me da matematika(mascavleblis cigni).indd - Ganatleba
30.01.2013 • Views
Share Embed Flag

me da matematika(mascavleblis cigni).indd - Ganatleba

me da matematika(mascavleblis cigni).indd - Ganatleba

me da matematika(mascavleblis cigni).indd - Ganatleba

SHOW MORE
SHOW LESS
ePAPER READ
DOWNLOAD ePAPER
ganatleba.org

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

START NOW

,,qarTuli saswavlebeli’’<br />

<strong>me</strong> <strong>da</strong> maTematika<br />

maswavleblis wigni<br />

eTer svaniZe

e<strong>da</strong>qtori: ciala kvaWaZe<br />

mxatvari: elene naveriani<br />

kompiuteruli uzrunvelyofa:<br />

lela kobiaSvili<br />

c qarTuli saswavlebeli 2009<br />

gamomcemloba `qarTuli saswavlebeli~<br />

v. beriZis q. 2,<br />

Tbilisi, 0108<br />

tel: 99 86 33<br />

e-mail: aecgs@mail.ru<br />

Sinaarsi<br />

Sesavali ..................................................................... gv. 3<br />

saxelmZRvanelos Sedgenis zogadi<br />

principebi ................................................................ gv. 4<br />

saxelmZRvanelos miznebi, amocanebi <strong>da</strong> mosalodneli<br />

Sedegebi ......................................................... gv. 5<br />

erovnuli saswavlo gegma .............................. gv. 8<br />

saxelmZRvaneloSi warmodgenili Tematikis<br />

mimarTeba miznebTan <strong>da</strong> SedegebTan ............ gv. 11<br />

saxelmZRvanelos struqtura<br />

<strong>da</strong> Sinaarsi .............................................................. gv. 16<br />

swavlebis modeli <strong>da</strong> <strong>me</strong>Todebi .................. gv. 24<br />

gakveTilebis savaraudo CamonaTvali<br />

I nawili ................................................................... gv. 28<br />

II nawili .................................................................. gv. 36<br />

<strong>da</strong>narTebi ................................................................... gv. 46<br />

2

Sesavali<br />

samyaro harmoniuli mTlianobaa, ro<strong>me</strong>lSic yvela mimdinare procesi erTmaneT-<br />

Tanaa <strong>da</strong>kavSirebuli <strong>da</strong> bunebis kanonzomierebas emorCileba. am mTlianobis sivrceSi<br />

kacobriobac moiazreba. samwuxarod, misi saqmianoba <strong>da</strong> ganviTareba arsebuli mTlianobis<br />

rRveviskenaa mimarTuli. am proble<strong>me</strong>bis ga<strong>da</strong>Wra ki SeuZlia mxolod ganaTlebul<br />

sazogadoebas, ro<strong>me</strong>lsac Seswevs unari sakuTar Tavze aiRos pasuxismgebloba kacobriobis<br />

momavalze. swored amaSi mdgomareobs ganaTlebis procesis umaRlesi mizani<br />

_ aRzardos Rirseuli a<strong>da</strong>miani, ro<strong>me</strong>lic Tavis movaleobad CaTvlis sazogadoebisa <strong>da</strong><br />

garemos harmonizaciis procesSi Tavisi wvlilis Setanas.<br />

34-e sajaro skola (`qarTuli saswavlebeli~) ukve 14 welia am principiT avi-<br />

Tarebs saswavlo process <strong>da</strong> mdgradi ganviTarebis farglebSi moiazrebs ganaTlebis<br />

miznebsa <strong>da</strong> mosalodnel Sedegebs.<br />

`qarTuli saswavleblis~ mTavar mizans warmoadgens maRali zneobisa <strong>da</strong> inteleqtis<br />

mqone pirovnebis aRzr<strong>da</strong>, ro<strong>me</strong>lic `... Tavis ers emsaxureba keTilgonierad <strong>da</strong> cdilobs<br />

Tavis samSoblo aRamaRlos gonebriv, qonebriv <strong>da</strong> zneobriv, amiT is umzadebs mTels<br />

kacobriobas saukeTeso wevrebs, saukeTeso <strong>me</strong>gobars, xels uwyobs mTeli kacobriobis<br />

ganviTarebas, keTildReobas.... yoveli mamuliSvili Tavis samSoblos un<strong>da</strong> emsaxuros<br />

mTeli Tavisi ZalRoniT, TanamoZ<strong>me</strong>Ta sargeblobaze un<strong>da</strong> fiqrobdes <strong>da</strong>, ramdena<strong>da</strong>c<br />

gonivruli iqneba misi Sroma, ramdena<strong>da</strong>c sasargeblo gamodgeba mSobeli qveynisaTvis<br />

misi Rvawli, imdenadve sasargeblo iqneba mTeli kacobriobisaTvis~ (vaJa-fSavela `kos-<br />

mopolitizmi <strong>da</strong> patriotizmi~).<br />

samyaros Sesacnobad <strong>da</strong> masSi sakuTari adgilis gasacnobiereblad aucilebelia <strong>me</strong>cnierebis<br />

sxva<strong>da</strong>sxva <strong>da</strong>rgis SekavSirebul, erTian sistemaSi moyvanili problemuri <strong>da</strong><br />

logikurad ganviTarebadi swavleba.<br />

swavlebis procesSi mTavari misia akisria or enas _ mSobliur enasa <strong>da</strong> maTematikas.<br />

enas, ro<strong>me</strong>lze<strong>da</strong>c vazrovnebT, (mSobliuri ena) <strong>da</strong> enas, ro<strong>me</strong>lze<strong>da</strong>c azrovnebs mTeli<br />

samyaro (maTematika).<br />

swavlebis procesi yovelTvis un<strong>da</strong> iTvaliswinebdes im cvlilebebs, romlebsac dro<br />

<strong>da</strong> sivrce karnaxobs sazogadoebas. bunebrivia, es moTxovnebi un<strong>da</strong> aisaxos saskolo<br />

saxelmZRvaneloSic.<br />

Cveni saxelmZRvanelos adresati XXI saukunis bavSvia, romlis Se<strong>me</strong>cnebiTi interesi<br />

mniSvnelovna<strong>da</strong>a gazrdili. amdenad, swavlebis procesi swored aseT bavSvebze un<strong>da</strong><br />

iyos orientirebuli <strong>da</strong> akmayofilebdes maT mzard interess, mudmivad uRviZebdes cnobismoyvareobas.<br />

swavlis procesi mimzidveli <strong>da</strong> xalisiani maSin xdeba, Tu saswavlo<br />

masala, misi miwodebis for<strong>me</strong>bi <strong>da</strong> <strong>me</strong>Todebi Seesaba<strong>me</strong>ba bavSvis inteleqtualur dones.<br />

interesis gaqroba ki swavlisadmi uaryofiTi <strong>da</strong>mokidebulebis safuZvelia. iakob gogebaSvili<br />

momxre iyo imisa, `rom swavlebis Sinaarsi periodulad ivsebodes axali <strong>me</strong>c- <strong>me</strong>c-<br />

nieruli aRmoCenebiT <strong>da</strong> am gziT swavleba <strong>da</strong> ganaTleba fex<strong>da</strong>fex misdevdes cxovrebas<br />

swavlebasa <strong>da</strong> aRzr<strong>da</strong>Si xorcieldebodes realuri ele<strong>me</strong>nti.~<br />

3

Cveni azriT, swored am principiT Seqmnilma saxelmZRvanelom un<strong>da</strong> <strong>da</strong>ainteresos<br />

bavSvi <strong>da</strong> gazardos swavlebis xarisxi.<br />

mdgradi ganviTarebis ZiriTad Sedegs warmoadgens gaazrebuli, socialurad mniSvnelovani<br />

moRvaweoba, ro<strong>me</strong>lic mimarTulia kacobriobis, garemosTan harmonizaciis<br />

misaRwevad.<br />

saxelmZRvanelos Sedgenis zogadi principi<br />

mocemuli saxelmZRvanelo ganixileba rogorc “qarTuli saswavleblis” <strong>da</strong>wyebiTi<br />

maTe<strong>me</strong>tikuri ganaTlebis organuli nawili.<br />

I safexuris maTematikis kursi spiraliseburad sxva sagnebis analogiura<strong>da</strong>a agebuli.<br />

saswavlo procesisadmi amgvari <strong>da</strong>mokidebuleba bavSvebs saSualebas aZlevs, erTi<br />

<strong>da</strong> igive masala gansxvavebuli moculobiTa <strong>da</strong> siRrmiT aRiqvan swavlebis yvela safexurze.<br />

rogorc samyaros Secnobis enas, maTematikis Seswavlasac samyaros erTianobis<br />

idea udevs safuZvlad (mag. ariT<strong>me</strong>tikuli moq<strong>me</strong>debebis erTdrouli swavleba <strong>da</strong> maT<br />

Soris kavSirebis <strong>da</strong>dgena, samyaros for<strong>me</strong>bsa <strong>da</strong> geo<strong>me</strong>triul figurebs Soris kavSiris<br />

<strong>da</strong>naxva, .......).<br />

es zusti <strong>me</strong>cniereba iswavleba ara rogorc calke aRebuli, ganyenebuli disciplina,<br />

ara<strong>me</strong>d, rogorc sxva disciplinebis sayrdeni <strong>da</strong> safuZveli.<br />

Cveni mizania, <strong>da</strong>vanaxoT bavSvs maTematikis kavSiri gare samyarosTan <strong>da</strong> misi<br />

gamoyenebis aucilebloba yoveldRiur cxovrebaSi.<br />

am saxelmZRvanelos I klasis kursSi mocemul situaciebSi, amocanebsa <strong>da</strong> savarjiSoebSi<br />

gamoyenebulia sxva<strong>da</strong>sxva disciplinis ele<strong>me</strong>ntebi. aseTi midgoma uyalibebs<br />

bavSvs samyaros mTlianobis xedvis unikalur stils, zrdis maTematikis mniSvnelobas<br />

<strong>da</strong> xdis mas universalurs.<br />

maTematika I klasi<br />

garemos<strong>da</strong>cva<br />

musika<br />

astronomia<br />

buneba<br />

4<br />

samyaros<br />

geo<strong>me</strong>tria<br />

informatika<br />

logika<br />

ekonomika<br />

sqema #1

maTematikuri ganaTlebis sawyis safexurze geo<strong>me</strong>triis kursis Setana SesaZleblobas<br />

iZleva gavacnoT bavSvebs samyaros Se<strong>me</strong>cnebis gansaxvavebuli xerxi.<br />

bavSvis azrovneba Tavis sawyisSi aris xatovani, emociuri azrovneba. is am asakSi,<br />

realur samyarosTan erTad agrZelebs cxovrebas fantastikur, zRaprul samyaroSi<br />

amitom <strong>da</strong>wyebiT etapze swavlebis erT-erT ZiriTad mizans warmoadgens umcros klaselebSi<br />

saxeebiTi azrovnebis, grafikuli informaciis aRqmisa <strong>da</strong> gaazrebis unaris gan-<br />

viTareba.<br />

pirveli nabijebi am mimarTulebiT, bunebrivia, un<strong>da</strong> <strong>da</strong>iwyon sagnobrivi suraTebis<br />

gaferadebiT, romlis procesSi isini gaiazreben maTTvis ukve cnobil sivrciT <strong>da</strong>mokidebulebebs.<br />

grafikuli <strong>da</strong>valebebis Tan<strong>da</strong>TanobiTi garTuleba ki ayalibebs figuris aRqmisa<br />

<strong>da</strong> agebis unars.<br />

<strong>da</strong>wyebiTi swavlebis procesSi umniSvnelovanes rols asrulebs sivrceSi orientacia.<br />

aqe<strong>da</strong>n gamomdinare, maTematikis am kursSi geo<strong>me</strong>triis swavlebis mizans warmoadgens:<br />

• masStaburi, warmosaxviTi unaris ganviTareba;<br />

• kavSiri samyaros for<strong>me</strong>bsa <strong>da</strong> geo<strong>me</strong>triul figurebs Soris;<br />

• sivrciTi <strong>da</strong> geo<strong>me</strong>triuli figurebis paraleluri swavleba;<br />

• sivrciT <strong>da</strong> brtyel figurebs Soris gansxvavebisa <strong>da</strong> kavSirebis xedvis unari.<br />

saxelmZRvanelos miznebi, amocanebi <strong>da</strong> mosalodneli Sedegebi<br />

termini saxelmZRvanelo Tavisi mniSvnelobiT gulisxmobs aqtiuri swavlebis,<br />

TviTswavlebis process, wigns ki xelmZRvanelis, warmmarTvelis funqcia ekisreba.<br />

saxelmZRvanelo “ <strong>me</strong> <strong>da</strong> maTematika”<br />

• integrirebulia <strong>da</strong> Seicavs samyarosmcodneobis, musikis, ekonomikis, astronomiis,<br />

informatikis, logikis, ele<strong>me</strong>ntebs.<br />

• mravalferovania.<br />

ariT<strong>me</strong>tikul, algebrul <strong>da</strong> geo<strong>me</strong>triul masalaSi gaerTianebulia<br />

• kombinatorikis;<br />

• logikis;<br />

• algoriTmis;<br />

• simravlis;<br />

• albaTobis;<br />

• geo<strong>me</strong>triul gar<strong>da</strong>qmnaTa Teoriis ele<strong>me</strong>ntebi.<br />

5

• sainteresoa<br />

sainteresoa.<br />

Seesaba<strong>me</strong>ba Tana<strong>me</strong>drove bavSvis interesebs.<br />

• aqtualuria.<br />

• aqtualuria.<br />

Seesaba<strong>me</strong>ba bavSvis moTxovnebs.<br />

saxelmZRvanelos mizania<br />

• bavSvis pirovnebis sulieri potencialis, misi Semoq<strong>me</strong>debiTi Taviseburebisa <strong>da</strong><br />

sagnisadmi interesis ganviTarebisaken orientacia;<br />

• bavSvs Seuqmnas safuZveli maTematikis siRrmiseuli SeswavlisaTvis;<br />

• bavSvs <strong>da</strong>anaxos maTematikis mniSvneloba samyaros SecnobisaTvis;<br />

• bavSvi uzrunvelyos erovnuli saswavlo gegmis Sesabamisi codniT.<br />

saxelmZRvanelos amocanaa:<br />

bavSvs ganuviTaros<br />

• logikuri, algoriTmuli, kritikuli, sistemuri azrovneba;<br />

• masStaburi <strong>da</strong> warmosaxviTi xedvis unari;<br />

• <strong>da</strong>moukideblad orientirebisa <strong>da</strong> Semoq<strong>me</strong>debiTi unari;<br />

• obieqtebis klasifikaciis unari;<br />

• codnis praqtikaSi gamoyenebisa <strong>da</strong> axali codnis <strong>da</strong>moukideblad miRebis unari.<br />

gaafarTovos<br />

bavSvis Tvalsawieri<br />

xeli Seuwyos<br />

• azrovnebis iseTi stilis Camoyalibebas, ro<strong>me</strong>lic aucilebelia eleqtronuli<br />

gamomTvleli manqanis warmatebiT gamoyenebisaTvis;<br />

• TvalsaCino-xatovani azrovnebis <strong>da</strong>kavSirebas sityvier-logikur azrovnebasTan<br />

• arCevanis unaris ganviTarebas.<br />

6

aswavlos<br />

• rogor aRmoaCinos <strong>da</strong> moipovos codna.<br />

<strong>da</strong>exmaros<br />

• sakuTari Tavis realizaciaSi, TviT<strong>da</strong>mkvidrebaSi, pirovnebad CamoyalibebaSi;<br />

• msjelobis, azris Camoyalibebasa <strong>da</strong> argu<strong>me</strong>ntirebis unarebis ganviTarebaSi;<br />

• dialogis, sxvisi mos<strong>me</strong>nis, sxvisi azris <strong>da</strong>fasebisa <strong>da</strong> sakuTari<br />

azris <strong>da</strong>cvis procesSi;<br />

• bavSvis niWis gamovlenasa <strong>da</strong> ganviTarebaSi.<br />

mosalodneli Sedegebi<br />

moswavleebma SeZlon:<br />

• sakuTari saswavlo saqmianobis organizeba;<br />

• sxva<strong>da</strong>sxva wyaro<strong>da</strong>n informaciis Segroveba;<br />

• informaciis logikuri ga<strong>da</strong>muSaveba (analizi, sinTezi, abstragireba, Se<strong>da</strong>reba,<br />

klasificireba, ganzogadeba, analogiis gatareba, <strong>da</strong>skvnebis gakeTeba, sakuTari<br />

msjelobis <strong>da</strong>sabuTeba);<br />

• sakuTari saswavlo moRvaweobis Sefaseba <strong>da</strong> koreqtireba;<br />

saxelmZRvanelo uzrunvelyofs moswavleebis momzadebis dones, ro<strong>me</strong>lic gaTval<br />

iswinebulia erovnuli saswavlo gegmiT.<br />

7

wlis bolos misaRwevi Sedegebi:<br />

maT. I mimarTuleba:<br />

ricxvebi <strong>da</strong> moq<strong>me</strong>debebi kanonzomierebebi <strong>da</strong> algebra<br />

1. erTmaneTs usaba<strong>me</strong>bs<br />

ricxvebs, ricxviT<br />

saxelebsa <strong>da</strong> Sesabamis.<br />

2. iyenebs rigobriv<br />

ricxviT saxelebs<br />

<strong>da</strong> ricxvebs, rogorc<br />

Wdeebs (“iarliyi”).<br />

3.akavSirebs Tvlas,<br />

ricxvebs Soris<br />

<strong>da</strong>mokidebuleba <strong>da</strong><br />

Sekreba-gamoklebis<br />

erTmaneTTan.<br />

4. afasebs <strong>da</strong> a<strong>da</strong>rebs<br />

raodenobebs.<br />

5. ganavrcobs warmoadgens<br />

<strong>da</strong> a<strong>da</strong>rebs<br />

sagnebis periodul<br />

ganlagebebs<br />

(mimdevrobebs).<br />

wlis bolos misaRwevi Sedegebi <strong>da</strong> maTi indikatorebi<br />

mimarTuleba: ricxvebi <strong>da</strong> moq<strong>me</strong>debebi<br />

8<br />

geo<strong>me</strong>tria <strong>da</strong> sivrcis<br />

aRqma<br />

6. amoicnobs <strong>da</strong> aRwers<br />

brtyel figuras.<br />

7. gamosaxavs brtyel<br />

geo<strong>me</strong>triul figurebs<br />

<strong>da</strong> amoicnobs<br />

obieqtTa urTierTmdebareobas.<br />

maT. I. 1. erTmaneTs usaba<strong>me</strong>bs ricxvebs, ricxviT saxelebs <strong>da</strong> Sesabamis<br />

raodenobebs.<br />

Sedegi TvalsaCinoa, Tu moswavle:<br />

• irCevs <strong>da</strong> qmnis mocemuli ricxvis Sesabamisi raodenobis grovebs <strong>da</strong>, piriqiT,<br />

ricxvs usaba<strong>me</strong>bs Sesabamisi raodenobis grovebs;<br />

• qmnis toli raodenobis saganTa mowesrigebul erTobliobas maTi <strong>da</strong>wyvilebiT;<br />

• kiTxulobs <strong>da</strong> wers ricxvebs;<br />

• gamosaxavs maT sxva<strong>da</strong>sxva modelis gamoyenebiT;<br />

• gamoyofs miTiTebuli ricxvebis Sesabamisi raodenobis jgufebs grovaSi (mag.<br />

gamoyofs aTeuls grovaSi).<br />

maT. I. 2.<br />

iyenebs rigobriv ricxviT saxelebs <strong>da</strong> ricxvebs, rogorc<br />

Wdeebs (“iarliyi”)<br />

Sedegi TvalsaCinoa, Tu moswavle:<br />

erovnuli saswavlo gegma:

mimarTuleba: kanonzomierebebi <strong>da</strong> algebra<br />

maT. aT. I. 5. ganavrcobs, warmoadgens <strong>da</strong> adrebs sagnebis periodul gan-<br />

lagebebs (mivdevrobebs).<br />

Sedegi TvalsaCinoa, Tu moswavle:<br />

• mimdevrobis mocemuli frag<strong>me</strong>ntis mixedviT avsebs am mimdevrobis ramdeni<strong>me</strong> Tanmimdevrul<br />

Ria pozicias;<br />

• a<strong>da</strong>rebs erTnairi sagnebiT warmodgenil or mocemul mimdevrobas (romlebSic sagan-<br />

Ta raodenoba tolia) <strong>da</strong> Sesabamis SemTxveveaSi miuTiTebs im mimdevrobebs, romlebic<br />

ganlagebis erTsa <strong>da</strong> imave wess emorCileba;<br />

• sityvierad mocemuli wesis mixedviT, mimdevrobiT ganlagebas mxolod erTi atributiT<br />

gansxvavebul sagnebs (mag. erTi zomis burTebis aseT mimdevrobas: wiTeli burTi,<br />

lurji burTi, wiTeli burTi...).<br />

Sinaarsi<br />

1. sagnebis saSualebiT warmodgenili perioduli mimdevrobebi.<br />

mimarTuleba: geo<strong>me</strong>tria <strong>da</strong> sivrcis aRqma<br />

maT. I. 6. amoicnobs <strong>da</strong> aRwers brtyel figuras.<br />

Sedegi TvalsaCinoa, Tu moswavle:<br />

• yofiTi <strong>da</strong>niSnulebis sagnebSi an maT ilustraciebSi uTTiTebs <strong>da</strong>saxelebul<br />

brtyel figurebs;<br />

• SearCevs miTiTebuli figuris models Sereuli grovi<strong>da</strong>n;<br />

• aRwers miTiTebul geo<strong>me</strong>triul figuras (mag. asaxelebs mocemuli mravalkuTxedis<br />

wveroebis raodenobas).<br />

maT. I. 7. gamosaxvas brtyel geo<strong>me</strong>triul figurebs <strong>da</strong> amoicnobs<br />

obieqtTa urTierTmdebareobas.<br />

Sedegi TvalsaCinoa, Tu moswavle:<br />

• miTiTebuli wesiT aerTebs ramdeni<strong>me</strong> wertils sibrtyeze an/<strong>da</strong> moniSnavs gzas mi-<br />

TiTebul obieqtamde martiv sqemaze;<br />

• sworad pasuxobs kiTxvebze obieqtTa urTierTmdebareobis (marjvniv/marcxniv, zemoT/qvemoT,<br />

win/ukan) Sesaxeb;<br />

• uTavsebs sxva<strong>da</strong>sxva brtyeli figurebis modelebs erTmaneTs nimuSze mocemuli gamosaxulebis<br />

(naxatis) misaRebad;<br />

• ro<strong>me</strong>li<strong>me</strong> xerxiT (mag. aplikaciiT an naxatis saSualebiT) qmnis <strong>da</strong>saxelebuli<br />

formis brtyeli figuris models an gamosaxulebas.<br />

Sinaarsi<br />

1. brtyeli figurebi: samkuTxedi, xuTkuTxedi, eqvskuTxedi, wre;<br />

2. martivi sqe<strong>me</strong>bi sibrtyeze (mag. wirebiT SeerTebuli wertilebi).<br />

9

• iTvlis win/ukan nebismieri ricxvi<strong>da</strong>n, ganmartavs 11-<strong>da</strong>n 20-mde ricxvis saxeldebas;<br />

asaxelebs mocemuli ricxvis wina <strong>da</strong> momdevno ricxvebs;<br />

• saganTa mowesrigebul erTobliobaSi asaxelebs miTiTebuli sagnis rigs;<br />

• mocemuli TanmimdevrobiT an/<strong>da</strong> miTiTebul poziciebze ganaTavsebs sagnebs;<br />

• iyenebs nuls <strong>da</strong> mis aRmniSvnel simbolos Sesabamis situaciebSi.<br />

• ganasxvavebs <strong>da</strong> asaxelebs erovnuli fulis niSnebis (monetebs, banknotebs) 20-is<br />

farglebSi.<br />

maT. I. 3. akavSirebs Tvlas, ricxvebs Soris <strong>da</strong>mokidebulebasa <strong>da</strong><br />

Sekreba-gamoklebis moq<strong>me</strong>debebs erTmaneTTan.<br />

Sedegi TvalsaCinoa, Tu moswavle:<br />

• sityvierad aRwers Sekrebis/gamoklebis/tolobis <strong>da</strong> Sedegis cnebebs sxva<strong>da</strong>sxva<br />

konteqstSi (mag. “<strong>da</strong>vumatoT,” “movakloT”, mimateba _ gazr<strong>da</strong>; gamokleba _ Semcireba,<br />

gacalkeveba, gansxvaveba);<br />

• axdens Sekreba-gamoklebis TvalsaCinod demonstrirebas, gansazRvravs gansxvavebas<br />

(mag. “ramdeniT gaizar<strong>da</strong>/Semcir<strong>da</strong>?”) <strong>da</strong> aRwers ricxvebs Soris <strong>da</strong>mokidebulebas.<br />

• zepirad angariSisas iyenebs 1-s toli bijiT Tvlas, an sxva xerxs <strong>da</strong> axdens Sekreba-gamoklebis<br />

moq<strong>me</strong>debaTa urTierSebrunebulobas demonstrirebisas modelis gamoyenebiT;<br />

• mocemuli grovisaTvis asaxelebs am grovis, miTiTebul raodenobamde Sesavsebad<br />

saWiro, <strong>da</strong>matebiT raodenobas; zepirad asrulebs 10-is gavliT Sekreba-gamoklebas <strong>da</strong><br />

axdens gamoyenebuli xerxis TvalsaCinod demonstrirebas.<br />

maT. I. 4. afasebs <strong>da</strong> a<strong>da</strong>rebs raodenobebs.<br />

Sedegi TvalsaCinoa, Tu moswavle:<br />

• <strong>da</strong>uTvlelad asaxlebs zust raodenobas erTgvarovan, mcire zomis saganTa grovaSi<br />

(raodenoba ar aRemateba 5-s) <strong>da</strong> amow<strong>me</strong>bs Tavis pasuxs;<br />

• akavSirebs “-iT” <strong>me</strong>toba/naklebobas Sekreba/gamoklebis moq<strong>me</strong>debebTan <strong>da</strong> axdens amis<br />

modelze demonsrtirebas;<br />

• saganTa <strong>da</strong>wyvilebiT a<strong>da</strong>rebs raodenobebs grovebSi, iyenebs Sesabamis terminebsa <strong>da</strong><br />

aRniSnvnebsa (>,

saxelmZRvaneloSi warmodgenili Tematikis Sesabamisoba<br />

mizanTan <strong>da</strong> SedegTan<br />

Tema Mmizani Sedegi<br />

<strong>me</strong> <strong>da</strong> samyaro bavSvis mier garemomcveli<br />

samyaros maTematikasTan<br />

kavSirSi gaazreba;<br />

samyaros mTlianobis aRqma;<br />

Se<strong>me</strong>cnebiTi azrovnebis<br />

ganviTareba.<br />

dro <strong>da</strong> maTematika maTematikis mniSvnelobis<br />

gaazreba;<br />

Se<strong>me</strong>cnebiTi azrovnebis<br />

ganviTareba.<br />

erTi <strong>da</strong> erTaderTi erTisa <strong>da</strong> erTaderTis<br />

kavSirisa <strong>da</strong> gansxvavebis<br />

<strong>da</strong>naxva;<br />

analitikuri azrovnebis<br />

ganviTareba.<br />

erTi <strong>da</strong> bevri.<br />

cota <strong>da</strong> bevri.<br />

raodenobrivi<br />

mimarTebani<br />

simravlis cnebis gaazreba;<br />

sistemuri azrovnebis<br />

ganviTareba.<br />

mTeli <strong>da</strong> nawili gaiazros mTelisa <strong>da</strong><br />

nawilis <strong>da</strong>mokidebuleba;<br />

sistemuri, logikuri<br />

analitikuri azrovnebis<br />

ganviTareba.<br />

cifri <strong>da</strong> ricxvi cifrsa <strong>da</strong> ricxvs Soris<br />

saerTosa <strong>da</strong> gansxvavebis<br />

<strong>da</strong>naxva.<br />

11<br />

moswavle erTmaneTs usaba<strong>me</strong>bs<br />

ricxvebs, raodenobebs, <strong>da</strong> rigs<br />

1.2.<br />

acnobierebs maTematikis,<br />

rogorc universaluri enis<br />

mniSvnelobas.<br />

iazrebs erTisa <strong>da</strong><br />

erTaderTis kavSirsa <strong>da</strong><br />

gansxvavebas;<br />

1.1<br />

sityvierad gadmocems<br />

raodenobas;<br />

iazrebs terminebs cota <strong>da</strong><br />

bevri;<br />

xe<strong>da</strong>vs <strong>da</strong> iazrebs maT Soris<br />

kavSirsa <strong>da</strong> gansxvavebas;<br />

1.1; 1.4<br />

yofs mTels tol nawilebad;<br />

iazrebs maT Soris<br />

<strong>da</strong>mokidebuilebas;<br />

nawilebis <strong>me</strong>t-naklebobas.<br />

asxvavebs <strong>da</strong> akavSirebs<br />

cifrebs <strong>da</strong> ricxvebs.<br />

1.1

naturaluri<br />

ricxvebi;<br />

erTniSna <strong>da</strong> orniSna,<br />

luwi <strong>da</strong> kenti<br />

ricxvebi;<br />

rigobiTi ricxvebi<br />

Tvla 100-is<br />

farglebSi<br />

20-is farglebSi ricxvTa<br />

awyoba <strong>da</strong> <strong>da</strong>Sla;<br />

erTniSna <strong>da</strong> orniSna luw<br />

<strong>da</strong> kent ricxvebs Soris<br />

msgavsebisa <strong>da</strong> gansxvavebis<br />

<strong>da</strong>naxva;<br />

100-is farglebSi ricxvebis<br />

Secnoba.<br />

100-mde Tvla, ricxvTa<br />

<strong>da</strong>saxelebebi;<br />

ricxvTa Tanamimdevrobis<br />

gaazreba<br />

100-is farglebSi aTobiTi<br />

<strong>da</strong> ocobiTi Tvla;<br />

Tvla bijiT win <strong>da</strong> ukan;<br />

Tvlis principebis aTviseba<br />

0-is Tvisebebi gaacnobieros 0-is Sinaarsi<br />

<strong>da</strong> mniSvneloba.<br />

lari. amocanebi<br />

larebze <strong>da</strong> TeTrebze<br />

laris Semadgenlobisa <strong>da</strong><br />

agebulebis <strong>da</strong>naxva.<br />

sistemuri <strong>da</strong> analizuri<br />

azrovnebis ganviTareba 1,2<br />

12<br />

usaba<strong>me</strong>bs ricxvebs,<br />

ricxviT saxelebs, rigs <strong>da</strong><br />

raodenobebs;<br />

gamosaxavs ricxvebs<br />

sxva<strong>da</strong>sxva modelis<br />

gamoyenebiT;<br />

uTiTebs erTeuls <strong>da</strong> aTeuls<br />

ricxviT CanawerSi;<br />

u<strong>da</strong>rebs erTmaneTs luw <strong>da</strong><br />

kent ricxvebs <strong>da</strong> amoicnobs<br />

maT;<br />

amyarebs rigiT mimarTebas<br />

naturalur ricxvTa mwkrivSi:<br />

1.1<br />

iTvlis kiTxulobs wers<br />

<strong>da</strong> a<strong>da</strong>rebs ricxvebs 100-is<br />

farglebSi. 1.3<br />

1,2,1,3<br />

moswavle iyenebs 0-s<br />

Sesabamis situaciebSi;<br />

1.2<br />

ganasxvavebs, asaxelebs, <strong>da</strong><br />

iyenebs erovnuli fulis<br />

niSnebs;<br />

xsnis martiv amocanebs<br />

larisa <strong>da</strong> TeTris<br />

gamoyenebiT;<br />

1.2

iT - <strong>me</strong>ti/naklebi;<br />

jer - <strong>me</strong>ti/naklebi;<br />

imdenive ramdenic<br />

martivi gantolebebi<br />

<strong>da</strong> utolobebi<br />

raodenobebs Soris<br />

kavSirisa <strong>da</strong> gansxvavebis<br />

<strong>da</strong>naxva. evristikuli<br />

<strong>me</strong>Todis gamoyenebiT<br />

msjelobis unaris<br />

Camoyalibeba.<br />

tolobebsa <strong>da</strong> utolobebSi<br />

ucxo komponentis povna.<br />

azrovnebisa <strong>da</strong> analitikuri<br />

ganviTareba;<br />

mimdevrobebi warmoidginon, Sea<strong>da</strong>ron<br />

<strong>da</strong> ganavrcon sagnebis an<br />

naxat/figurebis periodul<br />

ganlagebebi.<br />

warmosaxvisa <strong>da</strong> sistemuri<br />

azrovnebis ganviTareba.<br />

1.5<br />

figurebis <strong>da</strong>jgufeba<br />

maTi Tvisebebisa <strong>da</strong><br />

niSnebis mixedviT;<br />

feri, zoma, forma<br />

jgufis mTlianobis<br />

<strong>da</strong>naxva <strong>da</strong> misi aRqma sxva<br />

mTlianobis nawilad;<br />

sagnebsa <strong>da</strong> figurebs<br />

Soris gansxvavebebis <strong>da</strong><br />

msgavsebebis <strong>da</strong>naxva;<br />

martivi kanonzomierebebis<br />

<strong>da</strong>dgena;<br />

obieqtebis klasifikaciis<br />

unaris ganviTareba.<br />

logikuri <strong>da</strong> analitikuri<br />

azrovnebis ganviTareba.<br />

13<br />

moswavle qmnis toli<br />

raodenobis saganTa<br />

mowesrigebul erTobliobas<br />

maTi <strong>da</strong>wyvilebiT <strong>da</strong> adgens<br />

zed<strong>me</strong>t <strong>da</strong> nakleb raodenobas,<br />

iyenebs simboloebs: >,

saazrovno <strong>da</strong><br />

logikuri amocanebi<br />

sivrciTi <strong>da</strong> droiTi<br />

mimarTebani<br />

logikuri terminebis<br />

gaazreba;<br />

azrovnebis iseTi for<strong>me</strong>bis<br />

Camoyalibeba, rogoricaa<br />

analizi, sinTezi, analogia,<br />

ganzogadeba, azrovnebis<br />

moqniloba <strong>da</strong> miRebuli<br />

Sedegebis kritikuli aRqma.<br />

orientireba sivrcesa <strong>da</strong><br />

droSi;<br />

orientireba badiT <strong>da</strong>farul<br />

sibrtyeze;<br />

garemoSi orientirebis<br />

unaris ganviTareba.<br />

sivrce <strong>da</strong> sibrtye brtyeli <strong>da</strong> sivrciTi<br />

geo<strong>me</strong>triuli figurebis<br />

samyaros for<strong>me</strong>bTan<br />

Sesabamisobis aRqma;<br />

sivrciT <strong>da</strong> brtyel<br />

figuraTa Soris gansxvavebis<br />

<strong>da</strong>naxva;<br />

sivrciTi warmodgenebis<br />

ganviTareba.<br />

wertili <strong>da</strong> are wertilis, rogorc ZiriTadi<br />

geo<strong>me</strong>triuli figuris<br />

mniSvnelobis gacnobiereba.<br />

gansazRvros wertilebis<br />

mdebareoba ares mimarT.<br />

samyaros for<strong>me</strong>bsa <strong>da</strong><br />

geo<strong>me</strong>triul figurebs<br />

Soris kavSirebis <strong>da</strong>naxvis<br />

unari.<br />

wiri, monakveTi gaacnobieros wirTa<br />

mravalferovneba;<br />

14<br />

agebs <strong>da</strong> iazrebs martiv<br />

sqe<strong>me</strong>bs;<br />

xsnis martiv saazrovno <strong>da</strong><br />

logikur amocanebs;<br />

fiqrobs, adgens logikuri<br />

msjelobis jaWvebs.<br />

<strong>me</strong>xsierebas, yuradRebas,<br />

azrovnebas, <strong>me</strong>tyvelebas,<br />

warmosaxvas <strong>da</strong> algoriTmuli<br />

msjelobis unaris<br />

ganviTareba.<br />

aRwers obieqtis mdebareobas<br />

<strong>me</strong>ore obieqtTan mimarTebiT<br />

Sesabamisi terminebis<br />

gamoyenebiT;<br />

moswavle xe<strong>da</strong>vs Crdils<br />

mdebareobas ganaTebis<br />

Sesabamisad.<br />

a<strong>da</strong>rebs <strong>da</strong> ajgufebs sivrciT<br />

<strong>da</strong> brtyel figurebs. xe<strong>da</strong>vs<br />

maT Soris gansxvavebas;<br />

1.6 1.7<br />

xe<strong>da</strong>vs wertilis mdebareobas<br />

sibrtyeze <strong>da</strong> sivrceSi;<br />

ganasxvavebs Siga <strong>da</strong> gare<br />

areebs;<br />

uTiTebs SigniT gareT<br />

<strong>da</strong> sazRvarze mdebare<br />

wertilebs;<br />

1.7<br />

moswavle ganasxvavebs<br />

sxva<strong>da</strong>sxva saxis wirebs<br />

1.7

sxivi <strong>da</strong> kuTxe bunebaSi sxivisa <strong>da</strong> kuTxis<br />

amocnoba;<br />

kuTxeebs Soris gansxvavebis<br />

<strong>da</strong>naxva.<br />

mravalkuTxedebi gaarCios <strong>da</strong> aRweros<br />

brtyeli geo<strong>me</strong>triuli<br />

figurebi.<br />

si<strong>me</strong>tria garemomcvel obieqtebs<br />

Soris si<strong>me</strong>triul obieqtTa<br />

amocnoba;<br />

si<strong>me</strong>triuli geo<strong>me</strong>triuli<br />

figurebis gacnoba.<br />

15<br />

asxvavebs sxivsa <strong>da</strong> kuTxes<br />

1.7<br />

xe<strong>da</strong>vs kuTxeebs Soris<br />

msgavsebasa <strong>da</strong> gansxvavebas;<br />

a<strong>da</strong>rebs, ajgufebs <strong>da</strong> aRwers<br />

brtyel geo<strong>me</strong>triul figurebs<br />

1.7<br />

cnobs bunebaSi <strong>da</strong><br />

geo<strong>me</strong>triaSi arsebul<br />

si<strong>me</strong>triul sagnebsa <strong>da</strong><br />

figurebs;<br />

warmoidgens <strong>da</strong> avlebs<br />

si<strong>me</strong>triis RerZs;

saxelmZRvanelos struqtura <strong>da</strong> Sinaarsi<br />

Zal<strong>da</strong>taneba Zal<strong>da</strong>taneba saWiro saWiro ar ar aris, aris, radgan radgan TviTon TviTon wigni wigni<br />

sasiamovnod sasiamovnod hxdis hxdis Tavis Tavis kiTxvas. kiTxvas. (iakob (iakob gogebaSvili)<br />

gogebaSvili)<br />

yoveli saxelmZRvanelo bavSvisaTvis saintereso un<strong>da</strong> iyos. igi saintereso iqneba<br />

im SemTxvevaSi, Tu is<br />

Seesaba<strong>me</strong>ba:<br />

• dros <strong>da</strong> sivrces;<br />

pasuxobs:<br />

• epoqis moTxovnebs;<br />

iTvaliswinebs:<br />

• Tana<strong>me</strong>drove bavSvis inteleqts;<br />

exmareba:<br />

• bavSvs garesamyarosTan urTierTobaSi.<br />

I klasis maTematikis saxelmZRvanelo Sedgeba sami nawilisgan:<br />

moswavlis wigni I <strong>da</strong> II nawili;<br />

samuSao rveuli I <strong>da</strong> II nawili;<br />

maswavleblis wigni.<br />

moswavlis wigni<br />

moswavlis wignis Sedgenisas vxelmZRvanelobdiT Ziri-<br />

Tadi principiT: Cven uars vambobT ,,mza codnis’’ miwodebaze<br />

<strong>da</strong> bavSvisaTvis aucilebeli _ aRmoCenisa <strong>da</strong> Ziebis<br />

gza migvaCnia aucilebel pirobad misi azrovnebis ganvi-<br />

TarebisaTvis.<br />

,,erTferovneba ,,erTferovneba sikvdilia, sikvdilia, mravlaferovneba mravlaferovneba sicocxsicocxleo. leo. es es azri, azri, marTali marTali didebisaTvis, didebisaTvis, orkec orkec <strong>da</strong> <strong>da</strong> samkec samkec<br />

marTalia marTalia patarebisaTvis, patarebisaTvis, ro<strong>me</strong>lTa ro<strong>me</strong>lTa buneba buneba iTxovs iTxovs sxsxva<strong>da</strong>sxvagvarva<strong>da</strong>sxvagvar STabeWdilebas, STabeWdilebas, sxva<strong>da</strong>sxva sxva<strong>da</strong>sxva sazrdos sazrdos gonebigonebisas.’’ sas.’’<br />

(iakob (iakob gogebaSvili)<br />

gogebaSvili)<br />

am saxelmZRvaneloTi muSaobis dros bavSvi Tavs saTamaSo situaciis centrSi aRiqvams.<br />

sxva<strong>da</strong>sxva saswavlo amocanebis amoxsnisas acnobierebs sakuTari aqtivobis<br />

mniSvnelobas. codna mas Ziebisa <strong>da</strong> aRmoCenis gziT miewodeba. am gziT miRebuli codna<br />

myari <strong>da</strong> safuZvliania.<br />

wignSi mocemuli saswavlo masala mravalferovania, erTmaneTs enacvleba fotoebi,<br />

naxatebi, komiqsuri tipis ambebi, savarjiSoebi.<br />

16

migvaCnia, rom zomierad miwodebuli masalis SemTxvevaSi bavSvis ga<strong>da</strong>tvirTvis<br />

mizezi xdeba ara raodenoba, ara<strong>me</strong>d saswavlo procesis xarisxi.<br />

SemoTavazebuli saswavlo kursis <strong>da</strong>xmarebiT SeTvisebuli masala bavSvs saSualebas<br />

aZlevs gaiazros codnis <strong>da</strong>niSnuleba.<br />

moswavlis wignis sawyisi gakveTilebi<strong>da</strong>n bavSvebs eZlevaT <strong>da</strong>valebebi, romlebic<br />

azrovnebis kreatiulobas uwyobs xels, aviTarebebs ara marto gonebas, ara<strong>me</strong>d qmnis<br />

<strong>da</strong>debiT ganwyobas, ro<strong>me</strong>lic Tavis mxriv, swavlis motivacia xdeba. is saSualebas<br />

aZlevs moswavles Seicnos sakuTari Tavi <strong>da</strong> SeZlos TviTSefaseba, gaarkvios Tavisi<br />

pozicia, Camoayalibos TviTkontrolisa <strong>da</strong> TviT-regulaciis Cvevebi.<br />

<strong>da</strong>valebebi<br />

<strong>da</strong>valebaTa sistema agebulia sirTulis donis zrdis mixedviT ise, rom pirvelklaselma<br />

masze muSaoba SeZlos u<strong>me</strong>tesad <strong>da</strong>moukideblad. maswavleblis roli imaSi<br />

mdgomareobs, rom <strong>da</strong>exmaros moswavles <strong>da</strong>valebis azris gagebaSi: waukiTxos mas <strong>da</strong>valebis<br />

teqsti, ganixilos masTan erTad. gaarkvios rogor gaigo igi <strong>da</strong> saWiroebis<br />

SemTxvevaSi <strong>da</strong>exmaros <strong>da</strong>valebis ganawilebaSi.<br />

saxelmZRvaneloSi Setanili <strong>da</strong>valebebi<br />

• xels uwyobs <strong>me</strong>xsierebis, yuradRebis,<br />

azrovnebis, <strong>me</strong>tyvelebisa <strong>da</strong> warmosaxvis<br />

unaris ganviTarebas;<br />

• ayalibebs swavlis Cvevebs;<br />

• xels uwyobs ganaTlebuli pirovnebis<br />

formirebas;<br />

• maTgan moiTxovs Semoq<strong>me</strong>debiT midgomas<br />

(“moifiqre”, “monaxe”, Seadgine”, “SearCie”,<br />

“<strong>da</strong>xate” <strong>da</strong> a.S.) <strong>da</strong> aviTarebs ara marto gone<br />

bas, ara<strong>me</strong>d nebisyofasac.<br />

17<br />

saSinao <strong>da</strong>valeba<br />

aviTarebs<br />

• pasuxismgeblobas;<br />

• <strong>da</strong>moukideblobas;<br />

• <strong>da</strong> arCevanis unars.<br />

• bavSvisTvis logikuri <strong>da</strong> algoriTmuli azrovnebis ganviTarebis sistemis Camoyalibebis<br />

es etapi mTlianad agebulia iseTi <strong>da</strong>valebebis upiratesad gamoyenebaze,<br />

romlebic sagnobriv masalaze muSaobis saSualebiT, mimarTulia xatovan-TvalsaCino<br />

azrovnebis aqtivizaciisa <strong>da</strong> ganviTarebaze, rac am asakSi bavSvebis azrovnebaSi wamyvan<br />

rols asrulebs.<br />

• wigni isea organizebuli, rom grafTa gacnoba xdeba gansxvavebuli amocanebis<br />

amoxsnisas ise, rom amocanaTa pirobebSi grafi ar aris moxseniebuli.

• garemomcveli samyaros kompiuterizacia mTeli rigi Cvevebisa <strong>da</strong> unarebis ga<strong>da</strong>fasebis<br />

aucileblobas iwvevs. gansakuTrebul mniSvnelobas iZens moq<strong>me</strong>debis gegmis<br />

Sedgenis <strong>da</strong> ganxorcielebis unari, amoxsnis variantebis SerCeva, miRebuli pasuxebis<br />

marTebulobis Sefaseba, mocemuli wesebisadmi <strong>da</strong> algoriT<strong>me</strong>bisadmi mkacri <strong>da</strong>qvemdebarebis,<br />

kvlevis organiz<strong>me</strong>bis unari. SemoTavazebuli kursi am unarebis ganviTarebasa<br />

<strong>da</strong> skolaSi informatikis Semdgom <strong>da</strong>nergvazea orientirebuli.<br />

• <strong>da</strong>wyebiTi klasebis moswavleebisTvis maTematikisadmi interesis gaRviveba, maTi<br />

maTematikuri niWis gamovlena <strong>da</strong> ganviTareba SeuZlebelia saswavlo procesSi arastan<strong>da</strong>rtuli<br />

<strong>da</strong> saxaliso amocanebis gamoyenebis gareSe. maTi amoxsna saSualebas iZleva,<br />

ganvaviTaroT bavSvSi azrovnebis iseTi saxeebi, rogoricaa analizi, sinTezi, analogia,<br />

ganzogadeba, azrovnebis moqniloba <strong>da</strong> aCvevs maT miRebuli Sedegebis kritikul aRqmas.<br />

vinai<strong>da</strong>n arastan<strong>da</strong>rtuli <strong>da</strong> saxaliso amocanebis amoxsna swrafad ar xdeba <strong>da</strong><br />

u<strong>me</strong>tes SemTxvevaSi miiRweva ramdeni<strong>me</strong> mcdelobis Semdeg, es aviTarebs miznis <strong>da</strong>JinebiT<br />

miRwevis unars, anu xels uwyobs pirovnebs mniSvnelovani Tvisebis _ nebisyofis gamomuSavebas.<br />

rac mTavaria, aseTi amocanebis amoxsna bavSvs aZlevs mZlavr emociur muxts,<br />

rasac iwvevs, erTi mxriv, Sedegis miRweva, xolo, <strong>me</strong>ore mxriv, amoxsnis araordinaluri<br />

gzis monaxva.<br />

is, raze<strong>da</strong>c fiqri gviwevs, raze<strong>da</strong>c ga<strong>da</strong>wyvetilebas vRebulobT, raSic bavSvis<br />

inteleqtualuri aqtivobaa Cadebuli, ukeTesad amaxsovrdebaT. izrdeba ra saswavlo<br />

procesSi <strong>da</strong>moukidebeli azrovnebis xvedriTi wili, mcirdeba masalis aTvisebis dro,<br />

paralelurad izrdeba aTvisebis xarisxi.<br />

• swavlebis pirveli wli<strong>da</strong>n mniSvnelovani adgili ukavia Tana<strong>me</strong>drove maTematikis<br />

ZiriTad cnebas _ simravles <strong>da</strong> masTan <strong>da</strong>kavSirebul zogierT sakiTxs. jer kidev skolamdel<br />

asakSi aqvs bavSvs warmodgena simravleze. saxelmZRvanelom ki un<strong>da</strong> SeZlos misi<br />

ganviTareba <strong>da</strong> gaRrmaveba swavlebis pirveli wli<strong>da</strong>nve.<br />

18

weriTi <strong>me</strong>tyveleba<br />

• aucilebelia fanqriT wera, fanqari iSleba <strong>da</strong> Secdo<strong>me</strong>bi advilad swordeba;<br />

• yvela weris savarjiSo azrovnebasTanaa Serwymuli;<br />

• cifrTa gaazrebis <strong>me</strong>re iwyeba maTi wera;<br />

• jer xdeba cifrTa vizualuri aRqma <strong>da</strong> Semdgom iwyeba maTi weriTi Seswavla;<br />

• moswavles moeTxoveba kargad aiTvisos ujriani bade, sworad eWiros fanqari,<br />

marTebulad werdes cifrebs;<br />

• pirvel xanebSi pataras uWirs koordinacia. amitom mas ar moeTxoveba cifrebis<br />

lamazad wera;<br />

• Tavi<strong>da</strong>n weriTi savarjiSoebi klasSi keTdeba, Semdeg ki saSinao <strong>da</strong>valebad. dro<strong>da</strong>dro<br />

mowmdeba weriTi kultura.<br />

zepir<strong>me</strong>tyveleba<br />

_ msjelobs <strong>da</strong> logikurad gadmoscems azrs;<br />

_ wers maTematikur karnaxebs;<br />

_ igonebs, xatavs <strong>da</strong> logikurad gadmoscems maTematikuri amocanis azrs.<br />

saxviTi <strong>me</strong>tyveleba<br />

,,yvelam ,,yvelam kargad kargad icis, icis, rom rom sagani sagani gasinjviT gasinjviT ise ise arasdros arasdros<br />

Seiswavleba, Seiswavleba, rogorc rogorc <strong>da</strong>xatviT, <strong>da</strong>xatviT, sakuTari sakuTari xeliT xeliT<br />

gamosaxviT.’’<br />

gamosaxviT.’’<br />

(iakob (iakob gogebaSvili)<br />

gogebaSvili)<br />

naxati bavSvisTvis informaciis miRebisa <strong>da</strong> ga<strong>da</strong>cemis erT-erTi yvelaze nacnobi<br />

wyaroa, amitomac saxelmZRvaneloSi naxatze muSaoba swavlebis erT-erTi aqtiuri<br />

<strong>me</strong>Todia:<br />

• bavSvi qmnis mowodebuli naxatis mixedviT ricxviT gamosaxulebas <strong>da</strong> ricxviTi<br />

gamosaxulebebis mixedviT qmnis naxats.<br />

19

samuSao rveuli<br />

moswavlis rveulis Sinaarsi mTlianad Seesaba<strong>me</strong>ba saxelmZRvanlos Sinaarss.<br />

samuSao rveuli warmoadgens maswavleblis <strong>da</strong>mxmare masalas. is Sedgenilia samuSao<br />

baraTebisa <strong>da</strong> Sefasebis furclebisagan.<br />

• swavlebis pirvel etapze arsebiTia ara is, <strong>da</strong>valeba swora<strong>da</strong>a Sesrulebuli, Tu<br />

ara, ara<strong>me</strong>d is, rom masSi <strong>da</strong>Svebuli yvela Secdoma Sesworebulia bavSvis mier.<br />

moswavleebi <strong>da</strong>moukideblad asruleben <strong>da</strong>valebebs, bavSvebi amow<strong>me</strong>ben mas klasSi <strong>da</strong><br />

<strong>da</strong>Svebul Secdo<strong>me</strong>bs asworeben, am dros aucilebelia moswavleebisaTvis fsiqologiuri<br />

garemos Seqmna. (,,<strong>me</strong> SemiZlia’’; ,,<strong>me</strong> gamomdis.’’)<br />

samuSao baraTebi<br />

• amow<strong>me</strong>bs maswavleblis mier codnis ga<strong>da</strong>cemis xarisxs.<br />

• amow<strong>me</strong>bs aTvisebuli codnis xarisxs;<br />

individualuri samuSao baraTi<br />

samuSao baraTebis gaTvaliswinebiT maswavlebeli adgens TiToeuli bavSvis codnis<br />

xarvezs, agrZelebs maTTan individualur muSaobas <strong>da</strong> amow<strong>me</strong>bs maT codnas.<br />

Sefasebis furceli<br />

• afasebs moswavlis mier aTvisebul codnas.<br />

20

logo

products

Resources

Company

Terms of service
Privacy policy
Cookie policy
Cookie settings
Imprint
Change language
Made with love in Switzerland
© 2024 Yumpu.com all rights reserved

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!