iagor simonis Ze balanCivaZe skolisaTvis mzaobaSi Seferxebis ...

akaki wereTlis saxelmwifo universitetipedagogiuri fakultetixelnaweris uflebiTiagor simonis Ze balanCivaZeskolisaTvis mzaobaSi Seferxebis formebipirvelklaselebTan da maTi daZlevis pedagogiurfsiqologiuriTaviseburebanisadisertacio naSromiganaTlebis mecnierebaTa doqtoris akademiuri xarisxismosapovebladsamecniero xelmZRvanelebi:jemal jinjixaZepedagogiur mecnierebaTa doqtori,soxumis saxelmwifo universitetissruli profesoriimer basilaZeganaTlebis mecnierebaTa doqtori,akaki wereTlis saxelmwifo univeritetisasocirebuli profesoriquTaisi2009 weli1

s a r C e v iSesavali ________________________________________________________ 3Tavi I. pirvelklaselTa mzaobis pedagogiur-fsiqologiuri Tavisebureba$1 pirvelklaselTa swavlebisaTvis mzaobis zogadi daxasiaTeba ______ 8$2 pirvelklasel moswavleTa fizikuri ganviTareba _________________ 14$3 pirvelklasel moswavleTa inteleqtualuri mzaoba ______________ 20$4 pirvelklaselTa pirovnuli mzaobis pedagogiur-fsiqologiuridaxasiaTeba ____________________________________________________ 27I Tavis daskvnebi da rekomendaciebi _______________________________ 34Tavi II. pirvelklasel moswavleTa skolisaTvis mzaobis Seswavla$1 moswavleTa individualuri Taviseburebebis gamovlenis diagnostikurixerxebi ________________________________________________________ 36$2 skolisaTvis mzoabis kvlevis eqspres-diagnostikuri meTodi -______ 42$3 moswavleTa saswavlo unar_Cvevebis kvleva ______________________ 52II Tavis daskvnebi da rekomendaciebi ______________________________ 61Tavi III. moswavleTa elementaruli maTematikuri codnis donis dadgenada ganmaviTarebeli aqtivobebis dagegmva-organizeba$1 skolaSi Semosvlis dros pirvelklasel moswavleTa maTematikuricodnis donis dadgena ___________________________________________ 63$2 bavSvebSi raodenobis invariantobis wvdomis analizi da misi koreqcia________________________________________________________________ 70$3 zepiri angariSis gamoyeneba SemecnebiTi interesebis ganviTarebisaTvismaTematikis gakveTilebze ________________________________________ 91$4 moswavleTa inteleqtualuri unar-Cvevebis ganmaviTarebelsavarjiSoTa sistema ____________________________________________ 100$5 obieqturi Rirebulebis cnobierebis aRzrda maTematikis gakveTilebze_______________________________________________________________ 119III Tavis daskvnebi da rekomendaciebi _____________________________ 126Sedegebis damuSaveba ____________________________________________ 130saboloo daskvnebi da rekomendaciebi ____________________________ 135literatura ___________________________________________________ 138danarTi _______________________________________________________ 1452

S e s a v a l inaSromis aqtualoba. sazogadoebaSi mimdinaresocialurma cvlilebebma, axalma pedagogiurma paradigmam,inovaciurma procesebma ganaTlebaSi gamoiwvieszogadsaganmaTlebelo skolis reformis aucilebloba, ramacasaxva pova ganaTlebis koncefciis modernizaciaSi, ganaTlebisstandartebis SemuSavebaSi. Tanamedrove sazogadoebasgaTviTcnobierebuli aqvs diferencirebuli swavlebisaucilebloba, romelic gaiTvaliswinebs moswavlis individualurtipologiurTaviseburebebs.diferencirebuli swavlebis socialur-pedagogiuri dafsiqologiur-pedagogiuri aspeqtebi gamoikvlies m. fiSerma, a.kirsanovma, i. osmolkovskaiam, m. kolomenskim, v. orlovma.v. kruteckis, i. smirnovas, m. yolbaias kvlevebma gviCvenes, romdawyebiTi skolis moswavleebs axasiaTebT garkveuliindividualur-fsiqologiuri Taviseburebebi, rogoricaa _interesebisa da midrekilebebis mimarTulebaTa Tavisebureba dagansakuTrebuli niWi. magram fsiqologiur-pedagogiuri mecnierebiskvlevaTa farTo wris miRma rCeboda im faqtorebis monografiulikvlevis problema, romlebic uaryofiTad moqmedeben skolaSiswavlebisaTvis mzaobis formirebaze, maTi daZlevis didaqtikurixerxebis SemuSavebaze. problemis damuSavebis mniSvnelobasadasturebs skolis Semdgomi ganviTarebis prognozirebaditendeciebi (kerZod, pirovnebaze orientirebuli swavlebisgaZliereba diferencirebuli saSualebebiT).zemoT aRniSnuli faqtorebis safuZvelze SerCeuli iqnakvlevis Tema - `skolisaTvis mzaobaSi Seferxebis formebipirvelklaselebTan da maTi daZlevis pedagogiur-fsiqologiuriTaviseburebani~.kvlevis obieqti. skolisaTvis mzaobaSi Seferxebis mqonepirvelklaselebi.3

kvlevis sagani. faqtorebi, romlebic uaryofiTadmoqmedeben bavSvis skolisaTvis mzadyofnaze da maTi daZlevissaSualebebi (maTematikis swavlebis magaliTze).kvlevis mizani. koreqciul-ganmaviTarebeli swavlebisfsiqologiur-pedagogiuri safuZvlebis gansazRvra, rac emyarebadiferencirebuli swavlebis teqnologiur principebs dadidaqtikuri saSualebebis kompleqss maTematikis swavlebisSinaarsis, meTodebisa da xerxebis SerCevisas da xels uwyobspirvelklaselebis SemecnebiTi aqtivobis ganviTarebas.kvlevis hipoTeza. pedagogiuri moRvaweobis maRaliSedegi, romelic mimarTulia moswavleebis skolisaTvis mzaobaSiSemaferxebeli faqtorebis dasaZlevad, gaizrdeba im SemTxvevaSi,Tu iqneba gaTvaliswinebuli moswavleTa fsiqo-fiziologiuriTaviseburebebi, gamoyenebuli iqneba diferencirebuli swavlebisteqnologiebi, ùaxloesi ganviTarebis zonaze~ orientirebulimeTodebi, xerxebi da koreqciul-ganmaviTarebeli swavlebisprincipebi.kvlevis amocanebi:1. skolisaTvis mzaobis Semaferxebeli faqtorebisTeoriuli da empiruli daxasiaTeba;2. pirvelklaselebis skolisaTvis mzaobis fsilogiurpedagogiuriTaviseburebebis gamovlena;3. pirvelklaselebis individualuri Taviseburebebisgamovlinebis diagnostikuri xerxebis gansazRvra;4. pirvelklaselTa inteleqtualuri unar-CevebisganviTarebis mizniT didaqtikuri TamaSebis,savarjiSoebis da amocanebis sistemis SemuSavebamaTematikis swavlebis procesSi.kvlevis Teoriul-meTodologiuri safuZveli.meTodologiuri moTxovnebi pedagogiuri kvlevis organizaciismimarT, fsiqologiur-pedagogiuri debulebebi pirovnebis4

struqturis Sesaxeb, misi asakobrivi da invidualur-tipologiuriTaviseburebebi; debulebebi swavlebisadmi diferencirebulimidgomis mizanze, principebsa da safuZvlebze; zogaddidaqtikurida kerZo meToduri midgoma swavlebis Sinaarsis SerCevisas.Camoyalibebulma hipoTezam da kvlevis amocanebma gansazRvresSemdegi kvleviTi meTodebis gamoyeneba:• kvlevis problemebTan dakavSirebuli fsiqo-pedagogiurida meToduri literaturis Seswavla da analizi;• mowinave maswavleblebis muSaobis gamocdilebisSeswavla;• mizandasaxuli dakvirveba moswavlis swavlis procesze;• anketireba;• testireba;• monitoringis meTodi, romelSic igulisxmeba diagnostikada koreqcia;• eqsperimentaluri muSaoba maTematikis swavlebisas.kvlevis mecnieruli siaxle. Tanamedrove fsiqologiurpedagogiurimecnierebis konceptualuri debulebebis, koreqciulganmaviTarebeliswavlebis principebis da diferencirebuliswavlebis teqnologiebze dayrdnobiT ganvsazRvroT saswavloprocesis mimarT pirvelklaselebis mzaobis Semaferxebelifaqtorebi, maTi daZlevis pirobebi da, agreTve, maTematikurisavarjiSoebisa da amocanebis SerCevis didaqtikuri safuZvlebi,rac emyareba pirvelklaselebis individualur-tipologiurTaviseburebebsA da xels uwyobs maTi SemecnebiTi interesebis daunar-Cvevebis ganviTarebas.dacvaze gamotanilia Semdegi debulebebi:1. skolisaTvis mzadyofna ganisazRvreba bavSvis fizikuri,socialuri da inteleqtualuri ganviTarebiT, xolointeleqtualuri mzaobis umniSvnelovanesi maCvenebeliagonebrivi ganviTarebis done (misi konkretuli5

maxasiaTeblebia: azrovnebis siswrafe, myari yuradReba,gonebrivi Sromis unari), amitom, pirvelklaselebisskolisaTvis mzaobis Semaferxebel faqtorebad vTvliT:uaryofiT memkvidreobas, inteleqtualuri Sromisuunarobas, pedagogiur xelmiSvebulobas, metyvelebisarasakmaris ganviTarebas, SemecnebiT pasiurobas.2. swavlaSi CamorCenisEZiriTadi mizezebia: gadaxrebiganviTarebaSi, fizikuri ganviTarebis donis Seusabamobaasakobriv normebTan. aqedan gamomdinare, swavlebis sawyisetapze gansakuTrebuli mniSvneloba eniWeba moswavlisindividualur-tipologiuri Taviseburebebis gansazRvrasda sxvadasxva doneze diferenciaciis principebisgamoyenebas.3. pirvelklaselebis mier maTematikuri codnis aTvisebisSinaarsobrivi da procesualuri mxareebis erTianobisuzrunvelyofis efeqturi saSualebaa konceptualurisqemebis gamoyeneba, romlebic daefuZneba diferencialuriswavlebis principebs. konceptualuri sqema gansazRvravsmaTematikuri codnis dauflebis procesSi SemecnebiTqmedebebs, rac gamomdinareobs SemoTavzebulisavarjiSoebis da amocanebis donisa da swavlebiskonkretuli pirobebidan.4. maTematikis gakveTilebze baSvis inteleqtualuriaqtivobis unaris ganviTarebas xels uwyobs swavlebisteqnologiisa SerCeva, ganmaviTarebeli savarjiSoebis dadidaqturi TamaSebis gamoyeneba.Kkvlevis Teoriuli da praqtikuli Rirebuleba.rekomendaciebis micema dawyebiTi skolis maswavleblebisaTvis,raTa gamovlindes pirvelklaselebis skolisaTvis mzaobisSemaferxebeli faqtorebi da diferencirebuli midgomissafuZvelze SemuSavdes maTi daZlevis saSualebebi.6

kvlevis Sedegebis aqtualobas da dasabuTebasuzrunvelyofs fsiqologiisa da pedagogikis meTodologiebzedayrdnoba; diferencirebuli swavlebis teqnologiis principebisgamoyeneba; swavlebis procesSi miRebuli gamocdileba; kvlevismiznebisa da amocanebis misaRwevad gamoyenebuli meTodebiskompleqsis adekvaturoba; cdebisa da eqsperimentebisas miRebuliSedegebis analizi.kvlevis baza. q. quTaisis #1 da #3 dawyebiTi da #1, 7, 9,27 zogadganmanaTlebelo skolebis pirveli klasebi.naSromis aprobacia da kvlevis Sedegebis danergva.naSromis ZiriTadi debulebebi mosmenilia da ganxilulia sulxansabaorbelianis saxelobis Tbilisis saxelmwifo pedagogiuriuniversitetis (2005, 2006) da akaki wereTelis saxelobis quTaisissaxelmwifo universitetis (2005, 2006, 2007) pedagogikis kaTedraTa(departamentis) sxdomebze. disertaciis masalebis mixedviTwarmodgenili iyo moxsenebebi saqarTvelos mecnierebaTa akademiisganaTlebis Teoriis da praqtikis aqtualuri problemebissamecniero konferenciaze (2007), qsu-s samecniero konferenciebze(2007, 2008), q. quTaisis maswavlebelTa seminarebze (2005, 2007).naSromis struqtura. naSromi Sedgeba Sesavlis, samiTavis, ZiriTadi daskvnebis, bibliografiisa da danarTisagan.7

Tavi IpirvelklaselTa mzaobis pedagogiur - fsiqologiuriTaviseburebebi.$1 pirvelklaselTa swavlebisaTvis mzaobis zogadidaxasiaTebaskolamdeli asakis bavSvi, garkveuli azriT, ukve warmoadgenspirovnebas. man icis, romel qveyanaSi cxovrobs, romel qalaqSi andasaxelebul punqtSi mdebareobs misi saxli, rogori adgiliuWiravs adamianTa Soris (igi skolamdelia) da rogori adgilisdakaveba mouxdeba uaxloes momavalSi (is saswavleblad wavaskolaSi). skolamdeli bavSvi ukve erkveva ojaxur-naTesaururTierTobebSi da SeuZlia naTesavebsa da axloblebs Sorisdaikavos Tavisi socialuri statusis Sesatyvisi adgili. masSeuZlia urTierToba daamyaros mozrdilebTan da TanatolebTan,aqvs Tavis Sekavebis Cvevebi, SeuZlia daemorCilos viTarebas, iyosmtkice, Seudrekeli Tavis survilebSi. skolamdeli asakis bolosbavSvs esmis, rom misi saqcielisa da motivebis SefasebaganisazRvreba ara mxolod Tavis TavTan sakuTari damokidebulebiT(`me kargi var~), aramed, upirveles yovlisa, imiT, Tu rogorgamoiyureba misi saqcieli garSemo myofi adamianebis TvaliT.skolamdeli asakis bolosaTvis gansakuTrebul mniSvnelobas iZensmotivaciuri mzaoba skolaSi swavlebisaTvis. bavSvis, rogorcmoswavlis Semdgomi bedi didadaa damokidebuli imaze, ramdenadmomwifebuli da fsiqologiurd momzadebuli Sexvda asakobrivigaremos ase erTbaSad Secvlas.saskolo swavlebisaTvis bavSvis momwifebaSi S. CxartiSviligamohyofs sam aspeqts:A1. fizikuri momwifeba;2. inteleqtualuri momwifeba;8

3. socialur-pirovnuli momwifeba.swavlisaTvis fizikuri momwifeba gamoixateba, rogorc ZvalkunTovanisistemis imdenad ganviTarebaSi, rom bavSvma SeZlosswavlisaTvis saWiro moZraobaTa ganxorcieleba (magaliTad, werisada kiTxvis CvevaTa SemuSavebisaTvis wvrili kunTebis ganviTarebas,radganac isini uzrunvelyofen Tvalebis komodacia-konvergenciasda xelis mtevnis koordinirebul moZraobebs). aseve nerviulsistemaSi aRgzneba-Sekavebis procesTa urTierTwonasworobis iseTdabalansebaSi, rom bavSvma garkveuli drois ganmavlobaSi SeZlossakuTar moqmedebaTa Sinagani kontroli. Cveni azriT, Tu bavSviskolisaTvis fizikurad momwifebuli ar aris, skolaSi yofnam misjanmrTelobas SeiZleba mniSvnelovani safrTxe SeuqmnasskolaSi axladSesuli bavSvis swavleba iTvaliswinebsinteleqtualuri ganviTarebis garkveul dones: bavSvs aswavlianimas, risi aRqma, gageba, damaxsovreba, warmodgena da warmosaxvacSeuZlia. amitom, asakis Sesabamisad inteleqtualuradCamoyalibebul bavSvs TviTon masalis aTvisebaSi, saTanado SromiT,SeuZlia yvela siZnelis daZleva, magram, Tu bavSviinteleqtauluri ganviTarebis tempiT sakuTar asaks CamorCeba, igiTavidanve ver daZlevs masalas, ramac SeiZleba ganapirobos misiakademiuri CamorCena ara marto pirvel klasSi, aramed saerTodmTeli saswavlo cxovrebis ganmavlobaSi.swavlebisaTvis socialur-pirovnuli momwifeba gamoixatebabavSvis mzaobaSi -- aiRos Tavis Tavze moswavlis socialuri rolida seriozulad izrunos im moTxovnaTa Sesrulebaze, rasacsazogadoeba uyenebs, rogorc moswavles. yvela bavSvi, vincskolaSi sixaruliT Semodis da fizikuri Tu gonebriviTvalsazrisiT sruliad normaluradaa ganviTarebuli, ver axerxebskargad swavlas, mxolod imis gamo, rom ar SeuZlia aqtualurmoTxovnilebaTa impulsi CaaxSos da socialuri moTxovnebismixedviT imoqmedos. aseTi bavSvi mxolod im SemTxvevaSi iswavlis,Tu swavla misTvis saxaliso iqneba, swavlis mTeli procesis aseTi9

organizeba TiTqmis SeuZlebelia. ganskuTrebiT moumwifebulobasam aspeqtiT im bavSvebTan vawydebiT, romlebTanac ver moxerxda e.w.pirveli jiutobis (sami wlis krizisi) daZleva.saskolo swavlebisaTvis bavSvis momwifebaSi romelimeSeferxeba gviCvenebs, rom mis ganviTarebaSi aris disharmonia.disharmoniis daZlevas sWirdeba individualuri midgoma, bavSvisindidvidualuri Taviseburebebis gaTvaliswineba.saskolo ganaTlebis sistemaSi moswavleTa indidvidualuriTaviseburebebis gaTvaliswinebis gareSe SeuZlebelia pedagogiuriprocesis sworad ageba, radgan es ukanskneli, swored moswavlispirovnebaze orientirebuli, misi individualuri SesaZleblobebisgamoyenebas moiTxovs.saqme isaa, rom skolaSi yovelTvis arian bavSvebi,romelTagan zogi kargad swavlobs, raime xarvezebisa daCavardnebis gareSe, magram, maT gverdiT arian iseTebic, romlebsacswavla uWirT. swored aseTi bavSvebi uqmnian skolasa damaswavleblebs did siZneleebs. xSirad ar ician riT arisgamowveuli bavSvebis swavlaSi warumatebloba da rogor undaaigos maTTan pedagogiuri procesi, rom mdgomareoba gamoswordes.es sakiTxi metad aqtualuri gaxda, amaze miuTiTebs 90-ianwlebSi Catarebuli gamokvlevebic (i. gogebaSvilis saxelobispedegogiur mecnierebaTa erovnuli instituti). am drosSeswavlili iqna dawyebiTi klasebis 800 moswavle. aqedan 120bavSvs, anu 15%-s aRmoaCnda siZneleebi swavlebaSi. warumatebelibavSvebidan – 18% gonebrivad CamorCenili aRmoCnda, 15%-saReniSneboda smenisa da metyvelebis defeqti, 12%-s emociurnebelobiTsferoSi hqonda gadaxrebi, xolo naxevarze mets – 55%-saReniSneboda Seferxeba fsiqikur ganviTarebaSi.aRniSnuli sakiTxiT dainteresebuli iyvnen sazRvargareTac.magaliTad, Cexoslovakiis (113 gv. 10) fsiqologebi amtkiceben, romsaskolo asakis bavSvTa daaxloebiT 16% fsiqologiuriTvalsazrisiT ar arin srulad mzad skolisaTvis. amdenad,10

skolisaTvis mzaobis drouli Seafseba, maTi saqmianobis erT-erTisaxea.ganxiluli literaturuli masalis (45, 54, 56, 60, 105) analizigviCvenebs, rom swavlaSi siZneleebis mqone bavSvebi, romlebsac aramxolod gansxavevbuli faqtorebiT gamowveuli siptomatikaaxasiaTebT, aramed arsebuli mdgomareobis gamosasworeblad,gansxvavebul pedagogiur-meTodur RonisZiebebsac saWiroeben.swavlis dawyeba – es aris gardatexis momenti bavSviscxovrebaSi, cxovrebis axal wesze, moqmedebis axal pirobebze,sazogadoebaSi axal mdgomareobaze, mozrdilebTan daTanatolebTan axal urTierTobebze gadasvla. bunebrivia, es araris advili. gansakuTrebiT ki Znelia 6 wlis bavSvisaTvis. xSiradam rTul momentSi vawydebiT warumateblobas. ra ariswarumateblobis mizezi?gamokvlevebma gviCvena, rom moswavleTa umravlesobaSiwarumateblobis mizezi aris arasakmarisi momzadeba swavlebisrTuli procesisaTvis. mSoblebi xSirad fiqroben, rom 6 welsmiRweul bavSvebSi TavisTavad mimdinareobs skolisaTvis momzadeba.xSirad isini gakvirvebuli arian, rodesac winaswari gasaubrebis antestirebis Sedegad eubnebian, rom bavSvi ar aris mzad skolaSiswavlebisaTvis.dakvirkvebebma gviCvena, rom mSobelTa umetesoba yovel Ronesxmarobs, raTa maTi Svili moxvdes romelime prestiJul ansaavtoro skolaSi, magram arc erTi maTgani ar fiqrobs aris Tuara amisaTvis mzad maTi Svili. SeZlebs ki is am skolaSi swavlas?mSobelTa umetesoba am sakiTxs araadeqvaturad udgeba. kargi iqnebaTu mSoblebi dainteresdebian, Tu rogor mimdinareobs maTiSvilebis ganviTareba. bavSvis ganviTarebaSi raime Seferxebisdroul dadgenas Zalian didi mniSvneloba aqvs imdenad, ramdenadacmisi mTliani daZleva SedarebiT martivia skolamdel asakSi.TiToeuli bavSvis ganviTarebis gza aris individualuri,amdenad saskolo asakisaTvis bavSvebi modian gansxvavebuli codna-11

gamocdilebis, unarebis da Cvevebis maragiT. ra aris imisaTvissaWiro, rom bavSvi mzad iyos skolaSi swavlebisaTvis.aucilebelia bavSvi iyos janmrTeli, hqondes fizikurigamZleoba, winaaRmdeg SemTxvevaSi misTvis Zneli iqneba gauZlosdatvirTvas gakveTilebis dros da saerTod, mTeli sawavlo wlisganmavlobaSi.yvelaze metad moswavles unda hqondes skolaSi swavlissurvili e.i. swavlisadmi motivacia. misi upirvelesi mizani undaiyos gaxdes moswavle, Seasrulos micemuli davalebebi, iswavlos.aseTi survili bavSvebis did umravlesobas uCndeba skolamdeliasakis bolosaTvis.yvelaze mTavaria -- bavSvi gonebrivad kargad iyosganviTarebuli, rac aucilebelia saskolo codnis, Cvevebisdauflebasa da unaris gamomuSavebisaTvis. is aucilebelia agreTveinteleqtualuri saqmianobisaTvis optimaluri tempisSesanarCuneblad, raTa bavSvma SesZlos klasTan erTad muSaoba.pirvel klasSi Semsvlel bavSvs sasurvelia hqondes codnisgarkveuli maragi gare samyaros Sesaxeb – sagnebis, cocxali daaracocxali bunebis movlenebis, adamianebisa da maTi SromisTaobaze, imis Sesaxeb, Tu `ra aris kargi da ra aris cudi~.moswavleSi Camoyalibebuli unda iyos socialuri statusi:man unda SesZlos Tavis TanatolebTan erTad saqmianoba,Seasrulos maswavleblis moTxovnebi, akontrolos Tavisi qceva.maswavlebelsa da moswavles Soris yalibdeba urTierTobissruliad gansazRvruli tipi. maswavlebeli warmoadgens bavSvisadmiwayenebuli sazogadoebrivi moTxovnilebebis realur matarebels.klasSi moswavleTa Soris urTierTobani arsebiTad gansxvavdebasabavSvo baRis aRsazrdelebis urTierTobebisagan. skolaSiizrdeba maTi pasuxismgebloba, valdebuleba micemuli davalebisSesrulebisas.skolamdeli asakis bavSvebisaTvis erT-erTi ZiriTadi qcevisforma aris TamaSi. TamaSis dros (roluri iqneba es Tu siuJeturi)12

wesebis dacvis unari exmareba mas swavlebaSi. TamaSSi bavSvisxvadasxvagvarad amyarebs kavSirs gare samyarosTan, erTveba daTamaSobs sxvadasxva situacias – erT SemTxvevaSi is lideria,meore SemTxvevaSi emorCileba sxvas, mesame SemTxvevaSi erToblivsaqmianobas warmarTavs sxva bavSvebTan da ufrosebTan. amitomskolisaTvis mzaobaSi Zalian didi mniSvneloba aqvs bavSvma icodesTamaSi. winaaRmdeg SemTxvevaSi dawyebiT skolaSi swavlas is vermoergeba, ver Seegueba da SeiZleba bavSvSi Tavi iCinosnevrotikulma simptomebma (kaprizi, moswavleebisa da maswavlebliswinaSe SiSi, SeiZleba uaric Tqvas skolaSi wasvlaze).saskolo programebis SeTvisebaSi gadamwyveti mniSvnelobaaqvs bavSvis SemecnebiTi interesebisa da SemecnebiTi moqmedebisdones. bavSvs SeiZleba dadebiTi damokidebuleba hqondes skolisada maswavleblisadmi, moswavlis mdgomareobisadmi, misi uflebebisada movalaobisadmi, magram es sakmarisi ar aris warmatebuliswavlisaTvis. amasTan aucilebelia bavSvs izidavdes skolaSimiRebuli codnis TviT Sinaarsi, ainteresebdes is axali, rasacgakveTilze ecnoba da saerTod, Semecnebis procesi.skolisaTvis mzaobaSi gansakuTrebuli mniSvneloba aqvsSemecnebiTi moqmedebis nebismierobas, Tumca igi Camoyalibebasiwyebs umcros skolamdel asakSi, skolaSi Sesvlis momentisaTvisjer kidev ver aRwevs srul ganviTarebas: bavSvs uWirs didi xnisganmavlobaSi SeinarCunos myari nebismieri yuradReba, daiswavlosgarkveuli moculobis mqone mniSvnelovani masala da a.S.fsiqologTa did nawils miaCnia, rom bavSvis ganviTarebamoicavs rogorc fsiqikur struqturaTa, ise informaciisdamuSavebis xerxebis evolucias. es mentaluri struqturebi kinawilobriv genetikurad daprogramebulia da damokidebuliaindividuumis gonebriv simwifeze. fsiqologiaSi am mimarTulebiserT-erTi fuZemdebeli l.s. vigotski gamorCeulad interesdebodasakiTxiT, Tu rogor yalibdeba bavSvi imad, rac aris. am procesebisgadasaWrelad man gamoyo inteleqtualuri ganviTarebis ori13

sxvadasxva done. pirveli es aris ganviTarebis aqtualuri done,romelic ganisazRvreba bavSvis mier amocanis damoukidebladamoxsnis unariT, meore ki esaa ganviTarebis potenciuri done, rocabavSvs ZaluZs amoxsnas esa Tu is amocana ufrosebis daxmarebiT anufro niWier TanatolebTan erTad. ganviTarebis am or dones SorismanZils k. vogotskim uwoda uaxlesi ganviTarebis zona.l. vigotski xazgasmiT aRniSnavda, rom bavSvis srulyofiliinteleqtualuri ganviTarebisa da swavlebis SesabamisadwarmarTvisaTvis aucilebelia rogorc aqtualuri, ise potenciuriganviTarebis doneTa codna. vigotskisa da mis TanamoazreTaTvisinteleqtualuri ganviTareba urTierTgadajaWvulia bavSviscxovrebis rogorc socialur, ise kulturul yofasTan.Cveni mizani aris davadginoT bavSvis ganviTarebis aqtualuridone. es xorcieldeba skolisaTvis mzaobis eqspres diagnostikiT,romelsac vanxorcielebT e. varxotovas, n. diatkosa da e.sazanovis meTodikiT. es gvexmareba gavigoT mzad aris Tu arabavSvi skolaSi swavlebisaTvis. unda aRvniSno, rom es sakmarisi araris. im bavSvebTan, romlebic ar aRmoCndebian mzad skolaSiswavlebisaTvis, saWiroa SeviswavloT saswavlo unari, misigamokvlevisaTvis viyeneb profesor n. carciZis meTodikas. es orimeTodika bavSvis ganviTarebis Sesaxeb ukve gvaZlevs garkveulsuraTs. Cven ukve viciT, ra aqvs bavSvs kargad ganviTarebuli dasad aris Seferxeba, ra siZlieris aris is. Tu Seferxeba Zliaria,saqme gvaqvs CamorCenasTan, romelic calke saubris Temaa. Cvenisakvlevi moswavleebi arin mxolod msubuqi Seferxebis mqonebavSvebi.Sveicarieli fsiqologis J. piaJes ganmartebiT eqvswlianibavSvebi arian operaciamdel stadiaSi. isini sinamdvilis garkveulmxareebSi erkvevian intuiturad, sagangebo gonebrivi operaciebisgareSe. amdenad, maTSi naklebad aris formirebuli raodenobiscneba. es samive gamokvleva gvexmareba ukeT davgegmoT Cveni14

saqmianoba uaxloesi ganviTarebis zonaSi, raTa droulad damoxerxebulad miviyvanoT bavSvi ganviTarebis potenciur donemde.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom skolaSi warmatebiTswavlebisaTvis, skolaSi Semosvlis momentSi, bavSvs undahqondes fizikuri, inteleqtualuri da pirovnuliganviTarebis garkveuli done. magram xSirad ganviTarebis esdone ar aris sakmarisi saswavlo programebis aTvisebisaTvis.• moswavleTa warumateblobis mizezi aris arasakmarisimomzadeba skolisaTvis da mSobelTa araadeqvaturidamokidebuleba aRniSnuli sakiTxis mimarT;• saWiroa droulad davadginoT ganviTarebis aqtiuri done,raTa moxerxebulad miviyvanoT bavSvi ganviTarebis potenciurdonemde;• yuradsaRebia, rom mSoblebi da ojaxis wevrebi undadaexmaros bavSvs, Tavis Tavze aiRos moswavlis socialuristatusi. gansakuTrebuli yuradreba unda miaqcion bavSvisskolisaTvis momwifebas;F $2 pirvelklasel moswavleTa fizikuri ganviTarebaskolis winare asakSi bavSvis fizikuri organizmiganviTarebis sakmaod maRal dones gulisxmobs. damoukidebeliqcevis aqtebi, romelTac bavSvi garemos garTulebuli amocanebissapasuxod mimarTavs, misi ConCxis, kunTebisa da nerviuli sistemisSesatyvis mdgomareobas moiTxovs. amdenad, winamdebare periodSifizikuri organizmi intensiurad viTardeba.1-dan 6-wlamde asakis bavSvi weliwadSi saSualod 6,4santimetriT izrdeba simaRleSi da 2,5-3 kilograms imatebs wonaSi.bavSvis tani TandaTan ufro grZeldeba, xdeba da nel-nela ikveTebasxeulis formebi, Tavis forma tanTan SedarebiT jer kidev didia.15

Tumca skolaSi Sesvlisas, bavSvebis umravlesobisaTvis tani daTavi erTmaneTis proporciuli xdeba.d. uznaZis mixedviT 6-7 wlis bavSvi SedarebiT proporciuladizrdeba: fexebi maT SedarebiT ufro dagreZelebuli aqvT, _ axlaigi mTeli simaRlis 43-45 %-s Sedagens; Tavi ki sigrZis 1/6-s araRemateba. maSasadame, misi sxeulis proporciebi TiTqmis didisasaRwevs (didi adamianis fexebis sigrZe simaRlis 47-48 %-s udris,xolo Tavis _ 1/8-s). Casuqebuli, gamgrvalebuli, puntula bavSviaxla sul sxvagvari moCans: igi SedarebiT gamxdaria, kunTebiganmtkicebuli da ganviTarebuli aqvs, xolo qsovilebisagrZnoblad gamkvrivebuli.mecnierulma (9, 31, 35, 38) gamokvlevebma gviCvena, rom bavSvebigansxvavebuli siswrafiT izrdebian. am gansxvavebebis mizeziZiriTadad genetikuri faqtorebia, Tumca, garemomac SeiZlebaiTamaSos garkveuli roli. adamianis simaRles ori mniSvnelovanifaqtori gansazRvravs: eTnikuri warmomavloba da kveba. ratom ariszogierTi bavSvi uCveulod dabali? amis mizezi SeiZleba iyosTandayolili faqtorebi (genetika an dedis orsulobisdroindeliproblemebi), fizikuri problema, romelic Cvilobisas iCens Tavs,an emociuri problema. im bavSvebs, romelTac zrdis problemebicTandayolilia, xSirad hormonebiT mkurnaloben.dakvirvebebma gviCvena, rom fizikuri problema SeiZlebaganapirobos cudma kvebam da qronikulma infeqciebma. kargi kveba daSesaferisi samedicino mkurnaloba fizikur problemebTangamklavebis efeqturi gzebia. Seferxebulia im bavSvebis fizikurizrda, romlebic siyvarulsa da yuradRebas arian moklebulni, mZimestresis qveS imyofebian da hormonalur darRvevebs ganicdian.6-7 wlis asakis bavSvebSi wonisa da simaRlis matebaTandaTanobiT xdeba. es periodi simSvidiTa da stabilurobiTgamoirCeva. umcrosi saskolo asakis bavSvebi weliwadSi, saSualod,5-7,5 santimetriT izrdeba simaRleSi. Straci am periods sxeulisxelaxali dagrZelebis xanad Tvlis (6-7 wlis bavSvi weliwadSi16

daaxloebiT 10 sm-iT izrdeba). misi gamokvlevebi adasturebs, romzrdis energia, wina periodSi erTgvari Sesustebis Semdeg, kvlavimatebs.bavSvis fizikuri organizmisaTvis simaRleze metimniSvneloba wonas aqvs. winamdebare periodSi wonis yovelwliurimateba 1,5-2 kg udris, xolo meSvide welSi, rogorc zemoTaRvniSneT, 2,5-3,0 kg, maSasadame, wonis mateba meSvide wlamde imavetempiT midis win, rogorc wina wlebSi, xolo amis Semdeg _ kidevufro meti energiiT. wonaze gansakuTrebiT TvalsaCino gavlenaskveba axdens.mecnierulma (31, 35, 38, 56) gamokvlevebma gviCvena, rom winareperiodSi bavSvis Zvlebs elsatiuroba axasiaTebs. am asakSi ki,Zvlebis gamkriveba ise Sors midis, rom 6-7 wlis bavSvs xerxemlissakmaod mtkice forma umuSavdeba. amitom gvxvdeba SemTxvevebi, romxerxemlis gamrudeba ukve Cveni periodis bavSvsac etyoba.amave periodSi bavSvi kbilebis cvlasac iwyebs. jer massaZire kbilebi amodis (6 wlis bavSvs ukve aqvs oTxi didi saZirekbili. maSasadame, axla mas sul 24 kbili aqvs: 20 ZuZus kbili da 4-ic saZire), Semdeg ki ZuZus kbilebis cvla ewyeba. kbilebs imaveTanmimdevrobiT icvlis, rogoriTac amosdioda.mecnierulma (22, 31, 35, 38, 69) gamokvlevebma gviCvena, rombavSvis fizikuri ganviTareba mWidrod aris dakavSirebuli Sinaganisekreciis jirkvalebis funqcionirebasTan. amitom am asakis bavSvisfizikuri da fiziologiuri ganviTarebis Taviseburebaniganpirobebulia endokrinuli sistemis swori muSaobiT.mkerdukana jirkvali, romelic wina periodSi iyogabatonebuli, axla TandaTanobiT mniSvnelobas kargavs da axaljirkvlebs uTmobs adgils: farisebriv jirkvalsa da hipofizs. esukanaskneli, gansakuTrebiT 6 wlis bavSvis organizmSi, TvalsaCinorolis Sesrulebas iwyebs. albaT amiT aixsneba is garemoeba, romzrdis energia swored am dros iwyebs intensiur moqmedebas.farisebri jirkvlisa da hipofizis hormonebi organizmis JangviT17

unars uwyobs xels da wvis procesebs acxoveleben. unda vifiqroT,rom am periodis bavSvis tendencia sigamxdrisa da qsovilebisgamkvrivebisadmi jirkvalTa zegavleniT aris gamowveuli.swored am asakSi iwyeba Tirkmelzeda jirkvlebisgaZlierebuli zrdac. jirkvlebis hormoni kunTovan sistemazeaxdens gavlenas: amkvrivebs da aRagznebs mas. es garemoeba kargadxsnis zemoT xsnebuli asakis bavSvis fizikuri Zalisa dagamZleobis momatebas: axla igi gacilebiT mets moZraobs da ufroZnelad iRleba, vidre wina wlebSi.Cvenma dakvirvebebma gviCvena, rom bavSvis fizikurganviTarebaSi Zalian didi mniSvneloba aqvs motorul ganviTarebas.motorika gulisxmobs moZraobas ganviTarebisa da swavlebiskonteqstSi. skolamdeli asakis bavSvs TandaTanobiT uviTardebadidi kunTebis kontrolis unari. skoliswinare asakSi bavSvebikidev ufro gabedulebi xdebian. maT Tavisuflad SeuZliaT erTfexze dadgoma da xtunviT siaruli. eqvsi wlis bavSvebi Zalianswrafad darbian da uyvarT sxva bavSvebTan an ufrosebTansirbilSi Sejibreba.Sua da gvian bavSvobaSi, bavSvis msxvili motoruliganviTareba ufro TandaTanobiT da koordinirebulad xdeba.umcrosi saskolo asakis bavSvebs SeuZliaT iswavlon Zalian bevrifizikuri moqmedebis Sesruleba. magaliTad, sirbili, saxtunaozextunva, curva, velosipedis tareba da cigurebiT sriali.gamokvlevebiT davadgineT, rom bavSvebis zrdasTan erTadizrdeba misi unari, gaakontrolos sakuTari sxeuli. masTandaTanobiT ufro didi xniT SeuZlia erT adgilze jdoma dayuradrebis koncentracia. Tumca umcrosi saskolo asakis bavSvebijer kidev ar arian fizikurad bolomde momwifebulni da maT isevWirdebaT fizikuri aqtivoba. am askis bavSvebi erT adgilzejdomiT ufro iRlebian, vidre sirbiliT, xtunviT an velosipedistarebiT. amitom umcrosi saskolo asakis bavSvebi xSirad undaiyvnen CarTuli aqtiur saqmianobaSi. Cveulebriv, biWebi gogonebze18

ukeT asruleben iseT moqmedebebs, romlebic msxvil motorulunarebs moiTxovs.bavSvebis natifi (wvrili) motoruli unarebi mniSvnelovnadviTardeba adreuli bavSvobis periodSi. eqvsi wlis bavSvs SeuZliaCaquCis xmareba, dawebeba, Tasmebis Sekvra da sxva. Svidi wlisasakSi baSvis xelebi ufro stabiluri xdeba.fizikuri ganviTarebasTan erTad xdeba tvinisa da nerviulisistemis ganviTareba. 5-6 wlis bavSvis tvini mozrdili adamianistvinis cxra-meaTedis tolia. tvini da Tavi sxeulis sxva nawilzeufro swrafad izrdeba. Tavis zeda nawilebi, Tvalebi da tviniufro swrafad izrdeba, vidre Tavis qveda nawilebi, rogoric arisyba.mecnierebma daagines, rom 3-dan 6 wlamde yvelaze swrafadtvinis wina (frontaluri) nawili izrdeba. tvinis es nawiliadamianebi moqmedebis dagegmvis, axali davalebebis organizaciisada yuradRebis koncentracias ganapirobebs. 6 wlidan gardamavalasakamde ki yvelaze swrafad tvinis is nawilebi izrdeba, romlebicmniSvnelovan rols TamaSoben enis da sivrciTi mimarTebebisganviTarebaSi.tvinis TandaTanobiT momwifeba, romelsac Tan erTvisbavSvebis mzardi SesaZlebloba, Seimecnon da gamoscadon samyaro,xels uwyobs maTi kognituri unarebis ganviTarebas. magaliTad,ganvixiloT SemTxveva, rodesac bavSvi kiTxvas swavlobs. bavSvisTvalebidan informacia jer mis tvins gadecema. Semdeg is tvinisbevr sistemas gaivlis, romlebic Sav da TeTr formebs asoebs,sityvebis da asociaciebis Sifrebad gadaTargmnis (gadaamuSavebs).am procesis Sedegi bavSvis tuCebiT da eniT gamoxatulsignalebSi aisaxeba (bavSvi xmamaRla warmoTqvams danaxulinformacias).tvini organizebulia nervul wreebad, romlebic neironebsSeicavs. neironebs bevri gansxvavebuli funqcia akisria. magaliTad,erT-erTi nerviuli wredis niSvnelovani funqciaa yuradReba da19

samuSao mexsiereba. samuSao mexsiereba moklevadian mexsierebashgavs; igi warmoadgens im informaciis droebiT Senaxvis da marTvissistemas, romelic saWiroa rTuli kognituri davalebebisSesasruleblad, magaliTad, swavlis, azrovnebisa da gagebisaTvis.nerviuli sistemis wona igive ar rCeba, rogorc wina periodSi: igiTandaTanobiT izrdeba, wylis raodenobis Semcirebis gamo,mkvrivdeba da mniSvnelovani elementebis ufro did SefardebiTsricxvs Seicavs. magram mTavari es ki ar aris, armed is, rom pirvelrigSi nervuli sistemis funqcionaluri ganviTarebis amocanebidgeba: bavSvi axla Tavis Sekavebis gacilebiT met unar iZens; masSeferxebis gacilebiT meti Zala Seswevs, vidre wina periodSi.miuxedavad amisa, bavSvi jer kidev emociur arsebad undaCaiTavlos da, maSasadame, mis qcevas ufro metad emociuri gancdebiwarmarTaven, vidre qerqze momqmedi gamRizianeblebi,inteleqtualuri Sinaarsiis motivebi.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom umcros saskolo asakis bavSvTafizikuri organizmi intesiurad viTardeba, racxelsuwyobs maT skolisaTvis mzaobas;• bavSvis fizikuri ganviTareba mWidrod aris dakavSirebuliSinagani sekreciis jirkvalTa sistemis ganviTarebasTan. esgaremoeba kargad xsnis zemoT xsnebuli asakis bavSvisfizikuri Zalisa da gamZleobis momatebas: axla igigacilebiT mets moZraobs da ufro Znelad iRleba, vidrewina wlebSi;• bavSvis fizikur ganviTarebaSi Zalian didi mniSvnelobaaqvs motorul ganviTarebas, rogorc wvril (natif)motoruls, aseve msxvil motoruls. mas TandaTanobiTufro didi xniT SeuZlia erT adgilze jdoma dayuradrebis koncentracia.20

• fizikuri ganviTarebis erT-erTi mniSvnelovani aspeqtiatvinisa da nerviuli sistemis ganviTareba. am asakSiyvelaze swrafad tvinis wina (frontaluri) nawiliizrdeba. bavSvi Tavis Sekavebis gacilebiT met unars iZens• gasaTvaliswinebelia, rom am askis bavSvebi erT adgilzejdomiT ufro iRlebian, vidre sirbiliT, xtunviT anvelosipedis tarebiT. amitom umcrosi saskolo asakisbavSvebi xSirad unda iyvnen CarTuli aqtiur da ara pasiursaqmianobaSi.$3. pirvelklasel moswavleTa inteleqtualuri mzaoba.inteleqtis Sesaxeb samecniero gamokvlevebi aTeuli wlebiamimdinareobs, amJamad mainc ar arsebobs am cnebis iseTi ganmarteba,romelic srulyofilad moicavda adamianis inteleqtis mTelspeqtrs. qarTul sabWoTa enciklopediaSi weria: ìnteleqti (laT.intellectus – gageba, Semecneba, goneba), pirovnebis Tvisebaa, romelicazrovnebis unars, azrovnebis fsiqologiur safuZvelswarmoadgens~ (t.5, gv.172).ai, ras wers amis Sesaxeb fsiqologiur mecnierebaTasaerTaSoriso kavSiris prezidenti f. kliqsi: `Tu azrovneba arisprocesi, maSin inteleqti aris am procesis Tvisobrioba~, anuazrovnebis cnebaSi igulisxmeba is konkretuli moqmedeba, romelicinteleqtis meSveobiT warmoCindeba.arsebobs inteleqtis cnebis kidev erTi aspeqti – adaptacia(Segueba). v.Sternis mixedviT, Seguebadoba gulisxmobscxovrebiseul amocanaTa gadawyvetas, romelic xorcieldebaobieqtis mimarT gonebrivi moqmedianobis saSualebiT: ìnteleqti esaris individis zogadi unari, gacnobierebuli azrobrivimoTxovnilebebis mimarT; es aris gonebrivad Semecnebuli21

Seguebadoba realuri yofis axal pirobebTan da amocanebTan~(v.Sterni, J.piaJe).amerikeli swavluli, fsiqologi a. anastazi inteleqtsganmartavs ase: àm terminiT, Cveulebrivad, gamoxatulia unar-SesaZleblobaTa is kompleqsi, romelic aucilebelia arsebobisada warmatebisaTvis garkveul kulturul yofaSi~ [46, gv.16].d. veqsleris azri igive sakiTxTan dakavSirebiT mihyveba imSexedulebebis Sualedur xazs, romlebic inteleqts axasiaTebenrogorc azrovnebis unars da rogorc subieqtis gare samyarosTanSeguebadobis saSualebas: ìnteleqti es aris individisglobaluri da kombinirebuli unari adekvaturi moqmedebisa,jansaRi azrovnebisa da gare samyarosTan efeqturi urTierTobisa~[128, gv 243] .inteleqtis cneba dasavlur fsiqologiaSi ukavSirdebatestirebis meTodebsac. amis mixedviT inteleqti SesaZloaganimartos rogorc garkveuli wesiT Sedgenili testuriamocanebis gadaWris unari: ìnteleqti es aris is, rac izomebainteleqtualuri testebiT~ (e. boringi). aseTi Sexeduleba efuZnebaa. bines Sromebs, romelic bavSvis gonebrivi ganviTarebisdiagnostikas eZRvneba.amrigad, rogorc literaturulma gamokvlevebma gviCvena,inteleqtis cneba araerTgvarovania. is, erTis mxriv, ganixileba,rogorc gonebrivi ganviTarebis pirovnuli maxasiaTebeli, meoremxriv, rogorc axal pirobebTan Seguebis unari da bolos, rogorctestebis amoxsnis unari.inteleqtis cnebebis zemoT moyvanili masalidan naTlad CansmozardisaTvis misi mniSvneloba. skolaSi swavlebisaTvis bavSvisinteleqtualuri mzadyofnis maCvenebels warmoadgens azrovnebisada metyvelebis ganviTareba.22

azrovnebis ganviTareba.literaturulma (24, 67, 75, 125) gamokvlevebma gviCvena, romskolamdeli asakis bolosaTvis bavSvis gonebrivi ganviTarebisZiriTadi maCvenebeli aris masSi xatovani azrovnebisa daverbalur-logikuri azrovnebis safuZvlebis Camoyalibeba.xatovani azrovnebis roli SemecnebaSi Zneli Sesafasebelia.mravali saxis inteleqtualuri amocanebis amoxsna mimdinareobsnimuSis, magaliTis mixedviT. aseTi saxiT amocanis warmodgenagvexmareba gavigoT misi piroba, davakavSiroT is realobasTan,xolo Semdeg gavakeToT kontroli realur amoxsnaze.skolamdeli asakis dasasrulisaTvis bavSvs aqvs unari aramarto aRiqvas sagani srulad, Tavisi sxvadasxva saxismaxasiaTeblebiT, aramed SeZlos agreTve misi arsebiTi Tvisebebisada damokidebulebebis gamoyofa. maTSi yalibdeba TvalsaCinosqematuriazrovneba. es aris azrovnebis gansakuTrebuli saxe,romelic gamoixateba imaSi. rom warmatebiT iyenebs da igebs sagnissxvadasxva sqematur gamosaxulebas (gegma, maketi, martivi naxazebi).bavSvebi ufro advilad igeben pirobiT gamosaxulebas, vidreabstraqtul urTierTkavSirs: damokidebuleba winadadebaSisityvebs Soris, sityvaSi asoebs Soris, maTematikur sidideebsSoris da a.S. es uxsnis gzas bavSvebs iswavlon wera-kiTxva damaTematikuri saswavlo masalis TvalsaCino pirobiTigamosaxulebis ZiriTadi kanonzomierebebi.Tu bavSvSi aseTi azrovneba ar aris sakmarisadCamoyalibebuli, maSin pirvel klasSi mas uWirs sityvebisa dawinadadebebis Sedgena, amocanis pirobis sworad Cawera, sadacgamoyenebulia pirobiTi aRniSvnebi da isrebi.skolamdeli asakis bolos safuZveli eyreba verbalurlogikuriazrovnebis ganviTarebas. azrovnebis es saxe viTardebada saboloo saxiT Camoyalibdeba mxolod mozardobis (13 - 14w)asakSi da wamyvani aris zrdasruli adamianis azrovnebaSi.verbalur-logikuri azrovnebis ganviTareba xels uwyobs23

ganyenebul msjelobas, romelic agebulia logikis kanonebiT.skolaSi codnis sistematuri aTviseba ZiriTadad emyareba logikurazrovnebas.ufros skolamdel asakSi verbalur-logikuri azrovnebisZiriTad safuZvels warmoadgens TvalsaCino-xatovani azrovneba damisi bunebrivi gagrZeleba. eqvsi wlis bavSvs aqvs garemos martivianalizis unari; martivi msjelobebi. erTia, rom bavSvis gonebriviSesaZleblobebi Semofarglulia maTi codniT. bavSvis warmatebadidad aris damokidebuli mizez-Sedegobrivi kavSiris dadgenaze,romelic aisaxeba mis metyvelebaSi. isini iyeneben sityvebs: `Tu ki~;ìmitom, rom~; àmitom~ da a.S. misi msjeloba aris logikuri.logikuri azrovnebis ganviTareba gamoixateba metyvelebaSi,anu aisaxeba masSi. misi aTviseba xorcieldeba adre naswavlimniSnelobebis sistemiT, romlebic dafiqsirebulia sityvebSi daxorcieldeba ganzogadebebiT. aseT ganzogadebebs bavSvebi jerjerobiTar floben. logikuri azrovnebis sawyisebi gamovlindebasagnebis klasifikaciis dros. skolamdeli asakis bolos bavSvebsSeuZliaT sagnebis gaerTianeba jgufebSi: àveji~; `WurWeli~;`tansacmeli~ da a.S.verbalur-logikuri azrovnebis Camoyalibebis Semowmeba,sasurvelia sityvieri SeTnaxmebis savarjiSoebiT, romlisSesrulebisaTvis saWiroa TvalsaCino masalebi.jer erTi, sasurvelia gairkves, SeuZlia Tu ara bavSvsdaamyaros mizez-Sedegobrivi kavSiri. amisaTvis SeiZlebagamoviyenoT daumTavrebeli winadadebebis meTodika. SevTavazoTbavSvebs daamTavron frazebi. magaliTad: `Tu oTaxSi SemovitanT,yinvis natexs . . . ~; `biWi avad gaxda, imitom rom . . .~; `guSin wvimamovida, imitom . . .~ da sxvebi.meorec, bavSvis SesaZlelobebis Sefaseba SeiZleba gaerTianebuliobieqtebis SeTavsebis principiT. amisaTvis SeiZleba gamoviyenoTmeTodi `meoTxe zedmeti~. baraTze gamosaxulia 4 sagani, maTgan 3erTiandeba erT cnebaSi, meoTxe ki zedmetia. magaliTad, SeiZleba24

gamoviyenoT baraTi aseTi kriteriumebiT: 1) Sarvali, qvedakaba, kaba,gogona. 2) gvirila, RiRilo, pepela, ia. 3) karada, divani, baliSi,skami. da a.S. bavSvisagan moiTxoveba CamoaSoros erTi `zedmeti~,`SeuTavsebeli~. Tu bavSvi qmnis situaciur-garegnul gaerTianebas(`qvedakaba, kaba, gogona – imitom, rom is amaT icmevs~), maSasadamemxolod garegani, vizualuri warmodgeniT Semoifargleba, veraxerxebs maT Soris cnebiT kavSirs. mocemul magaliTSi sworipasuxia `gogona~, radgan danarCeni sami aris `tansacmeli~, anuerTiandeba am cnebaSi, swored aseTi sityvieri kavSirebi undamoaxdinon bavSvebma msgavs savarjiSoebSi. Tu amas bavSvi veraxdens, masSi arasakmarisad aris Camoyalibebuli cnebiTiazrovnebis safuZvlebi.zemoTxsenebulis mizezi imaSi mdgomareobs, rom skolaSiaxlad Semosuli bavSvis azrovneba sakmaod momZlavrebuliaimisaTvis, rom bavSvma, TvalsaCino warmodgenebze dayrdnobiT,sinamdvilis bevri mxare da sagnebsa da movlenebs Soris arsebulimimarTebebi Seicnos. magram bavSvis azrovneba jer kidev imdenadkonkretuli xasiaTisaa, rom ama Tu im zogad kategoriebzemsjelobisas, mas yovelTvis romelime konkretuli sagani aqvswarmodgenili, rogorc àmgvar~ saganTa warmomadgeneli. swored eskonkretuli warmodgenebi asrulebs saSualo bavSvobis dasawyisissafexurze cnebis funqcias bavSvis azrovnebis procesSi. amitom,bavSvi jer ver igebs iseT ganmartebaTa Sinaarss, sadac sagnisarsebiT, magram araTvalsaCino niSnebzea saubari.azrovnebis zogadi ganviTarebis done SeiZleba SevafasoTSemdegnairad: SevadaroT erTmaneTs TvalsaCino-xatovani amocanisamonaxseni da verbalur-logikuri msjelobis siswore. Tu bavSvsufro metad aqvs ganviTarebuli xatovani azrovneba vidrelogikuri, SeiZleba dazustebiT viwinaswarmetyveloT, romnaklebad ganviTarebuli msjeloba, TandaTan gamoswordebaSemdgomSi. unda aRiniSnos. rom amaze maswavlebels mouwevsgarkveuli muSaoba.25

daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom inteleqti erTis mxriv,ganixileba, rogorc gonebrivi ganviTarebis pirovnulimaxasiaTebeli, meore mxriv, rogorc axal pirobebTanSeguebis unari da bolos, rogorc testebis amoxsnis unari;• skolamdeli asaki bolos bavSvs ganviTarebuli aqvs xatovaniazrovneba. safuZveli eyreba verbalur-logiker azrovnebas.• saskoli asakis dasawyisSi bavSvs uyalibdeba TvalsaCinosqematuriazrovneba. am asakis bavSvebs SeuZliaT daamyaronmizez-Sedegobrivi kavSiri da uviTardebaT cnebiTi azrovneba;• gasaTvaliswinebelia, rom saskolo asakis bavSvTa xatovaniazrovnebis ganviTarebisaTvis mSoblebma da baRisaRmzdrelebma maTTan unda imuSaon rac SeiZleba metiTvalsaCino-didaqtikuri masalebiT. cnebiTi azrovnebisganviTarebisaTvis ki bavSvs daexmareba me-4 zedmeti da me-5zedmetis tipis savarjiSoebi.metyvelebis ganviTareba.skolaSi swavlebisaTvis bavSvis mzaobis erT-erTimniSvnelovani faqtoria – metyvelebis ganviTareba. masSiigulisxmeba: gamarTulad, Tanmimdevrulad, garSemo myofTaTvisgasagebad, sagnis, suraTis, movlenis aRweris, Tavis azrTamsvlelobis gadmocemis, ama Tu im movlenis, wesis ganmartebisunaris daufleba.verbalur-logikuri azrovnebis fesvebi, romlis gareSecSeuZlebelia skolaSi swavla, mWidro kavSirSia metyvelebisganviTarebasTan. mSobliuri ena SeiZleba iTqvas aris erT-erTiZiriTadi sagani dawyebiT skolaSi imdenad, ramdenadac is àRwevs~yvela sagnis swavlebaSi, aerTianebs da anzogadebs maT Sedegebs.sinamdvileSi, metyveleba warmoadgens safuZvels, romelzec igebamTeli saswavlo procesi. Zalian mniSvnelovania, rodesac bavSvi26

flobs monologs, Txrobas – Tavdapirvelad zepirs, xolo SemdegweriTs.gamarTuli monologi, Txroba – es ara mxolod calkeuliwinadadebebia, aramed gamonaTqvamebis erToblioba, romelicramdenime winadadebisagan Sedgeba. es aris farTo gagebiT teqsti(imis miuxedavad dawerilia es Tu warmoTqmuli), amitommonilogiuri metyveleba aigeba literaturuli kanonis Sesabamisadda ara salaparako enaze.gamarTuli monologi bavSvebisagan moiTxovs metTavisuflebas, azrianobas, vidre dialogi.bavSvisaTvis monologis yvelaze martiv formas warmoadgenssiuJeturi moTxrobis moyola, Txroba. masSi (aRwerilisagangansxvavebiT) naTlad Cans teqstis saerTo agebuleba: dasawyisi,Sua nawili, dasasruli rac amsubuqebs gamarTul metyvelebas.Txrobis unaris Semowmeba aucilebelia bavSvis skolaSimiRebis dros imdenad, ramdenadac Txrobas gansakuTrebuli adgiliuWiravs bavSvis saskolo saqmianobaSi. Tavdapirvelad es arismoyola, razec saubrobs maswavlebeli, Semdeg – bavSvis mierwakiTxuli saswavlo teqstis Txroba.SeiZleba SeTavazebuli iyos aseTi davaleba, mag.: ufrosebismier wakiTxuli teqstis (6-7 winadadeba) moyola. SeiZleba bavSvsSevTavzoT suraTebis TanmimdevrobiT dalageba, masze moTxrobisSedgena da a.S.Txrobis Sefasebis kriteriumebi SeiZleba iyos:1. Txrobis saerTo struqtura (dasawyisi, Sua nawili,dasaruli);2. gramatikuli siswore (winadadebis swori Sedgena, sityvaTaSeTanxmeba brunvasa da ricxvSi);3. gamomxatveli saSualebebis gamoyeneba;4. saubris bgeriTi mxare (tempi, sinarnare, intonacia).bavSvis metyvelebis Sefasebisas, sasurvelia gvaxsovdes, romzemoT mocemul winadadebebs kavSiri aqvT bavSvis mxolod aqtiur27

saubarTan. magram swavlebis procesSi CarTulia ara marto`laparaki~, aramed aRqmac.amdenad, monologiuri metyvelebis arasakmarisi ganviTareba ardaarRvevs saswavlo process. sxva saqmea, rom es naklovanebaicodes dawyebiTi klasis maswavlebelma swavlis dawyebamde, aramarto imisaTvis, rom SearCios swavlebisa da gakveTilzeurTierTobis formebi, aramed warmoSobili siZneleebisgadasalaxavad da sawavlo procesis saTanadod asagebad.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom pirvelklaselebSi skolaSiSesvlis momentSi, sakmaod aris ganviTarebuliTanmimdevrulad sakuTari azris gadmocemis unari;• bavSvis monologis martiv formas warmoadgens siuJeturimoTxrobis moyola. misi Sefasebis kriteriumebia: Txrobisstruqtura (dasawyisi, Sua nawili, dasasruli), gramatikulisiswore, saubris bgeriTi mxare, gamomxatvel saSualebaTagamoyeneba;• gasaTvaliswinebelia, rom mSoblebi da aRmzrdelebi xSiradunda Seecadon bavSvs moayolon Tavdapirvelad moklesiujeturi moTxrobebi, xolo Semdeg maTi sayvarelizRaprebi.$ 4. pirvelklaselTa pirovnuli mzaobis pedagogiurfsiqologiuridaxasiaTeba.bavSvis pirovnebis yvela parametris daxasiaTebidan daTaviseburebebidan gamovyofT 3 ZiriTad parametrs, romelic ufrometad aucilebelia skolaSi swavlebisaTvis, esenia:• ufrosebTan urTierTobis unari;• TanatolebTan urTierTobis unari;28

• TviTSefaseba, sakuTar TavTan damokidebuleba.ufrosebTan damokidebuleba.fsiqologiaSi dadgenilia, rom skolamdeli asakis bolosbavSvebi nimuSis mixedviT moqmedeben.nimuSis mixedviT moqmedeba –es aris is moqmedeba, romelic`xorcieldeba nimuSis Sesabamisad (imis miuxedavad mocemulia israime wesis an sxva adamianis moqmedebis formiT) da misikontrolireba xdeba am nimuSTan SepirispirebiT~ - (Д. Б. Эльконин.Психология игры – М. 1978г. с. 36)skolamdeli asakis bavSvebisaTvis ufro metaddamaxasiaTebelia uSualoba, impulsuroba, gulwrfeloba. saskoloasakTan miaxloebul bavSvebSi mcirdeba es Tvisebebi.dawyebiT klasebSi swavlebis warmateba didad arisdamokidebuli masze, Tu ramdenad muSaobs bavSvTan maswavlebeli,ramdenad swori iqneba misi midgoma da damokidebuleba bavSvebTan.amis gareSe SeuZlebelia gakveTilze mimdinare procesebisWeSmariti azris gageba.is bavSvebi, romlebic yvela aspeqtiT harmoniulad arianganviTarebuli swavlisaTvis, mniSvnelovan sirTuleebs awydebianaxal obieqtur viTarebasTan Seguebis TvalsazrisiT. bavSvmasrulad axleburi socialuri urTierTobebi unda daamyarosmaswavlebelTan, radgan swored is unda daexmaros am sirTuleebisdaZlevaSi. kerZod, pirveli klasis maswavlebelma pirvel dResveunda daamyaros yvela moswavlesTan kontaqti da agrZnobinosTavisi emociuri siTbo. rogoc S. CxartiSvili aRniSnavs, skolaSipirvel dRes miRebul STabeWdilebebs iseTi mniSvneloba aqvsadamianisaTvis, rom es mogonebebi TiTqmis mTeli cxovrebisganmavlobaSi ar ikargeba.Tu nimuSis mixedviT moqmedebis unari dabalia, maSin bavSviver aRiqvams sawavlo procesis amocanas. bavSvebi ver xedaven29

maswavleblis kiTxvebis miRma swavlebis problemebs da masaRiqvamen, rogorc `cxovrebiseuli~ uSualo urTierTobis sababs.aseT bavSvebs SeuZliaT xSirad Seawyvetinon maswavlebels, misceniseTi kiTxvebi, romlebic saerTod ar exeba gakveTils.unda aRiniSnos, rom skolisaTvis kargad momzadebuli bavSvi,mowodebuli aris Cveulebrivad aRiqvas maswavleblis roli. ammxriv rac ufro warmoaCens Tavs, rogorc maswavlebeli, miT ufrometad afaseben amas bavSvebi. cnobilia, rom dawyebiTi klasebismoswavleebi xSirad etrabaxebian erTmaneTs, rom misi maswavlebeliufro mkacria. simkacre, bavSvebis gagebiT, aris swored is Tviseba,romelic ganekuTvneba maswavleblis rolis arss, momTxovnelobasaigiveben simkacresTan. gavixsenoT, rogor TamaSoben bavSvebiskolobanas. rogor siamovnebiT uweren erTmaneTs orians, amyarebenklasSi disciplinas, amisaTvis ki iyeneben simkacres droTaganmavlobaSi bavSvebi rwmundebian imaSi, rom maswavlebelisinamdvileSi maT kargad epyroba da zrunavs maTze. Tu ase ar aris,maSin maswavlebeli aris ara mkacri, aramed avi, swavla arisautaneli da saerTod `sabavSvo baRSi ukeTesi iyo~.bavSvebis ufrosebTan nebismieri urTierTobis SeswavlaSeiZleba sxvadasxva xerxiT, magaliTad: àkrZaluli sityvebis~msgavsi TamaSi, rodesac bavSvebi pasuxoben ufrosebis kiTxvebs ise,rom ar iyeneben winaswar momzadebul sityvebs. msgavsi TamaSebisdros ufrosebis kiTxvebze bavSvebis pasuxebi da maTi qcevagviCvenebs, Tu rogor aRiqvamen aseT situaciebSi ufrosebispozicias, rogor upasuxon ùazro kiTxvebs~ ise, rom ar daarRvionTamaSis wesebi.bavSvebi, romlebic fsiqologiurad ar arian mzadskolisaTvis, Cveulebisamebr `keTilsindisierad~ pasuxobenufrosebis nebismier kiTxvas, magram arRveven TamaSis wesebs. maT arSeuZliaT yuradReba miaqcion im garemoebas, rom ufrosebisdasmuli kiTxvebi atarebs pirobiT xasiaTs, anu es aris FTamaSisgarkveuli wesi da maTze unda vupasuxoT am wesis Sesabamisad.30

aseTi bavSvebisaTvis mTavaria pasuxis `siswore~ da ara TamaSiswesebis dacva. marTalia swavla ar aris TamaSi, magram TamaSiswesebis dacva gvexmareba swavlebaSi. TamaSis meTodiT swavlebabavSvebisaTvis ufro misawvdomia da misi gamoyenebiT swavlaTandaTan gaxdeba qcevis ZiriTadi forma.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom bavSvis nimuSis mixedviTmoqmedebis dabali done xels uSlis aRiqvas saswavloprocesis amocana. wesebis mixedviT TamaSi gvexmarebaswavlebaSi da aqcevs swavlas qcevis ZiriTad formad.• pirvelklaselebs maswavlebeli hyavT gaidealebuli, didiamisi avtoriteti. maswavlebeli bavSvisadmi TavisidamokidebulebiT uqmnis swavlisadmi motivaciurdamokidebulebas;• gasaTvaliswinebelia, rom baRis aRmzrdelma da mSoblebmadidi yuradReba unda miaqcion bavSvis ufrosebis mimarTdamokidebulebas, maTi miTiTebebis mixedviT qmedebas.TanatolebTan damokidebulebabavSvis skolisaTvis pirovnuli mzadyofnis meoreumniSvnelovanes komponentad iTvleba TanatolebTan urTierTobisdonis gansazRvra. ufros skolamdel asakSi sxva bavSvebTanurTierTobis moTxovnileba aSkarad gamoxatulia. TanatolTakoleqtivi SesaZleblobas uqmnis bavSvebs gamoamJRavnondamoukidebloba, aqtiuroba, iniciativa da individualuriTaviseburebebi. koleqtiuri saqmianobiT yalibdeba TanatolebiTdaintereseba, uviTardebaT keTili damokidebuleba. sxva bavSvebTandamokidebuleba mniSvnelovania TanatolebTan decentraciis unarisganviTarebisaTvis. es aris sxvisi Tvalsazrisis gaTvaliswinebisunari, aRiqvas esa Tu is amocana, rogorc saerTo, romelic31

moiTxovs erTobliv saqmianobas, Sexedos sakuTar Tavsa da qcevasgverdidan, sxvisi TvaliT.skolaSi axlad misuli bavSvebi jer kidev ar ganicdian Tavsklasis socialuri jgufis wevrad. amaze isic metyvelebs, romkoleqtiurad micemul davalebebs isini sakuTar Tavze ar iReben,saWiroa TiToeuls cal-calke ganemartos risi gakeTebamoeTxoveba.swavleba koleqtiuri xasiaTisaa da iTvaliswinebsmoswavleTa urTierTsaqmianobasa da TanamSromlobas saerTosaswavlo amocanebis situaciaSi. Tu bavSvis urTierToba argamoirCeva gansakuTrebuli konfliqtebiT, Tu is SedarebiTadvilad amyarebs Tanatolebs Soris saqmian urTierTobebs,partniorobs maTTan TamaSsa da erTobliv saqmianobaSi. bavSvierkveva, rom saqmianobis mizezi yvela moswavlisaTvis aris saerTo,maSin darwmunebiT SegviZlia vTqvaT, rom sakmarisad arisganviTarebuli bavSvSi sxva bavSvebTan, TanatolebTan urTierToba,romelic aucilebelia skolaSi swavlebisaTvis.literaturuli masalebis (45, 88, 94, 119) gacnobisa dadakvirvebebis Sedegad miviReT, rom Tu bavSvSi TanatolebTanurTierTobis unari ar aris Camoyalibebuli, maSin mas gauWirdeba,mag.: Tanaklaselis pasuxis mosmena, sxvis mier dawyebulimonayolis gagrZeleba, adekvaturad moqceva sxva bavSvebiswarmatebasa da warumateblobaze (Suri, dacinva, xmaRalimsjeloba).bavSvebis TanatolTan urTierTobis donis dasadgenadSeiZleba davakvirdeT mis qmedebas koleqtivSi, sxva bavSvebTanerTobliv TamaSsa da saqmianobaSi.skolaSi Seyvanisas testirebis dros es amocana verganxorcieldeba. amdenad am sakiTxebisaTvis saWiro kiTxvebiSeiZleba davusvaT mSoblebs gasaubrebisas. ra Tqma unda, es araris sakmarisi. saWiroa TanamSromloba gvqondes sabavSvo baRisfsiqologTan da meTodistTan. dawyebiTi skolis32

maswavleblebisaTvis Zalian sasargebloa Tu bavSvis daxasiaTebaSiaRniSnulia misi urTierToba TanatolebTan sxvadasxva saqmianobisTu TamaSis (siuJetur-roluri da raime wesebiT) dros. esecSeiZleba mxolod im SemTxvevaSi, Tu bavSvi dadioda baRSi damisTvis fsiqologs (an aRmzrdels) micemuli aqvs daxasiaTeba.Tu Cven ar gvaqvs daxasiaTeba an bavSvi saerTod ar dadiodabaRSi, maSin am TvalsazrisiT Zalian sasargeblo daproduqtiulia, Tu dawyebiTi skolis maswavleblebi organizebasgaukeTeben skolaSi winaswar mosamzadebel jgufebs`progimnaziebs~, kursebs, romelic skolamdeli asakis bavSvebsmoamzadebs skolaSi swavlebisaTvis. rogorc wesi, msgavsi saxiTmomzadebisas maswavlebels aqvs saSualeba daakvirdes bavSvisqcevas sxvadasxva saswavlo da arasawavlo situaciebSi, yuradRebamiaqcios ufrosebTan da TanatolebTan erToblivi saqmianobis,urTierTobis Taviseburebebs.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom TantolebTan kargi urTierToba,erTobliv saqmianobaSi CarTuloba, xels uwyobs jgufurswavlebas. es mniSvnelovania, agreTve TanatolebTandecentralizaciis unaris ganviTarebisaTis.• yuradsaRebia bavSvis ganviTarebaze dakvirveba, kerZoddedmamiSvilebTan, mezoblebTan da megobrebTan urTieTobaze;• mSoblebma da ojaxis wevrebma xeli unda Seuwyon bavSvsxSirad miiRos monawileoba gundur TamaSebSi. TavidanvemivaqcioT yuradReba ramdenad egueba is sxvadasxvasituaciaSi TamaSs.sakuTar TavTan damokidebuleba.skolisaTvis pirovnuli mzadyofnis mesame komponentiwarmoaCens bavSvTa TviTSegnebis ganviTarebas, rac nawilobrivdakavSirebulia misi TviTSefasebis cvlilebasTan.33

skolamdelTaTvis yvelaze metad damaxasiaTebelia sakuTari Tavisada misi SesaZleblobebis araobieqturad maRali Sefaseba. `me –yvelaze Zlieri var jgufSi~; `Cemi naxati yvelaze saukeTesoa~ –aseTia skolamdelebis tipiuri gamoTqmebi. es xdeba ara zedmetiTviTdajerebulobiTa da qedmaRlobiT, aramed bavSvuriTviTSegnebis specifikis Sedegad. saWiro ar aris vibrZoloTbavSvis maRal TviTSefasebasTan, Cven kargad viciT, rom es arisara adekvaturi TviTSefaseba, saWiroa miviRoT pozitiuriTviTSefaseba, magram es unda moxdes TavisTavad, rogorc am asakisbavSvebis krizisis Sedegi.zogierT skolamdelSi SeiniSneba aramdgradi da zogjerdabali TviTSefaseba. Cveni azriT es migviTiTebs ara TviTSegnebisintensiur ganviTarebaze, aramed imaze, rom am bavSvebs maT garSemomyofi ufrosebisagan akliaT TanagrZnoba, siyvaruli dayuradReba. bavSvebi ganicdian yovelive amis deficits, isini Tavsver grZnoben daculad.mTeli skolamdeli asakis periodSi bavSvSi Camoyalibebulidabali TviTSefaseba, SeiZleba gaxdes skolaSi bavSvis CamorCenismizezi. is Sepyrobilia warumateblobis SiSiT, misi ukuduresigamoxatulebaa – saerTod uaris Tqma raimes gakeTebaze. aseTibavSvebi, rodesac moxvdebian skolaSi, uars amboben upasuxonadgilidan, uars amboben sakontrolo weris Sesrulebaze. aseTibavSvi mzad aris hqondes xulignisa da zarmacis saxeli, vidreswavlaSi warumateblisa. Sesabamisad xSirad tovebs saxlSiwignebs, rveulebs da sxvadasxva saswavlo nivTs.bavSvTa TviTSefasebaze warmodgenis miReba SeiZlebasxvadasxva xerxiT. mag.: SevTavazoT kibe, romlis yvelaze maRalsafexurze dganan jgufis yvelaze Zlieri bavSvebi, xolo sulqvedaze - yvelaze sustebi. vTxovoT Tavi dasvas im kibeze, romelicmas Seefereba. dakvirvebebma gviCvena, rom Tu tipiuri skolamdelebiTavianT Tavs dasvamen yvelaze maRal safexurze, 6-7 wlianebiTavianT Tavs dasvamen Sua safexuris cota zemoT. skolamdeli da34

umcrosi saskolo asakis bavSvTa TviTSefasebaSi gansxvavebaSeiZleba gavigoT, Tu CaveZiebiT, raSi xedaven isini TavianTiwarumateblobis mizezs. tipiuri skolamdelebi amboben, rom Robesisini ver gadaaxtnen imitom, rom Zalian maRali iyo, an vedro veraswien, imitom rom Zalian mZime iyo. umcrosklaselebi mzad arianmizezi eZebon ara marto gare faqtorebSi, aramed sakuTar TavSi,TavianT Tvisebebsa da SesaZleblobebSi.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom skolamdelebisaTvisdamaxasiaTebelia sakuTari Tavisa da SesaZleblobebisaraobieqturi Sefaseba. misi mizezi aris is, romufrosebisagan akliaT siyvaruli, TanagrZnoba, yuradReba,zrunva;• dabali TviTSefaseba SeiZleba gaxdes skolaSi bavSvisCamorCenis mizezi. asakis momatebasTan erTad ara adekvaturiTviTSefaseba gadadis pozitiurSi;• gasaTvaliswinebelia, rom skoliswinare asakSi, rogorcmaRali ise dabali TviTSefasebisas mSobeli frTxilad undamiudges mis gamosworebas;• dabali TviTSefasebis mqone baSvebi xSirad xvdebian CrdilSiswavlebis dros, sworad aq aris saWiro maswavleblis didiZalisxmeva. Sesabamisad mSoblebs xSiri kavSiri unda qondesmaswavleblebTan.I Tavis daskvnebi da rekomendaciebi• gamokvlevebma gviCvena, rom warmatebiT swavlebisaTvis,skolaSi Semosvlis pariodisaTvis bavSvs aqvs fizikuri,inteleqtualuri da pirovnuli, ganviTarebis garkveuli done.35

magram xSirad ganvitarebis es done ar aris sakmarisisaswavlo programebis aTvisebisaTvis.• moswavleTa warumateblobis mizezi aris arasakmarisimomzadeba skoliswinare periodSi da mSobelTaaraadeqvaturi damokidebuleba aRniSnuli sakiTxis mimarT;• arsebuli kvlevebis analizma gviCvena, rom:a)saskoli asakis dasawyisSi bavSvs uyalibdeba TvalsaCinoxatovaniazrovneba. am asakis bavSvebs jer kidev ar SeuZliaTmizez-Sedegobrivi kavSirebis damyareba. Bb) skolamdelebisaTvis damaxasiaTebelia sakuTari Tavisa daSesaZleblobebis araobieqturi Sefaseba, rac vlindebarogorc dabali aseve maRali TviTSefasebis saxiT. dabaliTviTSefaseba SeiZleba gaxdes skolaSi bavSvis CamorCenismizezi.• gasaTvaliswinebelia, rom skoliswinare asakSi dabaliTviTSefasebis gamo, bavSvebi xSirad xvdebian CrdilSiswavlebis dros, sworad aq aris saWiro maswavleblis didiZalisxmeva. interaqtiuri da jgufuri meTodikebi didaduwyobs xels swored adekvaturi TiTSefasebis formirebas.• bavSvis individualuri Taviseburebebis Seswavlas mSobeliunda ecados jer kidev skolis winare asakidan dawyebuli,raTa saTanado muSaobiT gamoasworos is xarvezebiromlebsac adgili aqvs.• mSoblebi da ojaxis wevrebi unda daexmaron bavSvs TavisTavze aiRos moswavlis socialuri roli. gansakuTrebuliyuradReba unda miaqcion bavSvis skolisaTvis momwifebas,bavSvis ufrosebis mimarT damokidebulebas, maTi miTiTebebismixedviT qmedebas. xeli unda Seuwyon bavSvs xSirad miiRosmonawileoba gundur TamaSebSi;36

Tavi IIpirvelklasel moswavleTa skolisaTvis mzaobisSeswavla$ 1. moswavleTa individualuri Taviseburebebisgamovlenis diagnostikuri xerxebiTanamedrove etapze, damoukidebeli qarTuli saxelmwifosmSeneblobis procesSi udidesi yuradReba eniWeba momavali TaobisaRzrdas. demokratiuli sazogadoebisaTvis damaxasiaTebeliapirovnebis individualuri SesaZleblobaTa gaTvaliswineba da maTiganviTarebisaTvis optimaluri pirobebis Seqmna. ganaTlebissaxelmwifo programis prioritetia bavSvTa individualuriTaviseburebebis gamovlena da amis gaTvaliswinebiT saswavloprocesis ageba, radgan es ukanaskneli misi individualuriSesaZleblobebis gamoyenebas moiTxovs. amiT is Zireuladgansxvavdeba unificirebuli da mkveTrad centralizebuliganaTlebis sistemisagan, romlis tipiuri magaliTi iyo yofilisabWoTa kavSiri. cnobilia, rom misi arsebobis bolo aTeuliwlebis ganmavlobaSi mTlianad gamoricxuli iyo bavSvTa Sorisindividualuri gansxvavebis gaTvaliswineba mizanmimarTulpedagogiur procesSic ki.individualuri TaviseburebebiT bavSvTa gansxvavebis ideaaxali ar aris, mas didi xnis istoria aqvs. mecxramete saukunisbolodan saTaves iRebs bavSvTa gadarCeva. gadavxedoT misiganviTarebis istorias. pirveli testebi ekuTvnis f. galtons. igicdilobda gonebrivi SesaZleblobebi Seecno `gazomviTa daricxobrivad~ (f.galtoni, 1879w.). galtonis ideaTa SemdgomganviTarebaSi wvlili miuZRvis j. qeTlis Sromebs, romelmacsaTave daudo `gonebrivi testebis~ farTo gamoyenebas. gonebrivi37

unaris ganviTarebis Tavdapirveli fsiqodiagnostikuri meTodikisavtorebi iyvnen bine da simoni, romlebmac SeimuSaves `gonebriviganviTarebis ganzomilebis skala~ - 1905wels. mecnierebaSi farTodgavrcelda da ganviTarda swored maTi ideebi da maT mierSemoTavazebuli inteleqtualuri testebis Sefasebis raodenobrivimaCvenebeli. amasTan, testireba ganixileba rogorc universalurimeTodi, gansazRvruli pirovnebis gonebrivi ganviTarebis imTandayolili donisa, romelic ganapirobebs individis miRwevebsada warmatebebs.gonebrivi ganviTarebis bine-simoniseuli skalis pirveliredaqcia iTvaliswinebda gonebrivad arasrulfasovani bavSvebisgamovlenas. a. bine wers: `doqtor simonTan erTad SevimuSavegonebrivi moqmedianobis sinTezuri Teoria. . . , anu gonebriv unar-CvevaTa sazomi meTodi, romelic cnobilia `metruli skalis~saxelwodebiT. igi iZleva imis dadgenis saSualebas, Seefereba Tuara ama Tu im subieqtis inteleqti mis asaks an uswrebs TuCamorCeba es ukanaskneli pirovnebis ganviTarebis dones, anu ra`xnovanebisaa~ individi gonebrivad~ (49 gv. 22).metruli skala ZiriTadad warmodgenili iyo ricxviTi,logikuri da verbaluri xasiaTis, agreTve drosa da sivrceSisaorientacio da mexsierebis ganviTarebis sazomi amocanebiT. maszericxviTi (ariTmetikuli) xasiaTis amocanaTa arseboba,ganpirobebulia maTematikis tradiciuli roliT moswavleTainteleqtis ganviTarebaSi.1908 wels maT gamoaqveynes sakuTari testebis pirveli seria 3-13 wlis bavSvebisaTvis. TiToeuli asakisaTvis Sedgenili iyo 5-7testi. sabolood testebis raodenoba dayvanili iqna xuTamde. isZiriTadad bavSvTa gonebrivi ganviTarebis dones ikvlevda.bine-simonis skalam miiqcia mTeli msoflios fsiqologTayuradReba; iTargmna mraval enaze. es testebi SemdgomSi l.termenma Tavis SromebSi ganavrco da daxvewa.38

gonebrivi ganviTarebis stenford-bineseuli skala arisgonebrivi ganviTarebis bine-simoniseuli skalis modifikacia.testis bolo redaqcia gamovida 1972 wels. testebi dajgufebuliaasakobrivi doneebis mixedviT. es testebi unar-Cvevebs ikvlevsfarTo masStabiT, martivi manipulaciebidan ganyenebul,abstraqtul azrovnebamde.es testuri meTodika gvaZlevs cnobebs cdispirTa Sesaxeb,konkretulad, maT mier amocanaTa amoxsnis xerxebis, maTiaqtivobis, motivirebis Sesaxeb.inteleqtis sazomi veqsleriseuli Skalebi aris inteleqtistestebis yvelaze metad cnobili jgufi da gankuTvniliinteleqtualuri ganviTarebis doneTa sazomad.1949 wels veqslerma SemogvTavaza skala 5-dan 15 wlamdeasakis bavSvebisaTvis. testi Sedgeba ramdenime subtestisagan. misierT-erTi mTavari Rirsebaa cdispiris mier subtestebis amocanebisSesrulebis Sinaarsobriv-Tvisobrivi analizi da maTiinterpretacia.fsiqodiagnostikaSi veqsleris skalaTa sayovelTao daxangrZlivi gamoyenebiT dagrovda sakmao cnobebi am meTodikebissaimedoobisa da validobis Sesaxeb.misi Sedegebis analizis Tanaxmad, veqsleris skalebigajerebulia zogadi inteleqtis faqtoriT. amas garda gamovlindasami jgufuri faqtori: verbaluri faqtori (subtestebi – leqsika,gageba-mixvedriloba, gaTviTcnobiereba, figurebis Sedgena),percefciuli faqtori (subtestebi – kosos kubikebi, figurebisSedgena), mexsierebis faqtori (subtesti – ariTmetika, ricxvismimdevroba).inteleqtualuri unarebis eqspres-diagnostikis meTodika(Методика зкспресс-диагностики интеллектуальных способностей) МЭДИС.inteleqtis testi 1994 wels SemogvTavazes e. n. Sceblanovam, i. s.averinam, e. n. zadorinam. testi gankuTvnilia 6-7 wlis bavSvebis39

inteleqtualuri unarebis sazomad. is Seqmnilia KFT 1-3-istestebis bazaze (Kognitiver Fahigkeits Test fur 1 bis 3 klassen, 1983), miunhenisuniversitetSi. igi gamiznulia gamorCeuli niWiT dajildoebulpirvelklaselTa SemecnebiTi unar-Cvevebis gansazRvrisaTvis.МЭДИС-is avtorebma miznad daisaxes iseTi testebiskonstruireba, romliTac gamartivdeboda moswavleTa saskolomzaobis dadgena. meTodika Sedgeba 4 subtestisagan, sadacTiToeuli iTvaliswinebs mzardi sirTulis 5-5 amocanas. amocanebiwarmodgenilia naxatebis saxiT da amdenad, wera-kiTxvis codnas ariTxovs. skolamdelebs Tavdapirvelad eZlevaT testebis SesabamisisawvrTneli amocanebi.aRniSnuli testebiT izomeba logikuri, verbaluri dasivrciTi aRqmis unarebi, agreTve ricxviTi simboloebiToperirebis unaric. aRniSnuli meTodikebis garda uamravi meTodikaamoswavleTa gonebrivi ganviTarebis dasadgenad, magram maTiCamoTvla da analizi Sors wagviyvans. amdenad, vnaxoT ra bedi ewiaindividualuri TaviseburebebiT bavSvTa gadarCevas Cvens qveyanaSi.20-30-ian wlebSi axalgazrda sabWoTa saxelmwifo dabunebrivia saqarTveloc bavSvTa gonebrivi doniT gadarCevisaTvistestirebis meTods iyenebda, magram axali testebi aq ar Seqmnila.ZiriTadad iyenebdnen bine-simonis adaptirebuli testebis seriebs.am droisaTvis maTi testebi farTod gavrcelebuli iyo mTelmsoflioSi, xolo testireba bavSvTa diagnostikis erT-erTiZiriTadi meTodi gaxda. bavSvTa gadarCevisaTvis testebs pedologiaiyenebda. 1936 wlis 4 ivlisis sak. k(b) centraluri komitetisdadgenilebiT pedologia, rogorc mecniereba aikrZala da masmiayoles testebi, rogorc misi ZiriTadi meTodi. aqedanmoyolebuli aTeuli wlebis manZilze testebis Zagebis metiaraferi iwereboda sabWoTa pedagogiur da fsiqologiur presaSi.70-iani wlebidan yofil sabWoTa kavSirSic daiwyes bavSvTagadarCevis meTodebze muSaoba (a. bodalevi, i. dobrovina, a.40

panasiuki, i. savenko, a. Cuki da sxva), magram am periodSi aRniSnulproblemas saTanado yuradReba mainc ar eqceoda da isgamokvlevebic mxolod pirvel cdad iyo miCneuli bavSvTafsiqodiagnostikis sakiTxebSi.80-iani da gansakuTrebiT 90-iani wlebisaTvis ruseTSi farTodgaiSala bavSvTa gadrCevis meTodebze muSaoba, am kuTxiT bavSvTakvleva. am sakiTxebze muSaobdnen: s. aganasevi, g. brelova, a. gaidi,k. zaxarovi, g. diakonova, e. romanova, o. potiomkina, o. usova, e.sokolova da sxva.Tanamedrove etapze, ruseTis ganaTlebis sistema bavSvTaindividualuri TaviseburebebiT gadarCevisaTvis iyenebs ara martoucxouri testebis modificirebul variantebs, aramed maT mierdamuSavebul fsiqodiagnostikur meTodebs (k. kravcova, e. kravcova,a. bugramenko, k. polovanova, e. suSkova, a. ivanova da sxva.).rac Seexeba saqarTvelos, bavSvTa diagnostikis sakiTxebiaTeuli wlebis ganmavlobaSi aqac ugulebelyofili iyo. amproblemisadmi damokidebuleba dRes CvenTanac Seicvala. amJamadsaqarTveloSi mravali ucxouri testi gamoiyeneba. maT gverdiTgamoCnda qarTuli testebic. magaliTad, pedagogikis kvleviserovnuli institutis sakoreqcio seqtoris gamgis, profesor nanacarciZis mier Seqmnili testebi, 5-12 wlis bavSvebisaTvis.zogadsaganmanaTleblo skolis dawyebiTi klasebismoswavleTa kontingenti sakmaod mravalferovania. bunebrivia,maswavlebels, romelsac saTanado momzadeba ara aqvs, uWirsmoswavleTa individualur TaviseburebebSi garkveva da maTTvisaucilebeli pedagogiuri garemos Seqmna.amdenad, Tavdapirvelad unda movaxdinoT moswavleTasaswavlo unar-CvevaTa diagnostika, xolo Sedegebis mixedviTdaigegmos Sesabamisi pedagogiuri RonisZiebebi, romelTa gareSecbavSvs ar SeuZlia warmatebulad gaarTvas Tavi swavlas. yoveliveaman, gvafiqrebina SegvemuSavebina iseTi diagnostikuri meTodika,romelic skolaSi swavlebisaTvis mzadyofnaSi Seferxebis41

gamovlenaSi dagvexmareboda. ganviTarebaSi mcire fsiqo-fizikurigadaxrebi yvelaze naTlad swavlis dros iCens Tavs, swored amsaqmianobaSi vlindeba bavSvis nakli. am kategoriis bavSvebs, romswavla uWirT, am sakiTxze aravin davobs. arc is aris sadavo, romswavlaSi warumateblobis mizezi moumwifebel unar-CvevebSi arissaZiebeli. unar-Cvevebidan am asakSi ZiriTadia swavlisaTvisaucilebeli unar-Cvevebi, romelTac saswavlo unar-Cvevebsuwodeben. unar-Cveva fsiqologiur literaturaSi ganisazRvrebarogorc `mzaoba praqtikuli da Teoriuli moqmedebisSesrulebisaTvis, SeZenili codnisa da cxovrebiseuligamocdilebis safuZvelze~.aRzrdisa da swavlebis procesSi bavSvebi euflebian iseTZiriTad unarebs, rogoricaa: dakvirvebis, damaxsovrebisa dagagebis. es is unarebia, romelTa gareSec swavla SeuZlebelia.skolaSi swavlebisaTvis mzadyofnaSi Seferxebis mqone bavSvebs,rogorc mkvlevarebi miuTiTeben, swored es ZiriTadi unarebi araaqvT saTanadod momwifebuli, rodesac moswavleebi xdebian. aqedangamomdinareobs maTi siZneleebi swavlaSi. Bunebrivicaa, Tu bavSvselementaluri dakvirvebis unari ar aqvs, Tu mas mexsierebaSi arSeuZlia Semoinaxos aRqmuli sagani Tu movlena da saWiroSemTxvevaSi aRadginos igi, ra Tqma unda aseT bavSvebs gauWirdebaTswavla da saskolo situaciisaTvis Segueba. es rom asea amaSiCvenma kvlevebmac dagvarwmuna. yvelaferma aman ganapiroba is, romdiagnostikis miznad avirCieT – saswavlo unar-CvevaTa kvleva.Tavdapirvelad SeviswavleT bavSvebis skolisaTvis mzaoba e.varxotovas, n. diatkosa da e. sazanovis meTodikiT. bavSvebi,romlebic ar aRmoCndnen skolisaTvis mzad, maTi saswavlo unarebiSeviswavleT profesor n. carciZis meTodikiT. ganvixiloTTiToeuli cal-calke.42

daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom bavSvTa individualuriTaviseburebebis gamovlenas didi mniSvneloba aqvs, raTa misigaTvaliswinebiT avagoT saswavlo procesi;• individualuri TavisebirebebiT bavSvTa gansxvavebis ideaaxali ar aris, is saTaves me-19 saukunidan iRebs, romelicTandaTan viTardeboda;• gasaTvaliswinebelia, rom bavSvis individualuriTaviseburebebis garkvevas mSobeli unda ecados jer kidevskolis winare asakidan, raTa saTanado muSaobiTgamoasworos is xarvezebi, romlebsac adgili aqvs bavSvebSi;• pirvelklaselTa individialuri unar-Cvevebis codna didaddaexmareba maswavlebels Sesabamisi pedagogiuriRonisZiebebis dagegmvaSi.$ 2. skolisaTvis mzaobis kvlevis eqspresdiagnostikurimeTodie. varxotovas, n. diatkosa da e. sazanovis mierSemoTavazebuli meTodika warmodgens mizanmimarTul diagnostikurkompleqss, romelic saSualebas gvaZlevs davinaxoT bavSvisfsiqikis is aucilebeli mxareebi, romlebic saWiroa skolaSiadaptaciisaTvis. ra Tqma unda arsebobs azrTa sxvadasxvaoba imaze,Tu ra unda vicodeT bavSvis Sesaxeb, am kompleqsSi ki mocemuliamokle diagnostikuri programa. aRniSnuli meTodikis avtorebiwlebis manZilze muSaobdnen am problemaze da Seadgines kidecprogramis es varianti, romelsac dReisaTvis warmatebiT iyenebensaqarTveloSi, kerZod, q.TbilisSi. e. varxotovas, n. diatkosa da e.sazanovis meTodikaSi garkveuli cvlilebebi Setanili iqna43

qarTveli fsigologebis a. kanjaraZis, s. baramiZis, T. kiknaZisa dam. Tofurias mier. aRniSnuli meTodikis Sedegebi Zalian exmarebafsiqologebsa da maswavleblebs, Sesabamisad gamoviyeneT Cvenc.diagnostikur krebulSi CarTulia testebi, romlebic ukvekargaxania miRebulia fsiqologiur praqtikaSi, aseve aris isdavalebebi, romlebic tradiciulad miRebulia pedagogebis mier,raTa gavarkvioT bavSvis skolisaTvis mzaoba. amave drosmocemulia logopediuri testi, romelic dagvexmareba gavarkvioT,xom ar aris raime gadaxra an defeqti metyvelebaSi. mzaoba arisori saxis: pedagogiuri da fsiqologiuri.pedagogiuri mzadyofna – es aris codnis, Cvevebis daunarebis maragi, romelic aqvs bavSvs skolaSi misvlisas. rogorcwesi aq igulisxmeba Tvlis, kiTxvis, saubris unari. aseTi saxisinformacia aucilebelia dawyebiTi klasebis maswavleblebisaTvis,romelTa xelSic unda gaiaros 6-7 wlis asakis didma nakadma. issasargebloa maswavlebelTaTvis, raTa man sworad dagegmosgakveTili. magram es informacia ar gvaZlevs swavlebis prognozissaSualebas uaxloes droSic ki.fsiqologiuri mzadyofna – es aris bavSvis inteleqtualuriganviTarebis xarisxobrivi maCvenebeli da misi pirovnebis zogierTiTaviseburebebi, romelTa gareSec SeuZlebelia sajark skolaSiwarmatebuli swavla. ra Tqma unda saskolo programis SemdgenlebiiTvaliswineben bavSvis inteleqtualuri da pirovnuliganviTarebis gansazRvrul dones. amdenad, am donis gansazRvraZalian mniSvnelovania bavSvis skolaSi miRebis dros.diagnostikuri kompleqsi Seqmnilia zogadsaganmanaTlebloskolebisaTvis. pirvel klasSi modian sxvadasxva ganviTarebisbavSvebi (inteleqtualuri da emociuri ganviTarebis sxvadasxvadone, gansxvavebuli cxovrebiseuli gamocdileba, sxvadasxvagvariindividualuri Taviseburebani). diagnostika saSualebas gvaZlevsdavexmaroT bavSvebs, maT mSoblebsa da bavSvis momavalmaswavleblebs.44

saboloo variantSi skolaSi swavlebisaTvis mzadyofnisdaignostikisaTvis saWiro kompleqsi Sedgeba Semdegi nawilebisagan:baSvis anketa da 11 subtesti bavSvTa diagnostikisaTvis. Cvensrulad ganvixilavT mxolod im subtestebs, romlebic uSualokavSirSia maTematikis codnasTan da agreTve imaT romlebic arianqarTulad modificirebuli.1. ùazrobebi~.mizani: bavSvTan emociuri kontaqtis damyareba (aq daSemdegac, sruli testi ixileT #1 danarTSi)2. `sivrciT-ariTmetikuli karnaxi~mizani: TvalsaCino-sqematuri azrovnebis (sivrciTiorientacia) diagnostika, wesebis mixedviT qceva. pedagogiuriaspeqti – 10-is farglebSi Camoyalibebuli Tvlis unarisdiagnostika.instruqcia: bavSvebs vaCveneb suraTs da veubnebi: `naxe, aqxatia biWuna~ da vekiTxebi:• Tu biWuna Tavisi adgilidan gadava marjvniv erTi ujriT, sadaRmoCndeba? ras ipovis iq? ramdens?• Semdeg am ujridan wava zemoT erTi ujriT. sad aRmoCndeba?axla ramdeni banani eqneba?Q45

• axla biWi midis erTi ujriT marcxniv. sad aRmoCndeba? axlaramdeni banani aqvs?• axla midis isev marcxniv erTi ujriT. axla sad imyofeba?spilom mas ori banani sTxova. ramdeni banani darCa biWs?• biWi wavida erTi ujriT qvemoT. sad aRmoCndeba? axla ramdenibanani aqvs?• bolos biWi midis qvemoT. ra Sexvda aq? is aZlevs 2 banans.ramdeni darCa?Sefasebasworad gaakeTa 1 - 2 moqmedeba0 qulasworad gaakeTa 3 – 4 moqmedeba1 qulasworad gaakeTa 5 – 6 moqmedeba2 qula3. `Tanmimdevruli suraTebi~.mizani: mizez-Sedegobrivi kavSiris dadgenis unarisa daTxrobisdiagnostika.4. `geometriuli figurebi~.mizani: TvalsaCino-sqematuri azrovnebisganviTarebis donis diagnostikada nimuSis mixedviT Sesrulebisunari. pedagogiuri aspeqti – geometriulifigurebis codnis diagnostika.insrtuqcia: bavSvebs vaZlev naxats,Sesabamis geometriul figurebs daveubnebi: àm figurebiT aawyve zus-46

tad iseTi, rogoric naxatzea mocemuli~.Sefasebasul ar gamouvida figurasworad aago Tavi, tani da fexebisworad aago figura0 qula1 qula2 qula5. ànalogiebi~mizani: mixvedrilobis safuZvlebis formirebis diagnostika.instruqcia: (es subtesti aris qarTulad modificirebuli,amdenad mogvaqvs srulad, ase aris danaCen SemTxvevaSic) `medagisaxeleb Sen sam sityvas. maTgan ori Seesabamiseba erTmaneTs,anu wyvilebia. Sen unda moZebno mesame sityvis Sesabamisi sityva,anu misi mewyvile~.• ZaRli cxovelia, gvirila . . . . ?• stafilo bostneulia, vaSli . . . ?• dRisiT sinaTlea, RamiT . . . ?• TvaliT vxedavT, yuriT . . . ?• wiwaka mwarea, Saqari . . . ?• telefoni rekavs, uTo . . . ?Sefaseba1 – 2 sworad Tqva 0 qula3 – 4 sworad Tqva 1 qula5 – 6 sworad Tqva 2 qula6. `logopediuri~mizani: asoebis warmoTqmisa da asobgeriTi analiziswarmarTvis unaris diagnostika47

instruqcia: 1. àxla getyvi sityvebs da Sen unda daSalonawilebad taSis SemokvriT. ai, magaliTad: `ma – gi – da~. Semdegmivcem sityvebs: karada; baliSi.2. àxla me getyvi sityvebs. Sen miTxari am sityvebSi pirveli dabolo bgera~.xval; kata; Sarvali; iremi.Sefasebabevri bgeras amaxinjebs da uWirs davalebisSes-ruleba. TviTon Secdomas ver asworebs,sWirdeba gamudmebiT daxmareba.2 – 3 bgeras amaxinjebs an eSleba I da IIdavalebis Sesrulebayvela bgeras sworad ambobs, sworad yofsnawi-lebad, sworad asaxelebs bgerebs (aneSleba, mag-ram TviTonve asworebs)0 qula1 qula2 qula7. àkrZaluli sityvebi~mizani: ufrosebTan Tavisufali urTierTobisa da wesebismixedviT qcevis unaris diagnostika.instruqcia: `modi viTamaSoT. me Sen mogcem kiTxvebs. CemskiTxvebs unda upasuxo ise, rom ar Tqva `ki~; àra~ da ar daasaxelo`feri~. kiTxvebis qarTul variants aqvs Semdegi saxe:1. Rame mze anaTebs?2. eqimi bavSvebs Tmas Wris?3. Zroxa dafrinavs?4. Sen biWi xar?5. balaxi TeTria?6. Tovli cxelia?7. kanfeti mwarea?8. Sen didi xar?9. cxens rqebi aqvs?10. pepela dacuravs?48

11. mgels kurdRlis eSinia?12. Werze siaruli SegiZlia?SefasebaarRvevs wesebs, gvpasuxobs (daufiqreblad)akrZaluli sityvebiT, an azrobrivad ar arisswori. swori mxolod 1-3 pasuxia.uWirs pasuxis gacema. ufro Cumadaa. Zneladpoulobs swor pasuxs 4-8 kiTxvaze.asrulebs wesebs. pasuxobs swrafad da sworad 9-12kiTxvaze.0 qula1 qula2 qula8. `gasaRebebi~mizani: kanonzomierebis dadgenisa da gamoyenebis unarisdiagnostika.9. `kiTxva~mizani: pedagogiuri aspeqti – asoebis codnis, kiTxvis unarisdiagnostika.instruqcia: bavSvs vekiTxebi icis Tu ara kiTxva. dadebiTipasuxis SemTxvevaSi mivcem wasakiTx masalas (SeiZleba gamoviyenoTI klasis wigni an Sesabamisi zomis asoebiT dawerili nebismierimasala). Tu man kiTxva ar icis, SevTavazeb baraTs asoebiT davTxov daasaxelos isini.a g l i vh o m k us n e b t49

SefasebaTu bavSvma icis 10 asoze naklebiTu bavSvma icis 10 aso mainc da gviCvenebs masTu is kiTxulebs damarcvliT, igebs wakiTxulsTu kiTxulobs gamarTulad, sityvebiT0 qula1 qula2 qula3 qulalimonaTimindorigvirilamandarini10. àdamianis daxatva~mizani: xatovani azrovnebisa da wvrili motorikisdiagnostika.11. `sityvebis Sedgena~mizani: TvalsaCino-sqematuri azrovnebisa da sityvierimaragis diagnostika.instruqcia: bavSvebs vaCveneb baraTs, sadac mocemuliasityvebi da veubnebi: àq dawerilia sityva `limonaTi~, is Sedgebaasoebisagan. am sityvis asoebisagan SevadginoT sityvebi, ramdensacSevZlebT mag, `nali~; `mona~; àTi~; `lomi~ da a.S. axlaSemogTavzebT sityvebs, romelTa asoebisagan Tqven unda SeadginoTsityvebi~.SefasebaTu bavSvi ver Seadgens verc erT sityvas 0 qulaTu bavSvi Seadgens erT sityvas mainc1 qulaTu bavSvi Seadgens or an met sityvas2 qula50

unda aRiniSnos, rom skolaSi swavlebisaTvis bavSvismzadyofnis diagnostika aris ara marto bavSvis arCeva skolaSi anspecialur klasebSi, aramed ufro metad misi saSualebiTmaswavlebels mivawodoT informacia momavali moswavlispedagogiur-fsiqologiuri Taviseburebebis Sesaxeb. aseTiinformacia saSualebas aZlevs maswavlebels icodes misimoswavlis Zlieri mxareebi da gaigos misi problemis buneba.testSi Semavali yvela davaleba rogorc vxedavT qulebiTfasdeba. davalebisaTvis maqsimaluri qula aris 3, minimaluri – 0.Sefasebis kriteriumebi aseTia:• bavSvi, romelic daagrovebs 18 da met qulas skolaSiswavlebisaTvis mzad aris.• bavSvi, romelic daagrovebs 16 an 17 qulas swavlebisaTvis`TiTqmis~ aris mzad. am dros saWiroa fsiqologTangasaubreba da SemdgomSi damatebiTi mecadineoba.• bavSvi, romelic daagrovebs 15 da nakleb qulas ar aris mzadskolaSi swavlebisaTvis.miRebuli Sedegebidan Cans, rom 2005 wels Seswavlili 135bavSvidan 47,7% mzad aris skolaSi swavlebisaTbis. 21,3% TiTqmismzad aris skolisaTvis, maT mxolod sWirdebaT fsiqologiskonsultaciebi. mxolod 31,1% ar aris mzad skolisaTvis. 2006 welsSeswavlili 152 bavSvidan 48,7% mzad aris skolaSi swavlebisaTvis.21.7% TiTqmis mzad aris skolisaTvis, maT mxolod sWirdebaTfsiqologis konsultaciebi,Mmxolod 28,3% ar aris mzadskolisaTvis.cdis pirTa anketebis analizis dros pasuxebi SeiZlebadavajgufod subtestebis mixedviT: 1, 3, 6 da 7 subtestebi gvaZlevssakmao warmodgenas bavSvis metyvelebis ganviTarebaze. yvelazemaRali 2 qulian Sefaseba aris Seusabamo suraTisa dalogopediuri testis dros, yvelaze metad gauWirdaTTanmimdevruli suraTebi, rac Seexeba akrZalul sityvebs51

umetesobas aqvs 1 quliani Sefaseba. aRsaniSnavia, rom Tu 2005 welsam subtestebSi bevri iyo 0 qula, 2006 wels maTi ricxvi SemcirdaerTi - oramde, ase aris sxva subtestebSic.2, 4 da 8 subtestebiT Cven vgebulobT Tu rogoria bavSvissivrciTi da maTematikis elementebis warmodgena. yvelaze kargadnimuSis mixedviT ageben geometriul figurebs, aq yvelaze metia 2quliani Sefaseba da arcerTi 0 qula. sakmaod kargad asrulebenmaTematikur sivrciT karnaxs, yvelaze metad uWirT gasaRebisdasruleba.5 da 8 subtestebi gviCveneben logikuri azrovnebisganviTarebas. yvelaze ukeT asruleben analogiebs, SedarebiTuZneldebaT sityvebis Sedgena. rac Seexeba kiTxvas, gamarTulikiTxva arc erTma icoda, umetesoba cnobda erTeul asoebs,garkveuli nawili asoebsac ver cnobda.mgavsi analizi daexmareba maswavlebels SesabamisadwarmarTos muSaoba moswavleebTan da miaRwios saTanadowarmatebebs.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom e. varxotovas, n. diatkosa da e.sazanovis mier SemoTavazebuli meTodika saSualebas gvaZlevsdavinaxoT bavSvis fsiqikis is aucilebeli mxareebi,romlebic saWiroa skolaSi adaptaciisaTvis.• pedagogiuri mzadyofna – es aris codnis, Cvevebis daunarebis maragi, romelic aqvs bavSvs skolaSi misvlisas.fsiqologiuri mzadyofna – es aris bavSvis inteleqtualuriganviTarebis xarisxobrivi maCvenebeli da misi pirovnebiszogierTi Taviseburebebi, romelTa gareSec SeuZlebeliaskolaSi warmatebuli swavla;• 2005 wels Seswavlili 135 bavSvidan 47,7% mzad aris skolaSiswavlebisaTbis. 21,3% TiTqmis mzad aris skolisaTvis, maT52

mxolod sWirdebaT fsiqologis konsultaciebi. mxolod 31,1%ar aris mzad skolisaTvis. 2006 wels Seswavlili 152bavSvidan 48,7% mzad aris skolaSi swavlebisaTvis. 21.7%TiTqmis mzad aris skolisaTvis, maT mxolod sWirdebaTfsiqologis konsultaciebi,Mmxolod 28,3% ar aris mzadskolisaTvis.• yuradsaRebia, rom moswavleTa anketebis drouli damuSavebada analizi didad daexmareba maswavlebels, Sesabamisaddagegmos saswavlo procesi da miaRwios warmatebebs;• saWiroa mSoblebis drouli informireba skolisaTvismomwifebisa da mzaobis sakiTxebze, es daexmareba maTmomavalSi, rac naTlad Cans Cvens SemTxvevaSic;$ 3. saswavlo unar-Cvevebis kvlevis meTodikakvlevisaTvis gamoviyene profesor n. carciZis meTodika.ECvensinteresebSi ZiriTadad Sedis, davadgonoT, Tu ra uWirs bavSvs daratom uWirs. Cvens mier gamoyenebulma meTodikam swored amkiTxvebs unda gasces pasuxi: ra uWirs bavSvs da ratom uWirs, raaris amis mizezi? Amis saSualebas ar gvaZlevs e. varxotovas, n.diatkosa da e. sazanovis meTodikaskolaSi swavlebisaTvis saWiro unar-CvevaTa kvleva, CemiazriT, pirdapir kavSirSia bavSvis fsiqikuri procesebisTaviseburebebTan. kerZod:dakvirvebis unari – bavSvis aRqmis ganviTarebisTaviseburebebze migvaniSnebs;damaxsovrebis unari – bavSvis mnemuri procesebismdgomareobas avlens;53

gagebis unari – azrovnebis procesebis ganviTarebis donismaCvenebelia;yovelive zemoT naTqvami SesaZleblobas gvaZlevs davaskvnaT,rom saswavlo unarebis kvlevas bavSvis fsiqikuri procesebisSeswavlasTan mivyavarT. Tu gamovavlenT bavSvis fsiqikuriprocesebis ganviTarebis Taviseburebebs, es did daxmarebasgagviwevs saswavlo unarebis Taviseburebebis daxasiaTebaSi.fsiqikuri procesebidan, Cemi miznebisaTvis sainteresoa: aRqma,yuradReba, mexsiereba, azrovneba, metyveleba. miRebuli SedegebiTbevri informacia gveqneba bavSvis saswavlo unarebisTaviseburebebis dasaxasiaTeblad.Cven ara marto saswavlo unarebi, aramed is codna-Cvevebi dawarmodgenebi gvainteresebs, romelTac bavSvs aZlevs ojaxi,sabavSvo baRi, skola da mTeli is socialuri garemo, sadac bavSvscxovreba uxdeba.amdenad, zogadsaganmanaTleblo skolis dawyebiTi klasebismoswavleTa saswavlo unar-CvevaTa diagnostikurma meTodikam undagamoavlinos:a) bavSvis fsiqikuri procesebis: aRqmis, yuradRebis,mexsierebis, azrovnebis, metyvelebis Taviseburebani;b) bavSvis codna-Cvevebis da warmodgenebis ganviTarebisTaviseburebani.diagnostikuri testebis Sedegebis damuSaveba xdeba, rogorcraodenobrivi, ise Tvisobrivi TvalsazrisiT. Sefaseba xdeba samimaCveneblis mixedviT:a) davaleba Seasrula – rac imas niSnavs, rom bavSvma sruladda amomwuravad gasca pasuxi dasmul kiTxvas.b) davaleba nawilobrivad Seasrula – niSnavs, rom bavSvispasuxi ar iyo sruli da amomwuravi.g) davaleba ver Seasrula – niSnavs, rom saerTod ver gascapasuxi an pasuxi mcdari iyo.54

am maCveneblebis gaanalizebis safuZvelze ganisazRvrebasaboloo jamuri qula, rac warmoadgenas gviqmnis bavSvis saswavlounar-CvevaTa ganviTarebis Taviseburebebze.warmodgenili meTodika testebis zogad principebzea agebuli.TiToeuli askisaTvis testis varianti specifikuria. sul 7variantia, romlebic gaTvaliswinebulia Semdegi asakebisaTvis: I. 5-dan 6-wlamde; II. 6-dan 7-wlamde; III. 7-dan 8-wlamde; IV. 8-dan 9-wlamde; V. 9-dan 10-wlamde; VI. 10-dan 11-wlamde; VII. 11-dan 12-wlamde.yoveli asakis testi 30 davalebas moicavs. davalebaTa mizaniagamoavlinos, rogoria konkretuli bavSvis aRqma (feri, sidide,forma, sivrceSi orientaciis unari, droiTi warmodgenebi da a. S.);yuradReba (koncentraciis unari, moculoba, simtkice da a.S.)mexsiereba (moculoba, simtkice, sizuste, nebismieri mexsiereba daa.S.) azrovneba (TvalsaCino-sagnobrivi, cnebiTi, ganzogadebis unarida a.S.) metyveleba (sityvis, winadadebis sworad xmareba da a. S.)codna-warmodgenebi garemomcvel sagnebsa da movlenebze (ra icisbavSvma Tavis Tavze, ojaxze, axloblebze, mis garemomcvelsamyaroze). aqedan gamomdinare, yoveli asakis testi (30 davaleba)dayofilia subtestebad: aRqma, yuradReba, mexsiereba, azrovneba,metyveleba, codna-warmodgenebi garemomcvel sagnebsa damovlenebze. sul 6 subtestia, romelic ramdenime davalebasmoicavs.subtestebSi davalebebis Sedgenis dros mkacrad arisdaculi principi: martividan – rTulisaken. yvela davalebasaxlavs is TvalsCino masala, romelic aucilebelia misSesasruleblad.testirebas vatarebdiT individualurad. amdenad, es meTodokaSeesabameba dasavleTSi farTod gavrcelebul klinikurmeTodikebs. gamokvleva mimdinareobda izolirebul oTaxSi(fsiqologis kabineti, saklaso oTaxi), sadac sxva pirTa Sesvlagamosvlaar xdeba.55

saSualod, erTi bavSvis testirebisaTvis saWiroa 30-40 wuTi.testirebas ar viwyebdiT uceb, bavSvis SemosvlisTanave. bavSvi jerunda ganvawyoT TanamSromlobisaTvis, SeqmnidiT keTilganwyobilsituacias da mxolod amis Semdeg viwyebdiT gamokvlevas. ar arismizanSewonili testireba Cautardes bavSvs, romelic daRlilia, anTavs cudad grZnobs.moviyvan testis mxolod im subtestebs, romlebic gvexmarebamaTematikis elementebis codnis dadgenaSi. minda aRvniSno, romqalnaton n. carciZesTan SeTanxmebiT zogierT testSi SeviTanemcire cvlileba, romelsac moviyvan winamdebare SromaSi.I. aRqma1. gadaarCie figurebi formis mixedviT.Catarebis procedura: magidaze awyvia erTi feris, sxvadasxvaformis geometriuli figurebi. sul 20 figura: samkuTxedi, wre,kvadrati, rombi (5-5 cali) bavSvs veubnebi: àq 4 sxvadasxva formis,gansxvavebuli figuraa. gadaarCie es figurebi formis mixedviT~.Sesrulebis dro – 120 wami.56

2. miageni figurebs, romlebic TavianT adgilze ar arian.Catarebisprocedura: bavSvsvuCveneb suraTs,romelzec 3 rigadgamosaxulia geometriulifigurebibavSvs veubnebi:aq yvelarigSi TiTo figuraSecdomiT moxvda,isini sxvebisagangansxvavebulia.miageni figurebs,romlebicTavianT adgilzear arian~.3. nawilebisagan mTelis Sedgena.Catarebis procedura:muyaoze daxazuli kvadrati4 nawilad aris daWrili.kvadratis nawilebi areuladawyvia magidaze bavSviswin. bavSvs vuCveneb furcelzegamosaxul kvadratsda veubnebi: ès kvadratia.Tu Sens win magidaze kvadratis4 nawils sworad SeaerTeb,miiReb aseTive kvadrats~.Sesrulebis dro –120 wami.57

UII. yuradReba1. yuradRebiT iyavi, araferi gamogrCes.Catarebis procedura: bavSvs vaZlev furcels, romelzecgamosaxulia geometriuli figurebi: samkuTxedi, wre, kvadrati,rombi. rigSi 10 figuraa, sul 5 rigia. erT-erT samkuTxeds TiTsvadeb da bavSvs veubnebi: ès samkuTxedia. yvela rigSi, yvelasamkuTxeds gadausvi xazi~.bavSvs am samuSaos vakeTebineb calke momzadebul furcelze,sadac miTiTebuli iqneba bavSvis vinaoba da Catarebis dro. es dasxva cvlileba, romlebic qvemoT meqneba mocemuli SeTanxmebuliaavtorTan. Sedegebi Caikvreba testirebis masalebSi. momzadebulmasalas aqvs Semdegi saxe:moswavlis saxeli da gvari ----------------------------------------------Sesrulebis dro – 120 wami.Catarebis TariRi ---------------------------------------2. Seavse ujrebi.Catarebis procedura: furcelze gamosaxulia ujrebi. maTSisxvadasxva raodenobis rgolebi da jvrebia Casmuli. bavSvs vaZlevdavalebas – TiToeul ujraSi rgolebis da jvrebis raodenobaSeavse 4-mde.58

Sesrulebis dro: -- 90 wami.moswavlis saxeli da gvari ----------------------------------------------Catarebis TariRi -----------------------------------------III. mexsiereba1. gaimeore ricxvebi.Catarebis procedura: bavSvs veubnebi: àxla CamogiTvli 4ricxvs. Sen isini daimaxsovre da Semdeg igive TanamimdevrobiTgaimeore. es ricxvebia: 1, 5, 3, 8~.mexsierebis moculobisa da simtkicis SeswavlisaTvissubtesti kidev Seicavs 2 savarjiSos, romlebic mocemuli maqvsdanarTSi #2IV. azrovnebaazrovnebis Taviseburebebis (TvalsaCino-sagnobrivi, cnebiTi,ganzogadebis unari da a.S) SeswavlisaTvis mocemulia 9 savarjiSo(ix. danarTi #2), magram me moviyvan mxolod imas, romelsac aqvsgarkveuli cvlileba ise, rom Caikras bavSvis testirebismasalebSi.4. labirinTiCatarebis procedura: bavSvs vuCveneb labirinTis suraTs.labirinTis dasawyisSi gogonaa gamosaxuli, labirinTis bolos kiskola. bavSvs veubnebi: `miiyvane gogona skolaSi ise, rom ardaajaxo Robes~.59

moswavlis saxeli da gvari----------------------------------------------Sesrulebis dro – 60 wami.V da VI subtestebis nawili(metyveleba da codnawarmodgenebi garemomcvelsagnebsa da movlenebze)gavakeTe calke testissaxiT ise, rom maTi pasuxebiCaidos saerTo monacemebSidanarTi #2 (danarCenisavarjiSoebi miewodebaucvlelad).Catarebis TariRi --------------------------testirebis dros vavseb ,,bavSvis Seswavlis rukas”. aseTi rukayvela gamosakvlev bavSvze arsebobs. ruka winaswar arisgamzadebuli da igi uSualod testirebis procesSi ivseba. ,,bavSvisSeswavlis ruka” – 5 grafisagan Sedgeba. esenia: davalebisdasaxeleba; davalebis Sesrulebis dro; davalebis SesrulebismaCvenebeli; miRebuli qula; bavSvis qcevaze dakvirveba.testSi Semavali yvela davaleba qulebiT fasdeba. yveladavalebisaTvis maqsimaluri qula aris 1, minimaluri – 0. zogierTidavaleba SeiZleba nawilobriv Sesruldes, am SemTxvevaSi Sefasebaiqneba 0-dan 1-mde romelime ricxvi.im SemTxvevaSi, roca davaleba droiT aris SezRuduli, TubavSvi vadaSi ver Caeteva, Cven pasuxis mxolod im nawils viniSnavT,60

omelic gankuTvnil droSi moeswro (testirebis procesSi ar arismizanSewonili bavSvs pasuxi SevawyvetinoT, es Zabavs mas dauaryofiTad moqmedebs Semdegi davalebis Sesrulebaze; amitombavSvs unda mivceT pasuxis gacemis saSualeba).calkeul davalebaze miRebuli qulebi ikribeba da viRebTjamur qulas. bavSvis mier miRebul saboloo qulas vadarebTSkalur monacemebs. imis mixedviT, Tu Skalis romel danayofSiTavsdeba qulebi, vmsjelobT konkretuli bavSvis saswavlo unar-CvevaTa ganviTarebis Taviseburebebze.cxrili #1qulebis klasifikaciaqulebiklasifikacia25-30 k a r g i20-25 s a S u a l o15-20 saSualoze dabali15-ze naklebic u d iaRsaniSnavia, rom am meTodiT vmuSaobT 1999 wlidan, magrammoviyvan mxolod bolo 2 wlis Sedegebs:cxrili #2saswavlo unar-Cvevebis Seswavlis SedegebiCatarebiscudisaSualozesaSualokargidrodabali2005 11,3% 35,2% 47,9% 6,14%2006 11,5% 37,3% 47,6% 3,5%testirebis Sedegad miRebuli dabali monacemebi ar undaSefasdes ise, rom amiT bavSvs raime ,,iarliyi” miekeros, piriqiT, es61

monacemebi pedagogma unda gamoiyenos bavSvTan Semdgomi sakoreqciomuSaobis dasagegmavad.fsiqodiagnostikur meTodikebs mxolod sadiagnostikodaniSnuleba ki ara aqvs, aramed bavSvis momavali ganviTarebisa daswavlebis prognozirebac akisria. am meTodikis SedegebiSesaZleblobas gvaZlevs, sworad ganvsazRvroT is sakoreqcioRonisZiebaTa sistema, romelic Seferxebis mqone bavSvis momavalganviTarebas daaCqarebs.daskvnebi da rekomendaciebi:• n. carciZis diagnostikuri meTodika swavlobs bavSvisfsiqikur procesebs: aRqmas, yuradRebas, mexsierebas,azrovnebas, metyvelabas da codna-warmodgenebs garemomcvelsagnebsa da movlenebze. es saSualebas gvaZlevs davadginoTTu sad aris problema da davgegmoT koreqciuli muSaoba.• gasaTvaliswinebelia, saswavlo unar-CvevaTa kvlevis meTodisakmaod sapasuxismgeblo da Sromatevadi procesia, magram isdidad daexmareba maswavlebels individualuriSesaZleblobaTa gaTvaliswinebiT sworad dagegmos saswavloprocesi da aamaRlos moswavleTa swavlebis done.II Tavis daskvnebi da rekomendaciebi• bavSvTa individualuri Taviseburebebis gamovlenas didimniSvneloba aqvs saswavlo procesis agebisaTvis. e.varxotovas, n. diatkosa da e. sazanovis mier SemoTavazebulimeTodika saSualebas gvaZlevs davinaxoT bavSvisinteleqtualuri da pirovnuli ganviTarebis is aucilebelimxareebi, romlebic saWiroa skolaSi adaptaciisaTvis. ammeTodikiT kavlevam gviCvena, rom Seswavlili 152 bavSvidan62

48,7% mzad aris skolaSi swavlebisaTvis. 21,7% Wirdeba mciredaxmareba skolisaTvis mzaobis kuTxiT, mxolod 29,6% araris mzad skolisaTvis;• bavSvebisaTvis, romlebic ar aRmoCndnen mzad skolisaTvis,mzaobis damatebiT Sesaswavlad gamoviyeneT prof. n. carciZisdiagnostikuri meTodika, romelic swavlobs bavSvis fsiqikurprocesebs: aRqmas, yuradRebas, mexsierebas, azrovnebas,metyvelebas da codna-warmodgenebs garemomcvel sagnebsa damovlenebze;• gasaTvaliswinebelia, rom saswavlo unar-CvevaTa kvlevismeTodi didad daexmareba maswavlebels individualurSesaZleblobaTa gaTvaliswinebiT sworad dagegmos saswavloprocesi da aamaRlos moswavleTa swavlebis done;• bavSvis individualuri Taviseburebebis garkvevas mSobeliunda ecados jer kidev skolis winare asakidan dawyebuli,raTa saTanado muSaobiT gamoasworos is xarvezebiromlebsac adgili aqvs bavSvebSi;63

Tavi IIImoswavleTa elementaruli maTematikuri codnis donisdadgena da ganmaviTarebeli aqrivobebis dagegmvaorganizeba$ 1. skolaSi Semosvlis dros pirvelklaselmoswavleTa maTematikuri codnis dadgenaerT-erT yvelaze rTul sagnad skolaSi iTvleba maTematika.pedagogiur-fsiqologiurma gamokvlevebma gviCvena, rom 6-7 wlisbavSvTa erTi nawili ar aris mzad maTematikis kursis Sesaswavlad.amis gamo mSoblebisa da maswavleblebis ZiriTadi mizania,saswavlo wlis dasawyisSi gaarkvion maTematikis ra elementarulicodna aqvs bavSvs da moamzadon is maTematikis saskolo kursisSeswavlisaTvis.moswavleTa umravlesoba dadis sabavSvo baRSi, romlisaRzrdisa da swavlebis programa iTvaliswinebs elementarulimaTematikuri warmodgenebis ganviTarebas. Cven maTematikuriwarmodgenebis Seswavla vawarmoeT Semdegi kiTxvariT:• 10-is farglebSi daTvla;• ricxvebis Sedareba 10-is farglebSi, romeli ricxvia meti(naklebi) meoreze, sagnebis gaTanabreba;• aTamde sagnis Sedareba sididis (grZeli, ganieri, maRali)mixedviT, maTi dalageba zrdis (klebis) mixedviT;• saganTa gansxvaveba formis mixedviT;• sakuTari Tavisa da sxva sagnebis mimarT sxeulTamdebareobis sityvieri gamoxatva;• kviris dReebis, dRis nawilebis (dila, SuadRe, saRamo, Rame)TanmimdevrobiT codna da a.S.rogorc praqtika gviCvenebs, am mxriv mdgomareobadamakmayofilebelia. SeiZleba bavSvebs cota uWirT sxeulTamdebareobis sityvieri gamoxatva, cota erevaT kvirisa da dRis64

nawilebis Tanmimdevroba, magram es ar aris didi problema,advilad daiZleva.elementaruli maTemetikuri warmodgenebis dadgenis SemdegSeiZleba gavarkvioT, Tu rogoria bavSvebis sivrceSi orientacia.rogorc wesi, 6-7 wlis bavSvi Tavisuflad axdens orientaciasmcire sivrceSi – oTaxSi, binaSi.bavSvi skolaSi Tavdajerebuli rom iyos, kargad undaaxdendes orientacias did sivrceSi.bavSvs unda SeeZlos pasuxis gacema Semdeg kiTxvebze:• romel qalaqSi (dasaxleba, sofeli) cxovrob?• miTxariT Tqveni misamarTi. romel sarTulze cxovrobT?• ramden sarTuliania Tqveni saxli?• ramdeni sarTulia Seni binis zemoT?• ramdeni sarTulia Seni binis qvemoT?• ra quCebi (gamziri) aris Sens saxlTan axlos?• ra transporti midis Sens saxlTan?Catarebulma gamokiTxvebma dagvanaxa, rom am kuTxiT iseTivemdgomareobaa, rogorc wina gamokiTxvisas. gamokiTxulma bavSvebmakargad ician misamarTi da TavianTi binis mdebareobamravalsarTulian saxlSi (Tu aseTi arsebobs, umetesoba sakuTarsaxlSi cxovrobs), magram eSlebaT saxlTan axlos mdebare quCebi,saxlTan mimavali transportis dasaxeleba.sivrciTi orientaciis garkevevis Semdeg, vadgenT rogoriasagnebis Sedarebis unari. sagnebis Sedareba Semdegi niSnismixedviT: grZeli-mokle; maRali-dabali; ganieri-viwro; sqeli-Txeli, zogjer sirTules warmoadgens. jer erTi, bavSvebiSedarebisas iyeneben zogad niSnebs (didi-patara). isini xSiradamboben ase: didi lenti? grZeli lentis nacvlad; didi boZi,patara boZi – maRali an dabali boZis nacvlad.bavSvTa aqtiur sasaubro leqsikonSi, rogorc wesi arissityvebi: maRali-dabali; grZeli-mokle; ganieri-viwro. magram65

cnebebi erevaT erTmaneTSi: maRalis nacvlad amboben grZeli;ganieris nacvlad – sqeli; Txelis nacvlad - viwro da a.S. Cemi dapraqtikosi maswavleblebis dakvirvebebma gviCvena, rom bavSvebisaubrisas xSirad iyeneben cnebebs maRali, grZeli, ganieri, sqeli –vidre dabali, mokle, viwro, Txeli. vfiqrob amis mizezia bavSvisaRqma, is ukeT aRiqvams did sxeulebs, amave dros kargad axdensmaT Sedarebas, vidre mcire zomisas.moswavleebs vekiTxebiT romeli ufro grZelia saxazavi Tufanqari? romeli ufro moklea, palto Tu kaba? skolaSimosasvleli romeli gza ufro grZelia? ratom? da a.S. msgavsikiTxvebi SeiZleba gamoviyenoT gaseirnebis dros, quCaSi, parkSi,tyeSi. praqtikul-sagnobrivi muSaobisas isini xalisiania,Sesabamisad muSaoba ufro saintereso da Sedegiania.Semdeg SeiZleba sagnebis Sedareba simZimis mixedviT. SeiZlebaSevadaroT carieli patara vedros wona, igive zomis wyliT anqviSiT savse vedrebis wonas. romeli vedro aris qviSian vedrozemsubuqi? romeli vedro aris wylian vedroze mZime? SevadaroT 1kg.marili da fqvili, romeli ufro mZimea? cxovrebiseuli situaciisSeqmnis specialuri TamaSebi xels uwyobs ganaviTaros da daxvewossididis cneba, sxeulTa formis cneba, bavSvebis sivrciTiwarmodgenebi, es amdidrebs bavSvis sasaubro leqsikonsa da codnawarmodgenebssamyaroze, anviTarebs maTematikur enas.ricxvze warmodgenis dasadgenad bavSvebs miveciT savarjiSoebiSemdegi TanmimdevrobiT:1. ramdeni sagania jgufSi?2. daiTvale erTi da igive sagani mwkrivSi an areulmdgomareobaSi. daasaxeleT maTi raodenobis amsaxveli ricxvi.3. daTvla 1-dan iqamde, sanamdec bavSvi SeZlebs. ukuTvlabavSvis SesaZleblobis mixedviT 5-dan; 10-dan; 20-dan; 100-dan.4. mocemul ricxvebs Soris Tvla. mag.: 2-dan 8-mde; 10-dan 6-mdeda a.S.5. ricxvebis Sedareba. romelia meti (naklebi)?66

vTxoveT bavSvebs Tvla awarmoon sagnebiT, yuradRebamivaqcieT imas, rom dasaxelebul ricxvTa saxeli emTxveodessagnis raodenobas. mag.: bavSvi ambobs èqvsi~, sinamdvileSigviCvenebs me-5 an me-7 sagans. xSirad bavSvebs uWirT Tvla Tu isinidawyobilia vertikalurad, daxrilad, mimobneulia. SeiZlebagauWirdeT, magram unda moviTxovoT daTvla awarmoontradiciulad macxnidan marjvniv an piriqiT.sirTuleebis dasaZlevad CavatareT Semdegi muSaoba:• davdoT (an davadebinoT) magidaze 5 TefSi. ramdeni TefSidevs (an dade) magidaze?• moutane dedas 5 kartofili, 3 stafilo, 2 Warxali. daiTvaleramdeni bostneuli moitane? ramdeni kartofili gaTaladedam ukve?• ramdeni kanfeti darCa axla yuTSi? ramdeni xilia axlalarnakze? da a.S.• daasaxeleT 5 (7, 3) -is mezobeli ricxvebi da a.S.• ra ricxvebs Soris aris ricxvi 3; 8 ? da a. S.ukuTvla SedarebiT rTulia, amdenad Tavdapirvelad SeiZlebakonkretul sagnebze Seasrulos da Semdeg ganyenebulze.magaliTad: daTvaleT fanqrebi. sul 6 fanqaria, erTi fanqarimovaSoroT da CavdoT yuTSi. darCeba 5 fanqari. aviRoT kidev erTifanqari, darCa 4 fanqari da a.S. dakvirvebebma gviCvena, romskolisaTvis mzaobaSi Seferxebis mqone bavSvebs eSlebaT ukuTvla.raodenobrivi warmodgenis dadgenis mizniT bavSvs vaCveneT 4-5didi buSti da 7-10 patara, davsvaT aseTi kiTxva: `sad aris metibuSti da sad cota?~ SeiZleba miviRoT aseTi pasuxi: `meti aris iq,sadac didi buStebia, cota aris iq, sadac patara buStebia~ esxdeba `piaJes fenomenis~ Tanaxmad.muSaobis Sedegad miRebuli gamocdilebidan dadginda, romraodenibrivi warmodgenebis ganviTarebis gareSe Zalian Zneliagaigon naturalur ricxvTa simravleSi ricxvis cneba.67

aodenobrivi warmodgenebis ganviTareba unda daviwyoTSemdegi cnebebis formulirebiT: bevri, cota, ramdenime.moswavleTa aqtiur leqsikur maragSi unda SevitanoTsityvebi: iyo, darCa, gaxda, erTad. kargi iqneba Tu moswavleebsvavarjiSebT iseTi winadadebebis Sedgenaze, sadac gamoiyenebasityvebi: bevri, cota, ramdenime.yuradReba mivaqcioT sityvebs: imdenive, Tanabari, erTidaigive.bavSvs SevekiTxoT:• `ramdeni yvavilia larnakSi?• bevria Tu cota? – bevri• ramdeni sokoa kalaTSi? – kalaTSi bevri sokoa da a.S.TvlaSi varjiSi SeiZleba sxvadasxva saTamaSo situaciisdros. SeiZleba bavSvma ixtunos da daiTvalos xmamaRla, ukravdestaSs da iTvlides da a.S.mTavaria bavSvma SeZlos Tvla mocemuli ricxvidan win daukan. aseTi varjiSiT bavSvi ufro ukeT gaigebs ricxviTi mwkrivisTvisebas. TiToeuli ricxvi miiReba mis wina ricxvs damatebulierTi, xolo Tu ricxvs gamovaklebT 1-s miviRebT win mdgom ricxvs.yuradReba mivaqcioT sityvebs: win, ukan, Soris, maxloblad.3-is win dgas 2. cifri, A dgas 3-sa da 5-s Soris, ra ricxviaA? 5-is Semdeg dgas 6 da a.S.raodenobrivi warmodgenebis dadgenis Semdeg, vswavlobTsivrciT warmodgenebs interqatiuri meTodiT. dasavleTis qveynebSi,romlebic mecnieruli siaxleebis praqtikuli danergvis saqmeSimeti moqnilobiT xasiaTdebian, SedarebiT advilad da farTodmoikida fexi swavlebisadmi axalma midgomebma da meTodebma,romlebic ukeT pasuxobs drois moTxovnebs. pedagogiuri muSaobisZiriTad principad miRebuli moswavleze orientirebuli swavleba,risi praqtikuli realizaciis saukeTeso saSualebad swavlebisinteraqtiuri meTodebia miCneuli. sayovelTao aRiarebiT, esmeTodebi uzrunvelyofs codnis mopovebis procesSi yvela68

moswavlis aqtiur monawileobas, ayalibebs moswavleSi kritikuliazrovnebis unars, aCvevs moswavles damoukideblad swavlas, axaliamocanebis gadaWrisaTvis saWiro informaciis damoukidebladmopovebas da a.S. rac mTavaria, aseTi swavleba, amzadebs moswavlessxva adamianebTan aqtiuri TanamSromlobisaTvis, radganinteraqtivobis arsi adamianTa Soris partniorul urTierTobebSia,sadac miznebis realizacia sxvebTan uSualo urTierTqmedebis gziTxorcieldeba.interaqtiuri meTodebiT swavlebis arsebiT momentsmoswavleTa erToblivi saqmianoba warmoadgens. swavlebis procesimTlianad orientirebulia moswavleze, romelic adre ukve miRebulcodnasa da gamocdilebaze dayrdnobiT, TanatolebTan erTad,aanalizebs Sesaswavl sakiTxebs, ayalibebs mis Sesaxeb garkveulmosazrebebs, gamoaqvs daskvnebi da a. S. am procesSi maswavlebeliaRar aris winaswar gamzadebuli codnis mimwodebeli. misi amocanaauzrunvelyos moswavleTa erToblivi saqmianoba. maswavlebeliexmareba moswavleebs erTobliv saqmianobaSi TiToeulis rolisgansazRvraSi, aZlevs maT saorientacio miTiTebebsa da miniSnebebs,yvela xelsayrel SemTxvevas iyenebs maTi Seqebisa dawaxalisebisaTvis. iZleva pedagogiur Sefasebebs. miRebuli SedegebimiiRweva moswavleTa erToblivi aqtiurobis Sedegad. maswavleblissaqmianoba am procesSi, romelic aq zogadad davaxasiaTeT,aRiniSneba terminiT `fasilitacia~. e. i. interaqtiur swavlebaSi,maswavlebeli aris ara codnis gadamcemi, aramed moswavleTa miercodnis miRebis procesis fasilitatori.swavlebis interaqtiuri meTodebia: jgufuri muSaoba,siuJetur- roluri TamaSi, gonebrivi ieriSi, diskusia da sxva.dawyebiT klasebSi yvelaze metad gamoiyeneba siujeturroluriTamaSi, gansakuTrebiT saswavlo wlis dasawyisSi daumcros saskolo asakSi, imdenad, ramdenadac am asakis bavSvisZiriTadi qcevaa TamaSi.69

vnaxoT rogor xdeba am meTodis gamoyenebiT sivrciTiwarmodgenebis dadgena. es SeiZleba TamaSis saxiT warimarTos. mag.:`daexmare dedas magidis gawyobaSi~. `dade larnaki yvavilebiTmagidis SuaSi, sayvaviles marjvniv dade puri, marcxniv – yveli.TefSis marcxniv dade Cangali, marjvniv – dana da a.S.~ SeiZlebaCavataroT TamaSi `gaawyve magida sauzmisaTvis~, aseT TamaSSi,romelSic didi interesiT CaerTvnen gogonebi. maTi umravlesobakargad erkveva orientaciaSi, zogs eSleba marjvena da marcxenamxare, rasac dinjad usworeben vaJebi.SeiZleba CavataroT TamaSi-gakveTili sivrciTi warmodgenebisgamosavlenad. aq SeiZleba ganvixiloT ramdenime TamaSi: `daalageaveji Tojinis oTaxSi~, `monaxe saTamaSo~, `sad daimalnen bavSvebi~da a.S.SeiZleba mivceT aseTi saxis savarjiSo:• `gaiare 10 nabiji win;• mouxvie marjvniv gadadgi 5 nabiji da a.S~.aseTi savarjiSoebi bavSebisaTvis Zalian saxalisoa imdenad,ramdenadac, es TamaSia. isini mxiarulad asworeben Secdomebs damxiaruladve xdeba Seferxebis gamosworeba.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom skolaSi Semosvlisas mzaobaSiSeferxebis mqone bavSvma icis 10-is farglebSi piradapiriTvla, saganTa gansxvaveba formis mixedviT, uWirs ukuTvlaTvla, rac Seexeba kviris dReebs, dRis nawilebs datransports romelic midis saxlTan, romlebic emsaxurebasivrcesa daDdroSi orientaciis Seswavlas, amaTze yovelTvisdadebiT pasuxs ver iZleva;• interaqtiur meTodebSi Sedegs vaRwevT moswavleTadamoukidebeli erToblivi aqtivobis Sedegad; isinibavSvisaTvis aris saxaliso da umtkivneulod xdebaSecdomebis gamosworeba.70

• gasaTvaliswinebelia, rom saswavlo procesis dagegmvisasmaswavlebelma unda gaiTvaliswinos didaqtikuri TamaSebi.maT SeuZliaT gamoiyenon Cvens mier Seqmnili didaqtikuriTamaSebis sistema an Seqmnan damoukideblad axali, mxolodgaiTvaliswinon, rom moswavleebi ufro kargad asrulebensiuJetur didaqtikur TamaSebs;$ 2. bavSvebSi raodenobis invariantobis wvdomisanalizi da misi koreqciaazrovnebisa da saerTod Semecnebis dispoziciuri safuZveliaris inteleqti, gonebrivi ganviTareba. im fsiqikur Zalebs Soris,romlis ganviTarebis donec bavSvis asakobrivi garemos SinaarssgansazRvravs, gonebriv ganviTarebas umniSvnelovanesi adgiliuWiravs. cxadia, fsiqikuri ganviTarebis process martointeleqtualuri ganviTarebis kanonzomierebaTa SeswavliT veramovwuravT, magram isic naTelia, rom ganviTarebis es aspeqtipirvelxarisxovan yuradRebas moiTxovs. bavSvis gonebrivganviTarebaSi cnobili Sveicarieli fsiqologi Jan piaJe gamoyofs4 ZiriTad stadias: senso-motoruli stadia; winaoperaciuli anuoperaciebamdeli stadia; konkretul operaciaTa stadia daformalur operaciaTa stadia. ganvixiloT TiToeuli cal-calke:1) senso-motoruli stadia (0-dan 2 wlamde)metyvelebis dauflebamde bavSvma SeiZleba ganaxorcielosmxolod is motoruli moqmedebani, romelic ar moiTxovsazrovnebis aqtivobas. marTalia, am moqmedebis ganxorcielebaSigarkveulad inteleqtic monawileobs, magram senso-motoruliinteleqti Tavisi xasiaTiT ar aris operaciuli, radganac bavSvisSesasrulebeli moqmedebani ar aris warmodgenis (azris) formiTmocemuli. `bavSvi iwyebs samyaros Semecnebas im fizikuri71

aqtivobis CarCoebSi, romlis ganxorcielebac SeuZlia. es stadiaazrovnebisa da metyvelebis aRmocenebiT mTavrdeba~ [19 gv. 16].2) operaciebamdeli stadia (2-dan 7 wlamde).2 wlis bavSvTan adgili aqvs simboluri funqciisganviTarebas – metyveleba, simboluri TamaSi, garkveuli tipisSinagani wabaZva, romelic warmoadgens xatovani azrovnebisganviTarebis safuZvels. simboluri funqciis bazaze SesaZlebelixdeba moqmedebis azris formiT mocema. farTovdeba inteleqtisfunqcionirebis sfero. awmyoSi Sesrulebul moqmedebas ematebawarsulisa da momavlis moqmedebebis gacnobiereba.senso-motoruli inteleqtisaTvis damaxasiaTebelipraqtikuli SeqceviToba aRar aris sakmarisi im amocanebisgadasawyvetad, romelic bavSvis winaSe dgeba. saWiroa axali,fsiqologiuri operaciebis gamoyeneba. bavSvs ar SeuZlia ucebganaviTaros es operaciebi.2-dan 7-wlamde bavSvisaTvis damaxasiaTebelia SeqceviTobisada Semonaxvis cnebis uqonloba. magaliTad, rodesac 4-6 wlisbavSvi erTi WurWlidan meoreSi, romelic pirvelisagan formiTgansxvavdeba, gadaasxams siTxes, is fiqrobs, rom siTxis raodenobaimatebs, Tu meore WurWeli pirvelTan SedarebiT ufro viwro damaRalia.davawyoT magidaze 6 wiTeli feris Jetoni. Semdeg mivceTcdis pirs cisferi Jetonebi da vTxovoT daawyos imdenive Jetoni,ramdenic wiTelia. 4-5 wlis bavSvebi Seavseben mxolod JetonebissigrZes. 5-6 wlis bavSvebi yvela wiTeli Jetonis qvemoT dadebencisfers, e. i. SeaTavseben Jetonebis raodenobas. magram sakmarisiaerT-erTi rigi gavSaloT, an SevkraT da bavSvi uaryofs wiTeli dacisferi Jetonebis raodenobis eqvivalentobas.am askis bavSvis msjelobebs raodenobaze sistematuritranzituloba akliaT. Tu mocemuli ori wyvili toli sidideebisa– A=B da B=C, bavSvs SeuZlia TiToeuli wyvilis toloba72

daadginos (A=B, B=C), rac Seexeba A=C, amis fiqsacias bavSvi veraxerxebs.3) konkretul operaciaTa stadia (7-dan 11 wlamde).am asakis bavSvebs SeuZliaT logikuri gziT gadaWrankonkretuli amocanebi, TvalsaCino warmodgenebisaTvis misawvdomsituaciebSi. maTi azrovnebis sayrdenia situacia àq da axla~.konkretul operaciaTa dauflebis Sedegad bavSvi swavlobsSeqceviTobis princips da xvdeba deduqciuri daskvniskanonzomierebas, rodesac es saganTa konkretul Tvisebebs Seexeba.raodenobis invariantobis cneba, romelic 7 wlamde asakisbavSvebs ar hqondaT (bavSvebi iyenebdnen, mag. aq Tixa ufro metia,imitom, rom ufro grZelia, an piriqiT), 7-8 wlis bavSvebs ukve escneba aqvT. isini raodenobis invariantobas SemdegnairadasabuTeben:a) sagani mxolod dagrZelda (gabrtyelebisas) da CvenSegviZlia mas pirvandeli forma davubrunoT;b) sagani dagrZelda, gagram is, rac mas moemata sigrZeSi,daaklda sisqeSi;g) araferi gamoaklda da arc araferi daemata.4) formalur operaciaTa stadia (viTardeba 11 wlidan 14-15wlamde).mozardi axerxebs azrobrivad gadaWras abstraqtuli dahipoTezuri amocanebi. amisaTvis mimarTos formalurreprezentaciasa da ganzogadebis operaciebs. am stadiaze TavsiCens axali Tviseba – hipoTezebiT azrovnebis unari.aq miTiTebuli asakobrivi sazRvrebi saSualo monacemebismixedviTaa gansazRvruli, variaciulia interindividualadac dakulturaTa Sorisac. saqme imaSia, rom swavlebis organozaciaZiriTadad saSualo monacemebs iTvaliswinebs, konkretulimoswavleebi ki am saSualos an CamorCebian, an win uswreben.saWiroa vicodeT asakobriv normasTan konkretuli moswavlisgonebrivi ganviTarebis donis Sefardeba, rac saSualebas mogvcems73

saswavlo amocanebis sirTulis xarisxi yvelasaTvis optimaluradSevarCioT.bavSvis SemecnebiT aqtivobaSi raodenobis invariantobiscnebis formirebas gansakuTrebuli adgili ukavia. Semonaxvisfenomenze miTiTebis gareSe SeuZlebelia skolamdeli asakisbavSvis azrovnebis daxasiaTeba. bolo aTeuli wlebis ganmavlobaSisazRvargareTeli bavSvis fsiqologiis erT-erTi wamyvani Temaa`raodenobis Semonaxvis~ cnebis formirebis Seswavla.bavSvis mier invariantobis cnebis formirebis rTuli damravalsafexuriani procesi J. piaJes mier iqna aRmoCenili.dReisaTvis fsiqologebi cdiloben Seavson da ganaviTaron J.piaJes Taoria. ufro srulyofilad gamoavlinon Semonaxvisprincipis formirebis procesebi da wanamZRvrebi da a. S.j. volvilis Tanaxmad, skolamdeli asakis bavSvi SemecnebiTixasiaTis amocanebis gadaWrisas emyareba konkretul perceptualniSnebs. am midrekilebas avtori `perceptul ganwyobas~ uwodebs.Semonaxvis cnebis formireba gulisxmobs `perceptuli ganwyobis~daZlevas da reaqciis axal tipze gadasvlas, rac dakavSirebuliasimbolur operaciebTan. analogiur Sexedulebas aviTareben j.bruneri, i. kesleri, b. riqseni, b. hameli.J. piaJes mixedviT miRebulia, rom bavSvi namdvilad mxolodmaSin eufleba raodenobis invariantobis cnebas, rodesac aramxolod aRniSnavs raodenobis invariantobas, aramed asabuTebskidec mas. raodenobis invariantobis srulfasovani cnebisaTvissimtkice da stabilobaa damaxasiaTebeli. amdenad, bavSvisSemecnebiTi aqtivoba unda ganvaviTaroT im donemde, rodesc isSeZlebda daufleboda invariantobis cnebas.vnaxoT, rogor ganasxvavebs J. piaJe bavSvebSi ricxvis cnebisformirebas stadiebis mixedviT, aq is gamoyofs sam stadias.ganviTarebis TiToeuli stadia gansxvavdeba erTmaneTisagansamyaros Secnobis TaviseburebebiT.74

J. piaJem es stadiebi aseTi eqsperimentebiT gamoavlina: mandaawyo 8 wiTeli muyaos naWeri rigSi ise, rom erTmaneTs SorisdaSoreba iyos TiTo santimetri. gamosacdel patarebs, ki uTxra,amoiRon yuTidan muyaos imdenive lurji naWeri. bavSvebis reaqciadamokidebuli aRmoCnda maT asakze. 5 da ufro naklebi asakisbavSvebma wiTeli naWrebi jer daawyves mWidrod, erTmaneTisgverdiT, daSorebis gareSe da Semdeg lurji naWrebi amoawyvesise, rom mieRoT igive sigrZis rigi. isini fiqroben, rom raodenobarCeba ucvleli Tu rigebis sigrZe erTnairia – es aris pirvelistadia. 6 wlis asakSi bavSvebi gadadian meore stadiaSi. isiniyovel lurj naWers deben wiTeli naWris pirdapir da iReben igivericxvs. es niSnavs imas, rom bavSvi TiTqosda Cawvda ricxvis cnebas.Tu Cven wiTel naWrebs Soris daSorebas gavzrdiT, bavSvi ifiqrebs,rom meti sigrZis rigSi muyaos meti naWeria, Tumca Cven maTiraodenoba ar Segvicvlia. am dros invariantobis wvdomis unarimeryevia, ar aris mtkice. 7 wlidan bavSvi aRwevs mesame stadias. amasakSi maT ician, rom naWrebis erTmaneTze daSorebiT, anerTmaneTTan axlos miweviT maTi raodenoba ar icvleba.gonebrivi operaciebi, rogorc piaJem uCvena umcros saskoloasakSi konkretul xasiaTs atarebs, magram yoveli konkretuligonebrivi moqmedeba avsebs bavSvis gamocdilebis sacavs da racufro mdidari iqneba es ukanaskneli, miT meti masala eqnebasubieqts xelT, inteleqtualuri ganviTarebis momdevno safexurze.TvalsaCinoebasa da konkretulobaze azrovnebis aseTidamokidebulebis gamo, umcrosi saskolo asakis dasawyisSi (6-7wlis) bavSvebi jer kidev ver swvdebian e.w. SeqceviTobis princips,romlis Tanaxmadac bunebis mTel rig procesebs iseve, rogorcadamianur moqmedebebsa da gonebriv operaciebs, Seesabameba misiSebrunebuli procesebi da operaciebi, riTac aRsdgeba pirvandeliviTareba. magaliTad, bavSvi ver xvdeba, rom gaRunuli mavTulisgasworeba aris gaRunvis sapirispiro operacia, rom gaartyelebuliplastilinis burTulas isev SeiZleba daubrundes pirvandeli75

forma da a.S., miuxedavaT imisa, rom praqtikulad aseT operaciebsTiTqmis yoveldRiurad ganaxorcieleben.azrovnebis am Taviseburebas ukavSirdeba is garemoeba, romsagnebisaTvis formis Secvlis SemTxvevaSi bavSvi ver xvdeba maTimasis ucvlelobas, maTi gafantvis an erTad Tavmoyris SemTxvevaSiraodenobis ucvlelobas da sxva. magaliTad, dabali, farToWurWlidan, maRal, viwro WurWelSi wylis gadasxmis Semdeg hgonia,rom wylis raodenobam moimata. gafantuli burTulebis erTadSegrovebis Semdeg hgonia, rom maTi raodenoba Semcirda da a.S. ammimarTebiT mravalricxovani eqxperimenti Caatara J. piaJem da ameqsperimentalur faqtebs mecnierebaSi `piaJes fenomenebi~ ewodeba.marTalia, Tavad piaJe miuTiTebs, rom gonebrivi ganviTarebiskonkretul operaciaTa stadiaze (7 wlis zemoT) es fenomenebidaiZleva, magram Cveni yuradReba miipyro im garemoebam, romzogierT moswavlesTan `piaJes fenomenebi~ am asakSic vlindeba,amitom gadvwyviteT, es sakiTxi Segveswavla dawyebiT klasebSi.cdebi Cavatare I-IV klasebSi anu 1993-97 wlebSi dabadebulbavSvebTan, 2004 wlis maisSi. sul Seswavlili iqna 200 bavSvi,TiToeuli klasidan 50-50.m e T o d i k a. yoveli cda tardeba individualurad.cdisaTvis winaswar momzadebuli maqvs 18 cali erTnairi feris dazomis Rilebi, romlebic dawyobilia mcire zomis erTjeradTefSze.bavSvs pirvelad vaCveneb Rilebs Sekrebili saxiT, Semdeg kimaT gavfantav. proceduras aqvs saxe: bavSvs Tavdapirveladganvawyob TamaSisaTvis, Semdeg vTavazob: ` --- modi viTamaSoT vinmesdabadebis dRe, visi dabadebis dRe viTamaSoT?~ xSir SemTxvevaSiasaxeleben megobris an mezoblis saxels. amis Semdeg kvlavvekiTxebi: `vin iqneba am dabadebis dReze celqi bavSvi?~ iubilarisada celqi bavSvis saxelebiT vTavazob siuJets: `Cven varT baias(ikas) dabadebis dReze. dedam daacxo namcxvrebi da moaqvsmagidasTan (vaCveneb TefSs da vuTanxmdebi, TiTqos es aris76

namcxvrebi), uceb celqi giorgi daetaka dedas da daayrevinanamcxvrebi (am dros Rilebi ise davyare magidaze, rom gabneuliyo).vekiTxebi: axla ufro metia Tu maSin meti iyo, roca TefSze ewyo?~TiToeul cdis pirze Sevavse Cems mier momzadebuli SemdegiSinaarsis oqmi, ixile danarTi #3Sedegebi aseTia:cxrili #3`piaJes fanomenis~ arseboba dawyebiT klasebSiklasi axla tolia axla metia axla naklebiaIV 64% 36% 0%III 56% 44% 0%II 42% 54% 4%I 34% 59% 7%gamokiTxuli 200 bavSvidan raodenibis cnebis invariantobaaris 109-sTan anu 54,5%-Tan, xolo cneba ar aqvs 91-s anu 45,5%-s, maTSoris axla metobas ambobs 93%, xolo naklebobas – 17%.raodenobis invariantoba aRmoaCnda 54,5%-s, anu 109-s. aqgamovyavi sami jgufi:1. bavSvebi, romlebic aRniSnavdnen raodenobisinvariantobas da mis asaxsnelad araviTar sityvierargumentacias ar gvaZleven (12,6%);2. bavSvebi, romlebic aRniSnaven raodenobis invariantobasda iZlevian erT sityvier argumentacias (45%);3. bavSvebi, romlebic aRniSnaven raodenobis invariantobasda iZlevian karg sityvier argumentacias (42.4%).gTavazobT ramdenime magaliTs: pirveli jgufidan moviyvan orbavSvs:c. p. (7;10) - axla ufro metia Tu maSin, roca TefSze ewyo?- axla tolia.- ratom fiqrob ase?77

- dums.c. p. T. b. (6;6) - axla ufro metia Tu maSin, roca TefSzeewyo?- axla tolia.- ratom fiqrob ase?- dums.meore jgufis bavSvebi invariantobis asaxsnelad iyenebdnenmxolod erT detals, mag.:c. p. n. j. (7;9) - axla ufro metia Tu maSin, roca TefSzeewyo?- axla tolia.- ratom fiqrob ase?gadmoiyara, magram raodenoba ar Seicvala.c. p. l. l. (6;7) - axla ufro metia Tu maSin, roca TefSzeewyo?- axla tolia.- ratom fiqrob ase?- imdenia, ramdenic iyo, ar damatebia.bavSvebis garkveuli jgufi iZleva raodenobis invariantobissrul dasabuTebas.c. p. T. r. (7;9) - axla ufro metia Tu maSin, roca TefSzeewyo?- axla tolia.- ratom fiqrob ase?- rac iyo TefSze igive gadmoiyara, arc moklebia,arc momatebia.l. l. (6;9) - axla ufro metia Tu maSin, roca TefSze ewyo?- axla tolia.- ratom fiqrob ase?- arc damatebia, arc moklebia.78

aRsaniSnavia, rom invariantobas umetesad ver xsnidnen I da IIklasis moswavvleebi da dumdnen, Tumca gvqonda SemTxvevebi zedaklasebSic (IIIkl. – 11,2%; IVkl. – 8,7%). analogiurad iyo erTiniSniT dasabuTebis drosac, rac Seexeba III jgufs, dasabuTebaTiTqmis zeda or klasSi modioda, Tumca I klaselebSic aRmoCndaaseTebi (3,3%).bavSvebi, romlebsac raodenobis invariantobis cneba ar aqvT(45,5%), SeiZleba sam jgufad daiyos: I. tolobas uaryofen, magrammis asaxsnelad araviTar sityvier arguments ar iyeneben, aseTiagamokiTxulTa 18,8%.mag.: z. W. (6;9) - axla ufro metia Tu maSin, roca TefSze ewyo?- axla metia.- ratom fiqrob ase?- dums.II. bavSvebi, romlebic tolobas uaryofen, magram misasaxsnelad mxolod erT sityvier arguments iyeneben, aseTiagamokiTxulTa 60,8%. mag.: g.s. (7;8) - axla ufro metia Tu maSin,roca TefSze ewyo?- axla metia.- ratom fiqrob ase?- daiyara da gaibna.r. n. (6;9) - axla ufro metia Tu maSin, roca TefSze ewyo?- axla metia.- ratom fiqrob ase?- roca gaibna, meti gaxda.III. bavSvebi, romlebic tolobas uaryofen, magram misasaxsnelad axdenen sityvier argumentirebas, aseTia gamokiTxulTa20,4%. mag.: S.k. (7;11) - axla ufro metia Tu maSin, roca TefSze ewyo?- axla metia.- ratom fiqrob ase?79

- TefSze erTad iyo da cota Canda, axla, romgadmoiyara gaibna da meti Cans.g.a. (6;9) - axla ufro metia Tu maSin, roca TefSze ewyo?- axla metia.- ratom fiqrob ase?- didi adgili daikava magidaze, amitom bevria.aRsaniSnavia, rom invariantobas uaryofdnen, magram umetesadver xsnidnen I da II klasis moswavvleebi da dumdnen, Tumca gvqondaSemTxvevebi zeda klasebSic (III-IVkl. – 22,2%). invariantobis ararsebobas erTi argumentiT umetesad amtkiceebdnen I da II klasismoswavleebi (I-33,3%, II-30,9%). analigiurad iyo invariantobis ararsebobis argumentuli damtkicebac.gamokiTxulTa mxolod 3% ambobda, rom axla naklebiao,magram sainteresoa ra axsnas akeTeben bavSvebi. mag.: g. r. (7,1) - axlaufro metia Tu maSin, roca TefSze ewyo?- axla naklebia.- ratom fiqrob ase?- gadmoiyara da moaklda.o. a. (6.9) - axla ufro metia Tu maSin, roca TefSze ewyo?- axla naklebia.- ratom fiqrob ase?- TefSze erTad iyo da bevri Canda.skolaSi cdebi CavatareT maisis bolos, amdenad mTeli wlisganmavlobaSi miRebuli gamocdilebis safuZvelze naklebad hqondaadgili piaJes fenomens. am problemiT imdenad davintersdiT, romgadavwyviteT, igive cdebi CametarebinaT sabavSvo baRSi,Seswavlili iqna 30 bavSvi. Sedegebi aseTia:80

cxrili #41998 wels dabadebulebi (5-6 wlis)dabadebis Tve toli axla meti axla sulnaklebi1—3 25% 75% 0% 100%4—6 0% 89% 11% 100%I naxevari 12% 82% 6% 100%7—9 0% 100% 0% 100%II naxevari 0% 100% 0% 100%sul jami 8% 88% 4% 100%vfiqrobT, saswavlo wlis dasawyisSi piaJes fenomens ufrometad eqneba adgili, gansakuTrebiT pirvel klasSi. amdenad, esSeviswavleT 2004wlis oqromberSi, sul Seswavlili iqna 160pirvelklaseli quTaisis sxvadasxva skolaSi. Sedegebi aseTia:cxrili #5kvlevis Sedegebi pirvelklaselebTanklasi axla tolia axla metia axla naklebia sulI 26,9% 61,1% 12% 100%moswavleTa pasuxebi identuria, amdenad calke ar ganvixilav.analizisaTvis ukeTesia SevaerTod CvenTvis saintereso asakisbavSvTa monacemebi:cxrili #6sxvadsxva dros miRebuli SedegebiCatarebis dro klasi axla axla axla sultolia metia naklebia2004w. maisi I 34% 59% 7% 100%2004w. maisi baRi 8% 88% 4% 100%2004w. oqtomberi I 29% 60% 11% 100%81

cxrilis analizis Sedegad naTlad Cans, rom Tu saswavlowlis bolos invariantobas aRiarebda 34% da Aar AaRiarebda 66%,saswavlo wlis dasawyisSi maCvenebeli aseTia: invariantobis wvdomaaqvs 29%-s, ar aqvs 71%-s. TiTqos procentuli maCvenebelierTnairia, magram gansxvaveba aris, amave dros unda aRvniSno, romsaswavlo wlis bolos Seswavlili iqna 50 bavSvi, xolo wlisdaswayisSi 168. sakmaod didia sxvaoba baRis SemTxvevaSi.invariantoba aqvs 8%-s, ar aqvs 92%-s.vfiqrobT, skolaSi Sesvla garkveul wilad did rolsasrulebs bavSvis momwifebis sakiTxSi. yuradsaRebia SeswavlilbavSvTa asakobrivi gansxvaveba. 2004 wlis maisSi SeswavlilpirvelklaselTa asaki iyo (7;3)-dan (8;2)-mde, xolo oqtomberSiSeswavlilTa - (6;2)-dan (7;1)-mde. rac Seexeba sabvSvo baRs, aq asakiicvleboda (5;8)-dan (6;2)-mde, bunebrivia misi maCvenebeli sxva veriqneboda.piaJes fenomenis koreqcias SevecadeT didaqtikuri TamaSiT.TviT saxelwodeba `didaqtikuri TamaSi~ garkveviT miuTiTebs immizandasaxulobaze, romelic TamaSis am formas gaaCnia. misTvisisaa damaxasiaTebeli, rom igi specialurad iqmneba pedagogis mierda emsaxureba bavSvis qcevis sasurveli mimarTulebiTorganizacias; es aris saswavlo TamaSi, sadac bavSvi euflebagarkveul codnas, iZens Cvevebs. didaqtikur TamaSSi qcevis impulsi,aris TamaSis moTxovnileba, rac bavSvis bunebriv mdgomareobaswarmoadgens.saskolo swavlebaSi TamaSis gamoyenebis Sesaxeb ori,urTierTsawinaaRmdego azri arsebobs: mkvlevarTa erTi jgufikategoriulad ewinaaRmdegeba saskolo swavlebis procsSi TamaSisgamoyenebis SesaZleblobas, meoreni aucileblobiT moiTxoven misgamoyenebas. unda aRiniSnos, rom orive am mosazrebas Tavisiobieqturi safuZveli gaaCnia. TamaSis gamoyeneba saskolo swavlebisprocesSi marTlac qmnis garkveul saSiSroebas. a. makarenko werda:`didi Secdoma iqneba uaxlesi perspeqtivis mxolod siamovnebis82

principze ageba, maSinac ki, Tu am siamovnebaSi mocemuliasasargeblo elementebi~ [97 gv. 76].k. uSinski werda: `...swavleba umjobesia daviwyoT cotamogvianebiT da Tavdapirvelad mas davuTmoT mcire dro, magramTavidanve gavmijnoT is TamaSisagan da gadavaqcioT bavSvisaTvisseriozul movaleobad. ra Tqma unda, SesaZlebelia bavSvs wera dakiTxva vaswavloT TamaSiT, magram vTvli, rom es mavnea, radganacrac ufro metad movaridebT bavSvs seriozul mecadineobas,misTvis miT ufro Zneli iqneba masze gadasvla. gavxadoTseriozuli mecadineoba bavSvisaTvis saxaliso – ai, pirvelsawyisiswavlebis ZiriTadi amocana~ [124 gv. 96.].Taviseburi gamarTleba gaaCnia sawinaaRmdego mosazrebasac.amas adasturebs is efeqturi praqtikuli Sedegebi, romelic Tanaxlavs TamaSis gamoyenebas swavlebis procesSi. ganwyobis TeoriisgaTvaliswineba mtkice Teoriul safuZvels uqmnis didaqtikuriTamaSiTa da didaqtikuri masalebiT muSaobas, romelzec didimuSaoba Catarda b. xaWapuriZis xelmZRvanelobiT.ganwyoba zogadi, centraluri mdgomareobaa. masSi CarTuliaindividis yvela Zala. mis bazaze aRmocendeba fsiqikuri procesebida xdeba mizanSewonili qcevis regulacia, individis ZalTagardaqmna garkveuli saxis qcevis gaSlis mimarTulebiT. ganwyobaar aris cnobieri mdgomareoba, igi misi safuZvelia. sistematuriaqtivobis Sedegad ganwyoba fiqsirdeba da gadadis farulmdgomareobaSi. `ganwyobis~ cnebis uznaZiseuli gageba metad didSesaZleblobas qmnis pedagogiuri procesis agebis TeoriulisafuZvlebis SeqmnisaTvis.didaqtikur TamaSebsa da masalebs aqvs TeoriuliwanamZRvrebi, elementaruli maTematikuri warmodgenebisganviTarebisaTvis, romelsac iZleva b. zaWapuriZe [9 gv. 89], esenia:1. saWiroa SemuSavdes didaqtikur masalaTa seria,romelic amocanaTa sxvadasxvagvarad dasmis SemTxvevaSi83

avSvisagan moiTxovs analizis, abstraqciis,saxeldebisa da sxva aqtebis ganxorcielebas;2. didaqtikuri masalis miwodeba unda xdebodesbavSvisaTvis wamyvani qcevis formaSi, e. i. TamaSissaxiT;3. aucilebelia dasaxelebuli aqtebis mravaljergameoreba, raTa funqciaTa momwifebis stimulirebamoxdes;4. didaqtikuri masaliT muSaoba unda xorcieldebodessocialuri kontrolis principiT da araTviTkontroliT;5. xelmZRvaneli sistematiur daxmarebas unda uwevdesbavSvs.gamoyenebuli didaqtikuri masalebisa da TamaSis efeqturobaunda ganisazRvros Semdegnairad:a. saWiroa eqsperimentuli zemoqmedebis dawyebamdearsebuli viTarebis zusti dadgena;b. unda moxdes zusti aRricxva imisa, Tu razegavlenas axdens eqsperimentul-pedagogiurizemoqmedeba;g. im cvlilebebis zusti aRrixcva, romelic amzegavlenam gamoiwvia.yovelive zemoT aRniSnulidan gamomdinare, udavoa, romdidaqtikuri TamaSis gamoyenebas pedagogiur-fsiqologiuriTvalsazrisiT didi mniSvneloba unda mieniWos. rogorc vTqviT,saWiroa Seiqmnas didaqtikuri TamaSis garkveuli sistema, romelicagebuli unda iqnes iseTive principiT, rogorc aigeba sawavloprocesi: bavSvs erTi da igive damokidebulaba unda eZleodessxvadasxva masalaze, sxvadasxva Sinaarsis saxiT. aseT situaciaSimasalisa da Sinaarsis variacia xelsayrel pirobebs qmnis ama Tuim mimarTebis wvdomisaTvis.84

amaSi mdgomareobs TamaSis didaqtikuri mizniT gamoyenebisarsi. swored aseTi organizacia aaxloebs TamaSs didaqtikasTan daamdenad SesaZlebelia vilaparakoT TamaSis didaqtikuridaniSnulebis Sesaxeb.am principebis gaTvaliswinebiT, SevecadeT agvegodidaqtikuri TamaSebis seriebi. am mizniT SevCerdiT piaJes erT-erTsakmaod cnobil eqsperimentze, romelic mowodebulia bavSvis mierinvariantobis cnebis dauflebis donis gansazRvrisaTvis. Senaxvis(invariantobis) principis dauflebis kvleva piaJes genetikurifsiqologiis erT-erT centralur problemas warmoadgens.`Senaxvis~ cneba gulisxmobs, rom sagani an saganTa jgufiaRiarebuli iqnes ucvlelad elementebis Semadgenlobis, an sxvafizikuri parametrebis TvalsazrisiT, miuxedavad misi formisa dagaregani ganlagebis cvlilebisa – erTi aucilebeli pirobisdacviT: mas araferi emateba da arc akldeba. piaJes koncefciisTanaxmad, bavSvis azrovnebis ZiriTad Taviseburebas umcrossakolo asakSi warmoadgens centracia, romlis arsi imaSimdgomareobs, rom obieqtTan kavSiris dros bavSvs ar Seswevs unarierTdroulad gaiTvaliswinos sagnis ramdenime Tviseba. igiiTvalsiwinebs mxolod mis uSualod mocemul mxares e. i. erTromelime Tvisebas: am sirTulis daZleva SesaZlebeliadecentraciis pirobebSi, romelic, avtoris azriT, viTardebaspontanurad, sakuTari Sinagani kanonebiT. kiTxvaze, SesaZlebeliaTu ara moZebnil iqnas raime xerxebi da meTodebi, rac daaCqarebdaim logikuri struqturis formirebas, romelic safuZvlad edebaSenaxvis principis dauflebas, piaJe uaryofiTad pasuxobs. masmiaCnia, rom am struqturaTa formirebis daCqareba arsebulistruqturebis aqtivizaciis gziT SeuZlebelia. misi azriT, amprocess spontanuri xasiaTi aqvs.Tu gadavxedavT am sferoSi Sesrulebul eqsperimentulgamokvlevebs, vnaxavT, rom umetes SemTxvevaSi bavSvebi Senaxvisprincipis dauflebas axerxeben mravalgvari, rTuli85

manipulaciebisa da saazrovno qmedebaTa ganmeorebis Sedegad.xSirad es procedurebi sakmaod damRlelia da SesrulebisTvalsazrisiT rTuli.cnobilia mravali eqsperimenti Senaxvis principisdauflebis donis kvlevisaTvis, romelic TviT piaJes mier arismowodebuli. Cven SevCerdiT erT-erT maTganze.cdebi CavatareT im pirvelklaselebTan, romlebTac ar aqvTraodenobis invariantobis wvdomis unari. sakontrolo cdiTerTxel kidev vadgenT aris Tu ara bavSvi raodenobisinvariantobis (Senaxvis) princips dauflebuli. am mizniT vimeorebTpiaJes erT-erT cnobil cdas – bavSvis win horizontalur rigSivalagebT 6 wiTeli feris kvadrats (23mmX23mm). figurebs SorismanZili 1,5 sm-ia. iqve awyvia aseTive zomis 10 yviTeli kvadrati. esganpirobebulia im garemoebiT, rom SesaZlebelia bavSvmahorizontaler rigSi ganlagebul 6 wiTel figuras, CvensmoTxovnaze: `miuwyve mas amdenive yviTeli kvadrati~, dados maTqvemoT gacilebiT meti an naklebi raodenoba. e. i. figurebsurTierTcalsaxa SesatyvisobaSi ki ar moiyvans (TiTos TiTos kiar miudebs), aramed meore rigs ufro mWidrod daalagebs. aseTSemTxvevaSi bavSvi raodenobas Tanabrad aRiarebs, Tu orive rigSipirveli da ukanaskneli figurebi erTmaneTis qveS aRmoCndeba. undaaRvniSno, rom aseT siZneleebs Cven ar SevxvedrivarT.zemoT moyvanili J. piaJes cdis dros c. p.-s eZleva Semdegiinstruqcia: `Sexede am wiTel figurebs, am yviTlebidan ki aiRe damaT miuwyve imdeni, ramdenic wiTeli figuraa. ai, ase~. mas vuCvenebTu rogor unda Seasrulos moqmedeba. amis Semdeg darCenili 4yviTeli kvadrati frTxilad gamaqvs bavSvis mxedvelobis aredan(darCenil figurebs TiTqmis araviTar yuradreba ar aqcevs). amisSemdeg bavSvs mivmarTav: àba Sexede~ da mis mier wiTeli figurebisqveS miwyobil yviTel kvadratebs erTad movagroveb ise, romhorizontalur rigSi wiTel kvadratebs gacilebiT meti adgiliukaviaT, vidre yviTlebs. `romeli metia, wiTeli figurebi Tu86

yviTlebi?~ -- vekiTxebi mas. is bavSvebi, romlebic aRiarebenraodenobis invariantobas, Tavisufldebian ZiriTadi cdebisagan.masSi monawileobas iRben, mxolod isini vinc obieqturad Tanabarraodenobas afaseben aratolad.amis Semdeg cdis pirs utardeba TanmimdevrobiT 5 cda, sadacigive damokidebulebaa mocemuli TamaSiseul situaciaSi sxvadasxvamasalisa da Sinaarsis saxiT. ganvixiloT I seriis cdebi calcalke:I cda: c. p. win vawyob 6 lurj wres horizontalur rigSi 1,5sm daSorebiT. `modi viTamaSoT, eseni viTom gogonebi arian~ -mivuTiTeb lurj wreebze. èseni ki viTom xaWapurebi~ - mivuTiTebiqve dawyobil yviTel samkuTxedebze. `modi davurigoT TiTogogonas TiTo xaWapuri~. c. p. saTiTaod iRebs yviTel samkuTxedebsda awyobs lurji wreebis qvemoT. `yvelas ergo TiTo xaWapuri ara?jer xelebi ar dagibaniaT – mimarTavs deda bavSvebs. aba, daawyveTxaWapurebi da xelebi daibaneT~ - vargZeleb ambis Txrobas, TanyviTel samkuTxedebs erTad vagroveb. àba miTxari, gogonebi metiaTu xaWapurebi?~ bavSvi gvaZlevs pasuxs, ris Semdegac vekiTxebiT:`ratom ggoniaT ase? an ratom fiqrobT ase? dasabuTebas moviTxovTyovel konkretul SemTxvevaSi.II cda: 6 TeTri wre da 6 yviTeli Zelaki. Sesabamisi siuJetiaseTia: ès TeTri wreebi viTom kurdRlebia, eseni ki stafiloebi,modi davurigoT TiTo kurdRels TiTo stafilo (bavSvsparalelurad urTierTcalsaxa SesatyvisobaSi mohyavs figurebi,keTdeba ise, rogorc pirveli cdis dros). am dros buCqebidanmgelma gamoyo Tavi. SeSinebulma kurdRlebma swrafad dayaresstafiloebi (Zelakebs erTad vuyri Tavs). aba miTxari, kurdRlebimetia Tu stafiloebi?~III cda: 6 mwvane Zelaki da 6 TeTri Rili. siuJeti aseTia (memxolod siuJets moviyvan, Tanmimdevroba da qmedeba iseTia, rogorcI cdis dros, aseve iqneba Semdegac): `modi viTamaSoT, es mwvaneZelakebi viTom biWunebia, es Rilebi ki burTebi. aba, davurigoT87

TiTo biWunas TiTo burTi. biWebma gahkres burTs fexi da erTadmouyares Tavi, ai ase. romeli metia – biWunebi Tu burTebi?~IV cda: 6 xis feri oTxkuTxedi da 6 TeTri wre. èsoTxkuTxedebi viTom galiebia, es wreebi ki Citebi. modiT CavsvaTTiTo Citi TiTo galiaSi. yvelas Sexvda TiTo galia ara? CitebiZalian mowyenili arian imitom, rom cal-calke galiaSi movaTavseT.erT keTil biWs Seecoda Citebi da gadawyvita gamouSvas. gauRokari. gaxarebulma Citebma erTad moiyares Tavi, ai, ase – Citebimetia Tu galiebi?~V cda: 6 mwvane Zelaki da 6 TeTri wre. ès mwvane ZelakebibavSvebia, eseni ki velosipedebi. modi, davurigoT TiTo bavSvsTiTo velosipedi. bavSvebi saseirnod apireben wasvlas, moemzadnenkidec amisaTvis, magram ... jer gakveTilebi moamzadeT da SemdegiseirneT – dauZaxa dedam bavSvebs. isini iqve erTad awyobenvelosipedebs, ai, ase – bavSvebi metia Tu velosipedebi?~II seria: sakontrolo cdis Semdeg (es cda yvela seriisaTvissaerToa da tardeba I seriis sakontrolo cdis analogiurad), amseriaSic tardeba 5 cda. am seriis Taviseburebas is garemoebawarmoadgens, rom cdebSi Sesasrulebeli moqmedeba aRar arisdakavSirebuli garkveul siuJetTan, igi TamaSiseuli siuJetisgareSe tardeba. c. p. eZleva igive masala imave TanmimdevrobiT,rogorc I seriaSi gvaqvs.I cda: c. p. win, horizontalur rigSi ganlagebulia 6 lurjiwre 1,5 sm daSorebiT, iqve erTad awyvia 6 yviTeli samkuTxedi,bavSvs eZleva Semdegi saxis instruqcia: `Sexede am lurj figurebs,am yviTelidan ki aiRe da miuwyve imdeni, ramdenic lurji figuraa.ai, ase~ - mivmarTav bavSvs. davalebis Sesrulebis Semdeg qvedarigis figurebs (yviTel samkuTxedebs) vagrovebT erTad, bavSvsvaZlev SekiTxvas: `romeli figuraa meti – lurji wreebi TuyviTeli samkuTxedebi?~analogiurad tardeba Semdegi cdebi sxvadasxva masalaze:II cda: 6 TeTri wre da 6 yviTeli Zelaki.88

III cda: ^6 mwvane Zelaki da 6 TeTri Rili.IV cda: 6 xis feri oTxkuTxedi da 6 TeTri wre.V cda: 6 mwvane Zelaki da 6 TeTri wre.III seria: sakontrolo cdis Semdeg c. p. eZleva 5 cdaSi erTida igive simboloebi (lurji wreebi da yviTeli samkuTxedebi)dakavSirebuli gansxvavebul siuJetebTan.I cda: c. p. win vawyob 6 lurj wres horizontalur rigSi.`modi viTamaSoT, eseni viTom gogonebi arian~ - mivuTiTeb lurjwreebze. èseni ki viTom xaWapurebi~ - mivuTiTeb iqve dawyobilyviTel samkuTxedebze. `modi davurigoT TiTo gogonas TiToxaWapuri. ai, ase~ da vuCveneb, rogor unda moiqces. c. p. asrulebssaTando moqmedebas, me ki vagrZeleb Txrobas ise, rogorc I seriisI cdaSia. bavSvebs vekiTxebi: àba miTxariT, gognebi metia TuxaWapurebi?~II cda: igive figurebi, ambavi kurdlebisa da stafiloebisSesaxeb.III cda: igive figurebi, ambavi biWunebis da burTebis Sesaxeb.IV cda: igive figurebi, ambavi Citebisa da galiebis Sesaxeb.V cda: igive figurebi, ambavi bavSvebisa da velosipedebisSesaxeb.rogorc vxedavT, am seriis cdebi imiT gansxvavdeba I seriiscdebisagan, rom erTi da igive simboloze igeba sxvadasxvaTamaSiseuli siuJeti.IV seria: wina seriis sapirispiroa im gagebiT, rom yvelacdaSi bavSvs eZleva sxvadasxva simbolo, romelic yovelTviserTsa da imave konkretul SinaarsTan aris dakavSirebuli. e. i.icvleba simboloebi, masTan dakavSirebuli Sinaarsi ki yovelTviserTi da igivea.I cda: 6 lurji wre da 6 yviTeli samkuTxedi, romelicTamaSiseul siuJetSi `gogonebi~ da `xaWapurebia~. instruqciaigivea, rac I da III seriis I cdaSi.II cda: 6 TeTri wre da 6 yviTeli Zelaki, ambavi igive.89

III cda: ^6 mwvane Zelaki da 6 TeTri Rili, ambavi igive.IV cda: 6 xis feri oTxkuTxedi da 6 TeTri wre, ambavi igive.V cda: 6 mwvane Zelaki da 6 TeTri wre, ambavi igive.e. i. erTi da igive konkratuli Sinaarsi yovelTvis sxvadaxvamasalasTan aris dakavSirebuli.amdenad, seriebis erTmaneTisagan gansxvavebas simboloebisada ambebis mixedviT aqvs Semdegi saxe:cxrili #7seriebis simboloebisa da ambebis cvlilebaseriebi simbolo ambaviI icvleba icvlebaII icvleba ar icvlebaIII ar icvleba icvlebaIV icvleba ar icvlebaTiToeuli seria Cuatarda 30-30 bavSvs, mxolod imaT, vinc araRiarebda raodenobis invariantobas. sxavadasxva seriaSimonawileobda sxvadasxva bavSvi. Sedegebi aseTia:mirebuli Sedegebi seriebis mixedviTcxrili #8I cda II cda III cda IV cda V cdaseria tolia metia tolia metia tolia metia tolia metia tolia metiaI 66% 34% 78% 22% 66% 34% 78% 22% 89% 11%II 34% 66% 45% 55% 55% 45% 89% 11% 89% 11%III 81% 19% 75% 25% 65% 35% 61% 39% 85% 15%IV 85% 15% 71% 29% 71% 29% 73% 27% 85% 15%yuradsaRebia is faqti, rom mTeli eqsperimentis msvlelobismanZilze cdebi imgvarad taredeboda, rom erT klasSi myofmoswavleebs ar eZleodaT saSualeba cdebisagan miRebuliStabeWdilebebi gaeziarebinaT sxva bavSvisaTvis. es gvaZlevs90

saSualebas vivaraudoT, rom arc erTi c. p. ar iyo winaswarinformirebuli imis Sesaxeb, Tu rogor tardeboda cda.cxrilis analizi gviCvenebs, rom I seriis cdebis progresiufro stabilurad mimdinareobs, am dros bavSvebi CarTuli iyvnenTamaSSi da Secdomas ar ganicdidnen. rac Seexeba II seriis cdebs –aq ufro metad aqcenti hqondaT gadatanili maTematikaze, radgansiuJeti ar iyo xatovani Sinaarsis. amdenad, Tavdapirvelad ufrometi Secdomebi iyo, romelic TandaTan daZlies. III seriis cdebiTiTqosda mosawyeni iyo, radgan siuJeti ar icvleboda. es daetyokidec me-3 da me-4 cdebs. aseve iyo IV seriis cdebic, oRond ufrostabiluroba iyo SenarCunebuli.cxrilze dakvirvebiT SeiZleba vTqvaT, rom didaqtikuriTamaSebiT saTanado Sedegs mivaRwieT. raodenobis invariantobissruli gamosworeba SeuZlebelia mxolod didaqtikuri TamaSebiT,amas miuTiTebda Tavad J. piaJec. mdgomareobis gamosaworebladZalian kargia g. beriSvilis, i. kotetiSvilis, b. sulakauris wigni– `maTematika I klasebisaTvis~, romelic Cvens mier iyogamoyenebuli. am wignSi mocemuli gakveTilebis nawils, sadacxdeba grovebiT Tvla, aqvs uamravi savarjiSo, romlebic diddaxmarebas gauwevs maswavleblebs.seriebis Catarebis Semdeg gavimeoreT sakontrolo cda. TuTavdapirbelad invariantobas aRiarebda mxolod 29%, xolo 71% araRiarebda, Catarebuli muSaobis Semdeg invariantobas aRiarebda69% - ar aRiarebda 31%. Cveni azriT, es ar aris cudi maCvenebeli.daskvnebi da rekomendaciebi:• gamokvlevebi gviCvenebs, elementaruli maTematikuri codniskvlevam gviCvena, raodenobis invariantobis wvdomis unarisSeswavlis aucilebloba. amisaTvis gamoviyeneT piaJes meTodida davadgineT: saswavlo wlis bolos raodenobisinvariantobis wvdomis unari hqonda 54,5%-s, ar hqonda – 45,5%-s. amave dros baRSi, Sedegebi aseTi iyo: invariantoba aqvs –91

8%-s, ar aqvs – 92%-s. amave wlis dasawyisisaTvispirvelklaselebSi Sedegi aseTia: inavriantoba aqvs - 29%-s,ar aqvs 71%-s.• TiToeul SemTxvevaSi gamovyaviT 3 jgufi: I. bavSvebi,romlebic ver axerxeben axsnas da duman; II. asabuTeben erTidetaliT; III. iZlevian srul argumentacias.• didaqtikuri TamaSi aris saswavlo TamaSi, sadac bavSvieufleba garkveul codnas, iZens Cvevebs. mis gamoyenebaspedagogiur-fsiqologiuri TvalsazrisiT didi mniSvnelobaaqvs. Tu Tavdapirvelad raodenobis invariantobis wvdomisunari qonda 29%-s, xolo ar qonda 71%-s, didaqtikuriTamaSebis Semdeg invariantoba qonda 69% - ar qonda 31%.• gasaTvaliswinebelia, saswavlo procesis dagegmvisasmaswavlebelma unda gaiTvaliswinos didaqtikuri TamaSebi.maT SeuZliaT gamoiyenon Cvens mier Seqmnili didaqtikuriTamaSebis sistema an Seqmnan damoukideblad axali, mxolodgaiTvaliswinon, rom moswavleebi ufro kargad asrulebensiuJetur didaqtikur TamaSebs.$ 3. zepiri angariSis gamoyeneba SemecnebiTiinteresebis ganviTarebisaTvis maTematikisgakveTilebzea) interesis cnebaaRzrdis erT-erTi aucilebeli saSualeba arisSromismoyvareoba – survili da unari kargad swavlisa, risTvisacaucilebelia moswavles SevuqmnaT iseTi piroba, rom man miaRwioswarmatebebs swavlis procesSi, igrZnos kmayofileba da xalisiarcodnidan codnisaken mimaval gzaze. es ki did stimuls aZlevsskolisaTvis mzaobaSi Seferxebis mqone bavSvebs. jer kidev XIX92

saukuneSi cnobili meTodisti s. Soxor-trocki Tavis wignSi `ra darogor unda vaswavloT ariTmetikaSi~, werda:` . . . moswavleTamaTematikuri codniT gamdidrebisaTvis aucilebelia, rom manSeigrZnos interesis cocxali emocia da kmayofileba. am interesiTsiamovneba, muSaobisas winsvlisa da sirTuleebis gadalaxvisprocesSi~.lolandis mixedviT interesi ganmartebulia, rogorcnebismieri yuradReba, romelic iwvevs sasiamovno gonebrivaqtivobas. peronis mixedviT, ki interesi warmoadgens masalaTaxarisxs, romelic ipyrobs adamianis yuradRebas da orientirebuliamis Semoqmedebaze. strogoni wers, rom interesi aris gonebrivi daemociuri aqtivobis gamomJRavneba. n. morozova da v. ivanovi weren,rom interesi esaa – adamianis aqtiuri, SemecnebiTi, aqtiur-SemecnebiTi damokidebuleba samyaroze.amdenad, interesi fsiqopedagogiuri gagebiT asaxavs uamravmniSvnelovan process: calkeulidan, mis TviTRirebulebamde, isgamoxatulia tendenciebSi, moTxovnilebebSi, urTierTobebSi.d. uznaZis mixedviT saskolo asakis interesi dayofili arisSemdeg etapebad: aRweris interesi, specialuri interesi,fenomenaluri interesi da bolos SemecnebiTi interesi.saskolo asakis dasawyisSi bavSvis interesi aRwerisaken arismimarTuli. es imas niSnavs, rom bavSvis yuradRebis centrSi esfenomenebi da SemTxevevebia mocemuli. aRwera ara marto imas exeba,Tu rogoria sagani, aramed imasac, Tu ra xdeba masTandakavSirebiT.saskolo asakis pirvel wlebSi Tavs iCens specialuriinteresic. gansakuTrebiT musikaluri, mxatvruli, zogjermecnieruli, kerZod, maTematikuri. magram yvelafer amas calkeindidvidTan aqvs adgili. ibadeba kiTxva: interesTa diferenciaciamarto individualuri farglebiT ganisazRvreba, Tu asakobrivixasiaTi aqvs? interesTa direnciaciis procesSi asakobrivi93

faqtoric mniSvnelovan rols asrulebs. magram es ar unda gavigoTise, rom TiTqos erT asakobriv safexurs erTi dargis SeswavlaaxasiaTebdes da meores meorisa.umcros saskolo asakSi bavSvs Zlieri inteleqtualuriinteresi aqvs, romelic axlis, misTvis jer kidev ucnobis garkvevaseswrafvis. magram saintersoa da gansakuTrebiT simptomaturi, romes axali, ara movlenaTa Soris arsebuli mimarTebaa, aramedTviTon movlenaTa Soris arsebuli movlenebi an sagnebia. aqbavSvis Tavisebur ganwyobasTan gvaqvs saqme, romlisTvisacsinamdvilis fenomenaluri Sinaaarsis wyurvilia damaxasiaTebeli.sainteresoa, rom 10 wlis Semdeg fenomenaluri interesi aRarZlierdeba, piriqiT, sustdeba. 12 wlisaTvis igi icvleba namdvilSemecnebiT interesSi, gadadis mimarTebaTa wvdomis interesSi.saskolo asakis dasawyisSi iRviZebs SemecnebiTi intersi,gviani bavSvobis Semdeg is gadadis mtkice SemecnebiT intersSi,romelic obieqturi sinavdvilis mtkice sistemuri bunebis wvdomaseswrafvis. obieqturi Rirebulebis cnobierebas dawyebiT klasebSiunda CavuyaroT safuZveli (amaze qvemoT iqneba saubari).g. SCukinas azriT interesi warmoiqmneba moTxovnilebissafuZvelze, interesis formireba yovelTvis ar iwyebamoTxovnilebis gacnobierebiT. interesi SeiZleba warmoiqmnasstiqiurad, emociuri mimzidvelobis cnobierebis gareSe.interess Zalian didi mniSvneloba aqvs adamianisSemoqmedebaSi. amdenad, bednierebas adamiani ganicdis maSin,rodesac aqvs cxovrebaSi raime interesi. i. pavlovi interessganixilavs, rogorc Tavis tvinis qerqis aqtiurobis process.k. uSinski werda: `ZaldatanebiTi swavleba, romelicmoklebulia yovelgvar interess, moswavleSi klavs codnisdauflebis survils. amave dros miuTiTebs, rom ar SeiZleba mTeliswavleba warimarTos intersze dayrdnobiT. swavleba moiTxovs didmuSaobas da nebelobis gazrdas~.94

g. SCukina ganasxvavebs interesis or saxes: uSualo interesida gacnobierebuli intersi. uSualo interesi es aris ZiriTadadsaqmianobasTan dakavSirebuli interesi: Semecnebis procesTan,codnis miRebasTan, Sromis procesTan. gacnobierebuli interesi,es aris interesi saqmianobis procesis SedegebTan dakavSirebuli.pirovnebis aqtiuri da produqtiuli saqmianobisaTvis didimniSvneloba aqvs am interesTa swor Tanafardobas.g. SCukinas azriT pedagogikaSi Zalian didi mniSvneloba aqvsSemecnebiT interess, rogorc interesTa erT-erT yvelaze ZiriTadsaxes. misi gansakuTrebuloba imaSi gamoixateba, rom obieqti arisara sagnis Sinaarsi, aramed codnis miRebis procesi. SemecnebiTinteress miekuTvneba SemecnebiTi aqtivobis sxvadasxva saxe. misimeSveobiT gansakuTrebulad mimdinareobs inteleqtualurisaqmianoba, am dros mJRavndeba: amocanis amoxsnisadmi mzaoba,aqtiuroba ZiebaSi, mixvedriloba, kvlevisadmi gansakuTrebulimidgoma.SemecnebiT aqtivobas axasiaTebs emociuri gamoxatva:gakvirvebis emocia, axlis molodinis SegrZneba, warmatebisSegZneba.SemecnebiTi interesebis birTvad iTvleba SemecnebiTiprocesebi. Kk. uSinskis gamoTqmiT, es aris interesis sruli mizani.me veTanxmebi k. uSinsks im sakiTxSi, rom SemecnebiTi interesi arisswavlis ZiriTadi motivi, masSi igulisxmeba moswavleTa dadebiTidamokidebuleba skolisadmi, swavlisadmi.SemecnebiTi interesis gansakuTrebul Taviseburebad iTvlebais, rom centraluri saqmianoba aris iseTi SemecnebiTi amocana,romelic moiTxovs adamianisagan aqtiur Ziebas an Semoqmedebas. ai,ras wers b. ananievi - ` . . . swavlis procesSi warmoqmniliinteresi, gonebriv saqmianobas aqtiurs xdis ara marto mocemulmomentSi, aramed mimarTavs mas Semdgomi inteleqtualuriamocanebis amoxsnisaken, e.i. organizebas ukeTebs SemdgomSemoqmedebas~.95

SemecnebiTi interesi yalibdeba TandaTan, didi xnisganmavlobaSi da ar SeiZleba aRmocendes uceb, skolaSiSesvlisTanave, Tu skolamdel asakSi sakmaris yuradRebas armivaqcevT maT aRzrdas. gamocdileba gviCvenebs, rom yvelaze metsiZnelebs dawyebiT skolaSi ganicdian ara is bavSvebi, romelTacskolamdeli asakis bolosaTvis aqvT codnisa da Cvevebisarasakmarisi moculoba, aramed isini, romlebic avleneninteleqtualur pasiurobas, romelTac ar gaaCniaT survili daCveuleba ifiqron, gadawyviton amocanebi, Tu is ar arisdakavSirebuli bavSvis saintereso romelime saTamaSo ancxovrebiseul situaciasTan. ase magaliTad, erTi pirvelklaseliver pasuxobs kiTxaze: ramdeni iqneba ors mivumatoT erTi. igiambobs xan òrs~ xan `xuTs~ magram rodesac mis winaSe daayeneswminda praqtikuli amocana: ` ramdeni fuli geqneba, Tu mama moqcemsor lars, xolo deda erT lars?~ - bavSvma TiTqmis daufiqrebladupasuxa: `rasakvirvelia sami!~Cven viciT, rom mtkice SemecnebiTi interesebis formirebasxels uwyobs sistematuri skolamdeli swavlebis pirobebi. magramam pirobebSic bavSvebis nawili amJRavnebs inteleqtualurpasiurobas da mis dasaZlevad saWiro xdeba individualuri muSaobamaTTan, gansakuTrebiT skolisaTvis mzaobaSi Seferxebis mqonebavSvebTan. rogorc aq moyvanili magaliTi gviCvenebs, TubavSvisaTvis davaleba an amocana iqneba saintereso, saxaliso -aseTi zepiri varjiSi mas xdis ufro aqtiurs da motivirebuls.SemecnebiTi interesi aris yvelaze Rirebuli motivimoswavleTa saswavlo saqmianobaSi. is aZlierebs da aRrmavebs sxvamotivebs, rogoricaa: codnis miRebis SesaZlebloba, axlis gageba,warmatebebi swavlaSi da a,S. amas didad uwyobs xels zepiriangariSi.b)zepiri angariSimaTematikis swavlebis meTodikaSi gamoyofen zepir da weriTangariSebs. zepirs miekuTvneba gamoTvlebi 100-is farglebSi, an96

iseTi SemTxvevebi, romelic masze daiyvaneba. es SeiZleba iyos 100-isfarglebs zemoT (mag.: 900X7 es SemTxveva iqneba zepiri, radgan isdaiyvaneba 9X7 gamravlebaze). werilobiTs miekuTvneba yveladanarCeni SemTxveva gamoangariSebisa, rodesac ricxvebi 100-zemetia.dawyebiTi klasebis maTematikis gakveTilebze zepir muSaobasaqvs Zalian didi mniSvneloba – es SeiZleba iyos maswavleblissaubari klasTan an ramdenime moswavlesTan, an msjelobamoswavleebTan ama Tu im davalebis Sesrulebis Sesaxeb da a.S.zepiri muSaobis am saxeebs Soris SeiZleba gamovyoT zepirisavarjiSoebi. is ZiriTadad ukavSirdeba gamoTvlebs, amitom mas,,zepir angariSsac” uwodebdnen, ukeTesia gamoviyenoT termini,,,zepiri savarjiSoebi”.gamocdili pedagogi o. zaiceva Tavis naSromSi ,,zepiriangariSis roli gamoTvliT Cvevebis formirebasa da bavSvispirovnebis ganviTarebaSi” wers: mniSvnelovanisa da aucileblisdamtkiceba ar xdeba zepiri savarjiSos dros. Mmas Zalian didimniSvneloba aqvs gamoTvliTi Cvevebis formirebisaTvis, numeraciazecodnis daxvewisaTvis da moswavleTa pirovnuli TvisebebisganviTarebisaTvis. Aadre naswavli sakiTxebis xSiri gameorebamoswavleebs ise anviTarebs, rom gamoTvliTi Cvevebi miyavsavtomatizmamde. zepiri angariSi ar SeiZleba iyos gakveTilisSemTxveviTi etapi, mas meToduri kavSiri aqvs ZiriTad TemasTan daatarebs problematur xariaTs.zepiri savarjiSoebi mimdinareobs kiTxva-pasuxis formiT,klasis yvela moswavle erTdroulad erTi da igive samuSaosasrulebs. zepiri savarjiSoebi aucilebelia agreTve moswavleTaazrovnebis aqtivizaciisaTvis. Mmisi SesrulebiT viTarebamexsiereba, metyveleba, yuradReba, naTqvamis gagebis unari, swrafireaqcia. maRal Sedegs rom mivaRwioT dawyebiT klasebismaTematikis gakveTilze zepir varjiSs yoveldRiurad unda daeTmos5-10 wT.97

dawyebiTi klasebis maTematikis gakveTilebis ZiriTadimizania mimdinare masalebis Seswavla. Ggarda amisa maTematikisgakveTilebs sxva miznebic aqvs, rogoricaa ganvlili masalisganmtkiceba da momzadeba axali masalisaTvis, Cvens SemTxvevaSi kiSemecnebiTi interesis gazrda. amas, Zalian didi mniSvneloba aqvs,yvela moswavlisaTvis da gansakuTrebiT skolisaTvis mzaobaSiSeferxebisMqone bavSvebisaTvis. amdenad, didi mniSvneloba aqvssavarjiSoebis SerCevas gakveTilebisaTvis. zepiri savarjiSoebisefeqturi gamoyenebisaTvis didi mniSvneloba aqvs misi adgilisgansazRvras gakveTilis msvlelobisas, sxvadsxva cnebisa TuCvevebis formirebisas.zepiri savarjiSoebis saxeebi1. matematikuri gamosaxulebis mniSvnelobis povna.gamoTvliTi samuSaoebi SeiZleba iyos sxvadasxva saxis.SeiZleba SevTavazoT ricxviTi maTematikuri gamosaxuleba an asosSemcveli gamosaxuleba, sadac mocemulia asos ricxviTimniSvneloba, magaliTad:- ipoveT 7-isa da 4-is sxvaoba- ipoveT a-b gamosaxulebis mniSvneloba, sadac a=10 b=7- saklebia 9 (7), maklebi 6 (4), ipoveT sxvaoba- 6 gaadideT 3-iT.- ra ricxvs unda gamovakloT 8 (12; 7), rom miviRoT 2 (2; 3)- Cavifiqre ricxvi, gaadide 5-iT da miiRe 12. ra ricxviCavifiqre?dawyebiTi skolis zeda klasebSi mizanSewonilia gamosaxulebaSiiyos ramdenime moqmedeba erTad, mag;- 45 : 9 + 10 (18 : 9 + 3)- 400 – 6X5 (40 – 6X5)- 47 + 16 – 15 (6 + 3 - 4)90 gamoakeliT 72-isa da 8-is ganayofi. gamosaxuleba SeiZlebamivceT cxrilis saxiT:98

saklebi 5 6 9 12 15 19Mmaklebi 2 2 2 2 2 2sxvaobagamosaxulebis mniSvnelobis povnaze savarjiSoebisSesrulebis ZiriTadi mniSvneloba imaSi mdgomareobs, rommoswavleebs daexmaros gamoangariSebis martivi CvevebisSemuSavebaSi.2. maTematikuri gamosaxulebebis Sedarebaaq SeiZleba iyos sxvadasxva varianti. TavdapirveladskolisaTvis mzaobaSi CamorCenis mqone bavSvebTan ukeTesiadaviwyoT ricxvebis SedarebiTmag: SeadareT 7 da 3; 4 da 9; 15 da 25.Semdeg SeiZleba SevitanoT martivi gamosaxulebebi.6 + 4 * 4 + 6; 2 + 7 * 2 + 5; 20 – 18 * 20 – 15,aseTi savarjiSoebis daniSnulebaa Teoriuli codnisganmtkiceba ariTmetikul gamosaxulebebze, maT Tvisebebze,tolobasa da utolobaze da sxva. is aseve xels uwyobsgamoTvliTi Cvevebis gamomuSavebas.3. leqsad mocemuli amocanebibavSvebs Zalian uyvarT leqsebi. maT uRuZravT did SemecnebiTinteress leqsad gamoTqmuli amocanebi. unda aRiniSnos, rommsgavsi saxiT mocemuli amocanebi sainteresoa, nebismieriklasis meTematikis gakveTilebze. skolaSi muSaobisas viyenebdiprof. g. CaCaniZis krebulebs, romlebmac Zalian didi Sedegimomca. asevea dawyebiT klasebsic. magaliTad:sisxam didliT me da Tinam qaris CamonayariavkrifeT da movitaneT kargad blomad kakali.imwamSive dauZaxeT Cveni ezos ymawvilebs,da kakali Tanasworad yvelam gavinawileT.oTx biWsa da xuT gogonas gvergo TiTo-TiTo,99

sul ramdeni iyo netav Cemo kargo Tiko?xelSi mqonda xuTi msxali,ridiT mTxova kaxam,muwilade ori caliramdeni maqvs axla?oqros feri WuWulebi axvevia dedas,oTxi frTebqveS SeyuJula, orsac zurgze vxedav;magram bati mdinarisken ratom iSvers kisers?Turme erTi nabolara Wyumpalaobs isevsul ramdeni WuWulia mipasuxe myisve.koba sami wlisa gaxlavT, zeinabi –aTis;Zmaze oriT ufrosia SuaTana fati.aba, erTad ramdenia wlovaneba maTi?mezobels xuTi vaJi yavsTiTo vaJs TiTo daikoramdeni Svili hyoliaegeba miTxra maiko?sul 12 feradi fanqari aqvs ninosda surs ramdenime kidev SeiZinos.TiTo-TiTo aCuqes giam, liam, baCam.ocis Sersulebamde Tqvi, ramdeni darCa?amdenad, msgavsi saxis zepiri savarjiSoebis Sesruleba xelsSeuwyobs moswavleebs ukeT Seiswavlon programuli masalamaTematikaSi, gzadagza moaxdinon misi ganmtkiceba. zepiriangariSis gamoyeneba uyalibebs maT keTil ganwyobas saswavloprocesisadmi. yovelive es xels uwyobs SemecnebiTi interesebisgazrdas.daskvenebi da rekomendaciebi:• gamokvlevebma gviCvena, dawyebiTi klasebis maTematikisgakveTilebze zepiri muSaoba umuSavebs moswavleebs gamoan-100

gariSebis martiv Cvevebs. umtkicebs Teoriul codnasariTmetikul gamosaxulebebze, maT Tvisebebze, tolobasa dautolobaze da sxva;• misi gamoyeneba uyalibebs moswavleebs keTil ganwyobassaswavlo procesisadmi. yovelive es xels uwyobs SemecnebiTiinteresebis gazrdas;• yuradReba unda mieqces imas, rom zepiri savarjiSoebisefeqturi gamoyenebisaTvis didi mniSvneloba aqvs misiadgilis gansazRvras gakveTilis msvlelobisas, sxvadsxvacnebisa Tu Cvevebis formirebisas. misi gamoyeneba uyalibebsmoswavleebs keTil ganwyobas saswavlo procesisadmi.yovelive es xels uwyobs SemecnebiTi interesebis gazrdas.$ 4. moswavleTa inteleqtualuri unar-CvevebisganmaviTarebel savarjiSoTa sistemamsoflio, Tanamedrove etapze araerTi problemis winaSe dgas.es im gardaqmnaTa procesebia, romelic moiTxovs pirovnebissrulyofil formirebas, RirebulebaTa gadafasebas, uaxlesorientirTa Tamam arCevans.es gvibiZgebs dawyebiTi klasebidanve warvmarToTmizanmimarTuli muSaoba moswavleTa inteleqtualuriSesaZleblobebis maqsimalurad warmosaCenad, ramac undagansazRvros momavali Taobis Semdgomi keTildReoba. esaucilebelia skolaSi Semosuli yvela bavSvisaTvis, gansakuTrebiTki skolisaTvis mzaobaSi Seferxebis mqone bavSvebTan. am sakiTxebzesakmao gamokvlevebi aqvs prof. i. ruxaZes. amdenad, moviyvan zogaddebulebebs da im savarjiSoebs, romlebic avtorTan SeTanxmebiTgamoviyeneT.Tanamedrove swavlebis mizania, zRva informaciis miRebis,misi kritikuli azrovnebis gamoyenebis unar-CvevaTa gamomuSaveba.swored amitom skolaSi prioritetul pozicias ikavebs101

ganmaviTarebeli swavleba, romelic elkonin-davidovisa dazankovis saswavlo sistemebiT xorcieldeba. ganviTarebisfsiqologiaSi am orma mimarTulebam, romlis avtorebi arian, erTismxriv d. b. elkonini, v. v. davidovi da meores mxriv l. v. zankovimisi mimdevrebiTurT, Tavis droze warmatebiT gansazRvra daCamoayaliba dawyebiTi ganaTlebis srulyofis strategia.elkoninisa da davidovis xelmZRvanelobiT Catarebulifsiqologiuri kvlevebi gamiznulia, upirveles yovlisa, saimisod,rom dadgindes, ra saxis fsiqologiuri axalwarmonaqmnebia maTiTeoriuli azrovneba. l. v. zankovisa da misi mimdevrebis Teoriisdidaqtikuri safuZvlebi ki ikvlevs ganmaviTarebeli swavlebisSinaarsis, formisa da meTodebis problemaTa gadaWris xerxebs.l. zankovis saswavlo sistemis Zireuli amocanaamoswavleebis zogadi ganviTareba, romelic gulisxmobs gonebis,nebisyofis, grZnobebis srulyofas. es ki Tavis mxriv, safuZveliamoswavleTa codnis da unar-Cvevebis aTvisebisa. aRniSnulisistemisaTvis damaxasiaTebelia Teoriuli codnis metad warmoCenada swavleba swrafi tempiT, maRal doneze.dRes udides mniSvnelobas iZens saswavlo masalisadmi iseTidamokidebuleba, roca es ukanaskneli moiazreba, rogorcinteleqtualuri ganviTarebis saSualeba.inteleqti `problemaTa Semecnebisa da gadaWris erT-erTiZiriTadi faqtoria, romelic gansazRvravs nebismieri saqmianobiswarmatebas da safuZvlad udevs pirovnebis unarianobas~ (9, gv. 139).naSromSi arsebiTad gamoiyeneba cneba ùnar-Cveva~. unar-Cvevafsiqologiur literaturaSi ganisazRvreba, rogorc `mzaobapraqtikuli da Teoriuli moqmedebebis SesrulebisTvis, romelicsruldeba swrafad, zustad da Segnebulad, SeZenili codnisa dacxovrebiseuli gamocdilebis safuZvelze~ (9, gv. 346).n. a. menCinskaiasa da n. d. bogoiavlenskis SromebSi - `swavlisproblemebi da moswavlis gonebrivi ganviTareba~, `codnisganviTarebis fsiqologia skolaSi~ - saazrovno saqmianoba102

ganixileba, rogorc mravalwaxnagovani movlena, romelic Sedgeba e.w. `Sreebisagan~ - codnisa da unar-Cvevebisagan. codna, TavisiarsiT, warmoadgens azrovnebis zedapirul Sres; gacilebiTsiRrmiseul Sres ki ganekuTvneba saswavlo saqmianobis mravalgvarixerxi, igive saazrovno operaciebis Sesrulebis unarebi. saswvlosaqmianobis pirvel etapze saazrovno operaciebi erwymian saswavlomasalis aRqmisa da damaxsovrebis process. Semgdom etapzegonebrivi operaciebiT xorcieldeba sakuTriv saazrovno aqtivoba.am mkvlevarTa mier dadgenilia, rom inteleqtualuriunarebis warmatebuli daufleba damokidebulia saazrovnioperaciebis (sinTezi, analizi, abstragireba da a. S.) formirebisxarisxisa da ganzogadebis doneze, romelTa meSveobiTacxorcieldeba codnis aTviseba da Semecneba.inteleqtualuri unar-Cvevebis formirebis n. a. menCiskaiasa dad. n. bogoiavlenskiseul koncefcias aviTarebs e. n. kabanovamileri,ganixilavs ra moswavleTa zogadinteleqtualur unar-Cvevebs,rogorc gonebrivi aqtivobis saSualebas da saswavlo procesissafuZvels, romelic gamoiyeneba umcroslkaselTa sxvadaxvasaswavlo aqtivobis sferoSi, sxvadasxva Sinaarsobrivi datvirTviT.ìnteleqrualur unar-CvevaTa~ cnebasTan azrobrivad axlosdgas Tanamedrove didaqtikis mier aRiarebuli cnebac`zogadsaswavlo unar-Cvevebi~, anu is unarebi, romliTacvsargeblobT, rogorc konkretuli saswavlo sagnebis swavlebisasskolaSi, ise yoveldRiur cxovrebaSi.zogadinteleqrualuri unar-Cvevebi (iseve, rogorczogadsaswavlo unar-Cvevebi) skolis moswavleebSi yalibdebanebismieri saswavlo sagnis Seswavlisas. TiToeul sagans Tavisiwvlili Seaqvs saswavlo procesSi, romelic ganpirobebulia,rogorc ama Tu im mecnierebis, ise uSualod saskolo sagnisspecifikurobiT, Sinaarsobrivi xasiaTiTa da misi SeswavlismeTodebiT.103

am mxriv udidesi SesaZleblobebi gaaCnia maTematikas.Tanamedrove codnaTa struqturaSi maTematika ikavebs gamorCeuladgils. mis specifikurobasa da Taviseburebebs xazs usvams bevrigamoCenili maTematikosi: d. poia, a. n. kolmogorovi, g. v. dorofeevida sxva.Cveni meTodikuri sistemis Teoriuli sayrdenia inteleqtismodelebi. kerZod, l. terstoniseuli inteleqtismravalfaqtoruli modeli gamoviyeneT umcrosklaselTainteleqtualuri unarebis Camosayalibebeli rogorc programis, isemeTodikis pirvelwyarod, xolo d. gilfordiseuli inteleqtismodeli ki gaxldaT umcrosklaselTa inteleqtualuri aqtivobisorganizaciis ZiriTadi orientiri.Cven SevimuSaveT umcrosklaselTa unarebis ganviTarebisprograma da gamoikveTa is sawyisebi, rac eqvemdebareba mecnieruldakvirvebebsa da Sefasebas. magaliTad, testirebis an droisromelime monakveTSi mimdinare Semowmebaze dakvirvebis Sedegad,maswavleblisaTvis advilia Tvalyuris midevneba logikuri,gamoTvliTi, verbaluri da sxva inteleqtualuri unarebisganviTarebis doneTa mimarT.inteleqtualuri unarebis ganviTarebis programa uTuoddaexmareba maswavlebels zustad da Segnebulad SeafasosmoswavleTa zogadinteleqtualuri ganviTareba. informaciisdamuSaveba, iseve rogorc, sazogadod, nayofieri gonebrivi muSaobaSeuZlebelia, Tu ki adamians ar aqvs ganviTarebuli azrovneba:logikuri azrovneba; algoriTmis zusti da sruli Sesrulebisa daalgoriTmis Camoyalibebis unar-Cvevebi; abstraqtuli daspecialuri Sinaarsis mqone testis wakiTxva-gaazrebis, teqstisCamoyalibebis, sakuTari azrebis gamarTulad, Tanmimdevrulad dadalagebulad gadmocemis, argumentebis, azrovnebis kritikulianalizisa da sinTezis, daxarisxeba – dajgufebisa da ganzogadebisunarebi da a. S. yovelive amas SeiZleba vuwodoT zogadi saazrovnoda verbaluri (enobrivi) unarebi.104

dawyebiT skolaSi inteleqtualuri unarebi undawarmoadgendes gansakuTrebulad specialuri swavlebisa dayuradRebis sagans, radganac saskolo swavlebis gamocdilebisTanaxmad, isini spontanurad ar viTardebian.dawyebiT klasebSi maTematikis swavlebis Cvens mierSemoTavazebuli meToduri sistema iTvaliswinebs:• umcrosklaselebis pirveldawyebiTi ricxviTiganswavlulobis Camoyalibebas, ganpirobebulssaxelmwifo saganmanaTleblo standartiTa da saswavloprogramiT;• saazrovno unar-Cvevebis ganviTarebas, romelicgamsazRvravs moswavleTa gonebriv potencialsdawyebiTi skolis damTavrebis Semdeg;• moswavleTa inteleqtualur aqtivobasa da winsvlas,rogorc garemomcvel samyarosTan SesabamisiurTierTdamokide-bulebis, socialuri gamocdilebisSeZenis umTavres pirobas.umcrosklaselTa inteleqrualuri SesaZleblobebisformireba Sinaarsobrivad emyareba ariTmetikul, algebrul,geometriul masalas, agreTve inteleqtualuri unar-CvevebisganmaviTarebel davalebebsa da savarjiSoebs. ariTmetikuli,algebruli da geometriuli – e. w. `sameuli~ gvevlinebamaTematikuri Sinaarsobrivi kursis ZiriTad matareblad, radganacmaTi saSualebiT ganisazRvreba Sesaswavli masalebis, Temebisa dasakiTxebis moculoba.amdenad, sworad SerCeuli davlebebis sistematuri gamoyenebagamiznulia bavSvis inteleqtualuri aqtivobisa da unar-CvevebisgansaviTareblad. am saxis davalebaTa Sesruleba moiTxovsganuwyvetliv Zalisxmevas, codnaTa srulyofas, inteleqtualursimwifes. amgvari davalebis SesarulebiT moswavleebi euflebianinteleqtualur xerxebs, rogorc Semecnebis gansazRvrul105

meTodebs, Rrmad acnobiereben SeZenil codnas, mis gamoyenebiTsa dapraqtikul Rirebulebas.maTematikis swavlebis procesSi mizanSewonilia, masalaSeirCes im saxiT, romelic maqsimalurad uzrunvelyofs TiToeulimoswavlis aqtiurobas yovel gakveTilze. am mxriv prioriteti undamieniWos moswavleTa praqtikul saqmianobas. aseTi midgomisaucilebloba gamomdinareobs umcrosklaselTa fsiqologiuriTaviseburebebidan. bevr maTgans ar ZaluZs aiTvisos axali codnamxolod maswavleblis monayoliT, naCvenebiTa da miTiTebebiT.calkeul moswavleTa CamorCena, rasac maswavlebeli xsnisganviTarebaSi SeferxebiT, xSirad gamowveulia imiT, rom sakmaodcudad aris organizebuli bavSvis praqtikuli aqtivobisganviTareba. maTematikis swavlebis procesSi arsebobs sxvadasxvasaSualebebi am problemis gadasaWrelad. saamisod mizanSewoniliagamoviyenoT mravalricxovani savarjiSo da praqtikuli davalebebi– kostruireba, xatva, gaferadeba, geometriuli figurebis gamoWrada a.S.maTematikis swavlebis nebismier konkretul etapzesavarjiSoTa sistema swavlebis is aucilebeli saSualebaa, romlisgareSec SeuZlebelia umcrosklaselTa mier saprogramo masalissaTando doneze daufleba, amasTan maTi yovelmxrivi aRzrda daganviTareba.miznobrivad da gegmazomierad Sedgenil savarjiSoebzebevradaa damokidebuli ara mxolod maTematikis swavlebis efeqtida moswavleTa Sesabamisi aRzrda-ganviTareba, aramed swavlebisSemdgomi safexurisaTvis umcrosklaselTa praqtikuli momzadeba,SeZenili codnis gamoyenebis unari.maTematikis tradiciuli dawyebiTi kursis SinaarsissaZirkvels Seadgens sami umTavresi Sinaarsobriv-meTodurimimarTuleba: ariTmetikuli, anu mTeli arauaryofiTi ricxvebisa daZiriTadi sidideebis ariTmetika; algebruli da geometriuli. amsami ZiriTadi mimarTulebis meSveobiT warmodgenilia sakuTriv106

dawyebiTi kursis maTematikis Sinaarsi. isini gansazRvravenSesaswavli sakiTxebis moculobas da Sesabamisad, savarjiSoebs,romlebic uzrunvelyofen ariTmetikuli sakiTxebis, agreTvealgebrisa da geometriis elementebis aTvisebas moswavleTa mier.aqve aqtiuri da efeqturi pirobebis Sesaqmnelad mizanSewonilia,meoTxe mimarTulebis inteleqtualuri savarjiSoebis gamoyeneba.eseni yvela erTad qmnian araordinalur savarjiSoTa sistemas,romelic mTliand mimarTulia umcrosklaselTa inteleqtualuriunar-Cvevebis gasaviTareblad.inteleqtualuri unar-Cvevebis ganviTareba ar aris swavlebismxolod Tanamedrove Sedegi, aramed piriqiT, saskolo saqmianobissawyis safexurze moswavleTa aRzrda-ganviTarebis erTob mTavaramocanad gvevlineba. amis dasturia is, rom mxolodinteleqtualur savarjiSoTa Taviseburebaa rogorc sakuTrivmaTematikuri masalis efeqturi gamoyeneba, ise umcrosklaselTaSemdgomi inteleqtualuri simwifisaTvis xelsayreli pirobebisSeqmna.inteleqtualuri unar-Cvevebis gasaviTrebeli savarjiSoebitradiciuli swavlebisagan gamocalkavebuli ki ar aris, aramedfriad sasikeTod zemoqmedebs, rogorc TviT saprogramo masalisaTvisebis dinamikaze, ise saazrovno procesebis aqtiurganviTarebaze.umcrosklaselTa inteleqtualuri simwifis mastimulirebelisavarjiSoTa sistemis struqtura, Seicavs savarjiSoTa ramdenimearsebiT qvesistemas, esenia:1. inteleqtualuri unar-Cvevebis ganviTarebismastimulirebeli gamoTvliTi xasiaTis savarjiSoTasistema;2. logikuri unar-Cvevebis ganmaviTarebel savarjiSoTasistema;3. sivrciTi azrovnebis ganmaviTarebel savarjiSoTasistema;107

4. verbaluri unar-Cvevebis ganmaviTarebel savarjiSoTasistema;adaptaciuri unar-Cvevebis ganmaviTarebel savarjiSoTasistema qvesistemad aRar gamovacalkeveT, vinaidan zemoTCamoTvlili oTxidan, TiToeuli qvesistemis savarjiSo,garkveulwilad, ayalibebs umcrosklaselTa adaptaciur unar-Cvevebsac.I. inteleqtualuri da gamoTvliTi unar-Cvevebis ganmaviTarebeli savarjiSoTasistema.inteleqtualuri da gamoTvliTi unar-Cvevebis ganviTarebisefeqturi saSualebaa kanonzomierebaTa gansazRvra, romlismixedviTac Sedgenilia mocemul ricxvTa mimdevrobebi.am saxis savarjiSoTa didi raodenoba eyrdnoba Sekrebas,gamoklebas, gamravlebasa da gayofas. yvelaze Zneli probleba,romelsac awydeba moswavle am amocanaTa amoxsnisas, mdgomareobsimaSi, Tu rogor gansazRvros swori pasuxis misagnebikanonzomiereba.sawyis etapze mizanSewonilia mzaobaSi Seferxebis mqonemoswavleebs SevTavzoT yvelaze martivi savarjiSoebi:I savarjiSo: mocemulia ricxvTa mimdevroba: 1, 3, 5, 7, ?kiTxvis niSnis magivrad CawereT saTando ricxvi.am davalebis pasuxi ar uWirT moswavleebs, vinaidan adviladamCneven, rom ricxvTa mocemul mimdevrobaSi yoveli momdevniricxvi oriT metia mis win mgomze.II savarjiSo: mocemulia ricxvTa mimdevroba: 2, 5, 8, 11 ?kiTxvis niSnis nacvlad CawereT saTanado ricxvi.108

moswavleebi amjerad advilad arkveven, rom ricxvebi izrdebasam-samis mimdevrobiT da amitom pasuxia – 14. dasabuTebaSemdegnairia:TiToeul ricxvs akldeba mis winamdgomi. sxvaoba yvelgansamia, e.i. swori pasuxia – 14. es kaninzomiereba erTnairad adviliadasadgenad rogorc mocemuli rixvTa mimdevrobis, iseukumimdevrobiT angariSisas.III savarjiSo: mocemulia ricxvTa mimdevroba: 1, 2, 3, 6, 4,5. am mimdevrobaSi romeli ricxvi arRvevskanonzomierebas?bavSvebi advilad xvdebian, rom es ricxvi aris 6, radganmimdevroba zrdadobis mixedviTaa dalagebuli da mxolod 6arRvevs maT rigs.mimdevrobaTa ganxilvis Semdeg, romlebic warmoadgenenariTmetikul an geometriul progresebs (dawyebiT klasebSi, raTqma unda, es terminebi ar fiqsirdeba) mizanSewonilia ufrorTuli savarjiSoebis SeTavazeba.IV savarjiSo: mocemulia ricxvTa mimdevroba: 2, 3, 5, 8, 9, 11,14. romeli wesis dacviT aris Sedgenili ricxvTa aseTimimdevroba?xSirad mimdevrobis wevrTa warmoqmnis kanonzomierebisSemCneva sakmaod rTulia. ricxvebi izrdeba, magram rogor? aseTSemTxvevaSi maswavlebeli ganmartavs, rom xandaxan ricxvebismimdevroba Cndeba ara romelime erTi da igive ariTmetikulioperaciis SesrulebiT, aramed raime Sablonis meSveobiT. amasTanrTuli savarjiSoebis (testebis) Sedgenisas iyeneben gansxvavebulSablonebs. zemoT miTiTebul ricxvTa warmoqmnis kanonzomierebasmoswavleebi angariSoben Semdegnairad: 3-2=1; 5-3=2; 8-5=3 da a.S.angariSisas SesamCnevi xdeba, rom mimdevrobis yoveli momdevnowevris misaRebad yovel win mdgom ricxvs jer mivumatoT 1, Semdeg2; 3 da a.S.. am msjelobis mixedviT SeiZleba gakeTdes aseTi naxazi:+? +? +? +? +? +?2 3 5 8 9 11 14109

omlic Sevsebisas miiRebs Semdeg saxes:2 3 5 8 9 11 14.savarjiSoTa Semdeg jgufSi Segvxvdeba iseTi amocanebi,romlebic mxolod Tvalis erTi gadavlebiT Tu gamoiyureba,rogorc maTematikuri, sinamdvileSi, arsiT sulac ar aris aseTi.nimuSad gamoviyvanT Semdeg amocanas: ori bavSvi xatvis wrezedadis. TiToeuli, naxatis daxatvas mounda sami saaTi. sulramdeni saaTi xatavda orive?erTi SexedviT es umartivesi ariTmetikuli amocanaaumcrosklaselTaTvis. arsebiTad SeumCnevelia dagebuli `maxe~analogiur amocanebSi, amitom Cveulebriv iwyeben amoxsnas, aradasaangariSo am davalebaSi araferia, saWiroa mxolod naTqvamisgaazreba.+1 +2 +3 +1 +2 +3aseT SemTxvevaSi maswavlebeli ganmartavs, rom amocaniTsulac ar aris aucilebeli Semowmdes maTematikuri codna.savsebiT SesaZlebelia, rom amocana sruliad sxva saazrovnounarebis Sesamowmeblad iyos gamiznuli.II.logikuri unar-Cvevebis ganmaviTarebelisavarjiSoTa sistema.inteleqtis warmatebuli formireba bevradaa damokidebuliganviTarebul logikur azrovnebaze, amitom umcrosklaselTainteleqtualuri unar-Cvevebis Camosayalibebel amocanaTa sistemaSiCvens mier Setanil iqna logikuri amocanebi.110

aseTi amocanebi aviTarebs logikur azrovnebas, masSiigulisxmeba: dakvirvebis, Sedareba-Sepirispirebis, klasificirebis,informaciis analizisa da sinTezis, kanonzomierebaTa da arsebiTTvisebaTa gamovlenis, daskvnebis, umartives ganzogadebaTagamotanis unarebi. es amocanebi garkveul wilad siuJeturixasiaTisaa. xSirad masSi isaxeba yoveldRiuri cxovrebis realurisituaciebi. erTi SexedviT, erTmaneTTan TiTqmis arafriTdakavSirebul garemoebaTa Sesaxeb, rigi gamoTqmuli azrebiTa dalogikuri daskvnebis meSveobiT, SesaZlebeli xdeba yvelaaucilebeli cnobis dadgena.bevr bavSvs uZneldeba logikur amocanaTa amoxsna, TumcaxSirad am amocanaTa formulireba sakmaod martivi daerTsaxovania, xolo amocana ar iTxovs gansakuTrebul specialurcodnas. ganvixiloT Sesabamisi amocanebi:I amocana: Tu ki skolaSi gogona ufro gvian mivida, vidrebuWuna, maSin biWuna ufro . . . . . . misula, vidre gogona.moswavle valdebulia gamotovebul adgilze Casvas is sityva,romelic amocanas Seesabameba da kanonzomierebas ar daarRvevs.amisaTvis pirobis gaazreba saWiroa, radgan Sedareba-SepirispirebasTan gvaqvs saqme da aq gamogvadgeba sityva àdre~.II amocana: qveviT Casvlisas lifti romel sarTuls ufromale gaivlis, mexuTes Tu meTerTmetes? ramdeni sarTulia maTSoris?elementarul dakvirvebasTan gvaqvs saqme, aTvla zemodanqvemoT unda vawarmooT. Tu ki TerTmetidan qvemoT daviTvliT,TerTmeti axloa, vidre xuTi, sarTulebs Soris sxvaoba, ki 11-5=6.maT Soris yofila 6 sarTuli.III amocana: baia da isaki krefdnen sokoebs. erTi agrovebdaqamas, meore ki – TeTras. romel sokos krefda baia, Tu isakimSeagrova qama?111

es cnobebi gamiznulia situaciaSi gasarkvevad, konkretuladimis gansasazRvrad, rom Tu isakim Seagrova qama, maSin baiaSeagrovebda TeTras.IV amocana: liam, gogim da Temurma sxvadsxvagvarad gaatareskvira dRe. arTi iyo cirkSi, meore – TeatrSi, mesame – fexburTze.viciT, rom gogi fexburTis matCs daeswro, Temuri ar yofilacirkSi, gamoarkvieT vin sad iyo?mocemuli amocanis piroba mizanSewonilia warmovadginoTgrafikulad Semdegi saxiT.lgTcTfes monacemebi saSualebas gvaZlevs davaskvnaT, rom gogi iyofexbuTze, lia cirkSi, xolo Temuri TetrSi.V amocana: levani iraklize maRalia, irakli - giorgizemaRali. vin aris yvelaze maRali?es amocana am obieqtebis Sedareba-Sepirispirebis saSualebasiZleva. ase magaliTad: TeTri lenti cisferze viwroa, cisferi –wiTelze, romeli lentia yvelaze farTo?maRalilevaniirakligiorgidabalilevani iraklize maRalia miuTiTebs imas, rom sqemis saTaveSiunda moeqces levani, mis qvemoT – irakli. igive amocanis meorepiroba gvkarnaxobs – irakli maRalia giorgize – gvakarnaxobs imas,rom sqemaSi giorgi eqceva yvelaze qvemoT.112

mocemuli sqemis Sedgena bavSvebs exmareba amocanis sivrceSiwarmodgenaSi. amitom garda logikuri unarisa, mxgavsi amocanebigarkveulwilad xels uwyobs moswavleTa sivrciTi warmodgenebisganviTarebas.VI amocana: givi, goCa, zaza da kaxa gatacebuli arian sportissxvadsxva saxeobiT: erTi – curviT, meore - CogburTiT, mesame –fexburTiT, meTxe – WidaobiT. vin romeli sportis saxeobiT arisdakavebuli, Tu zaza da kaxa ar arian moWidaveebi, kaxa arcmcuravia, givi ki CogburTelia?aqac naxazis saxiT SegviZlia advilad gaverkveT situaciaSi:curva CogbuTi fexburTi Widaobagivi - + - -goCa - - - +kaxa - - + -zaza + - - -VII amocana: badri da rati erTdroulad gamovidnenTbilisidan quTaisis mimarTulebiT. ori saaTis Semdeg badri iyoquTaisTan ufro axlos, vidre rati, vin ufro swrafad moZraobda?msgavsi amocanebis amoxsnisas aseve mizanSewoniliagarfikuli sistematizatorebis gamoyeneba.ratiTbilisibadriquTaisiVIII amocana: sinze devs vaSli, msxali da komSi. raTanmimdevrobiT SegviZlia aviRoT xili. CamoTvaleT yvelaSemTxveva.rogorc cnobilia, kombinatorul amocanaSi laparakiaelementebis ama Tu im kombinaciebze, romlis elementebis113

ganlagebaze, wyobaze, qvesimravleTa Sedgenaze, namravlis wesisgamoyenebaze.III sivrciTi azrovnebis gasaviTarebeli savarjiSoebissistemasivrciTi azrovnebis amosavalia obieqtTa feris, sididisa daformis aRqma. figurebis Sedareba feris, formisa da sididismixedviT.I savarjiSo: ra aqvT figuraTa wyvilebs erTnairi?gansxvavebuli?II savarjiSo: ra Seicvala am naxatze?meore da masame naxati miRebulia Semobrunebis Sedegad,meoTxe ki – gadabrunebulia.III savarjiSo: ra cvlilebebs amCnebT naxatze?figuris struqturis cvlilebis SemCneva, gamowveulia misielementebis raodenobis gazrdiT, Cveulebriv ar uWirTmoswavleebs da xalisiTac asruleben aseT davalebebs.114

IV savarjiSo: romeli figuraa naxazze zedmeti?V savarjiSo: romeli naxatia zedmeti?moswavleebi SeniSnaven, rom zedmetia pirveli naxati,ramdenadac is Sedgeba sami gansxvavebuli figurisagan,darCenilebi ki Seicavs or-or erTnair figuras.IV verbalur unar-CvevaTa ganmaviTarebel savarjiSoTasistemamaTematikis swavlebis nebismier konkretul etapzesavarjiSoTa sistema is aucilebeli saSualebaa, romlis gareSeSeuZlebelia umcrosklaselTa mier saprogramo masalis saTanadodaufleba, amasTan misi yovelmxrivi aRzrda da ganaTleba.mizanmimarTulad da gegmazomierad Sedgenil savarjiSoebzebevradaa damokidebuli ara mxolod maTematikis swavlebis efeqtida moswavleTa Sesabamisi swavla-ganaTleba, aramed swavlebisSemdgomi safexurisaTvis umcrosklaselTa praqtikuli momzadeba,SeZenili codnis gamoyenebis unari.115

verbaluri unar-Cvevebis gasaviTarebeli savarjiSoebi friadsasargeblod moqmedebs rogorc saprogramo masalis aTvisebisdinamikaze, ise saazrovno procesebis aqtiur ganviTarebaze.umcrosklaselTa inteleqtualuri simwifis mastimulirebelsavarjiSoTa sistemaSi verbalur unar-Cvevebs erT-erTi sainteresoadgili uWiravs.pedagogikaSi damkvidrebulia ramdenadme mcdari azri, romverbaluri unar-Cvevebi ueWvelad unda ganviTardes mxolod damxolod mSobliuri enis gakveTilebze. wera-kiTxvis,zepirimetyvelebisa da mosmenis unar-CvevaTa daufleba (Seswavla)SesaZlebelia da unda xdebodes kidec nebismieri sagnis swavlebisprocesSi, maT Soris maTematikis gakveTilebzec. saskolomaTematikuri ena gamoirCeva, rogorc azrovnebisa da Tanamedrovemetyvelebis kulturis elementebis ganmaviTarebeli saSualeba.cnobilia, rom sityvebi erTmaneTs ukavSirdebianmravalgvarad. verbaluri unar-Cvevebis gansaviTareblad gamoiyenebasityvieri amocanebi, anu amocanebi sityvebs Soris urTierTkavSirisyvelaze metad gavrcelebuli saxeebis Sesaxeb. maTi dawyvilebaSinaarsis, formis, aso-bgeriTi Sedgenilobis msgavseba-gansvavebaTaSesabamisad da a.S.Tavdapirvelad ganvixilav sinonimebisa da antonimebismagaliTebs. rogorc cnobilia, sinonimebad iTvleba sityvebi,romlebic Seadgenen sityvaTa erTi da igive Sinaarsobriv-Tematurjgufs, anu erTmaneTisagan formiT, bgeriTi SedgenilobiTgansxvavebulsa da mniSvnelobiT msgavs sityvebs. sinonimuriwyvilebidan sxvadasxva konteqsti, rogorc wesi, ixdens sityvismxolod romelime konkretul niuanss, sityvaTa semantikiskonkretul efeqts. swored amiT aris ganpirobebuli sinonimTamonacvleoba ama Tu im konteqstSi. rac ufro met mewyvilesmouZebnian moswavleebi sityvebs, miT ufro mdidaria maTi leqsika.sinonimuri wyvilebis umartivesi nimuSebia: mamaci-guladi, moxucixandazmulida a. S. antonimebad iTvleba sityvebi, romlebic116

urTierTsawinarmdego Sinaarsobriv Tematur jgufs Seadgens, mag.:mamaci-mSiSara, moxuci-axalgazrda da a.S.savarjiSo #1: mocemulia sityvaTa sinonimuri wyvili: sworimarTali;qvemoT miTiTebuli CamonaTvalSi moZebeneT miTiTebuliwyvilis Sesabamisi sityvaTa wyvili:a) zRva – mdinare;b) sinaTle – sibnele;g) matyuara – cru;d) adre – gvian.moswavleebi roca daadgenen, rom es sityvebi mniSvnelobiTerTi da igivea, advilad miagneben analogiur wyvils: matyuara –cru.savarjiSo #2: mocemulia antonimTa wyvili: guladi - mSiSara.moZebneT qvemoT miTiTebul sityvaTa CamonaTvalSi analogiurimniSvnelobis sityvaTa wyvili:a) sasixarulo – mxiaruli;b) mze – mTvare;g) mware – tkbili;g) mziuri - Tbili.moswavleebi msjeloben ase: guladi da mSiSara is sityvebia,romlebic erTmaneTisagan gansxvavdeba mniSvnelobiT. amitom mesamewyvilSi mware – tkbili, sruliad gansxvavebuli mniSvnelobissityvebia da es aris swori pasuxic.klasifikaciis xerxebis safuZvelia saganTa niSan-TvisebisgamokveTa da maT Soris msgavseba-gansxvavebaTa dadgena.savarjiSo #3: mocemulia sityvaTa wyvili: yayaCo – RiRilo.qvemoT CamoTvlil sityvaTagan SearCieT mocemuli wyvilis msgavsisityvaTa wyvili:a) wyali – yinuli;b) wiTeli – cisferi;g) mze – mzesumzira;d) yvavili – mcenare.117

`yayaCo – RiRilo is sagnebia, romlebic miekuTvnebian erTi daigive saganTa simravles – yvavilebs. wyali – yinuli, mze –mzesumzira, yvavili – mcenare, eseni yvela gansxvavebul saganTasimravles ekuTvnis. mxolod wyvilSi wiTeli – cisferi,gaerTianebulia saganTa erTi simravlis, kerZod ferebiselementebi.gansxvavebuli zomis obieqtebis gamoyeneba iZleva nairgvariinteleqtualuri savarjiSos Sedgenis saSualebas. mag.: borcvi –mTa, qoxi – sasaxle, navi – gemi, yoveli maTgani erTidaigive klasisdidi da mcire elementebia, anu erTmaneTisagan mxolod zomiTgansxvavebulni.savarjiSo #5: mocemulia sityvaTa wyvili: navi – gemi. qvemoTCamoTvlili sityvebidan SearCieT miTiTebuli nimuSis msgavsi:a) ZaRli – lekvi;b) foToli – xe;g) beRura – xoxobi;d) xomaldi – ialqani.navi da gemi sxvadasxva zomis sazRvao gadaadgilebissaSualebaa, anu erTi da igive klasis sagnebia. foToli xismxolod nawilia, ialqani – xomaldisa, amdenad erTi klasissagnebad ver CavTvliT. rac Seexeba wyvils `ZaRli – lekvi~, aqdamokidebuleba zomis mixedviT ki ar aris, aramed zrdis mixedviT– lekvisagan izrdeba ZaRli. swori pasuxia: beRura – xoxobi;beRura patara zomis frinvelia, xoxobi ki – gacilebiT didizomisaa e.i. beRura da xoxobi erTi da igive klasis sxvadasxvazomis sagnebia.gamoTvliTi xasiaTis masala, ricxviTi saxeebi, amocanaTaamoxsnis logikuri xerxebi da meTodebi, simboluri, grafikuli TumSobliuri enis elementebi, rac maTematikis dawyebiTikursisaTvisaa saxasiaTo, upirvelesad warmoadgens mZlavrganmaviTarebel potencials, swored maTi saSualebiT xorcieldeba118

ara mxolod sakuTriv maTematikis an danarCeni saskolodisciplinebis Seswavla, aramed umcrosklaselTazogadinteleqtualuri unarebis formireba.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom sworad SerCeuli davalebebissistematiuri gamoyeneba gamiznulia bavSvis inteleqtualuriaqtivobisa da unar-Cvevebis gansaviTareblad;• inteleqtualuri unar-Cvevebis gansaviTrebeli savarjiSoebitradiciuli swavlebisagan gamocalkavebuli ki ar aris,aramed friad sasikeTod zemoqmedebs, rogorc TviTsaprogramo masalis aTvisebis dinamikaze, ise saazrovnoprocesebis aqtiur ganviTarebaze;• inteleqtis warmatebuli formireba bevradaa damokidebuliganviTarebul logikur azrovnebaze, amitom umcrosklaselTainteleqtualuri unar-Cvevebis ganviTarebaSi gansakuTrebuliadgili uWiravs logikur amocanebs;• gasaTvaliswinebelia, rom dawyebiTi klasebidanve undawarvmarToT mizanmimarTuli muSaoba moswavleTainteleqtualuri SesaZleblobebis maqsimaluradwarmosaCenad, romelic uTuod daexmareba maswavlebelszustad da Segnebulad Seafasos moswavleTazogadinteleqtualuri ganviTareba;• maTematikis swavlebis procesSi mizanSewonilia, masalaSeirCes im saxiT, romelic maqsimalurad uzrunvelyofsTiToeuli moswavlis aqtiurobas yovel gakveTilze;• kargi iqneba Tu amocanebs siuJeturi xasiaTi eqnebaT da masSiaisaxeba cxovrebis realuri situaciebi;119

$ 5. obieqturi Rirebulebis cnobierebis aRzrdamaTematikis gakveTilebzemozardis formirebis saqmeSi mravali biologiuri dasocialuri faqtori iRebs monawileobas, romlebic erTmaneTsganapirobeben. amave dros maT aqvT sakuTari bunebis Sesabamisikanonzomiereba.bavSvi garkveuli fsiqo-fizikuri SesaZleblobebisganviTarebis potenciuri monacemebiT ibadeba, xolo is, Tu rogoriSinaarsi eqneba am ganviTarebas, sad da rogor gamoiyenebspirovneba, es mTliand aRzrdazea damokidebuli.mozardis Segnebul moqalaqed aRzrdis erT-erTimniSvnelovani faqtoria obieqturi Rirebulebis cnobierebisaRzrda. sanam uSualod aRzrdaze daviwyebdeT saubars, undaSevniSnoT, rom obieqturi Rirebulebis wvdoma cnobierebisfunqciaa, romelic amave dros, exeba individis ara erT an ormxares, aramed mTel pirovnebas. misi momwifeba-ganviTarebac mTelipirovnebis ganviTarebaSi aisaxeba.am konkretul SemTxvevaSi, obieqturi Rirebulebiscnobierebis, rogorc aRzrdis obieqtis cnebaSi, vgulisxmob iseTtendenciebs, roca umcrosklaseli igebs obieqtur sinamdvileSiarsebuli sagnebisa da movlenebis obieqtur mniSvnelobas. e. i.axerxebs, sagnebi da movlenebi Seafasos ara mxolod imis mixedviT,Tu ra mniSvneloba aqvs misTvis, anu subieqturad, aramedobieqturadac.bavSvebSi, rogorc cnobilia, dominirebs subieqturiRirebuleba, magram, amave dros, TandaTanobiT iRviZebs daviTardeba obieqturi Rirebulebis wvdomis unaric. misiganviTarebisa da ganmtkicebisaTvis aucilebelia mivagnoT CvenTvissaintereso asakis moswavlis qcevis obieqturi RirebulebissafuZvlebs. dakvirvebebma im daskvnamde mimiyvana, rom erT-erT aseT120

safuZvels warmoadgens sagnis bunebidan gamomdinare obieqturiaucileblobis danaxva.skolaSi axlad Semosuli moswavleebi sagnidan Tumovlenidan gamomdinare obieqtur Rirebulebas ver xedaven anZnelad xedaven, xolo amis gareSe obieqturi Rirebulebis wvdomasda aRzrdasac ver SevZlebT. pirvelklaseli ika zaris darekvamdemidis gareT imitom, rom mas ase surs. baia zaris darekvis Semdegar Semodis gakveTilze, radgan mas TamaSi ar daumTavrebia. gia SuagakveTilze iwyebs Wama da a.S. isini ver igeben ratom unda adgnenfexze maswavleblis Semosvlis an gasvlis dros, ratom unda iaronskolaSi yoveldRe da sxva.sagnidan gamomdinare obieqturi aucileblobapirvelklaselma unda dainaxos empiriuli masalebidan, wignebidan,cxovrebis praqtikidan, saswavlo-saaRmzrdelo procesidan, raTaigrZnon, rom maTi survilebis Sesrulebas marto ufrosebi ki aruSlian xels, aramed TviT sagnebisa da movlenebis buneba. amiTbavSvi ecnoba obieqturi aucileblobis faqts. es ki Tavis mxrivdid gavlenas axdens mozardis ganviTarebaze.d. uznaZe bavSvis ganviTarebaSi udides mniSvnelobas aniWebsobieqturi Rirebulebis cnobierebis aRzrdas. bavSvis mierobieqturi Rirebulebis wvdoma, d. uznaZis Tanaxmad, niSnavs imisgacnobierebas, Tu ra mniSvneloba aqvs sagans TavisTavad, subieqtismoTxovnilebisa da interesebisagan damoukideblad; sagnisRirebulebis aseTi gancda warmoadgens subieqtis qcevismotivaciur safuZvels (d. uznaZe, 1967).S. CxartiSvili miuTiTebs, rom adamianis qceva SeiZlebamotivirebuli iyos rogorc subieqturi, aseve obieqturiRirebulebiT. pirvel SemTxvevaSi adamiani moqmedebs ise, rogorcmisTvis sasiamovno iqneba, meore SemTxvevaSi iTvaliswinebs Tavisiqcevis Sedegebis sazogadoebriv mniSvnelobas da sakuTarimomavlisaTvis mis Rirebulebas. S. CxartiSvilis Tanaxmad, pirvelSemTxvevaSi impulsur qcevasTan gvaqvs saqme da mis mamoZravebel121

wyaros, aqtualuri moTxovnilebis impulsi warmoadgens, meoreSemTxvevaSi ki, saqme gavqvs nebisyofiT warmarTul anu nebismierqcevasTan (S. CxartiSvili, 1958).yvela sagnis swavleba, sxva amocanebTan erTad, miznad undaisaxavdes moswavleebTan obieqturi Rirebulebis cnobierebisCamoyalibebas, romlis safuZvels warmoadgens sagnis bunebidangamomdinare obieqturi aucileblobis danaxva.maTematikis swavlebisas bavSvebs sakmaod umwifdebaT sagnisbunebidan gamomdinare obieqturi aucileblobis danaxvis unari.maswavleblis pirveli da Zneli samuSao is aris, rom bavSvsSeagnebinos erTeulis cneba, rom es erTia, es ki ori da a.S.ricxvis aRqmas Tavdapirvelad bavSvi iwyebs simravlis daTvliT,Semdeg sagnebi icvleba misi pirobiTi aRniSvnebiT (TiTebiT,CxirebiT, geometriuli figurebiT da a.S.). orive SemTxvevaSi isinifizikurad arsebuli sagnebia da arseboben neba-survilisagandamoukideblad, sagnis bunebidan gamomdinare aucileblobis gamo.metad sapasuxismgebloa cifris Caweris swavleba, radgancifris, rogorc ricxvis gamosaxvis simbolos SemoReba, arisaxali abstraqcia, is ukve sagnobrivi ar aris. siZnelis dasaZlevadsaWiroa miviyvanoT am simbolos SemoRebis obieqturaucileblobamde. amis miRweva migvaniSnebs imaze, rom bavSvi dgasobieqturi sinamdvilis gacnobis pirvel safexurze. amis SemdegsaangariSos, Cxirebisa da sxva sagnebis daxmarebiT adviladgaigeben, rom 1+1=2 da ara 3 da arc misi Cawera ar gauWirdebaT.msagavsi samuSaoebis gawevis Semdeg moswavleebs aRar uWirTiswavlon ricxvis Sedgeniloba, Tu davanaxebT mis aucileblobas.ricxvis Sedgeniloba unda vaswavloT ara ori Sesakrebis, aramedyvela SesaZlo Sesakrebis jamis saxiT. magaliTad, ricxvi 7-isSedgeniloba SeiZleba vaCvenoT Semdegnairad:122

6 5 4 3 2 171 2 3 4 5 6ricxvis Sedgenilobis damaxsovrebisaTvis saWiroamoswavleebs, gansakuTrebiT skolisaTvis mzaobaSi SeferxebismqoneT, davanaxoT misi obieqturi aucilebloba. es ki SesaniSnavadCans gamoklebis swavlebisas. magaliTad, Tu moswavles undaamoxsnas 7-5, mas 7-s davaSlevineb 5-sa da 2-is jamad, 5-is gamoklebaniSnavs, rom darCeba 2. Zalian moswonT Semdegi Sinaarsisdavalebebi: ramdeni unda gamovakloT 7-s, rom miviRoT 6. ramdeniunda daumatoT 3-s, rom miviRoT 7 da a.S. aseTi savarjiSoebiamtkicebs Teoriul codnas, romlebic yvela tipis bavSvisaTvisaris misaRebi da saxaliso.ricxvis Sedgenilobis codnis obieqturi Rirebulebiscnobierebis aRzrdasTan gvaqvs saqme, rodesac vaswavliT erTniSnaricxvebis Sekrebas aTeulze gadasvliT. magaliTad, 6+7. aq 7 undadaiSalos xelsayrel SesakrebTa jamad 7=4+3. es imitom, rom 6-saTamde Sesavsebad aklia 4. Canawers eqneba saxe:6+76+746+4=1010+3=13 an6+ 7 = 10 + 3 = 133ricxvis SedgenilobasTan erTad iswavleba Sekreba-gamoklebiskomponentebsa da Sedegs Soris damokidebuleba. misi obieqturiRirebuleba is aris, rom Seiqmneba xelsayreli niadagi gantolebisswavlebisaTvis. ucnobi komponentisaTvis misi asoiTi simbolikis123

gamoyeneba xels uwyobs moswavleebSi ganaviTaros abstraqtuliazrovneba.gantolebas Tavdapirvelad moswavleebi xsnian sinjvisxerxiT. es advili SesaZlebelia maSin, rodesac saqme gvaqvs mciresididis ricxvTan. magaliTad, X+5=7 an 8-X=6. magram rodesac saqmegvaqvs did ricxvebTan, obieqturi aucileblobaa vicodeTmoqmedebis komponentebsa da Sedegs Soris damokidebuleba, riTackidev erTxel mtkicdeba am sakiTxis codnis aucilebloba.vTqvaT, mocemulia gantoleba: 8+X=22 amoxsna warimarTebaSemdegnairad:- ra aris X gantolebSi?- ucnobi Sesakrebi.- rogor vipivoT ucnobi Sesakrebi?- jams gamovakloT cnobili Sesakrebi.- e. i. X=22-8- X=14msgavsad warimarTeba danarCen sam moqmedebaze gantolebisSeswavlisas obieqturi Rirebulebis cnobierebis wvdoma.sagnis bunebidan gamomdinare, obieqturi aucileblobisa daobieqturi Rirebulebis cnobierebis wvdomaze dayrdnobiT,maswavlebels aRar gauWirdeba aswavlos Tanrigebad daSla,cxriluri da aracxriluri gamravleba-gayofa da sxva.dawyebiT klasebSi obieqturi Rirebulebis cnobierebisaRzrdis sakiTxTa Soris erT-erTi gansakuTrebulia patarebSicodnis obieqturi Rirebulebis SemuSaveba. am mimarTulebiTmuSaoba arc ise Znelia, radgan bavSvi ukve ganicdisinteleqtualuri Zalebis amoqmedebis moTxovnilebas. ammoTxovnilebebis dakmayofilebis paralelurad maswavlebeli undaawarmoebdes codnis obieqturi Rirebulebis wvdomis gamomuSavebas.bavSvis Sinagani SesaZlebloba saSualebs gvaZlevs, raRacSeiTvisos. Cven unda SevcvaloT SesaTvisebeli masala SinaarsiTa124

da saswavlo-saaRmzrdelo procesiT ise, rom bavSvs umuSavebdescodnis obieqtur Rirebulebas. es dagvexmareba SevagnebinoT mas,Tu ra mniSvneloba aqvs codnas da swavlas, amisaTvis saWiroasaswavlo procesi avagoT bavSvTa interesebis Sesabamisad.kargi iqneba Tu yoveli gakveTilis bolos, dainteresebismizniT daigegmos 4-5 wuTiani `sazrianTa 5 wuTi~, romelSicgamoyenebuli iqneba Semdegi Sinaarsis savarjiSoebi:1. wertilebis nacvlad CasviT saWiro ricxvi.10 =. . . + 4 6 =. . . + 4 . . . – 5 = 18 = 5 + . . . 9 - . . .= 4 . . . + 3 = 52. daakvirdiT da aRadgineT gamotovebuli ricxvebi.8+ = 10 + = 1443. SeamowmeT gantolebis amoxsna da axseniT Secdomis mizezi.15 – X = 5 X – 8 = 12 X + 5 = 14X = 15 – 5 X = 12 – 8 X = 14 + 5X = 10 X = 4 X = 194. ganixileT gantolebebi, gaarkvieT ras warmoadgens ucnobigantolebaSi da CawereT gamotovebuli moqmedebis niSani.X * 2 = 10 X * 7 = 10X = 10 : 2 X = 10 + 75. oTx Zmas hyavs TiTo da. ramdeni bavSvia sul ojaxSi?6. ramdeni samkuTxedia aq?125

moyvanili magaliTebidan yvela ar Seefereba pirvel klass,magram es imisaTvis, rom maswavlebelma icodes, ra unda gaakeTosSemdeg klasSi. zemoT mocemulma praqtikulma samuSaom gviCvena,rom am procesSi umcrosklaselebi da gansakuTrebiT mzaobaSiCamorCenis mqoneni, swvdebian Sesaswavl maTematikur masalaTaobieqtur Rirebulebas, rac motivaciur rols asrulebs maT mieram saswavlo disciplinis dauflebaSi.daskvnebi da rekomendaciebi:• gamokvlevebma gviCvena, rom bavSvi garkveuli fsiqofizikuriSesaZleblobebiT ibadeba, romelic undamomwifdes da ganviTardes misi bunebis Sesabamisiasakobrivi garemos kanonzomierebiT; yovel pataraSidominirebs subieqturi Rirebuleba, amave drosobieqturi Rirebulebis wvdomasTanac gvaqvs saqme;• obieqturi Rirebulebis wvdoma, niSnavs imisgacnobierebas, Tu ra mniSvneloba aqvs sagansTavisTavad, subieqtis moTxovnilebisa dainteresebisagan damoukideblad;• maTematikis swavlebisas bavSvebs sakmaod umwifdebaTsagnis bunebidan gamomdinare obieqturi aucileblobisdanaxvis unari, romelic didad exmareba moswavlesmasalis aTvisebaSi, mis ganmtkiceSi;• gasaTvaliswinebelia, rom skolaSi Semosvlisas bavSvidgas obieqturi sinamdvilis gacnobis pirvelsafexurze. amdenad, maswavlebeli yovelTvis undacdilobdes daanaxos bavSvs sagnis bunebidangamomdinare obieqturi aucilebloba, amiT masala ufromisawvdomi da dasamaxsovrebelia.126

Sedegebis damuSavebaTavdapirvelad pirvelklaselebTan gamokvlieT skolisaTvismzaoba e. varxotovas, n. diatkosa da e. sazanovis mierSemoTavazebuli meTodikiT, Sedegebi aseTia:cxrili #9skolisaTvis mzaobis kvlevis SedegebiCatarebis raodenoba ar aris TiTqmis mzad arisdromzad mzad aris2005w. 135 31.1% 21.3% 47,7%2006w. 152 28.3% 21.7% 48.7%Catarebuli gamokvlevis Semdeg kvleva-dakvirveba gavagrZeleTim cdis pirebTan, romlebic àr arian mzad~ skolisaTvis, anda`TiTqmis mzad arian~, 2005wels aseTi iyo 71 bavSvi, 2006wels – 78.maTTan SeviswavleT saswavlo unar-Cvevebi profesor nana carciZismeTodikiT. isini gavanawileT saeqsperimento da sakontrolojgufebSi. 2005 wels – eqsperimentul jgufSi – 47 moswavle,salontrolo jgufSi – 24, xolo 2006 wels – eqsperimentulSi – 53,sakoltroloSi – 25. Sedegebi aseTia:saswavlo unar-Cvevebis Sewavlis Sedegebipretesti / wlis dasawyisicxrili #10protesti / wlis bolodro jgufi cudi saSualozesaSualo kargi cudi saSualozesaSualo kargidabalidabalieqsp. 10,6 36,2 % 46,9% 6,3% 0% 25,5% 57,4% 17,1%2005w.%sak. 12,5% 33,3% 50% 4,2% 4,2% 29,2% 58,3% 8,3%eqsp. 11,3% 34,1% 47,1% 7,5% 0% 22,8% 58,4% 18,8%2006w. sak. 11,5% 34,7% 50% 3,8% 3,8% 30,8% 57,7% 7,7%AN127

ANam cxrilidan naTlad Cans, rom 2005 wels saeqsperimentojgufSi cudi maCveneblebis mqone bavSvebis raodenoba Semcirda100%-iT, saSualoze dabalis – 10,7%-iT; saSualo maCveneblis mqonebavSvebis raodenoba gaizarda 10,5%-iT, kargisa – 10,8%-iT.sakontrolo jgufSi cudi maCveneblebis mqone bavSvebis raodenobaSemcirda 8,3%-iT, saSualoze dabalisa – 4,1%-iT; saSualomaCveneblis mqone bavSvebis raodenoba gaizarda 8,3%-iT, xolokargisa – 4,2%-iT. 2006 wels saeqsperimento jgufSi cudimaCveneblebis mqone bavSvebis raodenoba Semcirda 100%-iT,saSualoze dabalisa – 11,8%-iT; saSualo maCveneblis mqonebavSvebis raodenoba gaizarda 11,3%-iT, xolo kargisa – 11,3%-iT.sakontrolo jgufSi cudi maCveneblebis mqone bavSvebis raodenobaSemcirda 7,7%-iT, saSualoze dabalisa – 3,9%-iT; saSualomaCveneblis mqone bavSvebis raodenoba gaizarda 7,7%-iT, xolokargisa – 3,9%-iT.M miRebuli Sedgebis siswore SevamowmeT stiudentiskriteriumiT, gamoviyene Semdegi formula:t =δ+ δM1− M− 2δ⋅δ2 2M1 M 2 M1M 22⋅rsadac, M1da M2aris qulaTa saSualo mniSvneloba pretestisada protestis dros, xolo δMda δ1Mstatistukuri Secdoma. isini2gamoiTvleba formuliT:= SMSMδ1N= M2M 2N,δ1sadac SMda S1 Maris saSualo standartuli gadaxra da2gamoiTvleba formuliT:128

SM 1=N∑i=12(X − M )iN −11SM 2=N∑i=1(y − M )iN −122xoloN∑ir =S= 1⋅Sr aris korelaciis koeficienti da gamoiTvleba:(X − y )iM 1 M 2i⋅ NgamoTvlebis Sedegebi aseTia:2005 weli M1=18,4, M2=21,5736,64593SM= = 16,01 = 4 S12,89 3, 61M= = =246464 43,6 3,6δM= = = 0,6δ0, 51 M= = =247 6,547 6,8r =− 70,54 ⋅3,6⋅ 47= −70,5676,8= −0,1saSualo maCveneblebs Soris gansxvavebaTa gansxvavebebisSesamowmeblad gamoyenebuli iqna stiudentis t kriteriumi:t =0,62+ 0,518,4 − 21,52− 2⋅0,6⋅0,5 ⋅ ( −0,1)=3,10,36 + 0,25 + 0,06=3,10,67=3,1= 3,870,82006 weli M1=19,2, M2=22,2652,42580,02SM= = 12,55 = 3,5 S11,15 3, 31 M= = =25252129

3,5 3,53,3 3,3δM= = = 0,5δ0, 51 M= = =253 7,353 7,3−160,1r = = −3,5 ⋅3,3⋅53160,5612,15= −0,3saSualo maCveneblebs Soris gansxvavebaTa gansxvavebebisSesamowmeblad gamoyenebuli iqna stiudentis t kriteriumi:t =0,52+ 0,519,2 − 22,22− 2 ⋅ 0,5 ⋅ 0,5 ⋅ ( −0,3)=30,25 + 0,25 + 0,15=30,65=30,8= 3,75Sedegebi SevitaneT cxrilSi:Catarebiswlebicxrili #11saSualo maCveneblebs Soris gansxvavebapretesti protesti stiudentis sandoobakriteriumiS t PM1SM12MM 22005 18,4 4,0 21,5 3,6 3,87 < 0,0012006 19,2 3,5 22,2 3,3 3,75 < 0,001cxrilidan Cans, rom wlis dasawyissa da wlis bolosmiRebul saSualo maCveneblebs Soris gansxvaveba statistikuradsandoa.Cven paralelurad davinteresdiT `piaJes fenomenis~arsebobiT, am mizniT SeviswavleT quTaisis sxvadasxva skolis 168pirvelklaseli. Sedegebi aseTia: raodenobis invarianTobasaRiarebs 29%, ar aRiarebas, anu `piaJes fenomeni~ dadasturda 71%-Tan. `piaJes fenomeni~-s koreqcias movaxdineT didaqtikuri TamaSiT.saxeldobr, SevimuSaveT didaqtikuri TamaSebis 4 seria,130

omelTaganac TiToeuli 5 cdas Seicavs. cdispirs utardeba erTerTiseriis 5 cda TanmimdevrobiT. seriebis Catarebis SemdeggavimeoreT sakontrolo cda. Catarebuli muSaobis Semdeginvariantobas aRiarebda 69% - ar aRiarebda 31%. didaqtikuriTamaSebis Catarebamde da Catarebis Semdeg mirebuli SedegebsSoris gansxvavebis Sesamowmeblad gamoviyeneT pirsoniskriteriumi (ix. cxrili #12):χ 2 =∑( ff21− f0)0sadac f 1aris miRebuli sixSire, xolo f0_ mosalodneli sixSirecxrili #12didaqtikuri TamaSis Catarebamde da Catarebis Semdeg miRebuliSedegebiaRiarebs ar aRiarebs χ 2pretesti 29% 71% 30,857 0.000protesti 69% 31% 17,633 0.000cxrilidan Cans, rom gansxvaveba statistikurad sandoa. es kiniSnavs, rom Cven mier SemuSavebuli didaqtikuri TamaSi uTuaodSeiZleba CaiTvalos `piaJes fanomenis~ koreqciis efeqtursaSualebad.pIII Tavis daskvnebi da rekolendaciebi• eqsperimentulma gamokvlevebma gviCvena, rom skolaSiSemosvlisas mzaobaSi Seferxebis mqone bavSvma icis 10-is farglebSi piradapiri Tvla, saganTa gansxvavebaformis mixedviT, uWirs ukuTvla Tvla, rac Seexebakviris dReebs, dRis nawilebs da transports romelicmidis saxlTan, romlebic emsaxureba sivrcesa daDdroSi131

orientaciis Sesawavlas, amaTze yovelTvis dadebiTpasuxs ver iZleva;• elementaruli maTematikuri codnis kvlevam gviCvena,raodenobis invariantobis wvdomis unaris Seswavlisaucilebloba. amisaTvis gamoviyeneT piaJes meTodi dadavadgineT: saswavlo wlis bolos raodenobisinvariantobis wvdomis unari hqonda 54,5%-s, ar hqonda –45,5%-s. amave dros baRSi, Sedegebi aseTi iyo:invariantoba aqvs – 8%-s, ar aqvs – 92%-s. amave wlisdasawyisisaTvis pirvelklaselebSi Sedegi aseTia:invariantoba aqvs - 29%-s, ar aqvs 71%-s. TiToeulSemTxvevaSi gamovyaviT 3 jgufi: I. bavSvebi, romlebicver axerxeben axsnas da duman; II. asabuTeben erTidetaliT; III. iZlevian srul argumentacias.• `piaJes fenimenis~ gamosworeba movaxdineT didaqtikuriTamaSiT, romelic aris saswavlo TamaSi, sadac bavSvieufleba garkveul codnas, iZens Cvevebs. mis gamoyenebaspedagogiur-fsiqologiuri TvalsazrisiT didimniSvneloba aqvs. Tu Tavdapirvelad raodenobisinvariantobis wvdomis unari qonda 29%-s, xolo arqonda 71%-s, didaqtikuri TamaSebis Semdeg invariantobaqonda 69% - ar qonda 31%.• garda didaqtiuri TamaSebisa Cven SevadgineTganmaviTarebel savarjiSoTa sistema, rogorc zepiriise inteleqtualuri da obieqturi Rirebulebis wvdomisunar-Cvevebis ganviTarebisaTvis. Catarebuli muSaobisanalizma gviCvena, Semdegi:a) dawyebiTi klasebis maTematikis gakveTilebze zepirimuSaoba umuSavebs moswavleebs gamoangariSebis martivCvevebs. unmtkicebs Teoriul codnas ariTmetikulgamosaxulebebze, maT Tvisebebze, tolobasa da132

utolobaze da sxva; misi gamoyeneba uyalibebsmoswavleebs keTil ganwyobas saswavlo procesisadmi.yovelive es xels uwyobs SemecnebiTi interesebisgazrdas;b) sworad SerCeuli davalebebis sistematiurigamoyeneba gamiznulia bavSvis inteleqtualuriaqtivobisa da unar-Cvevebis gansaviTareblad. essavarjiSoebi tradiciuli swavlebisagangamocalkavebuli ki ar aris, aramed friad sasikeTodzemoqmedebs, rogorc TviT saprogramo masalisaTvisebis dinamikaze, ise saazrovno procesebis aqtiurganviTarebaze;g) maTematikis swavlebisas bavSvebs sakmaodunvirTadebaT sagnis bunebidan gamomdinare obieqturiaucileblobis danaxvis unari. es kargad Canspraqtikuli muSaobiT. obieqturi sinamdviliscnobierebis wvdoma didad exmareba moswavles masalisaTvisebaSi, mis ganmtkicebaSi;• ganmaviTarebeli savarjiSoebis efeqturobisSemowmebis mizniT, ganmeorebiTi testireba Catardasaswavlo unar-Cvevebis kvlevis meTodiT da aRmoCnda,rom im bavSvebis raodenoba, romlebsac hqondaTSefaseba `kargi~ gaizrda _ 11,3%_iT da `saSualo~ _11,3%_iT; saSualoze dabali Semcirda _ 11,8%_iT, xolocudi _ 100%-iT.• gasaTvaliswinebelia, rom saswavlo procesisdagegmvisas maswavlebelma unda gaiTvaliswinosdidaqtikuri TamaSebi. maT SeuZliaT gamoiyenon Cvensmier Seqmnili didaqtikuri TamaSebis sistema an Seqmnandamoukideblad axali, mxolod gaiTvaliswinon, rom133

moswavleebi ufro kargad asruleben siuJeturdidaqtikur TamaSebs;• maTematikis swavlebis procesSi ganmaviTarebelsavrjiSoTa sistemis Seqmnisas mizanSewonilia, masalaSeirCes im saxiT, romelic maqsimalurad uzrunvelyofsTiToeuli moswavlis aqtiurobas yovel gakveTilze.kargi iqneba Tu amocanebi iqneba siuJeturi xasiaTis damasSi aisaxeba cxovrebis realuri situaciebi;134

ZiriTadi daskvnebi da rekomendaciebi• ganxorcielebuli kvlevis Sedegad dadgenili iqna faqtorebi,romlebic aferxeben pirvelklaselTa skolisaTvis mzaobas(kerZod: fizikuri, inteleqtualuri da socialuri) daSemuSavebuli iqna sxvadasxva saxis pedagogiuri pirobebi dasaSualebebi maTi daZlevisaTvis.• fsiqo-pedagogiuri mecnierebis miRwevebis da koreqciulganmaviTarebeliswavlebis kocefciebze darydnobiT,gamovlenilia da mecnierulad dasabuTebulia skolisaTvismzaobis ZiriTadi formebi: fizikuri, socialuri dainteleqtualuri. maTi gaTvaliswineba pirvelklaselTasaswavlo-aRmzrdelobiT procesSi, maswavlebels saSualebasaZlevs ufro efeqturad gadawyvitos pirvelklaselebisskolasTan adaptaciis amocana.• asakobriv normebTan fizikuri ganviTarebis tempisSeusabamoba saWiros xdis umcrosi klasebis moswavleTaidividualur-tipologiuri Taviseburebebis sistematiurSeswavlas, diagnostirebis Tanamedrove meTodebisYgamoyenebiT.• moswavleTa individualur Taviseburebebze dafuZnebulisaswavlo procesis organizeba SesaZlebelia diferenciaciisteqnologiebis gamoyenebiT, romlis mizansac Seadgensswavleba warimarTos TiToeuli moswavlis SesasZleblobisada ganviTarebis donis mixedviT. es xels Seuwyobsinteleqtualuri, emociur-RirebulebiTi da nebelobiTisferoebis ufro efeqtur ganviTarebas.• pirvelklaselebis mier maTematikuri savarjiSoebis daamocanebis amoxsna uviTarebs maT raodenobis invariantobiswvdomis unars.• maTematikaSi sworad SerCeuli saswavlo masala,savarjiSoebi, aviTarebs moswavleebis SemecnebiT interess,135

aaqtiurebs saazrovno operaciebis, rogorebicaa _ganzogadeba, Sedareba, abstrahireba; aviTarebs kreatiulimidgomis unar-Cvevebs sxvadasxva sirTulis amocanebisamoxsnis dros.• codna-warmodegenebis gazrda garemomcvel sagnebsa daralobaze, saswavlo TamaSebSi monawileoba aviTarebs daamdidrebs moswavleebis leqsikas, aviTarebs monologurmetyvelebas.• gasaTvaliswinebelia, rom saswavlo unar-CvevaTa kvlevismeTodi didad daexmareba maswavlebels individualurSesaZleblobaTa gaTvaliswinebiT sworad dagegmos saswavloprocesi da aamaRlos moswavleTa swavlebis done.• saswavlo procesis dagegmvisas maswavlebelma undagaiTvaliswinos didaqtikuri TamaSebi. maT SeuZliaTgamoiyenon Cven mier Seqmnili Tanamedrove didaqtikuriTamaSebis sistema an damoukideblad Seqmnan axali, mxolodgaiTvaliswinon, rom moswavleebi ufro kargad asrulebensiuJetur didaqtikur TamaSebs.• maTematikis swavlebis procesSi ganmaviTarebel savarjiSoTasistemis Seqmnisas mizanSewonilia masala SeirCes im saxiT,romelic maqsimalurad uzrunvelyofs TiToeuli moswavlisaqtiurobas yovel gakveTilze. Cven vTavazobT siuJeturixasiaTis iseTi TamaSebis gamoyenebas, sadac asaxuliacxovrebis realuri situaciebi.• dabali TviTSefasebis gamo skolamdel asakSi bavSvebixSirad swavlebis dros xvdebian CrdilSi. sakvalifikacionaSromSi maswavleblebs vTavazobT iseTi interaqtiuri dajgufuri meTodebis (didaqtikuri TamaSebi, gunduri muSaoba,ganmaviTrebeli swavleba d a.S.) gamoyenebas, romlebic didaduwyobs xels swored adekvaturi TviTSefasebis formirebas.136

• Cveni rekomendaciis mixedviT bavSvis individualuriTaviseburebebis Seswavla mSobelma unda scados jer kidevskolamdel asakSi da Cven mier SemoTavazebuli meTodikiTecados gamoasworos xarvezebi. mSoblebi da ojaxis wevrebiunda daexmaron bavSvs Tavis Tavze aiRos moswavlissocialuri roli. gansakuTrebuli yuradReba unda miaqcionbavSvis skolisaTvis momzadebas, ufrosebis mimarT bavSvisdamokidebulebas, maTi miTiTebebis mixedviT qmedebas. xeliSeuwyon bavSvs xSirad miiRos monawileoba gundur TamaSebSi.137

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danarTi #1skolaSi swavlebisaTvis mzadyofnis eqspresdiagnostika• sasaciloTia?1. ùazrobebi~.mizani: bavSvTan emociuri kontaqtis damyarebainstruqcia: bavSbvebsvaCveneb suraTs davebnebi: `naxeT, rogorinaxati maqvs~. isnaxulobs naxats, TuCumad aTvalierebs,an sulac ar reagirebs,maSin vaZlevdamaxmare kiTxvebs:• daaTvaliere suraTi?sura-• ratom aris sasacilo?• ra xatia arasworad?bavSvis qcevaSefasebaemiciurad aranairad ar reagirebs da molod CvenidaxmarebiT poulobs ùazrobebs~. Tavis gamoukideblobasarafriT gamoxatavs.reaqcia naklebad spontanuria, magramdamoukidebulad an cotaodeni daxmarebiT (1-2kiTxva) poulobs ùazrobebs~reagorebs cocxlad, uSialod, Cveni daxmarebisagreSe. eRimeba, icinis, advilad miuTiTeba yvelaùazrobebs~qula0 qula1 qula2 qula145

3. `Tanmimdevruli suraTebi~.mizani: mizez-Sedegobrivi kavSiris dadgenis unarisa da Txrobisdiagnostika.Sefasebainstruqcia: `me maqvsramdenime naxati, isiniareulia. daalage isiniSens win ise rogorcswori aris da Semdegam suraTebis mixedviTmogviyeviambavi~.Tu arRvevs Tanmimdevrobas, ar SeuZlia Secdomisgageba an TxrobaSi aris mxolod calkeulidetalebis aRwerauSvebs Secdomebs TanmimdevrobaSi, magram asworebs(TviTon an daxmarebiT) an Txroba uZneldeba dafragmentulia.alagebs TanmimdevrobiT damouikideblad, sworad,Tanmimdevrulad, logikurad. adgens moTxrobas.Sesabamisi0 qula1 qula2 qula8. `gasaRebebi~mizani: kanonzomierebis dadgenisa da gamoyenebis unarisdiagnostika.146

instruqcia: bavSvebs SevTavazeb furcels, romelzec daxatuliaramdenime gasaRebi da veubnebi: `Sexede, rogori gasaRebebi aris aqdaxatuli. xedav, isni sxvadasxvaa, magram maT Soris mainc arismsgavseba. dafiqrdi da gamoicani romeli gasaRebi ar arisbolomde daxatuli. Sen es gasaRebi unda daamTavro aq am anketaze~.SefasebaTu testirebis suraTze bavSvma arcerTi xaziar gaxaza sworad, ver moZebna msgavsebaTu testirebis suraTze 1 an 2 xazi maincgaavlo sworadTu 3 an 4 xazi gaavlo sworad0 qula1 qula2 qula9. `kiTxva~mizani: pedagogiuri aspeqti – asoebis codnis, kiTxvis unarisdiagnostika.instruqcia: bavSvs vekiTxebi icis Tu ara kiTxva. dadebiTi pasuxisSemTxvevaSi mivcem wasakiTx masalas (SeiZleba gamoviyenoT I klasiswigni an Sesabamisi zomis asoebiT dawerili nebismieri masala). Tuman kiTxva ar icis, SevTavazeb baraTs asoebiT da vTxovdaasaxelos isini.SefasebaTu bavSvma icis 10 asoze naklebiTu bavSvma 10 aso mainc da gviCvenebs masTu is kiTxulebs damarcvliT, gebulobswakiTxulsTu kiTxulobs gamarTulad, sityvebiT0 qula1 qula2 qula3 qula10. àdamianis daxatva~mizani: xatovani azrovnebisa da wvrili motorikis diagnostika.147

instruqcia: me bavSvs vaZlev mis anketas, vaCveneb adgilsdasaxatad da veubnebi: `gTxov, daxate aq adamiani~.SefasebaTu bavSvis naxati gavs #5-s an 6-sTu bavSvis naxati gavs #4-s an 3-sTu bavSvis naxati gavs #2-s an 1-s0 qula1 qula2 qulabavSvis Sefasebis anketas aqvs Semdegi saxe:bavSvis anketa #_______1. miTxari Seni saxeli da gvari__________________________________2. ramdeni wlis xar? _________________3. visTan erTad cxovrob? daasaxele Seni ojaxis wevrebi__________________________________________________________________4. sad cxovrob? miTxari Seni misamarTi__________________________________________________________________5. gyavs da an Zma? _____________________________________6. dedas ra hqvia? __________sad muSaobs? __________________________________________________mamas ra hqvia? ___________148

sad muSaobs? ____________________________________________________7. ginda skolaSi wasvla? _______ ratom? _________________________8. vin ginda gamoxvide? _______ ratom? ___________________________adgili bavSvis naxatisTvissubtestebitestirebis oqmi 0 1 2 31. Seusabamoba2. ariTmetikulsivrcobrivikarnaxi3. TanamimdevrulisuraTebi4. geometriulifigurebi5. analogiebi6. logopediurisubtesti1 2 34 5 67. akrZaluli1 2 3 4 5 6sityvebi 7 8 9 10 11 128. gasaRebi9. kiTxva,asoTa amocnoba10. adamianis naxati149

11. sityvebis SedgenaqulaTa jamitestis daskvna _______________________________________________________________________________________________________________________________saboloo daskvna _____________________________________________________________________________________________________________________________TariRi ________________fsiqologis saxeli, gvari _____________________________danarTi #2saswavlo unar-Cvevebis kvleva4. gamoicani ra aris daxatuli.Catarebis procedura: mebavSvs vuCveneb naxats,romelzecZaRliagamosaxuli,oRondaramTlianad, mxolodramodenime konturiT. bavSvmaunda gamoicnos ra arisnaxatze gamosaxuli.Sesrulebis dro – 20 wami.150

III. mexsiereba2. gamoicani ra daemata.Catarebis procedura: mebavSvs vuCveneb, suraTs.masze gamosaxulia: wigni,yvavili da manqana. vTavazobdaimaxsovros suraTze gamosaxulisagnebi. Semdeg amsuraTs viReb da bavSvs vaZlevsxva suraTs, sadac igivesagnebia gamosaxuli,oRonddamatebulia 3 axali sagnebic: naZvis xe, saswavlo CanTa daTojina. bavSvs veubnebi: `meore suraTze gamosaxulia igive sagnebi,rac wina suraTze iyo, Tumca damatebulia sxva 3 saganic. gamoicanira daemata meore suraTs~.dro pirveli suraTis damaxsorebisaTvis – 20 wami.3. ra Seicvala?Catarebis procedura: me bavSvs vuCvenebsuraTs. masze gamosaxulia: xelTaTmani,cigura, Ceqma, xeli (zeda suraTi).bavSvs vTavazob daimaxsovros suraTzegamosaxuli sagnebi. Semdeg am suraTsviReb da bavSvs vuCveneb sxva suraTs.meore suraTze gamosaxulia igivesagnebi, rac pirvelze, mxolod xelisnacvlad Txilamuria (qveda suraTi).bavSvs veubnebi: `meore suraTze erTisxva sagania, romelic pirvel suraTzear iyo. romelia es sagani?~dro pirveli suraTis dasamaxsovreblad – 20 wami.151

IV. azrovneba1. SeamCnie ra SeeSalaT.Catarebis procedura: bavSvsvuCveneb suraTs. masze gamosaxuliadaTvi, mgeli, melada mercxali. bavSvs veubnebi:àm oTaxidan sami erTmaneTismsgavsia, erTi ki gansxvavebuli,romelic aq SedomiTaris warmodgenili.moZebne romelia aq SecdomiTdaxatuli~.2. gamoicani sagani, romelic aq unda iyos.Catarebis procedura: bavSvsvuCveneb suraTs, sadacxilSi Sereulia burTi.bavSvs veubnebi: àq 4 sagania.amaTgan 3 erTmaneTismsgavsia, erTi ki gansxvavebuli,romelic aq ar undaiyos. gamoicani es sagani~.3. daawyve suraTebi ise, rom gamovides patara moTxroba.Catarebis procedura: bavSviswin magidaze 3 siuJeturi sura-Tia, romlebic areulad awyvia(yovel suraTs ukan TiTo qar-Tuli aso aweria: r, Z, e. eqsperimentisdasawyebis win sura-Tebi aseTi TanamimdevrobiTunda ewyos e, Z, r). bavSvs veubnebi:daawyve suraTebi ise, romgamovides patara moTxroba.152

Sesrulebis dro – 45 wami.4. miuCine yvela nivTs Tavisi adgili.Catarebis procedura: bavSvsvaCveneb suraTs, romelzec 4gogonaa gamosaxuli. gogonebisituaciisda mixedviT saWiroebenraRac nivTs. am nivTebissuraTebi calkea mocemuli.bavSvs vavaleb misces gogonebsmaTTvis saWiro nivTebi.Sesrulebis dro: – 30 wami.4. dRis monakveTebisgansazRvra siuJeturisuraTebis mixedviT.Catarebis procdura: bav-Svs vaZlev 4 siujetur suraTs.maTze gamosaxuliadRe –DRamis 4 monakveTi:dila, SuadRe, saRamo, Rame– TavianTi damaxasiaTebeliniSnebiT. bavSvs vaZlev davalebas:suraTebis mixedviTgansazRvros dRe – RamismonakveTebi: dila, SuadRe,saRamo da Rame.153

7. ra erTi sityva SeiZlebadavarqvaT?Catarebis procedura: bavSvsvaZlev suraTs, romelzecgamosaxulia sxvadasxva saxeobisxili: vaSli, msxali,yurZeni da marwyvi. bavSvsCamovaTvlevineb yvelas saxelwodebascal-calke daSemdeg vekiTxebi: `yvelaserTad ra erTi sityva SeiZlebadavarqvaT?~8. romeli sagani ara aris dawvilebuli?Catarebis procedura: bavSvsvuCveneb suraTs, romelzecdawyvilebuli sagania gamosaxuli.3 wyvilSi 1 kentisagani. bavSvs eZleva davaleba:`daasaxele, romelisagani ar aris dawyvilebuli?~9. suraTebis mixedviTweliwadisdroTa gansazRvra.Catarebisprocedura: magidaze4 suraTia,romelzec weliwadis4 droa gamosaxuli,Tavian-Ti damaxasiaTebe-154

li arsebiTi niSnebiT. bavSvs eZleva davaleba: suraTebis mixedviTgansazRvros weliwadis droebi.V. metyveleba1. ra SeiZleba vuwodoT?Catarebis procedura: bavSvs vekiTxebi: `ra SeiZleba vuwodoTadamians, romelsac sicili uyvars?~pasuxs vaZlev 4 variantad:a) jiuti, b) alersiani, g) mxiaruli, d) moCxubari.2. aba gamoicani?Catarebis procedura: bavSvs vukiTxav daumTavrebelwinadadebebs. bavSma unda moZebnos Sesabamisi sityva dadaamTavros winadadebebi.a) Tu ginda gaauToo TeTreuli, unda gaaxuro . . . . . . . . . .b) Tu ginda gaigo ra droa, unda daxedo . . . . . . . . . . . . . . .g) Tu ginda gaizomo temperatura, unda Caido . . . . . . . . . . .d) Tu ginda CaaWedo lursmani, unda daartya . . . . . . . . . . . .Sesrulebis dro – 60 wami.eweva.3. CamoTvale vin ra saqmianobasCatarebis procedura: suraTzegamosaxulia – durgali, mexan-Zre, gamyidveli, diasaxlisi damtvirTavi. yvelani asrulebenTavianT samuSaos. bavSvsvaZlev dabalebas: CamoTvalevin ras saqmianobs.155

VI. codna–warmodgenebi garemomcvel sagnebsa da movlenebze1. CamoTvale suraTzenaCvenebi cxovelebis, frinvelebisada maTi naSierebissaxelebi.Catarebis procedura:magidaze cxovelebis –cxenis, Zroxis, Txis, katisada frinvelis – ixvis sura-Tebia TavianTi naSierebiT.bavSvma unda daasaxelosisini.2. romeli ufro metia?Catarebis procedura: bavSvs vekiTxebi: `romeli ufro metia 1lari Tu 50 TeTri?~3. ra sagnebia darisTvis viyenebT?Catarebis procedura:suraTze gamosaxulia 3 jagrisi:a) kbilis, b) fexsacmlis,g) tansacmelis. bavSvsvekiTxebi: `daasaxele rasagnebia da risTvis viyenebT?~4. ra aris stadioni?Catarebis procedura: bavSvs vekiTxebi: `ra aris stadioni?~pasuxs vaZlev 4 variantad:a) avtomobilebis dasayenebeli adgili.156

) latariis gasaTamaSebeli adgili.c) TviTmfrinavebis dasafreni adgili.d) sportuli Sejibrebebis Casatarebeli adgili.5. romeli cxovels sWirdebasagani?Catarebis procedura: bavSvsvuCveneb suraTze gamosaxulunagirs. Tu ar icis, veubnebi:ès aris unagiri~. SemdegvuCveneb daTvis, ZaRlis,cxenisa da meliis suraTebs.bolos vekiTxebi: àm cxovelebidanromels sWirdebaes sagani?~6. yoveli nivTi Tavis adgilzedade.Catarebis procedura: magidazeawyvia 4 suraTi. maTzegamosaxulia a) tansacmliskarada, b) saswavloCanTa, g) magida, d) saTamaSokuTxe. amasTan, calke awyviaerTmaneTSi areuli – tansacmlis,saswavlo nivTebis,saTamaSoebis da WurWlissuraTebi. bavSvs vaZlevdavalebas: `yovel am nivTsmouZebne Tavisi adgili,daawyve Sesabamisi nivTebi157

zemoT dasaxelebuli 4 suraTisgverdiT~.Sesrulebis dro – 60 wami.7. ra aris mtkvari?Catarebis procedura: bavSvs vekiTxebi: `ra aris mtkvari?~ pasuxsvaZlev 3 variantad, saidanac bavSvma unda SearCios swori pasuxi:a) zRva, b) mdinare, g) tba.9. ra aris imereTi?Catarebis procedura: bavSvs vekiTxebi: `ra aris imereTi?~pasuxs vaZlev 3 variantad:a) mdinare, b) mTebi, g) saqarTvelos kuTxe.10. ra aris kavkasioni?Catarebis procedura: bavSvs vekiTxebi: `ra aris kavkasioni~?pasuxs vaZlev 3 variantad:a) qalaqi, b) mTebi, g) mdinare.V da VI subtestebi me gavakeTe calke testis saxiT ise, rommaTi pasuxebi Caidos saerTo monacemebSi. mas aqvs Semdegi saxe:saxeli da gvari _____________________ 6-7wlisaTvisV-1 ra SeiZleba vuwodoT adamians, romelsac sicili uyvars ?a) jiuti, b) alersiani, g) mxiaruli, d) moCxubari.V-2 aba gamoicani ?a) Tu ginda gaauToo TeTreuli, unda CarTo ___________b) Tu ginda gaigo ra droa, unda daxedo ____________g) Tu ginda gaizomo temperatura, unda Caido158

________________d) Tu ginda CaaWedo lursmani, unda daartya_________________VI-4 ra aris stadioni ?a) avtomobilebis dasayenebeli adgili ?b) latariis gasaTamaSebeli adgili ?g) TviTmfrinavis dasafreni adgili ?d) sportuli Sejibrebis Casatarebeli adgili ?VI-7 ra aris mtkvari ?a) zRva, b) mdinare, g) tba.VI-8 ra aris imereTi ?a) mdinare, b) mTebi, g) saqarTvelos kuTxe.VI-9 ra aris kavkasioni ?a) qalaqi, b) mTebi, g) mdinare.________TariRitestirebis dros eqsperimentatori avsebs ,,bavSvis Seswavlisrukas”.bavSvis Seswavlis rukamoswavlis saxeli da gvari: ----------------------------------------------dabadebis TariRi: ----------------------------------- skola -------------------159

testi #3DdavalebisSerulebisdro(wm)DdavalebisSesrulebismaCvenebelimiRebuli qulaBbavSvisQcevazedakvirveba# 2 3 4 5I. aRqma123miageniT figurebs, romlebicTavianT adgilze ar arianromeli droSa unda moaTavsdescariel adgilax?nawilebisagan mTelis Sedgena120jamuriqula12II. yuradRebaSeavse ujrebimoZebne da daasaxeli ricxvebiyuradRebiT iyavi, araferigamogrCes9090120jamuriqulaIII. mexsiereba1 ra daemata? 20jamuriqulaVI. azrovneba12ra erTi sityva SeiZlebadavarqvaT?daawyve suraTebi ise, rom 45160

345678910gamovides patara moTxrobaromelia zedmeyi?Cxirebisagan geometriulifigurewbis Sedgenaamocana-Tavsatexira aqvs saerTo?ra aqvs saerTo?risTvis aris saWiro?suraTis situaciaSi garkvevamoifiqre, romeli ricxvi undaiyosSemdegi?180120jamuriqulaV. metyveleba123ras uwodeben?romeli sityva ar aRniSnavsnaTesavs?mocemuli sityvebiT winadadebisSedgena60jamuriqula1234VI. codna-warmodgenebigaremomcvelsagnebsa da movlenebzeromeli ar aris xe?ra aris suraTze gamosaxuli?romel transporys ar sWirdebarelsebi?romeli ar aris musikaluri161

5678910instrumenti?weliwadis drois gansazRvrasuraTis mixedviT.romelia mxatvris samuSaoiaraRi?ra hqvia saRamos Wamas?ra aris sveticxoveli?gamoicani saidumlo ricxvebia?vin iyo vaxtang gorgasali?90jamuriqulasuljamuriquladanarTi # 3piaJes fenomenis Seswavlaoqmi # ____moswavlis gvari, saxeli: __________________________dabadebis weli, Tve, ricxvi: _______________________skola: ________________________________________ klasi:__________pasuxi:naklebiaratom fiqrobT ase?tolia axla metia axla____________________________________________________________________________________________________________________________________________________________________________________________________Catarebis TariRi: _____________________Camtareblis xelmowera: _____________________162

iagor simonis Ze balanCivaZe skolisaTvis mzaobaSi Seferxebis ...

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