1.1 001 01 innowpn.11 S11114:m01 spotninn 01409.4. otim ottit.4 in A30Aoasto :tits i! sa: n Altm pH s.1014:m01 in don; iit itIt.1ii..h)4 .1y011) 'HIlln1)1111; 11 :4! piiMatA WI If AA sp (pi 0n0,1,01? I! .10110(4 tlitanniaq,0auning ;nu soloa iti 83014:mai sluop pun ,rlis S ttua011iop 81,111 mil 11Ltion:m.1n11! th..ssa:mad 0141 14AA 'numoisula 111,0.1034. NI liPimitia!)!An inn no'Inout00.0in piliyA Jo alp Ali)Aoatila 111li)111? olii 111141 I! SI. 1171111alll pOj 0/%1011111! III mu '0311 i 03034 st an)t! maul mow? --imatin rilosro3(1 intim I! s! pni: moti 0 s! ol II! p0096.1(1 -notnatn* Alltyntiolo' 0141 Inoo3ssula untuintis inn: JitimaN (9960 pOiLli)filla tilt tin.1.111 .40 s.15)du(1 my 01 IswItuolit: ii,paods 1 014 sinau,010 . . inn potpaut - 8104304nm

litInol. sul.tiq irrohl ttilaq patat 111 inn Owing) 01 antjiip 1.10A0ast(1 atiloS 4430i11111! ,Ini!il 110.1.iiijol 01 NILO pOliiimil AISINWILA Hit AilAnait -WIN)! 'XIII i1034 Itntlinutiatixo ao 'tialtinutpal 0411.1-01(1tuat)(0 H000111.11s aw.104/1

7, 1 ilon-1:1S01) 1111 pm!' ) poin.lo(piin alp 11133110',1 811110110,1 -3111)111, .101;011/i) I :A10/10091( '0/14:111110110IIOS .0.111130.11S Att31111111 110110 0III0111 111 0111 01111P.h1111 SP11 1/111 pIIP '0,111:flIp5UPII 0111, 1.111!Ill u 10) ()intim p0Z1SP11(11111 P 1.11 poll innonnsui 0i U slum nip siunimei Sion(T)An imply»; Inapi0.1.41. dip lotr.mol HMO 8111011 10N031P)01111)10i AC1 e P V )10sPV) (911(j1 1107.1.1010V.IP111 0111 SS000.111 !;1. -'011.11S1111./i10/%11110.1 ill otp pawl ontionhos 'pun Alannel().1 -painillinn A(1 u(niurs(dien innlinui rpm inuit)(1 $)L1I in e inu)i) (11 o50dini um() I.II$aII.l$s input, (iitiileop 01151 .S01111 J0 11101(10.1(1 .I0A0m011 5III0111115.SM0111! 1111'1110111 "S(1111f0110001 .1011101111 Ipt41 AMU pP01 01 !Wall SIM.) .10 1UIpINIIN011 111(1 01 111.11 pUP .10.110 /C.10.100S1(I 1101110111 SUM() 1111 .10011 111011110.%110:) LI X11111.1P01 'pliP SP 1).1.1p1111.101 1111M 0.1011I signila(Lt paSnun111 ..s.i.)11:)ii.)1 HPIJ .Kunn pnilialtuf .10J ..10.I.10 - IP111 Anus H.101IY.)111).) pinf u0noil J0 U liuttileal 1)01110111 .101 S1011.1Piii 01 '80)1I1IS1U1 AIIP.10111 401)1.10.1d Sa1101111.10dd0 .110.1.in si SS010111.10A0N 11 I? OP] opl Imp ',In.') pun ))LI.)t.l)(1X) LII nip Aintni).10 Jp 'swan() (vim 1N1 .1AI.IIS 01 07,1101111111 411 1.10/V0;1;0118 lit 3110 APp l API) U101110.1(1 81.1t/110S 01 11110M i)(1 ;91?1; 0) APS 1p111 HP in() Xhivn.lis HPIJ 1(0 onni)0.1(1 ApnapiiiiOn 1011 .siciip.5s.)1.10.1.1a 11110(1 ((intim» sar01) Apinssa:inti 1011 ,-ins .10 i 5t1(rn.:vinulini.1 tion1 isoiN JO in) Aim 0/0/1 .111) 10 S.101 111(1 110.10 lama) unnii intim loll 01 01) in ()Jinni -tuns intles -shun diti, 'onion 1011 Os ifintil pup sm0i1ii .10J 0111 01 0)1PUI H.10140 SP 11 SI 0111 H.13U.II101 ii111U111 01 1.10(1 11.1011n1S r, 111 0111111; 1)UP OJ ISIS.10(1 -ni0pho) 0(10.) 1111M 01--S011P1S1111 »1411 10.113 11/111 1110,1A ofnioa(1s.h)(1 ()imp ()in Otini SOI1VS( 01 311 -1100 '1)0101)1S 'IS.11..1 0.1011i 0111r111.0111 JO 'ill1.111 111M 0111 /WPM NiltIt/111011 111111 1)0.111 01 aq 8(n.utp (no 100itns (cup pun 41 q8110.1 loinps 11hI Inn) i)(1 pniwinp 01)11n40i111 ulna alp *.in)ic m(111 tinniu anti:mai 'intaann S111110111 .10J III! MI4.10(11111 11.10A091M) Mil it SI tiatim onui Hun n pug 01 RU113/%0:flit() III 1011.10 01 0A011I 110 (ii Jails() palqns nip Jo dill s,intumni Imo sih)ou ()suns JO itynuipiiidui0onn pun '(pns(r.) nip si (Win atp polio painiadxn in pont) i0J kiatio:mnp S111101SUILII C1111PA nll 4j1atil! suo!isonh onnti icaoAoailp ;)*Ivi, . .. tiinp) tpinms) 01 nine.' snino) 110(pi 1 inn Hiputu JO nip -nitiiiitin , paini 0.11111PU JO nip Aion0niqj 'Minium;

e U=119 AIMODSIO A93.1.V.WLS

11,101191191, 610)1

intim unto .101)11;11,11ns Hu Jo atil Hitpitgl pruownilsol 141111118 'Mt ;)Atilttl HUM poso(loi(1 tI t1i0J.(op 2aNnaiJo. Immo:min ?Witt!) puo

) , . umwil ) (1961 pillIod Imo poi)!II) A.loAlr)sql sownoid splapnis alp 01 pun 30.1 Anuninclolo aninadds lianas inniwid,I Sian] 'sido9uoy.puit SIP toim .:c.tonaisin Joftommi ;911 o30111 Ifsipintillip 1).111,11001p ,1.13)1;osoto()(1 111n(1.011 anewull pup ;up a8un,I Jo -Ins, mop SI AN,Inns 11010,Joitixo 0,11 .paanpaa 5I191 ithww.) if.laAoasKI slo4411) (a:),o(i A.1,1 In Imp alp .1aI1mal onn ,S1110111118 -Xl 11,111M P 0111 111.A1 S00111301(1 011;111 111;1111 01 11101AP P 11m1(1.Eum) 41)111's-op-11m 111101 .0olp wain, tun 01 liutpunis.lopunsnuo, -nromin010;011 non jo ,;lan.1 pop, 111AS slualmis pull Amp am, 81nA0111 LII un annanpogiun II0ti.h),111) .tounam ) ((jail passnasip luo.lajpp 'Arto!A JO 1)01101j 51'M SILj .i.1.I.10:151(1 LIu!$LIel$LIo: IMO 111 1100111!) km/to:win dinfonol luima II! aulos 1)001!."5"01 lopio osi,oxiiit oto 1P111 S11101101S X11191410.1(1 HIM 0A;1111:11! .IIIII:)11.1V(1 (1,0)01 ,1.111hn(10 ,kAA toitit 111(13 ..11IXP!) 1111P 11M0.1t1 1111V 100.1.1 .1011110/1A 11141 11,111111:) A301E11;1(1 SI P .15ittioadtti1 oto jo AJamosta ',i`eionals Ifltj sun ion.so o91 .osiro JoJ.;)lettoq11.1 -st(I pinootti SI 01 iwilim:)(.99,9) ;191 XiI01anal-Hun1ana1 tionnmilmal rig ! S111,)I)1115 19 A4.1,1111n X01,110111 iiii9(10,1(1 XLL1AIOS )i1iA!l)I! lI oto .1(10(),IssiTi LII ,n11 .ssaa0.01 8uniOst,a.C.,s1uopnis sawInp? 14110m aq sluoimis 1911()1 Notimi 1110,9 sootiopmixo ji) Minna/90mq tvl tun I )SLIe)S jo ttio.9 !imp mot immol'illounpqrcluloaan ini0111 48000 alp AJam)..),NI sinp.taso.n1 !mini:111.11;am si)3111h)a0.01 imp inu,n)(1 aX111,1 01 ,splapois .s1101Iniopixa ))IIIIAA pawn, .N(E)slt icJ) st. posit(I (10 ;no owns 'olituoiliu aioul 1.1111 SI 1(9 11,1111A(11(1 ) point!! ri.lono:)SKI Ow! 11,110:):)il into SI tin tli aim itituntut JO twilettuoltii ut Atm tuol(inmi ntnAjos tIt)!$PI)$IS II 5.1a1)pl0a ley LI! ininapand ittapimd 11,011s II01 linvoina 01 nip ttrapioad iytim 111 IH)IIPILI.111.1 i)(1 .1,1111(.: Aunnap),1.1! '11,p01.1009 Jo '.8upana8qp SH pawn!) alp.*Ilsil 'potpolu alp Jalional um) Ian 01 )giThanpa.I. pinnal0111 110111,111,10.1ln J11(11 1118n11 uaivki uwillopit Aq S1001)1315 LII SI111 11P 'AVM fill1P(11:)11.110 111 0111 SS;-190.1(1 OAI1S '011111 41.10B0 inn? inari-{010tiarital Jnom pup 'Jnoi i1q) log to018I1! naam icnnoot;Rf pun riJano:ISKI 'spotpuur tot Su 11301a" oi alp tuop10.1(1 Jo 804a/0,31 100JJ atm unpuguniti 01 atil .10.1;11a 8u1s(I 041 A.lan0asm 'Ionpau, Jotodoi 148iut ituultioa sloop toim oto om,, ;nit pillint9 (9 lisin sonata.' in Jiato auusti all1 inia,tp.100 Ottivnitsi on)! am an its 10110%041 'pun moll onto( om ,Ino ,110!111106op 4tuapinal1 piII riiihntnbn no otO 'tion9(1 into i)Aam (ill MO noill1111.10JUI tam siminhoa Soqi into unati :115ni8 (nolo it oiquiontkpult oi(j11inlit(1 Nutsi p)pin3 kion0:9.9(1 Huipo:ratt 01 viiHn!) pun initroitit.pinom toim ay *qualm's 110 .1111111 SULIJO1 111011 itmonifi LIII $ posoduid II l)LIILI lib'! trisininidifti ilv olduntxo olnom. '0(1 Atim 1.001) aivi 01 Hum 'aims I i uti a(is id0clual win imiti i,Joia(mooti UJ inno 'mop% 0111 datuntoi ;no lit itetitn opittti tioinun)tio) nito ini()(1 Aq 14111,(1111 Aq Japlimitaq 411 WIN A.MA 'onottiothco linpittati Aiolo into 1.10(11.1011 .1110 J.1,01.11114%4) osou, Oion oy.iusotus 8..1O11111M 1i018.1:1A ppm!) ppiotin imim 01 pilau 11:1118 '1. liadtwa8i(1 JJO 11?S1)1111.111 III 011 15.111 ',E11111Sul 01) (Is Aq titup11A0.1(1 soluppniX 41! osill0 lluilAn tun luovimid s! ill! .11.Emp0.1 30,4 'apinnixo Auto itihnil 'APS (10.)N.. III plum Imo .1110 818011 padx.) 811 (,)1 in 9 111.01 pun will mul 00.11 'oseu nql Jinplioi popull 0111 81)11 1011 puouni ,ki.)111 iuRpo.1.1.1 autos ltlllIl ou.ainsw qu'An tIlul 8..11111:11!ol 811o1 01 p1.115.).1 .1111 Jo 01101S .81110111118 $1!,111111xo 511101 1() SIMIIMIX .1111,1Ptli OollosSo It) liyoA01S1(1 sion0 1110q 01 pimuuns pun .nii iil81.1 01 oil* !8.10.I.I.) 11.911. alp s.ropoi 01 .1.0 011,1, olNI.! pasuodso ul sun inlli - s! Ind .10 81411.1lio! 111.11! Jo 'oJI1 111 111 os11:) Jo pupil!) 'A.I.IAOusio 8!..111881. 1011 os pun n 8.111u1) 101,1 sUlpIsilu 81 psiunpu.i sr s! aliuni pun Jo 8110111..101(k.! Amu 11l poXp.uln dams 81uo111nimui J0 'pupil!) (110i8 1.10q8 Xu!p!timull soliqopled 1(larlomi.811!.1111:111,11830.1 li11mI08 'sow/urn, $l Julluvol Oton Isom osp.itoca pimitipul 1110011! MUll pun uolinn 01 ainiull.118 oto 'ioul 10.1 h tuopio.u1 -Avis souvulud 10. 'spurn 'AlainuitiJoilun ans jo 1mi 81 guns' imp s! 011 /cm 01 An0u1 intim item! -;nuis s! 111.1(11all pun ilaqm s! un it nu Juopuls s Ic11/111110.1:1 .A1,11111111S1 11111M .1(1 111111)111q111011P ()I APUI s!sotliffilic(l Ow) A11111-1011111o1 111111111r) .1111 111!..0) spoos m111.1101111 1118ts111 .1111 .1011101111 . V 1111:111.ro 111111111111111 III 0114 sSoliot11 1110(1 riaimousKt pun popIn!),, oui dull/jell! .10 i+.10AoOSI(1 uumiliusris denuaXnulilli -03(1 .43111).)..) ,10.1 .14.1air1iol III inn !mu.' 'IT:Alum! it s! s,auqultai -uodsua 01 Aup011 uoiliNlsop Isom .10 81191.11iol souuin.lu(hu) Jo policup ;no .11)J MI son!lualq0 11111111A11)111 111111 i1111 8S111:1 se .11011/in luolq0ad su(nunius sauminuos Imp wo.ij poinis 111110ftni.usu! sompo1010 ;nu. isniu 110 8u!p,u)uun stt! .10 Jog limo se Amu 'asp! 1.1m1n tu0.1.1 1141mo/taupe vial tun!) uo 'sluapitis !! tit atil ,laquiial 011M IsIllu, inn inapt!) olitilpinu 01 itu!Ipm S11/%11;1111111 OAR' iumui weinis!Xul huiounho.1 pullumpul inelitunpo tumid JOJ ifina poddirepunti itioplus samiusJaplin !up ouuni.elduie JO Sunnis pun 11111111AO 1NUI Sl11 sai111:1;141 'pun snyi JO $11!imu0.1d Joyanal -311 'Auptiniuluel swum; Aviv! Aanopitui dziunuuu autianui itenputinuniu ;no haimuusql pun pupil!) A.loAnusgi 8p0qiutu 8! ut! gimoitium Jo le Udl .01 sid pun n.losomi U 111.13011,11p iumpitioulin 111 alp Jo '1111)111fitallo pdu 11011111111111 11111111111:1LHIXO 8uPli1t1a tuu.ki J111111 I 111111111 tIoAIN umihm.ij 01 pun 01 'i).101(1x1) l 0LI Ism) .IE1111111;111 111 0A111/111 pun f111111.1111111 upuullilll U :11,1n.enuu.ap olds try

populn 'tiJoAo:NI(1 AJoAolsql Pup Hu on!loopu! 1+018011MIS .10J PIT itiviloduo ;mow saw.] 01 :sittaintis '14'3030131xa siazisatlitnis 11000:).y 'S.10>intu Pun .5J0inol1ito Apuci!? -8311111M 55011 JO .1111 sludImis oInt1pti.041 Iuulioduo saolopJ UI SUN) s ;magi .5o1801D.I1 Ailliolo!! mottiu!!!!Antili oi Alun tuO3J map Anui-aittdptiand solopnis Antu ati ameun 01. punituainnt )lp" tuditiO3(1 stt ..)10tiNt 30 autos JO sit ittni.I0dtut 'tquatuala H303110 Amu .10.31 imp 8tnlimittit10;1 tIOiltn0.10Jut samtai atm, 00010 01 't.uspopa otil SUOSI!13 .10J 11011 )M11:111.111(1 1101 ;131! atttituSto 30 1.3ann 'ant I130111 uoqualin iEnus /Oil) inotillm alp S.111011111IS ILIOUIOAIOAUI U331110.0 SWAIM 0011..11!SlIt!,11 got% atil '30yanal 0tp uossai %Kum oi n Anti imimptioa giovi imd(11?:)!In1I1L1uou pug polp8 quaimis pamoys IMO o.tom Al11'111 ii41! .tindtati4151 tit asinii sociAl Jo on!ionpu! 8uumo! soluOtiodxo U )tio oo.1801) Jo %willow! u! in!mt soatiouodx,l'istmitio:) popmaa 141131)015 isoIihus Ittll) ISOM 3,111 oplitun III 3010.) 0101 30 A3amEtsto pawn!) rf,tanO:nnu stuni13301thca ipHINI 0111 JapnaJ Amu loolop ull luo.o!doll! uotia!!!!!Jitioa glyvi sliopsu, ) i (z96 tuurotio.I LII tiaolm oti pu00J lug1 pop.miim smopois UI liodxa tiONSUI:1 0.10LIM U11 OAII:11111111 pOIJIOU1 HUM 1)01411 p0u330pad tin ipm sit p1dt1trniningti00 I sittopn no 001 Jo pmni t'n.q1:)11 liuptu!to OMJ 'aottomoti imnpoa 110n:11)11,11110..) 'NIA alp 6Atranpu! poylatu posit tit Apnis scAn 30two11 3OU AJOAO:Na pawn!) :A30nOosta 11 sum tt .1.1001 Poz!unti.lo ivolonpu! potlioui itnntiorl -31 ontump ./i800mis ;no Ittio:tas sitiointis imam JO JOOtios Hupaitio iittu U1I ;mom INIAionti! AA tip oti, potodul inoJj RiqI J isJu /cup u! 10011914 Amp NI) IOU JAM! D bop!!! JO oAwl/iou Nu!umoi lroatiolJodxo Aaq,L ;Liam hunpm 01 alitI t! toli 8u!p11eisJapun JO ay a)umpodul! JO aio.i.ogi imp -no ,Hiuop Jo!J(1 suouopodxo Arqd Iii tiu!igutio wino oi auutpuJud -onpul OM UM 01, ti,uuu1i9ns 09110I.110dXik.(1961.) paidUlaiitt 01 pilijOft1111,1I 111JU SJOIMJH 01 AilinhuiOolanut) sins Imp juPpodun.aill oi u! 110!111(11:)!!.111(1 'AJoAouslo uptutians sum .inosigrausun OH

,, paqiinsop ;unlit,' 8tii:nipoid s:Ipsi.hireiiint.) in ;nu splapilis HP ..timollo"

tu s.e.tos Aartiitutplit saipilis inuip, ()(_; 111111 ;Ipti.18 teuppqa ;11111Aet SPM 041X111.11111 AIIII!.1i1p1811(E) okt nionei ;qv otii1iyTh ;nuns "0 mil inleui imp -.1afu! ;ma" tpinet iti.lomns!p Witin,up .tiitnhul e1,1, 'll1V0,10001 030111 NPM 1,01.11)w in...1:H1 A11101101111) put! -Alutipnpnid omtin!tuillais tu1)3J----0/ml,H1 s.ttiupply) .r.)tiapuniil (OHIO *SailiJotpilti sithued put, 01.'slo0)0l minus .1!)91 -$idn'Atity.) unum tionpi vtau .10 t, 'flop tii tf:etim ti:118 !Tip 0.10M 4i)(11111.1?/11? inn thupwl.) poztt1P8.1() 4,1l11 *1)1flt A1O.IP.1 130.10.1111f8 1.111111 'POT Aj.ir.i posiP.1 polsoi simittindAti maJp 6,sa:numiqui peals /Soul .) ueati 01 .1;)""0 Ala1,9011110 paumitinsun ' .stinisiip P0 p.yetpaid P Hituis "0 pat11cuo.h9s sugo.ul imp_ pal .1.1;itinnott n patunistuiv 811!Avti snip:nun pauteidiKa oi lump U1 .8140issivisip 'slop" put! 'iopinglxin aqi ;mum -1111 In 01 811illim oppin uPoI IllIP 111111:1P 110M 0S0(1.11)(11,)111 JO .it11.1d.1(1.18111 AIM! in OAIOS111.1111 OO:10(Y) lb) tiotim II? mil rivp Jo] AAp8si3loti q:ms A.10A04S11) 0,10/N 01011?11.1!Al! 1)111!lltap (1) N0j1

'SW:110111,10:0N 11 111110A1 011 0.111110110,01 oi ;ipniauty.) tutu" s.utiuni:ms Ilf111 .101.A.10A0:1S10 01101!) A.10A06./SIO Alutissaanu.a.n! -anpum100 siJoilaH j,mit! 11961) in1n.111 ) 19961:J96 put! !unto() nati 0.1011,1, SI 00111 0:1110111A0 01 1.1(01111S ,1011110 0,14-1? .10 110x) 0.1nisod le still -own

"ANIVININ11S

lieuipilis pile 0)961) u! 8utzutiumins e uo Sulu:1mq A.10/t03111/ a. unileuitunx:4 JO tpoq alp milionupw swum.] Jo ayi ;mutual!! pue suoneamplop "t) ;up irnmaiquo:) peal ol ui oppideAuut -nlatue) tiois 00t1h1)(10) NI! 1101110; MUNI 010101101MM 113,11f0S0.1 suopnvis otintemq ;up' ihupluu! piluauluadxo 1uatuino,6 ;up bunonsw 'polonut si le" um snantiuluni aye osluomitu! 01 09 poen Ann"tiuilyour 111 Ulf piumuuJiltiXil 11) (L6L 1i767!/-ipsonu!

) (uz,61 paitiiMins imp so!unti!quiti alp iunpuoui UO anpanptu tiutuntaimi pue AXIAO:eig1 anuop utoJJ ato Stupunnn(e) Jo mseq :Knisaawd uoutipuuJo" "o indict' timing put! otp uopeawon JO -Ay 'Hosotpod popliam tug) 8)(:)O4A,titi! (9961) uo!Nopue! iunpuJ alutpu! tio!in)upon HI! pud Jo inn bilA034q(1 otpinu p1101 01 .11111111.1 10101.111ti t11011,101Ill1) Jo inn '11h)111.1 !9o(1s aq pawn 94 A411:11 141.1111,11101.111011:11h11 11110.1;4011:110±011.11 011101011 01q1U0NO3 u 011.1118 JO .101110.1 1010116.0110 Ulflp Ulf /(1.1111).10 liffil:HLO 'A.1111501..10

97, From the literature on Discovery and Guided Discovery,we may' conclude for the present that while some authorities hiivebeen per- suasive in their endorsement of these methods, there is littleevidence that the methods prqvi"deeffectiVe strategiesto improve students' reasoning abilities: However, this does not justifygeneralizing these reservations to all inductivestrategies. 4t-

-qc

27 .,

4 The Logicalinductive Striateg9 $ - ce

. , While the rationales for Discovery andGuided Discovery have merit. the'democratization of teaching-learningtransactions:and the enhance- ment of studentsreasoning, abilitiesit is questionable whether the use of these methods is.appropriatewith mist mildly retarded learners. Their cognitiv and affectivecharacteristics require the type of teaching-learning trahactions thatwill give them a better than even chance to succeed. Studies by Goldstein,Moss, and Jordan (1966), Ross and.. Ross (1973), Rpuse (1965), andTisdall (1962) nictitate thata systematic and predictable problem solving approachis needed since such an approach ismore nearly consistent with the abilities find eZ- ,periences of retarded leayners.. Systemat ic reasoning process mocials_are notnew to educationur to psychology. Dewey's concept of the scientific pulthOdof problem solving evolved, in effect, intoan orderly teachink-learhing process designed to promote and enhance thereasoning abilities of:students. He proposed five stages: .

1. Experience, the first contact withnew material. , 2. Problem, evolving a problem that is real to students. 3. Data, information resources derived from the student'spast and present experiences. 4. Hypothesis, a suggested solution to the problem basedon data, 5. Testing, verifying the validity of the hypothesis,

1 Others (GoilfOrd, 1907; Roseman, 1931; Wallas,1945) have presented psychological models for inductive prat=solving that iddicate the steps an individual takes from first confrontation witha problem to its u 4 29 .35 solution. While all of these model's focuson the individual, their structure and sequence permit them to be translated toa strategy for teach- . ing and learning. This has been done in the form of the LogicalIndite--.- live strategy.

ATTRIBUTES

There are six attributes of the I,ogical Inductivestrategy that differentiate it from discovery-lype strategies.

I. The strategy, offers teachers-and studbntsa strUctured procedure for teaching-learning transactions. e, 2. While the str-ategy is-structured, itis not rigid. Teachersand students have a number of entry points into the systOmand alterna- tives if the selected entry p4,t,proves to be unproductive: 3. While the method is structured it is not undemocratic. Th(i teacher's role is primarily that of stimulator and the student's roleis.that of responder. "I'eachers provokeresponse through their questioning. Students not only think through the problem andprovide responses: they also act as evaluators of their own productivity. 4. The structure of the Logical Inductive strategy permits the teacher to assess ,quickly how far along in the reasoningprocess each student has progressed. This 'allows the teacherto plan interventions that will make it possible fora student to take the "next step" in the reasoning proces. 5. The participat ion of the teacher at each step in theprocess allows quivk recognition of students' erf'orsor randomness in reasoning. This p'ermits the teacher to intervene to reduceerrorrepetition, digression, and frustration. ii The structure (440he Logical Inductive strategy doesnot restrict the student's ability to explore. The strategy makes it possiblefor the ^ teacher to particiPate in his explaations, but teacherpikrticipation is not required. It is the teacher's judgment that determineswhen, how, and under what imditions involvement withthe student's quest for information should take place.

The strWegy is not basedon the premise that there is a single correct pathto the solution of a problem or the acquisition ofa concept. Nor is itbased on the assumption that there is .a singlepredetermined solution: . The Logical Inductive strategy is appropriate foruse in both formal and informal problem solving situations. Formal situations:include those where traditional academic subjectmatter. is th e. content of the lesson, Informal situations often arise during studentq'free time in or (nit of school, Typically, the difference between formal and informal situations is the teacher's entry point into theprocess. In most formal situations, the teacher is instrumental in confronting-students witha problem, In informal situations, students often 'becomesensitive to problems that are part of tcheir Ownlihrexperiences. In lioth situations, the structure of the LogicalInductive method allows 'theteKher to judge the conditions for, andthe point of entry into, interactionswith the students.

THEORY

Gestalt theory Kovidesa sound theoMical framework for indktive reasoning dml.at the same time, an order'.'for. the.processas well. Typi- cal of learning theories, Gestalt Theory is complex and woethyof in- depth study: this chapter willfocus on those' features of Gestalttheory that are relevant to the developmentof an inductive teaching-learning

Learning Stages

Gestalt theory sayS. in effect, thatlearniag follows three stages:.Vass, Differentiation, and Integration. \.

Muss

At the Mass or awarenessstage, the reamer ifi confronted for the first time .with a -pro.blein2'. and finds.that it cOnsists ofan array of facts and concepts; Someare identified immediately asa function of prior learning arid experience. Others mightbe new. At this poin,t, it isnot clear to the learner how all of theelements of the problem relateto each other.

Differentiation

TO cope with the problem, the learnerbegins to sort out thv elements of the Vass, and to examine how theseelements are associtited with each other. At this point, theDifferentiation stag! has been entered 'and the learner first takesinventory of the elements of.the problem. He or she identifies-facts andconcepts and ties meaning to them by drawing ort earlier experiences. Thelearner also makes inferences about the factfi and concepts thatare new. Having identified the elements, the learner,Iliscards those thatare not relevant to the problem, then reassembletethe elem6nifs accordingto their relationship to each other in much thesame way that pieces of a jigsaw puzzleare fitted together. The processes ofsorting, identifyingnd reassembling the rblevent elements of the problem leadthe ktarner,to a more preciseun- derstanding of the problem and, inturn, allow him or her to state possible solutions to the problem,

1 Of

As understanding occurs and solutionsare generated by the learner, he or she is on the threshold ofthe Integration stage. Once firmly

e 31 s

Aware of the'meanings of the elements of the tiroblem and how they fit together, the leianer is well into the Integration stage. At this point the elements of the problem Itave become iptegrated into the indiyidual's knowledge bank io thoroughly that- similar problems can be solved quickly and with apirarent ease, -

Illustration of.the Learning Stages

Frorri.lifi'S description of thelearning stages in Gestalt theory it might ippear that this is a simple inmess. To dispel this impression,we will i'llustrate the stages usil the exiimple ofa teacher assigned to a new school at.the start ofa school year. Many teachers, new and'experideced, take positions in new schools each year. All are faced with the same array of problems insofaras set- tliq'in is concerned. There are-personnel issues, which may -ipdafle the climate of the school, thl characteristkAlif.4ie principal), thy "closeness- of the teaching,staff, among others There are proWurar iNsues such .asSie management of noninstructional duties, ordtring and obtaining supplies and materials, and policies governing .;peld trips. And there are problems with geography: learning to navigatelhe school. As afunction of their prior experiences as students, student ,teachers, and teachers, all teachers will have some general expecte- tion's as they t,ome to grips with the multitude of KA-terns they face. What they will neasis time to learn the specifics of their_new school

'setting so that they can adjust t(,them and eventually become an in-

tegrated part of the school. , Taking the most elementa y of the new teacher's problems, letus look at how. Gestalt theory iperates to help the teacher solve the problem of learning-6e geogra shy of the new school. We will jOin the t,iichere as he approaches the m in entr,ance to the tichool and enters.

4 ., "Where is my room and how is it k :ated withrespect tiiCmportant places in the school? Where will I find he princip il's office,teaChers' lounge, library, supplyroom, toiletsheirs a d ours), cafeteria, auditorium, etc.r , A . Mass Stage'

'Ilere I am inside the school. Corridors go off tmy right, left, and straight aheaq. There are doors leading torooms..utI don't know which are classrooms and which are 'other purpose'r s. On my immediate left 41 the school lice, so the principal's officeust be close by," Differentiation Singe

"I'll ask the secretary for my room number and how to get there. R

1 142.-T-down the central corridor, senind corridor,turn left. Here we-go, Ah. there's the library, and just beyondit is a fireextnguisher, Here's the first corridorno landmarkkeep going. Ilere'Sthe second corridor-,-turn left: First roorn is a Custodian's closet.Next, there's a classroom. Across the ,corridor isa water fountain and the girls' toilet; the hoys' is probably farther along. Room142here itis! There are double doorsat the end of the corridor. Maybe that'sthe entrance to the'cafeteria, I'll have to check thatout. 'I, . Now thatI know where my room is.I'll use it as a focal point to locale The teachers' loung9 and other place's.For now, rehearsal time, If I want to 'get the the library, I turn rightfromlny room, right at the central corridor,. and watch for the fire extinguisheron the right. The lbriry is"the next room.-

Clearly, the teachft is identifying.releVa-ntcues to the specific places he Wants to find and is drawingon his past experiences to interpret a novel situation. Note that he did not includethe color or texture of the floor or walls. .Obviously, they 'providedruidifferentiating cues because the texture and colorwere constant in all parts of the builcbil. The teacher will use the same differentiatingprocess to find his way to other places in the school. Ile will rehearsecues along the Way; and may give himself verbal instructions to.help him differentiate a\eroute to the teachers' hninge from the route to the supply room,.1-le'llmake skAor, mistakes:km. When he takesa wrong turn, he will reexamine.his cues to learn how and why he made anerror. And he'll revise his cups ac7 cordingly. With practice, the places he visits'most frequently become the first ones for-whichcues seem fade into the background. , For example, the fire extinguisher may becomeso inlegrated into. the gestalt of the hallway that he won't be ableto remember whether or not the grafitti on the glass cover was cleaned,off.

In tegro t ion Stow

At this 'stage, the new information has becomean integral part of the new teacber's knowledgobank. Now hecan travel from place to place without paying attent,ion Iii directionor location cues. In.fact,. he can put himself on automatic pilot and think about professional, personal, or social matters while he travels around the building: In the process, he. May itill make.errors but they will be fewer and IesS frequent,Oc- cally: he might forget a landmark. Sometimes, new etie9may be contused with cues that are relevant lc other locatibns because oftheir similarity. But, twain, practice. Will helto !educe errors and, in-time, the teachnr will navigate the schoolen ironment with ease.. In all probability, his integrated knowledge of the geography of the school will be combined with similarly acquired knowledge of the school's social structure and its customsandmores. For example, the

4 t 33 3 teacher will Combine the fact that'll('can use the library as a Shortcut to the teachers lounge with the knowledge That the librarianfrowns on this pracUce befae 2 p.m..imd he will avid theshortcut prior', to'that t i me.

RELATIONgHIP kTWEENGESTALT THEORY AND THE LOGICAiL INDUCTIVE STRATEGY

With the mass, differentiation, andintegration stagc's in inind,we can begin to eXplore the relaribnship between Gestalt theory andthe Logical Inductive strategy. Clearly, the bulkof the problem solvingac- tivitiesoccur during the flifferytiationstage. It is here that the actual .sorting; associaing, and reaspemblingof relevant facts and concepts takes place. Itis at the differentiati?m stage thata reasoning process -;can either facilitate problem s;dvingor, if itiS unsystematic, make it more difficult. As noted earlier. discoveay-type strategies'donot provide a structure that allows 4 an organized .way to deal with facts and coeciiptg. A LogiiA huluctive strategystrocluces the differentiatiim stage by providing a logical sequence to.deal with theundifferentiated array of information found in the mass stage of.a problem. S.

Recouping Sequence

The rivoning sequence provided in the DigicalInductive strategy consists of five steps: labeling. detailing, inferring,predicting-verify, ing, and generalizing. The .example used earlihr:which dealt with travel in ,Manhattan, will illustrate the ta,:tivity ateach ste"p. N Labeling

In this step, .the elements of the problem'ere identified:When we started to solve the travel problem,we first identified where we were in relation to where we needed to lot. Thenwe went on to name the ways we could get to our destination. We identified buses,sobways, taxis, and walking as possiNemeans of transpiirtation. lietoiting

In this step: the identified .(labeled) ehunentsof the problem are described to better distinguish (Omfrom each other..Semetimes simple details are required, for example, the tollman. In our eXample,, more complex and functional detailsare necesSary. Buses travel.. scheduled fixed routes with..periodicstops. They life surface vehicles affected by traffic conditions andcontrols.The cosi of bus travel is low. Subways travel helowAround. Whilethcy.travel scheduled fixed routes, subways are only minimally affected by traffic andtraffiCcon-: 'trots. The cost is the SUM as riding'', bus..Taxis are suttikce vehicles, , They iire no c)nfined to scheduledor f1Xed routes, Mat are subjeCt to.

34 31.1)1!JI pill! :)!JJP.II -510.111103 laAP.I.I. A() !XI!) SI JP.) ii118010.10)11 Until ii)AP.II 'JO .ApAmilis I! 00.11S 09P).1111; I! 111113invti '00 SI503 1'itt!tilotI Ill s! 4: Joitols. UM)) .IPIlllltIJA. 1P.Il 03 Sail I'liTli .1011!1.04 lima kg ay Il!llpIAII)lll 1 0

: IV sIt.11` iIM ail! 01 'dais. ApPoi ZIN0d0.1(1 010lI55Od 5001010S 0) .111.0 IN OM MillAa.l 'Ul0NO.Id_ ay t!!!!p papollo:) &p.m!) aill simmoi putt, hu!plqap sdalt; .om lira toNaq ()F, 'amnian.q,s .uotnnumojut pm! asooq:) 919!51!aj vuooda ua/o!) ay uo!pnwojtn may! 'sasnq am um am; Intp alp no. lass!? 'ins atp ;mono SN/13 tma awl in pnulinut :ism uo 'ains loAni! s1 Aril!!! any Aintriou /Wino! pig 1:)alqns 01 -PpIraidUll .11N/filial) pl.UP.1) SOU10:100 * oh - IA/Wag 0,II! umfo'Astou 'papmon inn nor .:)tnals APAM10S pue- 'aattamoj) Amp aanoa puno.IX :mow ify!dva imp. sasnq put? 18 ;no awns pfly.? 'spwIL apqm 'HaptiaA.aarjans Ima 0448qa m :nurai naq35,ti4p pott8 ..stuel Amu, WI! Joist!' Imp %maul pun but .:fli snt In! pnitta s48mqn5 pm Natp s.symnal-alm lipaa.flp 01 itatp -8upsap 'non I 'aana4MOI paittuq In 'Say :118 8d83.108insspd °Alp -xa,Ltot.0 9 amsuad NuillenA -i;! aaJJ-Iscra pun spuuad so 01 Ipti pinlx0 snow s:n110,1 0:flns am paint 01 10A8.11 P 8001 'alunfstp aqt dial aq -xa AiNtflpaa3 any iinttunstura pue ptm ttupq sn cil ano opnupsap . pam Jaipt atp pap.flod(18 'attof .a.mumayianA 11:111S 8 a:flimsy inai8 Auni fli ptnniaq ay siAtid 18:n k41pq108a JO alms Jo ino Hartitssup ano .;u0snai Ntll %ilprIIIM4 Illql IRIPSIXIll MU 8LIMPM 0.IP ST poo8 stunithl ),IP.1411 Mil gni_ 10 Anmqns as :tin) yinNo4.sir3tia.taju! uopmos amill unnq oi Jnoj.ttinal-pampal flit,'Omi snq JO mqns 1 OM 0.1li moll pa911 .qpni Al Nall ti1 paiiii. atp Japaq gunido . # ...... ktojiJaA-Nuq:qpoid ' '

.stql 8 $an;t4kt,uolaq;.. .. Nuppflu luatupttaum oi am-) pun:n(4011os tunp sliti ssauanoaaJja jo alp kratoki:) Ell thillel)illitil' SILU.101 s10 -38,.111100.1.S£Tp am mum alp 'suoq smapno. 01 Apttawsum tiNtam atp sapuanhastum JO , 'snta,,:stunsvibp'Jmtp Hupayaid ,pun Nuirip.tatt $118n1in se pinto!! , tym smovoltjaq liana unqatpaad Numonoitt, suonsont4 imp Moti alp sqnsai Km) uj *Paumptna'Aq atp ostm jo 360 'anvil iwamo4d irroJiom alp Nutptqap imp toot' tuimj dap; bqj pun.l:nq Annulus laituil jiMnpatio's ' ? sainoi ol; pa>of apias 1 tliiii*)s t QM II0 II tu a .qpvmodoa uu maim 91 11.18ai Jinpat JO Ap.flitpnv M .tpoq stu.mj floirstnui ON or mu) aqi uoputniiiiy saN'ooptut tmnpatpflt s,utup Jo wolindiy pun plmin JO.) atp suq putt ' my.* amps. qioq oN aiatim tim paau ol 'oN am amnopla mil Pa i 1)4* thin wcinto ,41i am cowls Ole& 8 Appqnqoad luptuanqs pun atp *Rua ititp Attmqns SI MO .10110I1 a:71010 jil inp inlinoa jo alp 'dm am Una tuopmm iinaan atp JO ino aa!otp thundtuoa'Aq atp painpailas nun 111111911' IliA011,1)001110 nokuti tinown i)ihnnunoona wilinlein 01 ino ptlettOttrud ItulAny pupil uo, p rut) !Kum MR JO,sonsaa' 'tiolopop.ipo onk 'dais ,. . . 1 ,,: illuoilligj.Apnitvoiil 7 ' 1 .'e fn 4 . , .:;, ' I' ' . , ' 4 11'1, 7. Gvnerutiziti.g

In this step, all of the information andexperiences are combined in order to identify the rule or Kiliciple thatunderlies the solution to Ons general type of Problem.Applying this step to our travel problem:Iwo were able to use Our experiences in Manhattan to facilitate solvinga similar type of problem in San Francisco. As we shalltin' frolli the'research on the I.ogicalInduclive strategy, generalizing is Memost abstract and, therefore, the most difficultstep in the process fvfore oftenthan not, several problems within thesame problem tyiw will have to be experiencedbefore a generalization emerges. For emple. a grtmp of mildly hamiicapped studentsmight hav(' t() plan mid take twoor three trips to different destinations-- when! subway and busare travel optionsbefore the generalization emerges that subways are generally the quickerway to travel. l'rocedurally labeling and detailingare data collecting stepS. The 'succeeding sq's are dataprocessingsteps. Clearly, lite effectiveness of the data processing steps is greatly affectedby the language iindIHT- ceptual ahilttivs of (he students. Theymust have the language available I() name and describe the'eleinents.of lite problem,hey als() need to underydand how the elements andAi('n.descriptors relate I() each other, and, how theyare relevant to the. problem, INith younger students, it is probable that teachers will haveto concentrate on building a. language .1sponsepotential and a perception of how thingsrelate In eitch other in di florenrsit nations:Ali-ofthis must occur befoee abstract reasoning,. typical Of inferring and predicting-verifying,can be at- tempted, 'ro help students mak(: the transiti)n from data collectingto (Inta processing. the leacher need's to 11(l 1) them develop reviewing behaviors that thvy can ube to constantlyreview labels anddetails as they begin to form inferences. In thisway, the data colleCted early in problem solving becomeilll information pool to be used in themore

advanced, 11.as( )11 i,ng steps. I) foll6ws, then, that (!arlyamPcontinning language development ana productive rthisoninA abilites are interdependent Since.thisis the. case, teacheys need tohave ir reasonably accurateassessmet each stud(mt's. vocabulary and .comprehensionin i)rdei' to piaprob ern solving iictivilies alappropriatelevels,ifstudonts become miredin a problem that istoo complex, progress beetmeslaborious, and confu- sion and frustration can result. This is nottosay that ev n'y student needs lb know.. every mord or. association beforea probtom, solving situahon is posed. If students havea reasonably adequate language has.e, they may be ahle to pickup the labels and.details theY laqk along the problern solviil route, Since the final stepin the 1:ogical Indvtive strategy,gbneralization, is pivotal to successful prohlein solvingit isimportant toexamine its role in the reasom Mgprocess. InduCtive reasoning has two goals: int- mmliate and long range. The immediate gokl,solvingthe probhtm at

44 !mon intim/s! sio! nomj passoaso) 0)5 ?1101 08111!,1 4I1.1 JO 800(0/10.'ll!0X 501;011.1d HP IIP 01110:W10 JO S001111),10(1X0 IIIIM 111.10A05 papp.1 st JiUlil iplaopp 01 mu!jip Sul], zu1,11 uatim ' 3131 IPII1)IA31 1511111 0.1(0A.) 010 01113 Jot op1):unm1 'Ailuapuodaput ul alp ;15,10(:) J0 PIO 100111S pun ;41( 'soallo1Jadxo JM aim( on [moo liginni ;aims Solna am 4. .Aipomp silitmlaums iil!tu IO,i .put!Itoapull ;)41 tpvt put! s.a3010.1a11m Jo v op.) ';.!?.:)) :)30J0(1 0, nionxo Joon 1101 1,,:) 0./11 0.1P 1;14010111.10A011 ;qv 01 Ii A101010 .Alo1\!palio MOA JO 410 1311103 10pi 3110 wasami sl.)A0I ill ';illuunpuni 'JaAannoll J) onn pm{ 01 in! plimq All:);),01) A10.1.) apu m) op1Iu1!m1 pup oiw pP iu) am omit] pamipai 11 ,TiPzP,', ;)moimutu.) uo mu) mArm) inu0s om uP:) azwi.cm pup mum; OM 1011116 nu! (al ..roolau una . , m Avid! ohno se .papaati 'Alanpulls Almon ow.) in! paddvalplino sphyllis ltpinvi tiOillJ 1)111! '501111:011.101 1 '.10.10M01 Olt 30 .101191A 1110311(1 3:i/10.1411W tleda44 ol ,-,!:olun on Jo 4111 aim! Salm pun 514(11.90I,01 IMO P III:11011S 1118101 p;h01 I! ')100/1,1 I! 110A '3 JO 01 SJP0A ,E111.131 JON 51 I! 4O!51;od 00 trwal on Jo ay papaao sapu pun sapf!aulJd III 11:015 P 11111 ow Num 1u0pnis upn (P) omxis 1111 mil pdpooll 11011PluJOJut ut 514 JO 3011 0}IN1M0111 1)1111:11IPt1 M11.11) 10 II (q) 11111 'A1IA111,40S :1111i).10:10P (11 041 51)I1P11101) JO P JIIII100,0111 .01a1(log1 ail] 50, Almon paddva!puno splapois pan 01 uJnoi Amur 01 uospaJ tiXimmil alpqmturtut 01 sulapimd asPo3:)0! ;04 icupql!40,u1 Imp 1pm HI 1 Amy 'aim eiJoisip pLR! um!oi 11010)1:nini sapu pun pun pp uo liapipiumi Aatp UP:, .AII0apthul1pui i!ti,i, supatu Imo (pm Amp paau tulontiqua) -mu(1 i 0:0 [limn ipa,1 put! stuoplomi tipm plum)! 810/10111 IIP III luninslan asuas ;no 1101 nzun.lialA dais solasa.ulai aqi -opt- wn, In ) .shationJp;on 0:maim(); ol atil NtiohraaJd .sdals on Jo qa!qm dap 00100J in mil uli)pimul In 'pupil suO)liviqpiaua8 am aJOul 'amlusgo Aotti, Awl iiplo aX.100b) Puy Alopiduup) aumstu) pnicupullJ sa!iiild0,R1 Ji 0til iu,)pititi $0 01 ;)pip 110001011! 51101 puagamium:) h11101111? 'pa/tat; Jtoptirs S1110190.01 pUP )111.I1S1101 0 unmaia,) aim au '41ciptiod ati AitnR!cpuu pup ri1txa1ituo3 .am paIO!plifol .J! wain ill!tunlaJ ay tioonzottJatia8 'dais 010 ludpnls s,Inadtin 'patinJuO:),10 anNunv umsaub. tp!tim paau 01 'Hi pals)! Aq ;nil Jay:mai it! tutil pl!Od :apniaul sa00 )111 wapitis -.lapin) 1)0015 ay iulaploml sa0o aq Jo ails iiinlisJaptin ay bid 'ma! Intl lou atp pla Jo si ato ovi!ato.id apIJ ald!auticho nuOthntio 001 to ato s.plap A(ain) -flu aaua!Jadxa 01 aq si 1! ipazp180:hu os peoson ni 1i s! ato H,Jatunal atop puoicao Otoa i,sompindna 'Jo s! I! ;yosuod pup atp -nis map. suailas!!) ato apli JO nig z!vi!aupd mato inn ingJaA NOT; oi altos J! yli,ApitaJaqoa Huttonito ii,h1MS1111 01 zisotp stloosanb saapthaa 1041 N.101131101 'massy pun AlluioNUO:) ssiissisiJ moti Amp am Suploanos pun ill011;11 1I101 ifii)111) Aptiaoed titopSomaJ stmosanh pun saw) pull iaq NuouJodJoan! (1 smapnis azonI8J0 oto HUIY1tINI MP, alUILI atp -J0JJIR a:ma '00,1, ;no s,Jotralho plJaana uo!r.,yalas 10 stualgoad pun puolostma tunnuttatuavitto JO mil Sultiosna,I ssoamni op% oH n guoi /Om p,IUMM Hu!;)0pi)J uv wiNtqum 'A Ao1)!aads0 patwodull onsaa 'Jo ato atm.! qa.! uo ato plaItio'i anoaupto Pialmos pomoto null totiapnls ino (dope ;/010111.11 tilf u Illalgoid X1111AION 1001 U1 0111 01.1J1109 JO motiiSunualso 01 11 MI VI ' HDI1V3S3N SHSVII NO.1 31-11. 110190'1 HALLOCKINI ADILVHIS

somidtonssI! (11)1q0.1d )iu!nius s! ipuurup.I.pq pup -(101)n4)p Ipulauk (flan] uuuppunoty .10j np Ip:)!;1(ri lurulpui (l)w am Aps pup dip 111.11110.10 RIIIA101; ssirmid am (mow Imo !! s! olutImisifs $1111' 04. 11 soss.)J80,01 tooJj oldtuts Aili1it5Por.911 )G9(1110):) 5di95 dm alpto au$ (100(1(111)Sm! win (10!!pol.1(9to 1)00!pli Ill ($1p.) (10)s sI ifipssoloo Ill .111/.10 (11 FIA0111 Ixot! :10401 dins (I! all tthipload Normos -s%):)0.1d ()sip osmium] Iptli u! 1o:1(pm] fi Iitutu) 55.1:10.1(1 s! "IplootodopAop !mg 191 so:)(1,1d 5 s! (9401p10.1 09! ptlisiftld pup tomo.di $11 op *$.1111.1..iplipi,Nqull .,1A1 otuossp Imo Alt.1111m11 oP 111A1po1 p 4,1;01 1(1001,),\001:Ip .10 114 onJP(1 siu 11111) (101ti 110,110A III 41101(10.01 11111A10% w,ualpimo s!sifieuv Jo !epos suolionps (SSNID)

()J. suolulumssp iptp uloppud .tl!Alus s! tpoq inuur.),InJoul pup IpluoulduloAup NJa($u.).l.P,) puP (lotus (t,z,m,) posn s,uo,Ippti,r) skstilpuv .p) rums lpIcus s(Im (sv:)) piputop ifq "fiJaquou.p..)

pup pup)IN 1 spivt 1110.1.1 1,s0,1, ) (7,a; ssv;) poldvp jo lut:ms -uj o1Ilo.1,9 (um 'um op '8011I '000101 pup 'qupol p ism pou'd!sup , .insp,uu pu..)us A:nlopriuur) pup plouusnIpp S1111ti 11011,1010J 511111/0 ) SSW 00111111(11 (31 50.11111111 Jo 5111111101.10111 1011! 1101110101 51101110 110.111!.1,11' Ill Al1l.11'.1 pi pulus wapp),H1 suuqpnos pUp.(4)3 (1.),Ippip 111 soXp 9 zi 'sJpoic pais)! 0) putrisdi 0) ;up amps souios suousont) 111001' 1111!0 '0,111111d 0111 1.0101.15111b 0.1;1/1A 1101181501) 01 1111111 MO,. 5.1111111 11015,10A JO 11'11M 51!M iiI11.001111?11 10 0111 *11.1111101 I! 111001011115 impvt .1111!11 001 01 0E11 '110111111115 111111 11 1101111110.111 M011,10 4)y! nollPops ,)(1,1101111 .1),LNIos0.1 atm s,tto.Iputu) sisu0dsoa palp,11s1lo1.1lo1) .11091 solly(IP '1!0$01)..lautu '10101 1:)i;10J(1 'pup (11 u assai luopG) ilz!ft)JiltiaN I('tuJojo! 1101 100(Ip 11:)pu .)111 1)0,040 ituaos ulappLut .suoupnus X.I.)(pwo,p,) pup 5.1111.11.IS 1;11111N.1 1109 puttlui otp 1109(10110ml Lulu 0J)1J! s! p A1ool.10114 j() sdols (I! inn I1i:)!l an!popol AS010,10; Joj tualuoad 11111AI0s A09,1, Polio] Imp tiippul 1)01).1190.1 I)101:) u().1 papoao 0110! 01(itt 9:)1911! p0.1.10) sioup! (1$ s81.1011 pop oIdood 0.10j0(1 /foul 19110:) 4lpinom1

lupAdi lop sip! pump! Imim $ A.ILJ 1)1111 .1119!)(p11 :1();1 'aidfillIM) putp polJaat1 0$ aq 01(jt! (9 Ap1101)! tut 1304) SI! U 11011 otile()J0(1 101gA010.1 sit!!!0!) juiuo.i LII mum aq I!) 'I)01!:)! 'Aizututu!s ...attraJojaq 0.10m 01(itt 01 :))itttu snatlautjo! pump: ;up 110.11)10J),, umplomi lioututfp; fiaty pap000 oto 11191001J0ju! potuttti otp Jotioto sdals JO Xtujoqui j..X101090, 09 A!!!!:qu 01 111110.1(1 401M uo,pasug glii/1111g 111 0111 gd018,11/M01 Ili 41111 11111&111 W0111111111 /01001,118 pill 091 /fume 01 iri!iNinli)X !NNW 11(11 0:npladt1Iol 111 flP j() au! H011)0:h)Jd Jo S0011111 01111111 11o!tmitio,16 loopturfai)Jauu gl 106 0111 g w)A., JAPq MIl.I1,$ 4)JOJ)( nori tura 'Illurv putt Iptivi ,aJojaq tiOic tun 11113 101100g Imp ovi!uu!ad :salphIp seoaans ajduqs .06 Nuo!1 N111.1111 upoupuuni Joi AptuNuo.19111 Xi;iduJoa

, S p sup '05 Jo umpload Suimos pplotis ospt .popoddos v 30tpotovouun.mop Ion to0ppm1 Ittioa;t_ypinap ogi s30i:Lotos0,1 p0mituPx0 mot) 010 s,u03pptp 508I1 poptiaa .tiotp -J0JJ0(1 0MP111 Willi) 1110190,101 liutAlos (1015 icoq1 fitotoJ pop 0 -L.pup gplo imoM apip 510(111 )1)1A0.111 1)11)) 8111104) .10.1 0111 1mM1 118 $U0)11111 Ing i1.10M apron 50.1 IP 041 plod Api1tipoirxr 0.10)111 x0pituo3 'sdopi LI) 0111 1 1 puP 71 .U!OA smo 0.1om opiP Amyl littrop '304u1 pup pipoJil Mogi? otp po.mpol 811011P11115 ..10A0M01 Alm) P Hums Jaquinu Jo 1sOppitp wapitis in 0tp Apnis .10m 0p1p OlItut '4* 1U7.tpta0o08 'soot, SUM pOddnti polio.; mu 041 4041duinsse unp mapioid 814/4os s! 1luot401010A0p .ssommi ppq ;up iotp poviciptit? dootiop,ppo 40010.A104 08e fun? oatieuuopad Xtittn 041 fe:480rI omumpuf 'Alimells 83044003!) putt glints °sly -x0 poutow 041 do11ot04P10,1 tioomtIoq painspoto pun ttioppixt snimatonN sotpois Il .0:itiiR1130.1.10d fliwodo3 p1I'aupt8is u00m10q ditriNtiotwl '8utppo.11,ot? sdptpod JoJ Tittf Jo 030111! awid.ttioa wouoJto mit 03041 sPq 11004 P kithiptiai ol 0741%101108 sitp wpm (1oom)! ! sso3:i Jo pimps soiLil .0:notto301,10101. 04.1, 13040,lltos0a 111100J A1LII) HUHN 1P1.1,1 1.)(1 110,1M piLIIISIN)111 ditr1101 0:111081.1101III 111II? ii11)11.111 pap.11)10.1 ,1.I;111.11N11 010 P:41-to1 0A40npuf 'totILL2A8opt.ils 041 prj IPIJI pue Ierms (-)1 m0144,101 U!AfO11 0.1e nom paptI03 1111111 0311 pull ipi0os p?:ilSopluo.or 1)8p tooppmd Soinpis 1jsoXXnI pop &whams. SI1011P7.111),1011a8 1110011? *NI $I! I) 61 1111 Sildifi JO 10ollas 0:WV9'" Amu 001 wwumun illp os.our) Jo ISM giotrodposo.i polOu a8uittp UI oqi 1%4 JotAptioq Jo 041 'tiaJp11110 sv iot1I 04.1m)0(1 0Joul ;Hume Jo mil -404sonb 8to '0:iti0nh0s 041 miapit40 tie809 awdtailtitt sitoip;0ob putt 01 ani8 03o110 010vituo0 .8.10/voon? J10111, 00uptitionod 'ponoximi ow s,10to 010,1 pmpouittop sp otp s,thupptui ovu p0rupdx0 &Italy atp sal LIOIIL'II II piuttoddp imp aunts iiippto p0pJlliim sJatuttal imitnn ;Tr 1:01a1) alp ontianptil Davos ptw 01 ilSn AptioptIodaptii Jo otp oauttpins,,iatttuittxo 8.toquazia!Vsti pop tpitus paJapistm 0E0 pup alp Appwssod ilutii;o1 uorwolis popooad tt !sloth Sulup144 40,1 alp 00u0i3ad Aina.u0apptp 1))1eiod.140u! s!tp U01100 Mu! IOW Ilo!N 0 ; V SS way' JO etp Aqiuniam JO Øn99npul ailpaistoux biNuu) tiutul-; puff 43 U00.1 HiiN (E6I) ptitptito pa Otp Uotpn.u.toJul pito Hut,ilip pit to soli Pa Hoo J0 0111 SSIL/a atij 1);)SIAil.1 'S181111).10:19I1 0111,1AA (1l aim Panutitio0 jaid piun wpm; tooppiid imoiwiliiN pun 111I main Aatp:a.mpiriodd apetu imonos sim!s!A0.1 0tp a:alumni; JO 0111

inti, maplua mu 1:0 60.111 SuM p1ll!Ao.1 00.1E11 Jo. . plaNiud .111pUllt; WappLut 111111p; IWO! litOJJ tpitpsk II 01111.0046 Jo alupu!ia (Ito!levyltlatio?1) Pino:! 41111 uoimItla

(g. OAPI1 1i).1t11 SOA101,10(1X0 gum .mpuus suonnutps !Lupo! riat11 0.10M 110)181! 01 UP 0/.111!.1011.11(1 1:1P,INIP 0111.1 IMO 11011(1(11? 01 Ot11 'tit1011PI4lS

11410;111,1, 11(1SIA.).1 tiPM .1s111!3:111 11 cu 1111!1.10(11U1 p0M011P uoappli..) tiut`e? a:yoquodxo um.IJ poinadiu suinnonn u! attios poop.' sadril 'Jo sOlop,m.I'd a.l.y.loo :foul unLIJ"p7.!pmatiah Jim!! .suauin.lodxo (. 1.1s V 1101.11110SAJO S0.1111:1111 SPM 110111A9.111 monis Sul ;nil %num!) -nios sum! tr 11Antoj Jo ay pdiniwd .!!!!:)os umpload suotumus sum, dais pa/vow 0111 11,111111p (4 A11,10A ogi A:)e.unrn. Jo .uotn uuno!poad pump! moll o! ,Ittlus toPo !Pups Inn !! win 111001 don; pnil .i111)1:1111 (I1 iit11 1011.150. IS,11 uoISIWNIlfj. palpi8.).1 II! mil 1,10v3odlolin Jo e -a!paut uohlvniudA-no!, (1018 (qui otil 15:09 atumpul Atiolvals 85 inn dais . 8utpiyaul .110111'ZI1P.1,11101/1 , .111.1, MOIA.1)1R11 11.1:)(3.1d 0.111 811M. 1101.11110111 pl11! impundxo 0)1 opykoid .lonoo uonniluoJoup Jo ,un s,uoapptia Xt1iti0sno.1 .somptp! 51,1001 .1.10/11 'Annanchlds 011PUI u! trudiunstp uoompo 8111111)1A1p111 ?MON .1.1.1M 8II1/1141 icipumip upni ow ulam0.1d Stonius sso;nud pun osoin ()gm oionn Nu!Any Anuaup quAn oln lualum Jo otn . im.InIo!d .suuunupq ...... )t trn.:.1 Jo ,n0 stunsuw.! .1,511.101 110.1111:M.118 inn isol 'uowniks 'slut!, u.nim 0)1 )111 udippir) lopuudsdi poinpluis 'movuoiti! .110111 -.10pild .EMPIU popLioati tiP owtroisa jo al.ato is0J!Limu 8uplosno.1 Aumcie .1opun ' ,i!!! ,rnInpinK Jo otp ;.uunulpxo 8!11,1, adA! Jo !nunrivmpod s! .wpous oi 0 11411 Ju splopuis u! popodx,) uunusser' sHunios ;Liolinn 180111 Jo ma SI umiquid litnAws 0.)1limip 4(1 ay ..liniapai .nti. 5idtp.wd1403 0,10m icipmbd pin1.1a3u0;) tu!* Nutssassn otn /Sully? Jo papielai slatunal ui osil inn pr,u`thri 6Awnpul AS111!,11ti -UUCLII1111 A1111,11) 110A Ansi 1151.1.1 1510 111t1M 1 NUIS1 0111 'SSV) }1.10(1U00.1!) '1)UU lliIIIIS 1111110J 1P,111 0111(1ti 19 in11 110:1111111:1 01 1100108 A1(141) 01/1 gum posnoi:hy /411111.11ti Alunpollii iiti inn 'auutuunto Ainu, posttip SUOWinl!S .inpuns u! osuin inn P !1!. pa.mouns uunJud Jo otn al es. 01 mune otp uoappto ut sonpiniiuddu vomt tpinuan sulapiwd 10 .1141l11 unno v 5.111111'.1 11.111?,111R10111.111 Amur ol ado3 tocM pito dais% u! ato pr.Ori -U1 .1A11:111p Alliliniis SPM. polo.nhoun SP ull xoput. jo flos ponimu! .. -uudapui map liutuositaa Appon - . . osatu. sotiony pun suolpppn ouio:sni n moo 'ISai mu poi, .10 inn e I 11911 Ju I /.0 All: ompum Mpopyonoi II) 1 1)11\11 08 pountu ol Amp -mum 11011 01 IiIi 10IPUI :suao) iitn iumussostat Jo un- ptuap.io o3uanhos Jo uoppmi titunios midis 11.lin1Uoull1)) :LL61 KNHIU10.1!) pUll Vurs 1 :11L6 goals inlit liJi(tuiimt) 'Nail illtr, INO(IJKL Jo ill11 119.1111140.1 Nom 01 upIN II! .10J uunnul !mu!!! inn Hu!mullul suonsolth ul il tcnOJOX!.paJoui umu JOU MR11 Will 1/11110.1 1111 .1111.1Pil pi ii11111

ow otn u! ato p!..)!Hol iSHOIHIN iplappan.lint.i i , -'° 11? i1111 ;1111010d (1.)1S 11 il1U+1111);IJi1m1 JOJ tifia3:111fi I1 IXOU AL1113 111111 ti101) 81(11 thli11111(1 plado.! Jioni! I1 tptio Sulpoignms oxv inn sduis pdiol !Inn:mini) ANainJus iainniatudonviol) sack! inn a JO in4!tioluumu1 atin Awn pop.uom HJUI1IUII °Anti Il Plut.muct UO .00qi to liana to diouoLlojimI dois i)1n i,iftIoluJis .0(4 304)40) 110.14)4!14:) puol oi .1011011 51' 111301.10(1 11100 ,;!dois ;13v u0.1png0.10p40 0.10)11l oppi oi 108 oft 811101110.0 81111011110(1011111 110111 .1011111108 113 110.10j1

Afp1410,1 p.11.1010.1 8,1011,100f 1100A11081 0111 NMI! Jo (3 pop ti sittitic :mom otp spolons In sop Apilis .10 0111 T11,1001;01 otp XII1S0 NN11LL if108010 1011nind wimp 1)111)014 In mtp .10113nd tp1M -s.sv;) Apnis 010 u! 0111 luattiori ampnpui !4(1;118 84oi1'il8 0,IOM 4)01101 01 ou 41r1t4:on,10n4 0141 !quiz pannotis imp 58 aqi IcXo.i 1111 550080.00a 8111111.800.10u! N01(111nr) los Jo tiuulostio.1 stunnuod0 syni 080. punni imp in.sso:Ems 11:!!!0 1101S SIIM 1! -0,10,111 ,10.1 ,1115S0111 X1111111110111' 01 110SP0,1 II! 41111 1)(011 301.101111 '4101S S011, -1110,101111 11101 SI 011118 III! 1001,10111111 111110111fpl! 1101111! 8PA+1 pain,10dio011! nun- poisoi 1101iniu!.10.\-Innimpaid ina s(1018 liu!spdInot) 0111 11!:001.. ;-0np1li 0,111 ri1011!Jis 0,10 SI, NM0H01

I .HZIIVII3N39 - Ad1113A I HadNI IIVL313 1311111

j, 11.1110f .101j1.111/11 .10 1011 ,sluOpnis anunmopod Nunn) 0111 110001 411 1111P snm AX011'.11s '11!010111(101.1.\01) s.10q0.11!0s0.1 possassn -"10.1.0111 (1114511o11 1100A410(1 0811 pun aannuiJoJi011 maul, sins0.1 iiiptiouax pownon ooninputy.) Imp 030(41 s! -0' u.talludoplivatudulatop 01 Aipinu 4)011,11!10.1 .8.1011.11,04 30(1 10.1 00tInui 81I!8n 180ittils.0115 Hy Jo 014$ 110.1prup 0,10M 111.0%11:1118 lI 014$ &mogul pun 8u!Inti0p !! 111180.1 imp $um .sdals 1001818000 qi!An 0 .10!1.11 4i0l liu!sn inp ssv:.) ii) 084 110,11141110111M will alp isalittnoA noippon :no LI, NNII 03.1M Janio auto 1ç111118 sinoic 080t11 otort puindp!pud 11! atii ssv;) 8I!!!)000:ms 'sdois own 61,101014 A111(1 till inuqv 111111.10dUll AnAAJnni 4Sn0.1141 0111 u0appu0 piann roiso 0A!S U -awls inoiu Jo oul JO Inalgoad sosuodsoj 0141 cf pun DI Jil0A spio 0.10m 1QU tool )flu0 'atm:101mA log kno. puinlIma Jairsu8 lima sasu0ds0.1 apptu 14 utupptp otim tq,aiamt fumy( Jo 'NINO Jamo uoappqa JOM 0810 anaq appl opossu :up Riunatoi spud yr 149110 'ulatoo.nl putt .notp's sas1!od10,1 3.10M 0,1061 UNMAN 'SI100 !Iv JO aqi 1h1,11111111, 0,10M 01111? I alum mum; so:miuojo! inoqu 01111810d 11M SA 01 ii/1jOS otp pun Os Jono maltwid II ot000pototiptil atjs ssouasupdoiddn Jo otp topotios ato otn, fit pup 01 .tuopplid JIMA 1i1)10 U01.10 ilAUR ./qUO ift .10 0Arq so;n10.10Ju! Inn! pooiliNtid JomtoJ Jol pat .sa:maJaJto ;nu 1 1 111111 7,1 11110A tippl 'wool Di S )A! ft Japtaa mouton Jo litrautuoJto tuoysi mop tatty 'ont Soy yitmi pal(E) attp8 putt maLotoo 111Eit.1,10JUI pun pamoto tut ss:waininein JO swim:Mimi:Imp JO ono uounlos atwpuo sivotu to mit tixto utupittia Ut mu HatiultoJtiittapio 13 putt 1,1 ancrit Aux; Jo It -i.k 1 saatimaitn ing Isom Apnonbaij pangs qI imumojUi II sum jai.uoa pon al,ty Allugy CII Olo111 1:10.1,10:1 sinua.laju! paininitu :s.):)no.tojui JSltl 110.1111111:1 0.10111.0.10M oJos jo IV oql 11P 1() Jtfi ..u.a.tpi4) Nan% apr (n awn; au() isaq alios tun .tnapio.ul iv ay 8untij!Jim-liutiatpadd 'dais /fay alam apip asn tualgoid uouniosai sainold tualjtioa .10 pato.' itoy los umin

11"111'101011(1.111:) 01.11' OS11' SP,JA 1111!:111111XIS .101:111 }P ;)111 IS0M 41111.11S(111 10A01 Jo otii .),\!1:)npui .1111 11011PZIIP.1011.,qi '(1)1S .WM0,4 \ .1M11110A II1.114111:) ,1.10A1 olgt, 01 01411)(1.1(10.0(1101 1st!' 1iiitil ()pm polst! 01 Illm)1,10(1 sitiv Adis Au 'Isplitio.) tiXtnitilip .topio ttimpluta -.taint» .\ pools iptim sPA% noilm 01PIS paim1),),1 m)jAltatii ail() Ol? -1.1d0.1(1.(1P sias 11o1IPZ111'.101101 1110.11 Il jo pa,nikant tuqpio.id 'Suotiptips 'azupututtls twins pup ono inp .1a8tino/i p sot, .1,tann ()I ail!, 1,)(11)iv pup pplap spud JO 11101(10,1(1 O111 ppti X1101'.11!(IOS 111PA010.1 S10(1111 11111! 1411P1011 110.1J OS0111 11'111 sum, pattwas own put a saltia.rojti! lump, XtitAi()% 'ttlapio.td tia.ipion 111 0111 01M)1111 01.11! (1110A .1,1,1A1 01(11! 10(11,1 1111011 Imp fljttti .sa:)110.1,)pi! J!,)til "f ti,1\110.10.1 ..10,10M011 110MOUIS P jo sa:)((14;) .103 (liLjoI ati putt ppti 'tti\)pio.tol icatil AA:n.1.111) Sunij!Jan stun limy? aqi polo .p) din 11()!040,s Aatii pini impalas atu, isapio tniapptia U UtJ Apnis imam oi ape? ota) iiP sdais,atil do ol atii tio!prz!ipJatia8 dais. ./fiannaajja atu, aJtionl. jo Sti!Joinai alp ittaimis ain.i8ait1! -xi) hLIill tiowritiaLlad .iiiJ!t1lt IUHI St1Iip10.1(1iithuomp 01111 I! ,1011111.1 -Upd .00111 X111410111111 '11011111(IS SPAA ooi ,n)j Jill W11111 t71 .11131i S1110 11 110,1 IP111 11(1P ;111111'.1(1 91111,811.1(101)A011 MIS 1)1111 1(111 U00(1 11 iiiitl jo L1i .tI).ti)iIt intunipanpa .saatli)(Jadxa ) I( tfl tnni.tod JO atp otp tniapptia ;mini% turni8 -do sainuni.tod u (Wu an!puptif Ailuapuildapuckiaituis JO ,(411 '.1;)(1!Itip\i). spAlt i(1n paiaa(b)ini puil I11L.1I ifOtp paut,n)j.n),d \TI? Aatii ikuop Jain»! :up a:).119)018 jo 'Jatutunxi) 'Apepuns iou-sPivt j),)11,)(hatill ivy tlimppty) ()Ulm pug panuittuoulap tut Any) ()I aipdruitip suoinmill) tit ay paJnianais minAJaitli pun oqm 11,111M ONO (II Orui MHOS t I 111111011P 8111111.10J SU01111Z1Iiii,101108 i)Jotu -adtuiin mai tn. atii inaptiadainn. titonios-tuingthul 'soul jo ati s.tiaipptia sastuds.).1 ;moth) painansoidos uo sop tuniJod jo pPt. poi until kup trai Jain») ay irauttinti8 JO NI '.tilltutpcit tint, -8114i SIS011 111111 0.1.11.11 tam mum; Janoiciatta uto.tj ato ptunpiLlIs Stuisni -uni!B 11()!I oi ay ittaptiadoinn utolgomi los (tit Xt 'uotitmils apit) uv\ otjuo tnupptia ilJa14 jIlj pun puny tlI sivatuina jo 111 01110S 1.0.101111111111 D11111 HOM 1101110SO4d S(114110 `,10A01%011 .1),111U11 -(4)1(1111) S01.1 Jo SOS110(1S11.1 110111111(i\OJOM Jo1 u! iqj pturtionm -.101111 SMOIA SO0080011 (1.10M pi0i\Sit 1110(111 I till stlitti.ouirt immix Att alp oidoad tit old uatim Ilyttotptitt Attuapilocloput pumas imp mil tp multi! padouHt asatu ;mot1 awls saw) di ay inpnis Huotiunin; lUIfl imam pal:into)) u! '14ainilld iv alp '8ulaaajul 041 ititzlie.100.0S %dais 5,u0.1pn1J) 50511(3(150.1 cuann 01(10),01A.0.1010 pun lont001sAstm limp peg 000q )111 limp 80),101) poiniatms ttop.uni JO MO 1501 .)4A, oalpptio picmpoid Jottnai 4011010S 01 041 '800)pload pue 041 )olounlos 01 001 popttal 0.10111 '40.1:100:1 0.1011.1, SPM Min ssal Hos -:30.19) 10 041 titukpi0A-;-tinunpaid 110is N 1s0) Jo 041 00.tplop -um) unms soonuiptod-0 p0!..11 A.jois 1003J inp 00)04050J sp.nr) untp 01 paps alp isoo 0141)40.01 itorinios humplup mina lout ponanal Anog -01 050 0tp utolgo.ni 041 Juninii)s0J 50.1nont Xtp.mp paniunuis 1,0n1 JO alp ism 0.10tvi A1.11,010 01(1311.10;354) ifq inn -Am Amp polios 041 sainpui minui ,00q1 pm) 001)9010s Aq ;)111 Auto A010 paq!Jasop Army 041 100110.0 p11100 aq p0A1oso.) 0solu, 110,INI11:1 OJOM ()S1i1 0111 Slum sou() mori 0.10m opp) 0711)10008 11 aim ohil 811)0.10/v4i 00)1010s JO) Inp 100)(113,01 1110.induto:) 041 Jo 0:Onnu.n4.10)1 alp 00apptp 00 ;op Omi siand JO 3111 11.1. 1)ilM0111! olp *ir11 g.o01:).0)0s0,1* 0)) 01eplain15 imp 041 ituipuodaptu ulopload `eitoAlos Appqn Jo Apnittout p01).1)10.1 s.0ou,11)01 Attu) at ssol pann until s) .1)041 p001010.,op Aupon o 10d (11.101 .101M0 01.11 UO11:10,111) 10 ..EnpOU 4:ms s! 01.11 SII;) UI uosiad /4011I Jo 0141 SHIM/W.1 0111 00.11111 110/111101d .10M01 SON00(18).1 11011 0.10111 pawn)) sostmdsai uatinn tp 0.mttn Apooptontopto Jo mu u1Ioc) 5,.0n11 '0aueppiti s /imp peg 00o4) u! J!inn oyna Apnis Jo wovpud linytios -000,e,) 1,10)) put) tpuus ) (9L61 IneXP polyp.) paansnow pun 0:01084 01 alp tunut 1); Stotiosum sioupqn Jo Aippul pop,m103 sJ1U.itii tlin8v pulto.i Imo 0.10to 5501 hi so,u6s ovienivn se sJ0lairmi1 11101(10,1(1. X111.110S INN) ic1111(11 111918010110.01:1 .08u in:opmukatil, uouna!plun Jo de.n 1LIPI.I Xtupuy lpm p'ossie)top UI pniap 0! 041 pcim l;y1 110s '0;) Jo] 011i '100100u1 07,111'4030J 111111 SII11 NI n Isom -8nano..)00 0) UI 0:)0101.01 'U0)11)01.104 0:nos 1! stviolln so 01 podx0 ingi papin10,1 -PO) ,5300 LII 440:01 8u1A10s s'ougnie 000 ono.nlio) se Aatn .aapp smt Si 0,001) 0Juli omit 041 (lop 00)jou 1" let .61 so e at8u)s soils!ple)so artentu 04I poplavni tivpu) inn .l.nr) IEM0.1

Aivuuuns jo otts preasali uo alp lea,8o1 ampnpui

010.1.4 oto onni sownis pailo(10J hi() ;nil )/%!Ianpui antal 000,0101 Amu

uloppud e 4 Xtunios 111:1111).01.101 liN030.1(1 011.1, 55090.0-0111 OBI InapuodapJagil UI Imp fifia1911S Ill ;up isannoi dais JOJ Xupdtualot tourn) in alp pot' .(101s ulopload tiounpin oin :Inituntuiolottop Amp am) p04010.1 pr)1}i010110.1113 4i).811 JO mu 'plop sum, lituptuJ gisotilins in4) tpoq 1;500)pnaa pun 30).ol a:11109301)(0 Ilan NJOIM1.1 IMO APII 01 0(1 -WE) 110.10105 50 0m idtuoun 0ouggua 10.1 1)apa1) juatunal N011111(1fl JAWS 'swavio.ol tuavpiad 0.01 tiuvq05 sauquin 1011 413 SIONOrd pa1q0J pnantinatu -u) 000084101 sn Amp In00101000aq0 '0Xn

46 SUMMARY

To this point, reasoning has liven described as a learned activity and research has been cited to show that mildly handicapped students, like otheN, can enhanceei r, reasoning abilities by learning and applying iiproblem solving s rategy. It was noted that the concept of an inductive approach to teaching and learnini is well rooted in history and that a resurgence in ,idvecacy of the use of inductive strategiesoccur- red followpigSputnikin the Atte 1950.5..Two once-popular strategies, 'Discovery and Guided Discovery,- were discussed whose stresson democratizing teaching-learning interactions in the classroom and enhancing the diwelopillent of reasoning abilities of students has in- fluenced current educat ional practices.' It was found that interest in

these inductiye strategies has ebbed since evidence of their effective- c ness has not generally met thedexpectations. that educators held for them. Further,it was suggested Ntat.these strategies would not be effective to teach mildly handicapped students because they lackpre-

dictAre sequence and structore. - The research cited, concerned with progtem solving tactics, showed that mildly handicapped students could learn problem solving tactics if these weie taught in a consistent and systematic Way. Too, itwas found that handicapped learners were almost as productive in creative learning.tasks as their nonharidicapped counterparts whop theywere taught i,ising a structured inductive strategy. Subsequently, the Logical Inductive strategy was described in detail with particulai: at tention to it's three stagesT---mass, differentiation, and integration; and to the five steps that comprise the strategy-7labeling, detailing, inferring. predicting-verifying, and generalizing. The research reported demonstrated that the sequence of the Logical In- ductive strategy is hierarchicaland that students'performance on problem solving tasks is developmental. The research alsb showed that chronological age isa better predictor of problem solving performance of mildly retarded learners than is measured intelligence. 4 mplementing theLogical Inductive Strategj

TenhinStrategiesand tacties, like almost alleducatiebal activities, gain meaning only when theyare put to .use.f or teachers,,edistussion of the theoretical aspects lching strategies and tactics-t*widesa, foundation for impleme .ation.,' discitssion is necessaty;:bUt.not sufficient; to meet a teacher'sneedS.' Attentionttgraiso be givento certain teacher characteristics andto the educhti na settings iNwhiCh , . the strategy Will be used. - From the earliet.Oiscussien of , . strategies,it is clear that-thbyare net , equal in ter*or:the amount-oftime and 'effort_ they requite ofthe: teless E.xPetiencet elfru "th--lpher.a 1rote teaching'; as a style, ist easier and time consuMing than i .dactive teaching.'gofor the keacher Who.- chooses to teaChinctuctively ihetemust be.the additiOnal commitment . to structuring SiiiqUenting, and assessingstudent performance Using.. the strategy. There Mustalso,be' a willingness on theleacher'spart to, relinquish sole leadershiP, Of Tall Owroom activitimi-Josive.the..:studepts a greater 1)401.404y role. ., . )... , .. We intuit also takeintoWcceuni-the."back to, basics"movement that is currently prevalent:4i ilye educatiOnalcomMunity. One' need' only look at the emerging competen0,testinS4novement for confirmation-of the pressure on boaAls of educationand,,school administratorsto in- crense the academic performance Ofstudents. In special education,we - are faced with a similar demand: the needte. raise ttiq academicper- formance of mildly handicappedandents so thaLtheycan be mai nst reamed. . .. If teachers need to improve academic achievementscores in order to satisfy the pressures placedon them, the temptation to "kictore" about both facts, and concepts isgreat, Althoue research suggests thatrules

45 II! S01(11:110.1(1 0.1P JlIiq pou.knoi n tualgo3(1 t3toni0's (on!ianPu!) -uo:) ixa :9!attignil N I .10(10p} sumis. (9961) soulnaads 10111 010,1 APO! :1.A10/1.0 01111 S1(1131103 SP P JO .S11101M1S IIII00S li0:)11013O(1 \ 0(11 SWISS! 0.1P 1011 JP01:1 I(1 011108 101 8.101111'01 Ot1I.118(1I1S 01. I! Ii110111!11. 1P111 SM011P tI10111 01 Ji1A0:1 u olj Jo 3!ttlapn:w plauto3 11:toth j '3anamot qi uotur.)!ThsnI Alt() s..)tu(t;)ati apppi).1:1 ot atii tuitixi) in.til lIA ;LH! littopm '.1olvto J! iou 'amsnpxi) on!rhil(lo Jo lituurutpit paddnatpung s.totunal s! julmixo !atil 3pu1pIru! !gills pun 'suptuipumul pinod. ooalin s1 son!palqo Jo uo!ur.topi) 0J -tiny pa(1(Initp ui)Jpi!tp °sin apopu! agi $(1 1lr.)1o1otpii pun typos .ut;utulo)nop Hoj alitina Jo inuow:utpi) i)A!I:))I(loI JO -tiny pa(1dy:tot. saauJnal opt! luno:rm sitiothaa imp (n) pioiaa liupplut utiopoii suo!spop utogn litotianio 'sa!`iiion.os pun (q) idopt! n a.00laada.! Jot 8totpnio sa!liionals spatjaa Jtj ow° siootps ,s1u01)1118 intu , !itio.3

1.143011.LS .1%16 1433NO3

Akpi pp i)sinil %Hoist pide otu 00!unanpa JO Aipptu poddea!pung -ros 'i8otuaio,4 i)mt au daal 8tou.Inal pun roxolotnifsd s:ms!aormant'ut UI puitu jA4 'avitunxo s! pigu8n -qns,0 itolunis Jogtuou JO podde:)!pung tquapnis ploy intokawos angeHau linkup% Jo 1!inii pun Imp J!aty piuonkoi so!ftualinitum 'Homwor)) (g961. Jot; sidiEnt09 aJapopo gunk '8u!timoi V Jnpulod pun Him !Hochman 39:Apotty,t. stip ummoid si !mug 8upopluiti samunpoddo JOJ -ant; icIpt=.)fdicisaatoeiv..ssin r)imos sIsni intli 0.1P Apinu9sno.! uNpAk -pil tuo) iumutprid JUPJ JO sjuapois pun am injam siuinutigniitImm .411i)in1ihapn UJ il!utiosea sp.p tquapnp; 80!mi pa:)uj p.):Intths tium imapina Jo i!atil sapooladuun pun jo Appyi ..paatrms situ adifi jo IJimo tianovide diati splapnis ppml an!i!sod JpS 100 Atwonet.s! JO Ittinuoacipui) 'aanannou qi sattiomus os.Inou jo Aep- Anp uoymunity ant24 spiapnis aligns soup pulytt SUOIIII1:10dX0 JOJ imunt.d.thpocrmtp intp loajjn-usrmum ijos 'Ido3um 4 intim odici jo o8nssinu soup n pyunot ifaituo.5 uoym sty fi.untuud -clO tc.ntusd UI Huttjanoi st Ay AVM JO I! oi0.1 iANoinais V /001 11 aqJ ampa9o.id . UP!) 0(1 A.h1A liutplanaa oyt -uoyanul . ' ' simptys intim ty sayt.taila.rd 1ir ,quppnis 'snoton "Wo p,opJA4 Onjj 'yyttly .11u t spin) iv) wittoplys *puodso,Loj / ,. sum. alp qualm's j! 6atp 1904103,ellt JO '130.4103U1 A; spawn lI spiaptyi Ay titywnso.id ,joypniu 'kyAnan

.Llint L. The message unties across loud and clear: lookto the teacher for what is to be learned, how itis to be learned, andto find out whether you have learned what or not you were taught. Asa daily experience, this view of one's role in school hardly fosters feelingsOf confidence,competence, and indipendenceapart frnm the reinforcement following orders. . ri!ceivod for Now.let us look at themessages conveyed by the.leacher inductive or, for that who uses matter, deductive teachingstrategies. These strategies, characteristically,are almost devoid of "teacher tions While teachers telling" ac-. ITIOtil often designate Thelearning objective and may even construct the problem that is the sciurce ofthe learning' ob, jective, it is the\studentswho identify kindstate the problem come of the teacher's questions. as an out- Too, it is the students,guided by the teacher's qqestions, whosolve the probleM andverify the appropriate-. ness of the solution before they move on to evolve the ruleor principle that goVerns 'the soluitionof Siipilar problems. -Unlike rote strategies whereteachers tell and are'told, inductive students do what they strategies allow the teacherto ask and permit stip-- Lnts.toparticipate as they ch`oose.If they are, for unready to participate some reason,- they are still involvedas they observe their classmates' participation. In time they may realizethat participation is doubly rewarded.First, studiMtsare rewarded for Simply respOnding. Second, if their yesporise is partThltyor wholly correct, they.are rewarded' with-a' "welldone," Wen ifa respons.e is incerrect, there 'no retribution. is Instea41, the teacher backtrackswifh them to assist they reorganize the as information 'about ,tfkeProblem and/or to thif pr,oblem, wIlereupon restate thby':iithr'rewarded frn-,taking'part in the res t ruct uryag, act Nities. Student,s---- and teachers'are equalsas they engage in inductftte pro6len'i solving. Theteacher's Message, irffierent No matter how in the strategy, is you seeyourselfj seeyou as an able person whocan succeed. Othurwisse,I wouldn't askyou. to ioin with me in' this Ovity." Daily experiences-of ac- receiving this kind ofmessage clin go .far to shore-up flagging selfconcepts-,While evklence ing can be constructive that inductive teach- in developing studentspositive-self concept is not overwhelMim-L thismay be because so little research cione on the subjA? has been The 'evidence thatis awailable,is worth however. noting, For example, thy studyof the. efficac. 4.of.special claSs placement (Goldstein: Moss-& jordan,1965) showed thatstudents in classrooms where the inductive strategy was the dominantteaching stylewere greater risk takers than studentsin classrooms where the styles were 1eaching more eclectic. To illustrate, thesestalents were asked answer* list of questions that tu started with questions thatall cbuld; answer, progressed to questionsso difficult that they could not bly answer them possi.- . correctly, and. then backto questions which they were capable of answering. The special Class 'students in 'theexperi- mentol group not onlyanswered theeasy preliminary questions but

47 osp! wow 1)cd O az)nnsun ay km iplaupp 'suoqsanb Aalp.uaqm aJam inn8u piquoiJuoa LIM suOqsanh APi L1IIi .oion 'Appqndna Amu -1109 panu!1 puodsm pun paJamsun UI 'isnilum u0synduum (100.18 to sffiapnig pimamsun is.m dno.01 JO SU011tial)b glIAA 95110 111(1 IlUlf:11JOUI WOW aAISUaJap, SP 'Aay. oaam pam0.1009 Imm iinaupp -suousanl) j, A04 papuodsai ytm 1.. Luop mum{ 01 rip? ay 1199upp suolis*mth lug 9Jou1 'Xilulopmituo Aaqi paatajtio9 I puodsaa An tot 0(1).1., maul al ay! Ja!spa tioolsalth 111 alp 1)119 Jo) ;NI lsai ;nuainJu(r) 1)1111 wh)q Alpr(l uminqs Imo /fay, mann Wimp! alvi .srto

atm, sun1a.1 Jo) mil .ipnis patuJyao;) 5uati9timad pnui s.latp.wasaJ sJanaN 8thsn ) (t41. .A.matn Suoimo)av al lp. sor)auppadxo:AJoato ormanuth aqi Joonnyoq Jo) .smapnis swapnis ,aton pTly Rpti tuomsrap sa9aauatha IL1L1I lialoaload sapumadxa J1 ssmans pinom aq amau di..poo!riut sun .Iam yoq bow) pal Iinamtp -saith pug oft1-51109 stuai)Ilsodiuo9 04m 111001:§tiPla %Ell101.10(1X9 IIlqI -0,Id Puy I! plata Ja4esataupi:)9tha aJapPj pinom 41):4pp 01 9(103 qpm itiqw0(11.; 01 ay sun_ apin'aom isan1) .511(1! XL0mOiloi 0a41 ainpuj Jammu? alp iplly.pp isanh stun Into piqhmaJd 'way 0,j, }nom! Iiinto!`ie lunssaidun imp aqi toq:H4ft0 A8apu1c paMmis qt!m jualum UI pTi6s04:nisd 'smut! Ii pploqs aq pappot try IlIJI uaJppqa tu alp du0.18.1Inuaw!Jadxa ()sin pauuopad Aunissa:ynls LII titilp_altuopirm JOUV ISJIJ z sniaA JO ay 'Apnis Amp aJam uo gum ind'y .0ay Je1iXa.1 ssnp sJoad a!pnuippn LiOqnulaul01 pun aaam ApUPAIJI11815 aTiodos UI magi Li! loin lualqwd '8up.olOs pn31d8 55113 siatpeal IIJ pup J!alp ,splapms panunqua SuplosnaJ Appcpl arm a:maJaii!p 10 may anquppinub litipp_qqf 'Appqn aqj sia4Inal imam osin jo alp ummdo putt .1!ay s!seqdula ppis -doianap vow u! '}un1u0,1 40m qauln ssat .uosuoilaiduim -all !opium) i ssal ii:maJaipp.apphinttuaJ L1 padse.s!ip J0 toy J -his ,somp a0napnan- sa:nuniadx:q yim A:nrqta Xpnis pampqs m04 sapunpadxa JOJ 'ssatnns atpuaydde panuaua8. Aq Auapnis saauaoadxo ui Ufl -anpu! Aianti poitlo!,lo tuocussup Ulla OU10:10(1 TU71111,1;108 SJONIOS(10 palm' Jam) sioapnis stion pIiq uoaq 01,1unianta.i LUpattionu! Olp 8up1Jnar8L0411:01 8u0o3esu4U1 un8aq modpq.ind Aay'sp pun0J IULII saanplq Ill aumq pun aJin1mat4a aJani Sumittpoiew Li! alp Iumussnia maps.. qualm's nitinaaq 'amnion 8urwitum saoquiol1..1 Jo otp stinp V pomp.] ipisai unuj 4puis pun s,Siaquaap3 pannoto pup n UX!I Imlay 00q.lodwd JO ay Bluopms utmqm Amp papal pidope alp priOtoi anoanput Mop; 01 a/Ts ay ulaigold 8 paivaHaid 01 way gqi Aq 'sJaii;uoxa Ij pin0m 'mad& ualp iq tquapnis oqm aincimand Lit 9m-h1Ims/ft; pun p100.101 szgt:nnucido u uuimmd Suvolos idupwApio 01 ay maisAti tog ospi idope Juj J!aup um0 tucqq0Jd huytton 'Hasodand pun. Appiuniin Ogn fl 'Ailuopuosiapul. Appp pun AllunuttErms *pip -90 .. . . . 5.011 tio n spu9dap aquom JO 'Haolanj lou atji paial jo Hillop a441t4p% 04; is -ti ao!.ur shtyit17)!Jatko .10.4 'apiunma ny Ai ;n11 sulannis u! Inp- A:pltjja 'ARI11.8 x71 piluatumad pLui . a.mm.'uost.uiduma o lootps Jalua " OXP. 1104M Amp maank Kul Apuopupa s magi Pataitssu tmo.Issiivroik 'tintus imou aio .10nomi qq alp 9 14qi .. II, Aprils sod onto Jo ;)Atie8ati 100q3s -xa s3ai1:itiaj, u! atn illiatioyad inwattp.iatka sossii19 p!p 01 1111M 01/1 ioti anet.; 0(100 1P11%11 0,\111Ili:111 tiOr111111! 11.11!MOI Pioyas HI! 01 iluitum SO11101.10thql un870atu ithquapitu! alp I ralY OA '. pliptli Miajnits tipm ;ini -ins H11.1011 . . , , ' . ' 4 I. s SOO S. t011rld u011PIII.I0j1/1 1! s! slat00801 appssod 01 ail mon liutatintoa alp .tun!nn issat Jo nn sluapnis , aiii;.o4 sIst.i 10!Lu 0;.)Linqua patn 'aRn jjas um ' 7 sr -ism), ,'(17iAn stietpad ay His. pla:moa jo atn 8tpuatOttans -xa saamplati tia.ippg3 tit atn pnuotutJadsxa :101. diuL03 elpew. 1i 01q0;Still drag) 01 AJ1 b aannsun, pi i.jo au su9nsanii pasod 01 :w)in 041 Apptf!ssod. 1, ifi ii1.111(1 SLIMIM .....,jOU U1001 08.0 HI! I! -0HUO3.i1AllOHOU plIT.H1la.',00t1iitIh IOU MOOS 01 at; atn OSP:1 JO) otim adoat uotiliflitpiT111;10ti silt:quip; ti!.0.0Jipi ineia.i ssatomp 11 pamaas prtp agog) 113511013 -Xa paatiatiad zito sad.iii ,jo a.mpin tii iiinn sulomssela win s! os gain') n ' Jo otti Ieuoile:mpo .1.1mi .ilailinaain 10) Atim .Autillof Loo) 'pdati oaappin otim (pod. pun into I asati saauat5tadx0 paauanutp an s1say imil Join!? Liu aqi .finn:)!.paatis )$;11 uaappya ,aiann 01 ;ippittu onoaw, JO 7 flas,..n.rnir in atn tpilunto r i , aplari appiaansun stiotionl) I It; iplaupp Htplinopoj ;Lippej tnim 7411 14a1pp11 .Stionsanb.' ' V r 'aulos s.lappai itpipu uousanh 01 injualupadxa,ato ,sitlaptns ssau8un1!m 1H1S510(1 'to spituann 01 amsuu ,. t;!tp 1iisn0yttio appssodup 'stionNanb iti.Swi - 1$;088os.,:lott ul! .ans!piaJon jps idaatm pun Optoa pm); 01 nos 7iA!lantiisap ,i,saati7.4satixa sr An 01 luattploianap zmI1att1)1p,p040 tuntoadde 'Ip.w.loid Stnnios ipautonl :ui oi titi!puotisaa .)ziakti St10110111/ 11 NI 14 01 1y:)70. into atn 1-Pipq tuapphui 8101os 'dims s! up Ipphya.td pal(1p 17 yontt NutomplAra 'dais .111.0.1l,Wt Cs. ;m1037Hiiitiapniiii'sntn, paumistuati 4... 01 8u!i:vi pull uagi ail] Apipinhiwup 81i1.41:mtp 11HOJ 4,11.g i FAI J '11041311 atm, pluutitisaith ;El 4, Aani.tio!AAnc.41!AA umnum.o.lam pal snm iou -u! pop atu. ;Liam paluasaati i.fpi prn At; inn J41111111?X0 piln all sluai'404s loti) ..p)til (Jaganin .01-st'oog..... viatil e antuou jo I Ulm), Isf suonsailb 7); pa8motoati1) oi tip oil; rcani.j.0q sppma amt, o pan!aaatosivannis Jaillou ampsod mt antinNati ism.; 00 JW(11 ft)(III stuannsue 'mum, atn sasuodsol 7NI.0) -xa f . , fllitout!Jigt smappls vo4V,!1) 1ia88ns ssauntetint JO ssauquetnooj u! alai '8und 01 a(1tv.) gnm atn. 'stionsimb sjittaistn Amp aJam pile oi )01.1 14.10.1511l.uppiw 'oilittlipm SJIP t alvt . Jorwrtfkig umoils MI ,,Hatii s!e,,pnis tptiwitiais!sum Jim map% jo annanpouh- tp pun ,,. tpappLid '8utiijoi; im ppum JOJONI oi aas -ung patide:pp swoons iciplpit ' ep ldoUll li 7jAnjassn A1(1(100%110.1 Nonoultin v mappud , pali11ss11t0 ss; Agnipttau! u .pattiosun ritj litpidtpoliti 01 Oft) 'utappimi ;NJ Anptietioad jo litnAlos j! s! jo oqi 'Ousea.13u! 01 " pftiOt0.1 ANainals.:)Anaupul HI dopAtni -titta!putiti,Apntu pad NUONJOd $)1 . 119110.1d(111 1,1101(j0Jd 8111/110$ SU0111 IMAN ' tat y tt ampood Id 41) '8(1)111n'

, fit ' /..11 of. , FOLLOWUP STUDIES

While it is important for mildly handicapped students to be competent in school, this importan& paleS alongsale the significance of. having them deirelop competencies that provide the haindation for their ad- justnasit 'to the mature world beyond dm school.IIis important 10 recognize lluitthe education provided these students during their school years has its real payoff once Ihoy reach school leaving age. Compared to Ihwhool years, an individual's adulthwid is far less structural, goals arriless well defined, suppirl and resources are less' accessibt4,, and the consequences of actions fl're far more dramatic. The. nature of theodult world requires a great deal of independence; in every aspect of living. j'he teacher is no losiger present to guide, to moti- vate, or to confirm the alipropriateness or inappropriateness of solutions lo real life problems. The individual who has, nor acquired problem solving skills and a self concept that allows him or her to cope with everyday problems faces a relakiwely limited lifestyle., A reasonably good picture of Ilw adaptability of mildly handicapped adults catt lie constructed from the reViews of research rewind in the literature ((ldstein, 1904: Tizard,19'74: Windle, .1962). While .the many followup studies cited varied in their designs and on the basis of changing economic conditions, nonetheless they showvd that mildly .handicapved persons had proportionately naire difficulty in getting and holding jobs, in their marital relationships, and in their confronta-. tions with du) law than (lid nonhandicapped perSons. Further,. as a _foundation for the development of -the Social lArning. Curriculum a survey was made of agenc0 serving mildly handicapped'adulhi who were havang loll related pi oblems. II was found that, in the majority ofit cases, thesproblems arose as a result of inadequate social skills. Foremost among these were reports of overdependence on others towo. 'I'he prAlems that removed Many mildly handicapped adults from the job market could be Irked to the inappropridler (less and/or absence of decision making abilities in.their personal, oc- . cupational, and leisure lime lives,. . II is i3flportant.0then,that asWe leanh reasoning skills to mildly.han- &capped students-as part of their Mirrisgrum, we also prepare them to use theSe skills in the future. In this senge, the strategies and tactics that tvachers ieie should be presented 'so that students wlopt them as problem solving tools in sChool anti, at the same time, integrate them asi. aids td social adaptation that they can lake into the adult 'Wo'rld. Smith Greenberi.6-(044, -research showed that an inductive leaching, sti'atemy- that is logical and systematic can he learned by mildly handicap-

\ -4. issi stialents and .nsed independently of leachera or other Adults. Thus, when wtj consider the question, "Isitworth. Ilfetime atul iffort required 10 teacb inductiVely'?" we find that the followup sludies and research suggest that it isparlicularly*When teacher-s want students to acquire rules and principles for imlependent problem solving.

50 ingm s! poi mg Si. sr os,!:)aJd piu8isop go! Jo Hiraggpal so!8opilis sP :oppssod p 00).1 gogm uoilpopm pup aspodso3 ;mu -ssagau tiJr. tuopli)ral Xiontoii 's.fotAPgog inn! olipulaisifs 0/91:mpu! tIdLlA oto Amissinou ut3p10.id Iiiranuzs sraptipqaq ;up X1IIAIOAO sapid IMP %11(11)111.1(1 ,LIP sp `..ol ipspg JOJ- tprapizipiJouoli Xottuporasuivol solptu it inguasso .101 Alppui poddprainuPg sluopuis 01 idpvii IpialioX ippip:raipo slitonos put! uoirrang sp 'sift) Soto up3 0! osogi .sXptilas 's! Xpituporasturvi !pip .asuas 01,iggitarai -pluo.qui);) sum] otp:graXi quip, pi.p)m rag Awl' podderaptniq ()I -aid ).11,d' glow ot lamp 'sipapAs 'ailiggivq:) sigopois pgrag imp; Sinia g! ramp lomps s.iao.ni:) prig og) Niugpo.1 soggpip Aotp ipm poop sp 'siin pup sJogopol Isom Juotv ,q)!Aoid. dip sagginpoddo 01 op ..os

9 Mii.1.3 A13011 01. Rsr, 31-11. A93IVILLS

.isovq Ji ppi 'pp Jo ow Iliti.)No.I0J go!ssir)sq) s! pappolgt 01 oiplu p osiri rag irpini pi ;imirai sp e Xing:wig ssoaiiid pup s! snooSiggimpo ig ..agi gpvio.U1 itipiiir\t\L ipouldoloA; Jo iiippin padderapiniq 'Sluapnis UI MI) -0.1(1 'SSivl II AllIll pourams imp 01 AM) ggpal tilan!loning s! sno!rappg pm? 'ssopoping AA go iglu) 0) Nuoi.u):)p ;pp lotiapol puoSog itiqm trar.) og -go tra.po.Naos ogi ..pramig,H) .sluoppis 10.11,4. SI Ill 11.10.1.1 091 Twig .oslia onnonpul Nig Xtrapipitims',)9.onrd pip! applanseigd JOJ siaitopol pue sumpuis ,):)go 01 pal Amp iffi!iag ;)ppgraggpro loon inn Diainais *will oip trapil,E) mg SopsrattioJaad Xipluogog appgjoJtuoa gipin ogi viRaiv.iis mu. Joti:mol 301 '01(11110)() 1111111 inl Strappin 01 ale) oil) isia JO Xinniaddp ssal pegi HP Xignmnot oi imp 'slualmis .10 OlIti SP1I ..01 .0(1 ./.1.0111S 111 of ill IiiVii $11 'sitiopiiis ol.om piriliJ gpm il tuopitud pup Imago moti diog 01 Onlos ..,.11 .JogiaraA ;pp Jogaval oi Olt aq oppi oi Ailop -iiiJ8 Ippurpp souralogios oil) parasol) sosuodsoa luoJJ till1011110; il.le IOU. SP. 01 .: 1911111 M.1,111.11 A.1111-SP .1,1P P 010.1 11010A 1f8011!.115; SI '1101i11 MM. U011 01 -131(111101 ..,1A18 11,111.119111 Utp 01 01 till1i1111.1)S IOS .MAO,U1091 H g8110J iods AMU MI .8goras '.1.1A.1MOII gogm alp porasop asuodsoJ s! log -um:rapJOJ 'Sul oip Joippol Ignogs ssossii stti Jo Jag um° 'iinginuragJod pm agi logapal Isli ogi i! igN!J iraogsnIti spm pippin in P Sum posi9goom) og) 4igilopitis 'Stitt), .pq alp 'Iotypial sapsinhoJaJd oi Hupp) spogiagi opitpui 4 angoPpu! Sirantig imuolupp0 11! s!ti Jo Jog Aupqr 0) atinuniu ogi 'ssa:)0Jd &um) 8tiqpivi oi mpg_ agi amp ii)paini oi wing gitiopnis -rigrald oind u! ;nil IMP 4411110..)0.1d XIII/t0THI )1111) illI1 IiILIVIIIS U129 ii! Anni4sogans aindvpiraid waigoid 11111AIOS 8;1111,A11:113 ',..iI1101111-1S. ".001 aA111.I 0) '1111111 SIUOU11141111111 OU1OS AMU. MI -(1111111) 1101111110.) 1101IM alp ialpllal AIIIi11111I NUM OAIO/111001 U1011) Uf Sulnios maigo.ral ihipAicip .:oolus mg 'wino ii Amu aq P israJ ow!' 0 gpAti '391101Jild AU11111 Jo li)110P11)*01i0III 'MOUE/SP:IMMO UP:1 O1110.JiHI .10810 1(E) 'S.101ll.J0(1111 UI '1911 0140 111111JOJUI ;mowing JO Jias idagium ! i m110111.11 JO otrag 0 e umpigs ol Imp si\lig utangn )ili s,Jogoimi goplJum . u! tgq Jo Jog . Appqii ip pawn() uo .1:inj . lo i saaippol Om spiopuis oAilq 01 imp.) fillpia.rinp pup ligElp11.0; fIllM IOU ll,10.111.111 i1.114111:111 HuitIONINIJ :saggppl HP gum flit uttunig 'sallupJiiii -Pis sinap ale.11semodp 080e.I jo 81gu0)sea.1 'Howley! -mew; sio:)pn)5 wAn mi Ten!) ol weal ogi .ichige.gs ill. ;el aaronn o1e1.103 51:Ods1' Jo ay icKgp,115 Inv ut %Imo) plw. InAn pool! ;.):momsse Oil eadmuls J!ain .51p)is II samilo M fli puol alown 'ljnoupp Ifue Jews 1011.iiew SSJJ80.u1 mow puoicaq JIll mei) li1eamne8 sda)s jo 8011.elei pue .8uwelop sillopepi anvil lied Jelem Allommp ilonn on podsn Jo :nu Mime.lis Jill uleindluig ;miela.1 80q88n.gs pup uogeJIHOJJ -1)!n0.e1 801' SJOAASIIII AVM °l IS .8110.1 oaojoji 801/.98 AJI 'aanonnoy 111I10111; Ajsges saAloslumn Amp :me lUll 8leo9 WHIM II -de III! II SI smod ieln OSSPIIIIII SLl ll.),H1 '11011:H?0,1 H] 1110111811111S.Jilli:HI:11 1P111 .1111 1:IPJ 11I111 'SIIP.i.1.1(1 'SI 010911111.10,110 1110(111 5OA1.1S111,1111 811111051I0.1 ,ieH(.11111 i1I AIM) so8eIs. ji A8011I.11ti utr, s.logaiNg iniew sithell8pnl iv 51111 o.inpunl

NE131:11119 S3

II si loll oviissod 01 .geol!:elle, He Jo mil steoltioad Imo Ilt8jui amlins osan0;) Jo `80111wo1 .icion!rinpul suonetoosyrano 1)l11! 'SIMI:11,10(Na 011105 SaIIII0111118 111111 pOSII Oj 1515511 1It mit (Ims ;Ii!popul .1i8a10.10 (e) 8loillield inn! (q) 811lpolo5 811N:wm -sa411:);?1(lo fitquintid

h11111111,1,1. otorniptil 811N:emi s! posit!! up mil 81.1!mo1loj :81e08

m mem sinopms ma5Limo .qinp ponj Jo .08palmoul Z IUPM 5111:y111S 01 UI u.leal MUll anIoa sulamoml (1.10101),1) ui n :II1P11101Sics pee 0AHanpumi 1: OM IIIPM siuppllis 01 meal mil soliu JO sigdpli!ml owa'pell ay) smeinios sassep jo uouiam '5,tualgoid "8.a 8o!8noein letiosJad .smnipt Hu1IIa8 'SJOII10 't? IIIPM sioppois Oil omob:m aqi jps amialejime) imp pin mow1 Lump *00101 AN lip a!mil titimplold lounpuodalm!

111111 'SW1:114010 oj uatin somiapadxo 141101.1H (HI injotiod pee 'anjsuatio.ehuo:) eirelmaadvA Nemo ppng auo. uodn J.1(1101111 111.81111.1H1S lattig leg] luamsom alp 8.1U(11)11 iliflhI JO mom, a8pal pee Houma:m.1(1 01 Ja148,N blotto! Jo Inavoid 8w/we; tile ale.1 iltawsum iniam fell Jo og .sompqn V la!nb aittiullso Jo ou41 ametnap.i Jo an!podeoid No9uo1Jiebta WM (HI :WPM AI HI ill11 tuovimid Nuittnol poau Joj icui unt;) Amu ,1,11101(I0Jd HHIHHHHI clip HJ.mq pile, ipHati:olientiuni U tippul ato ituoviant

7,9 Suutpeeillusaaps sampallo ;yin() Xaminp1 Joi 8inganal 'AnmJapon litlnaapis Stnyanin SOA11:101(10 'tiM01101 paan apt:iap mon ;up anti:sidso.ut sni inn Jo rinn!pe sf4-n-i-li,nOW,Joinin mil-s-nrapn-F; am !matt .111n:111 0.111:101(10 !;0111A0,1(1 1P111 SO111013AX.) pinnalaa alp -1111 piWaimpain alp ipoq lino! Ann.l spzian Jo otp .spiapins !minim alp swapop; pain1 01 oil ;Tr Annisanh 111111111 310111 aunpanon! Rpom MVPS 'Juni Jv q! '3a.N.).moti Amp 1)00U (11 01 0180(1 0,1111h111 811111; 111111 0Z11111.1011411 SP WM S01111/10(i1110'.) P '100M P JO Jeaii ()I S.1110ti 1110.1J M011 010111. P now,pitual simoi Aionisopixa no inewatinn! 10../ 01(11111')(0 0111 splapins Ion stuapnoid Anti! liti!Thiom 110M SS11(:) Sp010.1(1 ',10JJI1S nom 'J01111801 asonj. pawn!1 swls liwaq 'pannatnop 'Ilop9o.101 los Num a.ln saatlamnixa paprnwl! ssaappn asato stnapio.ni .10,10Mini am °sly mow! imp ;magi spiapnis wm 0,11I01 0111 S10011:114 1101? Anpanios APU1 oanJ Jimunis saanal.linixa u! ;up )/'% 1) Anunintum 550.1p( olio Jo wog Jo ;moo sooss! aM papi.s Jim Hunianin i.amiaalqo 511L1. si 1 vipun!J pun luanbaii JO .10.1 150111 1;1011:11101 WALL 0.1P 11(111:611 011 Asea SJOMSLII! 0.1. ployin isatilins imp nopo:njwinnsaaAo am ainsiltia ipoq alp arnpatuun )un Jo alp Vimj 5tump:m(11w 81nuanal so/in:0010 imp am! papapn; NIsn 9 Hi A93.LVNISk

!tom pill? Xlmn!!!!ii 1101.11:1010S.0111 JO 1;i1A11:10l(10 ;1111 om '110101(1111(E) .1011aP01 s! ,a,,,w.Ati!spiawils III $:H S)I$If! pito !pm peal oi Jo atim 8 .511!0 inatuRlInJ a.Niumlip, 'nolo spiosaida.1 lIP Jo minium Hp Ict.i.n my! MA JO S(1011;.0111 0111111 411Pds ra!Hol aAwnpul Atioui.ns 0.1, 1111.111;11111 /1A011 tin S111!) 0/01.)01q0 0(11111S 1111111M 11 11111111011-diS W1431111111 Ifh11111.11S 0111 X111A10110.1 SII0SS0( 0.1P '110111.10.1(1

by:L wavioid

011 :101111101 4;1111 1111110J 111111 IS0111 11 0111 1;111011111S 111 0111 Sta113 a.111 Ann Jnani! tnni.i,E) syhuis!! Jo a!atp inappud Amu tianouldn S11101(10.1(1 11,1,11110:1111, IMP tiriPM woos apie osn 'quo linunpianuoa pun opp!winr ,,51(H)L, VAION 010 kq '11101(10A 11011M 0S0111 0,11114001 -tionfolun tualgomi 01 .1)1041X111./110S 9110 1) 111111 ;141 sovn popathiann putt ovio,Osoputt ,"tiooIpoJI1) .10.4 %Omni) uo11M, Ippr..1 ppm) lou Opt301 smisvas an paddois 1Jom no alp !imp pawn paam twm awns nriaujesi 'Inapload 111111 apo4 inp.JOJ papipisqns Haosspni iontys 'Spiv pop,riatis III Nunota !no alp Amtlisaaau Jaiind Joj inp !mom! inn ;jai n tunssamtun UI oho oanjins JO otp 1Jom Nip!! asnn3aq MIN 111.) if1V.103111 110 0111 SP MO 14111 01101) 110M Ii.1088pfi ' Janatial popuhip IULII 8uipturpilapun an! idaanoa Jo ,..nownwaIns, wpm Ilion annpatuni! pue attill1,1'81101 pool! JO atp :sinapnis ilti1111:1all JO -woulun 41.111:1.1111/* inn! '3:11111I30(tkil &Lot i!Htuta, atninaaq NI papi0JjtMn tinm/ suouenwi 0110AJOA0 asiatim !IA% Tan! 1 Inuolluanuou 0 140 UU p

Lik r must choose an alternative way to accomplish our goal. fvlostof us navelearned tit) suhslitute either directly. indirectly, or by trial and or- For. The teacher selected as the lessonobjective ,to have the students learn the concept of substitution, with the eventiilltAoal Of evotving a rule ur OrinIple rg(!neralization) to assist lheni ithakink(kcisions whvii they necd to Nuhstitute. flow do we go from tho,:ory to practice? It low does a.teaeher begin to use the voblein lolving steps to enhance Students knowledgeand, at the same time. their ability to solve probhinsio.elependently? At this t here.are two option's. One is to ()outlive a real problem need- ing to hidlia picture when the most appropriate to61,-ilhaiinner, is unavailableAnother optionistodisplay the problem situation graphically and to iNur-k nut tho situation ver.bally,with the stuellints. 12,x1)erience has shoWn that the lattyr opt ig morArserviceable early inthe studentsprobleAi solving :activities, partionlarly when The teacher, is unsore that they possess the neeclvd:language and/Or experience to participate. Cuntrotitatm with real problem situaliotA is ; mon. utten apprupriate later in the sequence of lessons whenreal experiences can be used to reinflirce the ride or principlethat has heen evolved by the students_ 4.4 To illustrate how the teaaier and studepts interact systematically, we 'will use stimulus inctureti that wure used as part of the Test of the Hierarchy. of Inductive Knowledge (THINK). Viewing thestinuilns , picture, Figure I. Ow leiluher Can so! that the labels are: boy. man,

'174,

FIGURE 1. Stimulus irjcture. MIA

6/1 'Mr.! 'ti.I0M0f1 'SyMil/11,1p .11P(110(1) Itt.11111filI '9 .3A11.1 'soInvoi sopiou 1.1! mit o,1111o0 :opitrint 8ottp?4,IntItI 'thytuttI SM1 SPAC1,11,11) IIP(1100.I 111. 'OAP,/ tuamnu ixott oi au' t)0) 'ot1Patt8 sMIIIA 'swat put? ()?4, 'on

Jinutpol 1 tt.lomp ottp owns sittoplits tont ifi?ktl mnul out spy?' .101 s111.).11 pup 1 .,Int?it 1! gtr.).Utt:, ;pm! stun.; Imo aq -1:tot.onrs! 1 ;)} _usatit t;Idolol mit lzuptotti sithipnis .itt!?.;11 t? ;wt.! 'Slioluils i1 (Nit? ,liottAt? novo:flout op spolcio Intl opoplitor.) oi otij untotios ) alp (u.)1(10.1(1 ;glum s,h)1110 'op ).,)(1!!-; sio(111 pun? sputa!, oi oAtui p/111);) whinal()(1 littimi Jotrwal Illm tiava !pm 'Ittotuoittis put unril lountoppl? lihnu.):).1()Juhu ()I lout out Osuntithht olt?Ioa Apuoop ot 41,101(in.1(1 HIA1 fljPLLI ;mull stouptois!!) .ttalo:).)(1 smotil IIbti Xto.Not! IthIpnis avtloyaA , otalods;),! Joi 'inottIort.topo.).! st? gaup ,tto ssotti..),),I.Ity.) Jo mit .itsthulIa .(p(,)41 sod/ft Jo itt)ttio:mitotta p oat? -to! invi.1()(1 tetunwi sithl)nis ,1,11? 01 alti(hi)(1 i1walltil1.(1 Lu u.laitioad -AIM; n111 pi' I IA

pa)sintufs fouossal k ;.).1t1).)1(1 ill" .1(1 'total ()I ittoplunti (imt 'stotssit! ono tipm icipttit.rd wor .t;g1,1-.) poP tint,atit) in? ;)ftttpout.totto ional 'sstla tit ,Itil .411(ii 'sow) .tioss,t1 Jo 1? lo.,(1 .r.)11.)obits lo Jotutp.)1 (II paIltun'tni sotitittluo 11,11IXItia1) 1.')111.Nl11 sithlonts to I? its toollut ohlotlivt swot 10 S1111! ,1,11, tom poporm .11(loppAtt io .1to molt P mp spodu u(1 'ponicit; ptinti Imp dip oloviumi (looN tit .10,1p3tutt1l unti:latoplo $t onoti sithrpnis oitu!pains -do Aidipt,t(16.1(1 .1(ti tor) louttinh).?) slum tout 'tFuti knit atm euol )tml -001(10 !;I ()I APli WOW 0.110A) P 0111...1 IP111 S11,10A0 oASUNI.D0 'uotitlitNitts

mu kouttimi ssoi.) si potti prlin uompptiu 8ut'ittom !!! onv lumq L (fi (II ill,lltiltilIO:) .ti:IP,Iii 11I1Aft. ,1111, tilIIM).1 J(1 NNIIILAtil sloop 'tt.htuattot osato -tut; ow) Imp?! 1)111? 'polo!) Winntliii? !coy A.Ii1A lli Sillifiltil!li 01 (lp 'OS lidli.I. onphi lAal Apple.' mt.! Nuotioui tioulot101, ' ' 'sup!p!pota(1 putt 'tituntoutp.lott puo do? otti()s ordtwooli /Wm!! Itinaj XtIpputi suoil 0111 AtztioauttoN .1.)910,11 outtotola (loam .notit otop sotop(11? 11? nlyinovn 'Inoo inp _owl's ',non ,I.Nottil uhnit , PI ').town .itIttiot.t! 't(outIo.topIt i

.111)111i1111.111UI tita,11:)

anttputttaann s! stilti:) upon( (In p) uolplola ()Lim ).1H tioomia(4 simv Jo w pm! v.1 11!t1m thu )/1!11l(Ill 3(1 Mil 1111 .1111PS .hwti solopnis oloutoy.) Ju out !pm 'tttoinititount; aug000l .1tonitit /18.01?Joi iv I ino.htipp pond )simoaq alp; ;4311.11114811 ,Itil dill 111111 ati4pffiltini tilLyijitiwytttricJifF0aaii oty 'tquigomt flfl paloinoto; oftootisal IUtfl monoi i1.111t 111,10j JO 'til(11.13SMilti, PRIMARY IsEVEL LESSON

Tewher: (Shows class Figure I) Let's all take a good look at this picture. Now let's see if we can i1iiiflF all of the things in the picture. Who wants to start? O.K.. Eddie, you can .80 first. Ethlie: I see a boy. car, football, garage, some flowers. Tmic lwr (;ood, Ed Who else wants to try? Yes, Marcia,ti ahead.' Murcia: Isee a man raking leaves, somehushes, flowers, (The teacher notes that Marcia is, in some cases, combining labels and details, which represents a more mature .respons(' than labeling alone.) Teacher: Very good. Marcia. Now, let's all look at the picture again and see if Eddie and Marcia named all of the thimis in the 1 picture.. Bill. I seu your hod. Bill: The mail has no hair on his head and he's smoking a pipe. Teacher. Can everyone see the things that Billy named? Is he correct?i (;ood, s;ou're very observant. (Teacher singles- out student who characteristically gives limite(I responses.) Louis, can name some of the things that Edith!, Marcia' and Bill have named'? (Teacher encourages student to repeat as ma,ny labels as possible and does the same with One or Iwo other stu(lents.) IMP teacher has reached the detailing step. At this' point, he has Iwo options. Ile can (a) encourage the students to give details about all of the things namedif he is con- centrating On enhancing their labeling and detailing skills, * orb) draw from students only those details about eh,- melds of the \picture that have a bearing On solving the problem. In this case, the teacher wants to move ahead to the inferring step and win, therefore, focus on the ele-' ments of the pict(Im that will licit) to solve the problem.) Teacher: We said we saw a boy. Who can tell me something about the boy?

Eddie The Imy is wearing ;1 football sw(ater. .10 Teacher; Why do you say that, Eddie? Eddie: II looks like a football sweater .to me because of the num- 1)0.9. and the stripes on the arm. Teocher:,) hue. Does everyone agree with-ldje? TOm: I I is 'pants look like" football pant8.,7_, Teochor: Does everyone agree with Tom? Omit Let's hiok at the boy's face. What can Intl tell me?Claudi4.... Claudia: Ile looks like he might b mad or unhappy. Teacher. Everybody look at the bey. Do you' agree with Claudia'?

a lb% 11111 11,i4(m11111111411 1.011.14 111111.m. it ii) tlit. 41rItilinti iii lw Nvvvrthv I., Ow hi IIli.iI hi.. 'm11111,111111.4 Milt. Ial' i Irat 111.1 dui.; 1101 11411(01f l ill lu101.11totii 1,1i .1%'.4.111t.1111011 411111111 y 011.1111011vd III lOVIIIi11100 trIvvittil

JO (gets agreement) Fine. We saidwe saw a man. TO me, irtiore about theman. 'ham :Theman is smokinKa pipe and he's raking leaves, .Teacher:.Yes, he's raking leaves. What is-heraking the leaves with? (Mite that the teacher does not reinforcethe response "the man is.spoiting a pipe" since this is irrelmantto the solti- lion of the problem.) . l'om; /\ rake. Teocher: Does everyone see the rake? Tont.come up here and point oulthe rake to everyone. Cood foryou. Ymi saul you sawa football: Tell me something about thk! football. Mereiic The football isup on the side of the garage in theeave. 'Veer:tier Dees everyoneagree with Marcia? (Teacher si.nglesoutstudent who makes limited responses.) Robert. do you agree with Marcia?Where did she say the football was? liohert: ...pa the garage. Teacher:_Yes,'but whereon the garage? Marcia, tell us again where the football is. Marcie: It is lying in the eaveon the side of the garage. Teecher: Can you say that, Robert?. Hobert: (Repeats Marcia's statement) Teecher.(;ood for you. Now, we saidwe saw the trellis. Who can tell U11 something, about the trellis? Eddie: 'The trellis is on the side of thegarage near the football, It Was vines grawingon it. Teecher That's excellent Eddie. Cananyone add anything to that? Cleudio: , It looks to me like the trellis is partlyin the flowerbed. Teacher: Ilere, ( laudia, take the picture and showus what you inean, (( laudia points12_, the base of the trellis mid flowerbed surrounding it. The classconfirms her 41)serva- t ) Tetwher: Someone saitl hesaw a ear. Who can tell us something about 'the car? Mereio: The car looks like it's parked because,Ican't see anybody in it.lt looks like it's just sitting in the driveway, Teeclier: Does everyone agree with Marcia'? Cluod; (The teacher estimates that the studentshave identified the salient elements in the stimuluspictire and feels that stime of them may be reatly to put all of the (ata together and arrive at an inference, To facilitatethis, the teacher will ask the students to associatethe elements in the stimulus picture by reviewing in their bwnminds the 411 labels and details that they have justdiscussed.) Teecher: Ntw, let's all takeanotherpmdlook at the picture, Try to remember how we described the people andthings that 14

1",ri.),) ...10%

Om patunu pun 8.01 008 1 1 OUVOUIOS um) ontfi 80 On nap! Jo intim y sit .pouoddity '010,1, .100A puny tatm .citt

0 81001 oi JUl inm ic44,q stm SutO8 An01 nmpooJ pm) oy snm thlimmtp 1l Ill I oth tnn .00 30 0.8upiopi pun. 0 mann till Ito oyt 0800)8 Jooa put) 18)110.1 000 mil '0Alio :a!pp:11, otilinvq .otp ifoti putt inn 11001 ;Elam 810/flint yoloa Intm 001

1001001 1 1):111) 001 111110 mo.up II 001 g put) 10.0 lonis tit otp '0.100 :.1001110,1, )) 110/0! s0auolop0, InOge Intim 8P11 '18).1.008)0 ppt01('( ;.)q ism otp Alt0mh JO otp s):)10).liqut Ay M01.10.1 8ut 001m otn uoirfplio ook; ;a) 0 sol0n).1 01 otp soatioJOJ 10tp ;mom 1o1018 stILL um) o(1 01101) Ay liuppie 0111 splopnis p ;coy) o0.180 tptm Two 'oattoaolut All pi) :sant) '810tuni otp Jotiovol um) tiloy ;all topnis $ 010.10.1 itotp -10 .soouoioJ .10,4 'onituttxo yitm loodso3 ; 0o1Io.10J10 00p alp umu put) ;nil Aoti 0.tom aim) 1)110 otp mo.up ;n0 in)q tnity 01110 otip 'Joui otp .linumiol pfettut Ji. 110A 0.tom 810001 qopio IIM 00001110N putt 00A maJtp ,011 jjlOJ tin os imp 108 Ionts IlIUM pin0m 00A 'op mot] 10110M 110A ji:0! 111 S1111 'OW0 001 .1011:1001 S lit0mmip 00 alp SA:0101.1,0V) 10 001 $0100011; 01 DA110 111001 1111:10.1 11101 U0110 P tiottioti Oym s)leob II t1lo0081(1 outitssit $ 0100s -00dsaJ Aliptos .101 ii11011011 IOS oA .0 I '81.0Ani tit s!tp 'Atm 188011)0.1 otp soatio.toiti; 01 otii onitstle01.0.100.1 sotto Ati J.44.-.141&)fsti is sittoplt l my.tp 00(111 ism! 'strouot.linixo t011 layavoi s; Apeoi 0) 1st? .10J 0 In10aos lonoi Jo :0000111.I0Jut 'Alottuni luoutolvis p) ;nil Cutonputi :,100000,1, '110AA OM 111! 00411' 11101 mil icog mann 011i untilooj di) tio 01.0 J00.I Ay Jiostutti .10 otuos otpo sAati ouwo put) )1001 11 APMI! 1110.1.1 11111J 1)110 momn 0 lin 001AA 01) 110A luttp sty tuopimui i,st hood 0 1001 01 IAA 80 tn1n0til st 8E008 outoy 01 ioX 0 itiatmptius letnyt Osia 00 110/i 11011 )1 ,S1 11110110,11

i,1111(1 1110,1, 1109 110/f 1101 :1001 11 SM./0S 01 0111 10111 00 SWIM ot 0)8 1I 110(1 Itmop :1011:)Pad, '1)0(0, 11101, ittlytit op imA vittp :108101,A; I In tit .001 JI snAA 'out pplom ILIUM Atu 110(1 Iattti

110/0!) otp s,.lot10001 'oAttooltio Annunu 01 cilay inn sittopms al altuut, sttp su su otp .tationol tit .00ssol II ta, -00 '8;):)0;80)Jui 0J 11181,01 0ti fill 1011 ituttami 01 ;tont 111111, m00110.011 001 '110141i01 J101:11101 010 100 01)11/10.1d SJOAA1;1111! ,1011 Atp.ton nu Jo otn ,S111)111118 808110(1440,1 '1110811.101 -111

'01101S 011 00.111111; 141111 1911 oc.11/11 1111M '811100111% 80111101108 1)1A11011 A111111 ;)10.1 01 011 -111 10111 1401111101110S SP It 1.110),IX Jogottol poottly sty 810110:) 1001 1101 01 IPA 81101 810001010 1.11, otp snintutjs 1,10I 11 01 001 -1118 smolt 01 olnis otp 110)010.01 .10A 'altitutoco uotim otp sidapnis 1)01001.0)A0 lp on;i0o10; oX0s8out tit 8,Aoti,o10 %ton.; 091 Jatioltai polaoatp Jtotp 11011 01 sty oat)J 10011nm HutAtti soup) mow) sty 1100010.1dX0 ,10 0111 -11110111 1X01110) JO N111 JO 0111 1101880.01X0 1011'110111M 0111 010010.1d 80 11 0110011M Ti .k....i,:::: -,..-...._, . c 0'....-oil % . "4.4- , . , . the case of thi) inappropriate inferenceabout tilt role Of theman' in creating the prottlem; the teacher canes'upon the students' experience* to--14alp-them-s-t-tht: inappropriatenessof the inference. The lessons that follow,as 'the teacher pursues his earlier stated objective, would- he to have the students(a) recall the statement of the problem, and )\?.,o back to labeling;aid d(tailing; (1)) quicklyreview who and what wio involved, andwhin happened; And. (c)restate the problem. Al that point, the leacherMudd 'be, ready to[law!) into the next step, predicting and verifying and, fromthere, to generalizing ac-. livilies .r \Ale indicated earlier ka the teacherof the intermediatii class assumes that her students have thenecessary language to proceed with the lessen She feels that,t,hestssnulents don't need to spend timelabel- ing acid detailing the' picture. The pennity foroverestimating the abilities of students is not that great. 1A/hat follows isa more or4;ss typical.result when the teacher hasoverestimated the stude t$ abilities.

INTERMEDIATE LEVEL LESSON

Teueher Let's all take a good look at thispicture. (Pause) Whocan, tell us what bas happened in thepicture? The boy's father has asked himto help rake the lawn and the boi doesn't want' to. (Thisis theonly response the teat het can evoke from the class.) Tiincher. All right. let'sSee if Ralph is correa, Let's lake another good'hing look al the picl'ure 'and let'ssee if we can name all of the things thatwe see in it. Cl'he timelier is not gelling the kindsof responses that allow her to involve students in theinferring step Vroduc- Theriifore, she has backtrackedto the labeling -and detailing slaws whichwe dscribed with the primary class. All that was lostwere the few-moments i t took to at- tempt to draw antinference from the students.The transi- tion from tlw inference step back to the earliersteps; was ,u:complished quickly and smoothly.Now, let's takean example whe're the leachers estimateof the students' abilities was more acorale.) Tmeher. LeLS all look it this picture and when)youthink you know 1;0141 10 as happened,mete your hand. (At this 'point, the teacher can lest her assiimpt ion thatthe student has sufficient language and experience toenter this transaction on the inferring step. ()Ri!way to do this is to call upon Mu- *. dents who are among the least fluent andwho in previous'

lessons, were among the last tomove from the otetailingiti the inferring step. Ai least nt the heginnin$,the teacher can r- 54) ),) ;Rousse pop it. 111;(!yl litnlitnaq do ay ima 0,1P twit? 01 -saJ ptiod 'Alpa.1.10a atp tfopyteiald si qXiq pop atp amoti -woo ueo 3 tualad pundsaa ('Apo).1.10D '1,1agnm puey sem An pal sn Intim nwf Tiny) s! -deg

:lia(10)1 mu, st no sly Awj /Om moot" pun ay palm)$ (11) pue mes aup tit4wittool ayi .;),P :Jallooa,l, I pop saoq punos appssod 0940,ateef.Ona 'pimp! 'IlayoN pun pal 511 11)t0,1 110A .11111110(1(1101 011 SO:1S OW 1111111001 splem poi! moo s,ay -Japtiom XIII moti s,aq lit11011 loll 'timop sa(fti atio/caa,a yom soon atm/full oney , ittaJaipp i;110et1do soimr) peq1003 s! sty put )11 sem .litippum litoye ilegloOJ 1111..)P.101 111.1M0.11.0 avil pm! (10 ut, 110,ayl p(1t! I! dn 111 ;op 'oAea .iotiotm,i, 'No :sallett) JELL) aotioeal mon sinem 01 lamp ay) -ounJ tee' Jo qi Xiii Inn! u! ('aoua.laJti! intim st atp 0,1111:m1 letit l ve) 110A ,01 !ita!la(1 ay s! -num ;in! apply nio.IJ / lin(pooi aonoe.of put ietp MO.Illi 111Ni .111! 05 0.411-TIN11 II0j1 II 11010111 11fl-t1! 4.)Apa rtidi.11.111:) S.0q 11111,11?0M P 11111100J '111.10.10111 S.011 lit11.100M P -100.1 Hey .I.neams atp pup Ay Sem tini S.101)1110titi )100I A11111 INS .101)1110g% tipP(1 110 )t.. SILIP(1 1001 0.1001 011I IIP(11001 SIIIP(i 1110.11 pitp am Jeam 11! royos J...101:11)0 MO11 AlIPILI P1 tI(Ift% la,IJ pop sawn) s! ijoaa.10o llf Iti8!.1 08 pealle .solator) jetim asp i,litiniachtytts! sabintr,-) I satiAtinp Addequn asne:mq JtI sinem 01 laS alp 1111(i le-umop 3 Lusaop aas pit umop tipm . ) pm; tiom 1.1, pue ) sappy; anuti ItiaJaipp snap! -Inymploge spy .patiodd.eti Iul /cow op 00.18t? 00 lil11l1101110S II11 1100 ) 11110(1 111 Jilf).10 01 ;)/tionti! atp isa.r $0 atp atp 'sItiapnIs Jatpeal *Amu pod lona Jo otp sloop ol ion] pin() Amp aas ;op mpg! JO 1-huatuaa.18t! -al '/cati letim op noic Itipp /foto ila..01t! ,00 tipei lees AITT pop atp A0(1 splem a8 pe(l) 'umop Japoo,i, ou am A. 1)001 'rfaual lin aa.181! 10 pop ijupd .latineal (lay foist! yea ipplo 01 altysaa alp .tonss! :Jotpoo,I, salatty;) Ines pop alp s1001 ym op n0 Iddetpin tf )6 alp Mei sloty i,Addeytin :tagokv ato, ley I s! (Hy .1(1 nog 01 "ionai :Jago0a,l, ppm pplom ay poop 01 IoN atp peg Pimp 'AlaJes, 'AvRea pile dill:Ind) :1"(11)IN .1°1)01

, ou 1101c oat; R i,Jappel 'oN I itiop jmu. 'po(41 layetAi ) silod ay' !Nur! I1!e8e 01 ay 03118 saletu 01 astu)dsai )inas 01110(11 4/W1S ltV1 00.1811

'09

5e ( intn. 11 Jappni I P og atn IM isotir djati UI 8un1A ling IMO)) pl1P 01111S 11A+) onnti ou 'aami s! way Huttnifun norf Jos Ivy ay /Coq asn sn o'iltilisqns 01.3op.10 iof IIPq (olmop tiilm) uousontr's!to .1o1.ional otn sltionnis (nut ay 8utpnal's1 linufittan-tittnotpo.ill "('dais onmopti " pinoo dn uo swan pin? Ifpg ) ')1( M011 A1111111 100.1 111111 14110M 0() P po0X /cum oAlos )I d

moo mils no oto ino pun tiono.i inn 110q1001 . 'may . ,

:Jog000.1, !Iv ) sliod nn ssnio 1i811 motraos 'cum )a.Oin gum sun (tfonnlos. .ittv .ililpo i.stionsiWns 'Hp:). oi pimp 1st! .untu .1! .oli fi.11;:) !limo m0.1,109 sty iMILI 1)UP 1111 011011 11P11100.1 100 JO 0111 'OAPO j, :Jd ')10 .soon lan;) ApoOup asp ;mg P ,tiotisaMns ..(sosnnd) uv ANL, on imp! 4,4 ' '511111.saMins 'MON hum two no) sn Jo sAem. ',ill nninu lo8 Neu 'umop ol pinoo quino dIji dn 'stliodi ini pinoo nano uo %lir! ou mo,yociTinoo s.untu pun olod 'Limon poo11.410A moN s3oi Oos tptim st dip Isoti Atm anvil.; ay i)ottopio.td sty 'iutod Jotional sole) ay s long 01 8tntooll pun 'It!!!!!!lop tsdois 1001- in ay swan pun ion! in iln, AOI1 nor sn OW XtrItilotiu}s oy1,11)0u11 .stna,ti intim op orq ;meg M011)1 1110()1! 51041,01U 0.10.1011 ;1111 icog 110 .11. S1111110 ti1 X110.11ti 111011.0 01 plog nilift4 ium .1! II si noddIni jou lotionol .,ms.1Iu1 sty" loni yom Two.' ,sittonnis-oul stiOtinpuntunt000.! 811tpt0 out ssnro " olnui soono.loin! ilmille padolio'suonnios Lfl Jaw() 01 ism) Cuonnios Jotio003, ox,o/v\ pooAin niln swill! hat Ino.ni otnooptIn sdfou 1/1111 11411 1111 (01 .11A 1110.1.1 1111 .0iiP,11!N 1011AA

n4.1. 1111:) INV A011 0111 1111111 ,p.1 -tino m0.1.10() otn :Jail:mai, AtiPita lol sn oos p am 0mtti two() loa.tioo sAni(Ist()) tionnow.ton Ion! :a.111 a.inki (7 intim on norf oos :stiltilno, pamo.1.109 ;no olni nue iltunA,s! otp log IIA401) moN otim uno .am Ind pawl mocp oiti! atm SJois to tip oin s- Amq stti.811!liah II1 Innti ) ;NI xilionol soAni Iwyan.ssoi s,taynaut .10 a(4) wsnio sonlasal ttiX!.1,,illi inn u0 a.101il paounnim sluottilis , .10.) (.1.10ddns . .:1J111:) 0 Anvils! yin" otnos 1110.1.1 dioq Csaatno otii, /cog stim -Anid 8111 II" $111 1113(1100J 1/1111 11 1101111111 111 0111 'ilA110 oil nolunm Limon all ioX 00 pam03.ilili JL inin.c.s,untu pun plod I! 010 10 ay 'antro

) 1/01.0, .1.111^) um !ill! :Ji111000,1, nori. annoi SuplionION ijno imr,)) saop fou '.10m9un Jationaj, Sassaappn. .atutts ttonsanli 01 ' LU FIGURE 2. Ve0fication Picture. AP

(.1,IsS; 111;111..111;ms are Ilmt [hey have hirgotten the fact-of die lath,l('y.) Tvociter V1i did the boy.liave to use the rake? What is missiNg in4

Ow picture that'wmild hilyP iihu3e il much easier:for what. 4.- dui Ihr bos,- substitute the Eleunor: It Would have been easier-if hr lidd a ladder.

Tvucher (;o1)-(1, Sei Ow rakewas d Fur . (pauses lo eu- altis lit COMpleh` the' stiltelli(lli). A tillt(IPE TPOCIfer MOV("S alsti into gen(ralizing step.) Who'Ciin tell us why the tri:lbs' wits not a good substitute for a ladder'? lintwrt 1114,11151'it al101 lweak and boy might fall and. hurl himsolf. t 'reuche'r: lkiy. What shbuld we keep in mind whenever we baVe to P. titmielhingive need bul do nol have? Gan someone tell me.a rule'? (Our experiences phis the data front the CASS and THINK indicate that 00; it; a difficult lask foi younger students. Vurlher, the data indicate !hal more th4 one prohivm solving experience istiecessarybefore rules or principles begin to emerge. Nhive'rlheless, il15 41 following problem solvirig,and should be pur-

. qu(1d hil?!,)

EINI110r. lieVd to lisl!'A tiflbst hal% we should be sure lhieitit will not break or hurt,anyono.

02 : ./(-) 1

.. Jo() ;050)01.11101 si Sintql opt!' pits pplop, ii! tlimi itiottiold NinnieN suossoi s! 001 a.ity)s.lortili otik Apittityou itioia(itil tp dill ir.)!o.i --ottinli AXoitt,lis itio.lalyrwilmj. Aiiiio sitt!oil oioni :poirmisitil! olli illttiChipi this .111 out) 'Ito it 'titio.i1i itIt.I.I. (his 1(1 ..loillottp olotim oi ;tiptiolt mu .101o11'.Iis SI ihvpionjitp Ati ow s..1;ofdpii :!.iptullso JO mil ..m.liolo(itutr) jo mil stitv ji mil .1.3tu)p.3i .5oiptiitiso.1,1An p (lois .00) omi eNi...!Pt( polit:twil! ati III6'itiot 1).011sirliiim:11, .A.K.!!!!)! ji w 3,044144 'solitupisolopun sisit .101 spin poi, li'o ' sloX iouttlitio:t sioiipi Poe , .. soplop imp otuos ii!. .- 's0ltid.1.)1 oil att 0101:1 oil% ,rwiii . Sii..)!nl) of din ixou .tiois way log itospol .1o1 XitioX olio Tins ifplop st oi . tiit.lisuottioi4. otiJ jo din 'aim Joti:tvoi sp -.1.)N1o.lo.p1 'tilptuftisrEto:pirp..iolipIX '.1;!1ii.lij1io.. odatti, S.I II!,),Iti Di., ..,ill .si,maili 01,01110.,Imoi Imo Irmo, 5.1 pry", osooti:o RI, Ind . r Adio0111: 70.,v, s3011.)1,01 ur) !Ai soAlostii.111, 011), liwilpI.1.1),Th -P.mp;110:, .tko!, SI ..riivitmitl il, (111 moil 50011 0111 , iii'll, l)try,), ihAOC (Iv '.1Divisill? . -- ,... *pima. ih-liplittily, itsiPtIostioi moils .nuos jo aqi 9!is00D1t) spoils!! Jo 11,:jiXtri aN!ilttpui :Iiii!ippoi iv otil 8u!pcipi ipip 8timpial) 'tiliois Mil III!'.) 3.1.1;1$11(1 a3.1tiM S.It'ANIF.11.01) III aill!IlikIll 110 ii.IIIII1(11!:)0A ;LIP ;1111..1,01110g wi.1:E) u :sitiJimis -t;':.;o.ilio.R1 II s! p Jotimtai Ltiottilipni osotli .1,110. 0 sop010.0 Amp( .i.tp. .1I;9pt11ti III otuos otirsospA .1;4:ntm salmi] q:oilm, aim Jo Ill,11111lti JO .).11!.tilli,111IIIS ii1111:111 SI).141AA .10 tli icIIIItlI! (1) aq!,13801) 'sloilatti(h inq 00,..son'it iii!m, dip uossai iiti iitn.Avit 050111 (AIM i).10t1,1 0 iiiitioiltom loll (HIM i.1.II! ti siii.iptils piiou 1! 'Jowl 3tii Joirmol soimpti! dill s.titt 8111 A.11111(11!..MA 10 IIIIS III iillIppaI,I? .10 tii.I1?4M1?IlitlIII UOS;01 )9tilIM II $I .1Pior., ()I oto oll:will will i)oi jo Miptu, -mil sittopPis 1:titi aqj -ssa:tott ti.ip pop Ktit1ot1P1 :1111111,1.y 'sitils ;til Jo oils op..) AH:)!Ith lioniity) tun ilossol oitn. p Xiii?Witipi .ilossol w, ..)Alpaltio:stiossot spill sa8i0itila taw., iuditioatt iii..tios pi Iii1to.tp.,11 inn Ando sp.lom lulu . Nittiii tuovioad 8t1tni0s ' . SS,I.Iii().111 .11111110i0C1 . ... '). 4 dilliAA' alli 11011111111I tillOtitidi 110A.,) Iliikillti lie 11111? attli;111110.Id tviou jo stioir,to plip 'stiollipailiii! III ittol Istiltil Itil11 ii0I11 (I1) 10l1 ) a'14.101L0tUln1: 11!01(1A1 lti.111 S0.01100,1 0411 0/111:H11M4 1110110M1 dill, tillotiti0I 0.10L0 iii.mini : paud.1 I!. Xtilips o.loilivt oto pootitt sit,ii tioloami tie potistitiviso 1it..!!li0r1 a/413111)bl 81pii.IP1)i-?lupopdi '1.10maititt.li ,Joirtitoi..oill, otim s! -9!, rIttpoli -.i-ti still -Aii,liPlis ititiotis wild tit) hutApii 01 01.109,I0A0 I001.1)) ti1)111.1. It) 101.1.0.0 SV 0110.40(1 WO '3011.11!0 s.101131!11 putt sitiopnis :mug) oi soli itiiiii jp 1! im.101t out Holm ii!'poittut.iimpti! zuo,t sinJottomitit? di -119ttoi till! pint 11iiiii.woi ;Limon o.lpsolo.i iiio:)!II itaxii ;twos Imit.siotitmoi -011$ smolt iitmt ,tti iirpttioa oi attputtaans Aitattlos.otil .1!oi1i-jo im .;t.itio!rni!is!p .. _ . ito:timotioid II til ()I 1111!1.10(1110 '0100 ,10IA0M0l1 MID 111! .10 0111 sJotauj ivy ptim lit alp. Jo Apivt itivtihiolup ssiErnis '0.11? 01 %)1110ti 'I)ij)00j) 1014(1111; 01 .1)8t1Ol10 301,11.4101M 0 .1.0! Olt 111!0 Ili011l't;ih11111!.0418 14.10110k11 01 01101fitilt - 0.0411 4.10111,1 -.duo !ow,' ti! ;pp 4)v.1110..) mil jo Aino:Airp ion wilt; tuo,it if 3,10iii aioa ,..1 ..)!Iit.ctoinit lov.!,ihiaesittlil Ati ;Itt!tiattai suotimins imp Jim) .10j dio.rit 0, . .10 J.Iiii:m1 oi 1/ wow ipito,idttut antt.p.totilop timi ivy st .iiilm)uoisistio.:, itti!hol dnii:Illititi .sootOsiotai so:Itiot.i.olx.,.1 tiltm (pug mil $sv:) p.uu ILL NNI opoill tjom ow is Nowo otp tio $1,111:)1,01 Jo .%;)nalo MOilli -111141 ;soul sulapnis utia )AUli1 inoij AmiolmaddL, 10) dill _Imperil -ti(I!anied-ol 11,191.1 !Him .)91 lagandi Jo1110 sluapnis Ui itIol9om1 litnAlos 's;i!ontialt 011.1, .1311')P01 S(11 pipd/viod.,P awl in Jo litilladJ dinlisod aiituttla u! leaainintiaAsd sawmil titr) 0mo:win) ifol atil sp,w/voi 0J long. nollediallJed (liv!puolisazif pne Amen!) Jo dill .eilloilsaJ 8utdol; 3.1311M SOI:113111.1311 111. 3811181111 .10/p1.1P dill .111111 11110SS1' A111111k) SIMI two/iliac; siall pue puels.sl(taatur) u! dill littlin)suoJ dill Jarywol inn solo.; no )way soiatio!alpip -0.1(1 ' 8t1tpiA udtilid liniptAtput tip!tianilsill Jo aatIaeJol intlitm dIJI Jo8Jii; ittaigonl XitiAlos pcoitior) dm HIM ¶APMjP pddu o(1a). tinAri ip A.HoudX0Jaiati sivtotts tPtil ../cuP dip) Sslp drio.I8 Jo) ludsor,i(10.1 P otipP.1 jo IP:Oinjuirics(1. 111031 diJ AWAIIPI0.1 diontim .1.191.01 '.)ti(1A.r) 1110).1.1 ,n11 letOuttll rit di aiesom1 pun ttio4J dill ssaalis ok.inAIJIs f-)JytHel pratitolonoitia pue

IdAdietinn osio dtfl lotriPoi Amu, Moul toy) I pi litittimoi S111S1.1313011111 :01 Jo 11:/),1 111.11111S 3.13111 A1.1.1 0111,1113,1 S.101:111111.1(1 1110 S.11131)110 -11310(1

1111 (11 31111110111 III 111,11(111.1(1 foti 8111,1 No!lown! ttJJ 1.1, 1 I Ntsi itlitl) Amur -st xapit! u! sup ladolsaJ in m ludAd a lute mil noissitainp Imo pa/violin.; otti sallow\ -8Its rid8 1,14 mil da1ht:M.11s IMP ,nuanhos Jo) Iii:treio.; oinianpul

trwol 01 11111 UI 1 1)111! 1)31/111'..) ¶-.110X01111t. 1)1111(11 4.1i1:10141( A.10A03S11(1 .Sda)IPUS P ,1101I(11):)s.i.i) Jo /i8dIeJis s! powasold o.1h8!,.; ti; ILl 'rniettidgas ,itli sollitteladJ itiasoldoi Jotrwal stionau pip otil Jo Jo Jo) 'sitiopois sp,m) atij. !motile ti 'Itiapliis (111().18

1 111' ,13Ii 1 .1,131 1,\I ley am Itra18(r; ontianpul lI.Il Ai i.I1 ltf S110I1(10 Jo; dill dtredi I; sJaiii) /inpopxdu se Ham se Joel. 'iyhtuexo ludIn polio nossdj 'a/madly) oil; Jotpeol tura %mina ttioisifs le Riit) poseol dill ssainpeo.i o atil sluopnis 01001 .0ti ii ill11 titS 111P.1,11,1.1 dJP lop 11101111.10j 01 UP S.11110111i..1.1 alp Jalriitill 111411,.0-.1.iippd 11I uldisics o.l. S11 6ps 14111AP111U111 1)311113(1'S itossol ..d..opolg() dip 'zillanal sIsi! e tIonsaill) pauS!sol) ol Hallo 'sjdop.1 X.0 utla alue'n oto tina ilraos till jaanpul nos) (Iis (1 .,n1.1. sludpu op wit Intodsaa .1.)IpPol piloprinl -ILIIISSP .111 S301) 1011 .113111 1101111311P 3.11I ,),.011113.11111 1'111 ) (1' 311111 3/011 (9).10 A)1.11 111(1 staPI alp /Opole on Junin lutim Awn .oas J; tnalol0.n1 si din oill adlIN duo 'Xulpuoli"frio siao.IJoa notitions /io; Nuppitu posit:mi.; ./cialitiJoloJdoin ; uo thu Jogio oill J,predi paleuitisdadAn aill sotitinpi Jo) oti; ot; mit; twa ;doge 'uossal oleisda oto oinkladnio (); tuna; o11; sottwu Jo aqi paJopul Islaaiy) pue o8 uo 11101J imp 11110(1 iv t! amtu oto s..la.tpuol snood() oilt Alittillh) .10,1110(10 ' 'dloititexa otiLin puoaas tlosso; tunittpullis ;no Jotiano; sbd...) le :nil d.ailaJoilli dins oi)s) dais c ( limits! Jo otli ;wawa-loin! imoivi wend.; uloaxd Jo.; .s.a!pp...; I a; poplin:lints will oil; twill 44upuiti otll Nonni); pen tidag won inn Awl pip moJto lim11001 opio ail; Jo().1 iv sop 'lutool flhl Jatuntol ppioa (19is atil stioJP10,n1 Jo ay i °4 11VW. 11111,111\1 11.11111 1111..1.11,1 1. I to ii 1.11110Is .11111 .1 .111411'\.111111,

I )

Astino Nol Elti ii tlitItitis 111..11 atitlining N I ' of -111111.--

9...mmeemel tilltttt, 11.1.111111111101 .11.111.1,

roo st .0..11 t itnlotttgo.nro olualiuto tI ' titlitilti % Mr 11. smolIP01 I;.11 lilt ill di tik oit lo111111 11.11 111.1.01 anti fitIttstiiii

Vo Y

ttiktuttit en( het mutton

9 yft FIGURE 3. Inductive Problem SolvingSequence. class in order to ask Eddie what detailsin Ow picture led him lo his in- ferenceIt 'Would also ht. approjwiate fur the teacherto help Eddie profit from ogie.ruence .i.volha question studi a. -If you were the man 'and you knew that Itwas your faull that the football Was stuck in the rave, im,)111(1 you be raking leaves'? What woilldyou do'?." Hy drawing un Me (V1( lrii:tIll the mclure, along vitligeueralized appeal lo.fair play, the leacher helps Eddie andthe Class dispose,ofI distracting inference so 111,11 they canmove ahead I() 1110soluls)I1 of the problem. \Auk ^Hid of the Lycle,following the verification of ,the proposed solution. the leacher provides the -opportunity , for.sludenls I() evolve ; statement ol ,1 rule or mini tple relp lyeto the problelIl and the classf probtents. mst sok III isee -',1ep 5). WhvIhvy generalizilla is stated. die teacher Ownmoyes on to the neNd objective and the prokess continues

MIMI/tat:Z.

There are t111(1, obiectives Associated%Nith teadhing hy way of the Logi- cal Ind mil%str,degy. First, there is Ihe miiversal objectiveof inertias- mg the knowledge of mildly retarded sludents..Secon(l , there is the ob- ieLtive of te,whing in suchI way lhal students learn a:strategy lhal allows them) capitalize.on their knowledge. in thecourse of reasoning the st, uhtws Ito proldeins. Finally. thereis Ihe ohjeclive of having, students ;00.qui.re feelinwl about tinpliselvesthat will enconrage th(m) to solve prohlems independently The attainment of these ohiectives requiresmot.e than simply imple- menting certain leaching' INiniquesor using particular teaching rualerialq It I that the classroom liea place where leachers and students feel a tuuly o urpose and are able lo share liolhsuccesses dud failures This is not tosay lhal roles need lo be blurred or lhar responsibilities need to he ignondor surrendered. Rather, wilh ftill recognition of roles and responsibilities, thereis nevertheless a shared *feeling that%ye-r(, all on the same learn.: Withm this ( onlext, te'acher planning coilhe directed toward achieving the, skond and 1111111 obiedives. The cOnlen1 of learintigneeds to he releyanl both the immediate and long ramiematurational heeds of students Telacher uulginent prevails inmilking deciSiims about setting priorities and sewiencing imtitent. Keeinng thesgoalsand objectives of education in mind providesa framework for decision naking thgt lernIs both (TrdihIllly and consistency lo planning. hice the content of instruction has been identified,knowledge of students- ;ditties and liabilities is essentialin helping the feachor lo determine where hi initial() the strategy withstudents and how lo plan Ihe amount of content that will la,1111 of each acliVify or lesson. Along with knouing wild the contentof instruction will be, and what the OlaracIerislics of Ihr lenrnersare, il is eimally important to know how to manage the learningprocess tising the Logiefl ,. inductive strategy Tenchers need Io know theprocems thoroughly so that, step

06'.4 ny step, they can help students move' toward solving problvmsand learning the necessary rules. and principles tofunction productively Ihry rpich,school leavingage. If the leachyr is not well orgnized, the steps in problem solviNg will be ranth)in and.In some i;i1ses, cmi defeat the purpiNes of theinstruction. in thel.course of- . implementmg...the lAigicalInductive strategy, fii.nce and insight pa- are important teacher.attr.ibuts:Somestudents will hnJit hard to believe. th,it the leacher is sincerein believing thlit they ',are iAinipetent to share problemsolving ventures. Students reCurring nmd r \periences. if they (ire ClalVall:Vd lir the it'aC11:1,-; ctsrity Sortie students. althoughready alai 1V141144 to lack some ut. participate, inay thisu. knowledge requiredfor involvement, The leacher has hi talc(' till' tone to help themgaol ilie neceksary hack- ground Tilt. temptation to lake shortcuts.is presentunder both sets of conditions, it is Much easier to "tell- thanit is to ask key questions. 4 )1 course,since the inductive strategy isdevelopmental, achieving the desireihend the generaliztion--is certainly Ow most slep but there shoukf sonic'eumfort in knowing difficult as il that, as m to ai.hieve, once gained -itopens lip a broader range of problmi sok lag hir students and itu:reases the possibilityof their gaining an ICI' *HMO1111\11klurr.at independence. Finally the fai that this content ofjnstructiivi is. From the start, abstract fardas 111,8 ilaTOl.,11111at kr extelall'dgaps in instructin. Im- plementing Ole Logical Inductive strategy needsto bea day by day experience for ,leai het and students. Thelearning- of abstract rules.and ni.num1(44 is an emerging phenomenon:Theyemerge as an outcome of planned, and frequente5kperiences. There is no substitute. for continual iirai.oris if problinn solving abilitiesare to tleychp and to be isnilam ell as tiart of the mildly handicappedstudent's instructional prograni .

riv

1)7 4

References

, 'Bruner. 1.S The ,a.I of disimvery. ilurvard Education01 Itevivw, IOW, 314 1-32 . ,Iiroi er,I.S Toword a theory of instruction. Cumhridge MA: Harvard Illrersily PrISs. 196ti (:lark .. A 1), II).. & Clarice, A. Persoaallionnounication, May 19. 1992. Cannell,'ftI.. A social learning apprim4tt0 nlental retardation. In

1.,111 (Ed.), flondbook Of mental (lefil)eney. New York: McGrawHill. Itxt:t,

Ellinoteimi. li . delimg. I.E., Iplarid. II_ & Leach. E. M. Manual: A test of soend inference. Eugene. 'University, of flret{on, 1970.

.1:1fflakrs.I P A rrytew of research on imitative llehuvin Psychological fltilletin, 1969, 99, 319 307. ( ;age. N I.. The scleatific hosts of. the orl of teaohing. NewYork: Teacthers

Collegi Press. Columbia 11110/y1'01y, 11170. . ( ;agil, R M , & Brown, I. T. Some factors in the programmingof conceptual learning, lourmil of Experimentol Psychology, 1961. 62. 313-321. Glaser. R,. yarmb1 e4 ol illse:mfery learning. InI., S. ShMman Si E. K. Keislar (Eds.),1.,earn rig by discnvery: A criticeiloAra'isal. Chicago: Rand McNally,.119114. Gold. M VV. Sqinalos factors in skill training of the retarded Inc,usinpfux assembly Isioi- Acquisition, trapsfer and retention. Anioricanjournol on Mental De lc iency, 1972, 79;1117-520. ,- Goldstain, II, ,Ljaual and ociminitionaladjusti'nent. InII. A. Stevens & R. I leber, t Eilsp. Menlo! returdotion: A riAtiew ofresourch. Chicago: Univer- gity of Chit:pp) Press, 1994. ( .olifstein, I I( onslrucl ion' of a Social blunting Curriculum, roclIn on Excop-, . Noma Clillilr6a, 1969, 1(2). 41181 (;oldstrin, II.. KiliAiS, [ W.,.& Jordan, I. I. Timoffict :yulspockulcloss training Oil the deiri,,lop\eolot of mnionllyrelorded eliiiJnii g. tIS Office of Ethre- k...

\l, oft ' 4 Imo, Proiect N/o 419institute fin.Rese4Ircli on Exciiptional University cd lninuis,19415 Children, I ;nviiherg, SAssessment of mduclive probhmi solvingamong educable mentally rebirth/astudents. Doctoral 1117 dissertation, YeshivaUniversity,

Creenberg, S /4,/ timith, II. Development Ilierarchy of INductivit and validation of theVost of tlii Knowledge al (INK).Unpublished monograph. Curriculum Researili and Development Center in MentalRetardation, New York 1'tin.er,div1971i s------1(;ueun18.rgS/4 Smith 1 I.Structurdl validationof a behavior underlying an oultirtivy ._hierarchy . teaching nwthodology, publ_Ou'd Research Report #3.un- iname,cript, CurrnailtunResearch aml Mental Retardation. Development Centerin Yeshiva I Iniversity,1974 ;iiillord. jl Ilu. notion' of human 1987 intelligemp, Ni`W York.McGraw 11111, d licher. R. I: Klotor task performanceof high grail(' mentally as a hint bon ol the inagnitmh. retarded limb's id inceptive.American Journal Deficiency, 1959. 667.071 on Mental klausinmer. 11. S .14limper, II (.onceptual Iii F. Kerlinger development andinstruction. 8( I Carroll (Eds ).Review of rosearC r Peaco( k. 1974 cdtwatiun. Itasca. . Creenberg. S & Melnick;t1. Test mud nation& Childrenanalysis of sittionons. Unpublishedmanuscript, CurricultiM I levelopmentCenter in MentarRetardation, R se.arch and Yeshiva University,1972. 1.0;,411,1, Ic, . I.iiilI R & 1Vhite.R. K. Patterns of Ii1i't.tttII aggressive behavior in txper- I reatc(1 'so( fouiliol of Social Psychology, 1939,10, 41dand,R ISarason. Ili & Cladwin. Mentol subnormality. Huas, 1058 New York: ict'r. I Labeling the mentallyretorded. Ilerkeley Press-, 1973 Murini.I I& Ntorine C Discovery: /1 chollenge loteachers. Englewood.... (..1111)11 PrenticeIlan. 1973 qittiur: N & III', metal 11 Like andcross modality recognition 411 1,111;111ren in submit% Quorterly fournalof lixperimental Psychology, 1961.1:1, )1 I Or YlPiA & Milberg (II (Eds.), on teaching. Berkeley: ( i.i.44,101979 Mc- Ro% & Koss. SA Cognitive brat ng for the EMR child: 'ad% ing and planning Hituatinnal ;- American louriinlon Mental Deficiency, 'he psychology of the" inventor.Washington DC: laventors , 1931 with. r mill, learning find psychology, Englewood P119) 11.'19ea4 Cli(fs NI: of trainingprogram on the pi:mini:live rrment thinking of educe- lo'lardatesAniefi.cmi Journal NW 670 .44\ on Merital Deficiency,19115. 69, 61/4 Shtitglatt U S E it (Eds.), Learning by discovery: Acritical up-. ...go4 Rand McNally,191111. SibII. s construct valid4 of &process oriented(ISSesS- v*mpetency. Unpublishedminim:rip!, 1978.

t 4". a NOW VOCk: 1101i. .Kinehort & Swills, A_ W ,Lermiliing, lumougu und vugmhon., Wiw.oin. ltititl .. discovery: Itoview ofEduvotios Strike.I.A :11w logo: ol lvarolog . by Roston-ch. 1975. 45(.3 ). trti1.583. a* . linilding skillS tor autonomousdiscovery. "jlit.11111,111. 1 R Inquiry framing Merriti-Poimer Quorterlyof BoliOviottitmv.,,lopment.1981. 7,-147499. elementary sclmal Takt. 1 I. Te01.10 0); stmtemies (04,1eugnItivf functioning in San Era I I - chili/rill. Coopriatir,e ResearchProject Nio. 2404. Su) Francisco. LIM t) St.lh 01111'14C_ 1510 I . Titillan, IN PI mim.tivethinking III Ellarth:d Chlilktql.Exceptionol Childruti, . .1962. 29, :16-11 hothogs. lo A D. B. Clarke& A. Tizdril. )!Jun.:1001nel snebes PrOtilems and Ord edl. New N4 Clarki k his r. Mentaldeficiem:y. -Vie changing outbiult Vrk. Free l'r( s. 1974. IXalles..0 The irt Of tliought. London.1Nati.19,15..: . Technolog.y,4;rVern, 1,Veinter. R C. An analysis ofihscovery. Educational ...... 1.11E 1975. supplement.- Wind Iv.C. Priignosis ofinental snImormals. Monograh Ainericao journal on NelentalDeficiency, 191)Z. 1..140 In I. S. Shulman & . Witt rock. kl.) C..1-licb-arning by discovery hypothesis. appraisui. Chicago: R. krl%Lil. 1 Eds.). 1,1'0111111gby discovery: (1 critical . r Rand. MuNdlly. 19139 . . psychology. linglewijod Cliffs NJ: Wolin:in. II,It (Ed.). Ilondbook of general r--..), Prentice 11.111. 1975. .. ..

o, r'e3

I. it N..