dawyebiti klasebis matematikis davalebis...

dawyebiTi klasebis maTematikis davalebis

baraTebi

gamoyenebis instruqcia

am masalis momzadeba SesaZlebeli gaxda amerikeli xalxis keTili nebiTa da aSS saer

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TaSoriso ganviTarebis saagentos mxardaWeriT. masalis Sinaarsze pasuxismgebelia qemoniqs inTerneSenali ink. da da igi ar warmoadgens aSS saerTaSoriso ganviTarebis saagentosa an aSS mTavrobis azrs. es masala momzadda aSS saerTaSoriso ganviTarebis saagentos dawyebiTi ganaTlebis proeqtis farglebSi, romelic xorcieldeba saqarT

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velos ganaTlebisa da mecnierebis saministrosTan erTad.

am masalis momzadeba SesaZlebeli gaxda amerikeli xalxis keTili nebiTa da aSS saerTaSoriso ganviTarebis saagentos mxardaWeriT. masalebis Sinaarsze pasuxismgebelia SemdgenelTa jgufi da igi ar warmoadgens aSS saerTaSoriso ganviTarebis saagentosa da aSS mTavrobis azrs. Ees masala momzadda aSS saer-TaSoriso ganviTarebis saagentos dawyebiTi ganaTlebis proeqtis farglebSi, romelic xorcieldeba saqarTvelos ganaTlebisa da mecnierebis saministro-sTan erTad.

1

maTematikuri davalebis baraTebi

davalebis baraTis ganmarteba:

davalebis baraTi aris moswavlisTvis gankuTvnili savarjiSos werilobiTi aRwera da miTiTebebi, Tu ro-gor SeuZlia bavSvs maswavleblis mier misTvis micemu-li davalebis Sesruleba.

baraTebis dizaini iseTi unda iyos, rom bavSvebi waax-alisos problemis gadaWris, dafiqrebis, kiTxvebis das-mis, zepiri da werilobiTi komunikaciisa da TanamSrom-lobisken.

davalebis baraTi martivi eniT unda iyos Sedgenili, raTa bavSvebma advilad SeeZlon misi gageba. masSi dasmuli amocanebi unda iyos garkveuli da gasagebi rogorc maswav-leblis asistentisa da mSoblisTvis, ise bavSvebisTvis.

kargad Sedgenili baraTis maxasiaTeblebi:

• aqvs diferenciaciis potenciali imis gamo, rom iZleva sxvadasxvanairi midgomis, strategiisa da Caweris teqnikis gamoyenebis saSualebas,

• bavSvs aZlevs saSualebas winare unarebisa da cod-nis miRma kidev ufro win waiwios,

• amocanas SeiZleba hqondes erTze meti amoxsna an amoxsnamde misasvleli ramdenime gza,

• davalebis SesrulebisTvis saWiroa ufro meti, vi-dre ubralod faqtebis damaxsovreba da gaxseneba,

• bavSvs aZlevs saSualebas, rom warmoadginos maTematikuri ideebi werilobiT an modelebis gam-oyenebiT,

• bavSvs aZlevs saSualebas, rom dasabuTebulad im-sjelos an Seafasos sxvebis msjeloba,

• Seicavs mokle da gasageb direqtivebs.

2

baraTis struqtura:

• saWiro masalebi – is, rac moswavleebs dasWirde-baT davalebis Sesasruleblad.

• davalebis Sesrulebis gzebi – martivi instruqcie-bi, maTematikuri azrovnebis stimulirebisTvis saWiro Ria SekiTxvebi da miniSnebebi.

• mkafiod gamokveTili saswavlo sakiTxi, romelsac exeba baraTSi mocemuli davaleba - saswavlo pro-gramis dagegmvisa da moswavlis Sefasebis xelSewy-obis mizniT.

marTebulad Sedgenili davalebis baraTis nimuSi moswavlisTvis, romelmac ZiriTadi davaleba sxvebze adre daasrula:

maTematikuri davalebis baraTi

gamoTvaleT, ramdeni wlisaa TiToeuli bavSvi.

luka lali ana qeTi mari kaxa liana

= 2 = 3 = 1

3

pedagogiurad Seuferebeli davalebis baraTis nimu-Si moswavlisTvis, romelmac ZiriTadi davaleba sxvebze adre daasrula:


100%

ujredebian qaRaldis furcelze Camowere ricxvebi ukuTvliT 100-dan 1-mde.

maswavleblebis mier xSirad gamoyenebuli davalebis baraTebis nimuSebi

qvemoT ixilavT davalebis baraTebis magaliTebs, rom-lebic SegiZliaT nimuSebad da STagonebis wyarod gamoiy-enoT.

Ria davaleba


Seadgine amocana xoWoebis Sesaxeb, romelSic gamoyenebuli iqneba ricxvebis mimateba.

pasuxad unda miiRo ricxvi, romelic ar aRemateba 18-s.

4

davalebis baraTi sadiagnostiko SefasebisTvis


Cawere ricxvebi, romlebic Seicavs:

8 aTeuls da 6 erTeuls






davalebis baraTi swrafi moTelvisaTvis


Seavse cxrilis carieli ujrebi.

TiToeul mocemul ricxvs gamoakeli 3.

861112

5

baraTi gameorebisTvis


daalage mocemuli ricxvebi klebadobis mixedviT.

34, 68, 13, 84

46, 25, 47, 16

19, 15, 12, 5

baraTi jgufuri muSaobisaTvis


warmoadgine mocemuli wiladebi naxatebis saSualebiT.

23

35

1 4

5 6

28

4 7

5 9

1 2

6

baraTi moswavlis damoukideblad gavarjiSebisTvis


daxaze brtyeli figurebi da qves miuwere maTi saxelebi

1. marTkuTxedi

2. kvadrati

3. wre

4. samkuTxedi

baraTi mTeli klasis monawileobisaTvis


SeadgineT saklaso oTaxSi arsebuli nivTebis sia, romelTa sigrZe daaxloebiT Teqvsmeti

santimetris tolia.

7

baraTi „moifiqre da mewyviles gauziare“


Tvali gadaavle Seni Tanaklaselebis maisurebs. Seadgine diagrama, romelic

asaxavs sxvadasxva feris maisurebis raodenobas. Seamowmebine Sens mier Sedgenili

diagrama Sens mewyviles.

saSinao davalebis baraTi


Seadgine amocana zRvis varskvlavis Sesaxeb, romelic gamoklebiT unda amoixsnas. dawere amocanis Sesabamisi ricxviTi gamosaxuleba.

8

daval

ebis baraT

ebis gamo

yeneba gakveT

ilebz

e:

moswavl

eebi awesrigeben, ganmar

taven d

a afaseben saku

Tar

naazr

evs.

amoc

anebis amoxsna 3

ro

melia mo

mdevno

ric

xvi? 150, 155, 160, 165, 170, 175

ro

meli xer

xis gamoyenebiT

amoxseni amo

cana?

•d

avxate su

raT

i •vipo

ve kanonz

omier

eba •gaviT

amaSe amo

canaSi mo

cemu

li viT

areba

•gamo

vicani d

a Sevamowme •

Sevadgine c

xril

i •gamo

vTval

e u

kusvl

iT

•j

er amo

vxseni uf

ro

mart

ivi amoc

ana

amoc

anebis amoxsna

4r

igSi pirvel

i dgas, l

eqso ki

mis ukan, o

Txi mo

swavlis Semd

eg. r

igSi meramd

enea leqso

?

ro

meli xer

xis gamoyenebiT

amoxseni amo

cana?

•d

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ve kanonz

omier

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amaSe amo

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Sevadgine c

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mart

ivi amoc

ana

amoc

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1and

riam baR

Si To

Txmet

i vaSli mo

wyvita,

vanom –

aTi, gio

rgim –

eqvsi, xol

o er

eklem

– o

Txi. su

l r

amdeni vaSl

i mowyvit

es bavSvebma? r

omel

i xerxis gamo

yenebiT amo

xseni amo

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raT

i •vipo

ve kanonz

omier

eba •gaviT

amaSe amo

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er amo

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ro

mart

ivi amoc

ana

amoc

anebis amoxsna

2l

anas sakuW

naoSi saT

amaSoebis eqvsi yu

Ti

hqond

a. TiT

oeu

l yu

TSi sami saT

amaSo id

o.

sul

ramd

eni saTamaSo

hqond

a lanas?

ro

meli xer

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amoxseni

amoc

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ve kanonz

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amaSe amo

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xril

i •gamo

vTval

e u

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mart

ivi amoc

ana

9

moswavleebi ikvleven:

gaarkvieT, sworia Tu ara

ori Tanmimdevruli samkuTxa ricxvis jami mTeli ricxvis

kvadratia.


marTkuTxeds aqvs 2 simetriis RerZi.


6-is jeradebi martiv ricxvebze 1-iT meti an 1-iT

naklebia


oTxi luwi ricxvis jami 4-ze iyofa.


Tu luw ricxvs kent ricxvze gavamravlebT, kent ricxvs

miviRebT.


oTxkuTxeds ar SeiZleba 2-ze meti blagvi kuTxe hqondes.


20 TeTrze naklebi sul 2 Tanxaa, romelsac ver SevagrovebT 3 monetiT.


orniSna ricxvisa da misi cifrebis gadanacvlebiT

miRebuli ricxvis sxvaoba yovelTvis 9-is jeradia.

10

rogor gamoviyenoT maTematikuri davalebis baraTebi

risTvis viyenebT davalebis baraTebs?

davalebis baraTebi motivaciis amamaRlebeli da efeqturi saswavlo saSualebaa, romelic SegviZlia gamoviyenoT imisTvis, rom ufro efeqturad CavrToT moswavleebi maTematikur aqtivobebSi. arsebobs ram-denime mizezi, ris gamoc Rirs mxedvelobaSi miviRoT am faseuli saSualebis gamoyeneba:

• davalebis baraTebi moswavleebs motivacias umaR-lebs imiT, rom baraTze mxolod erTi davaleba we-ria. moswavles erTdroulad ramdenime davaleba rom hqondes gasakeTebeli, igi ubralod gadat-virTulad igrZnobs Tavs. Tumca, roca igive dava-lebebi davalebis baraTebzea ganawilebuli, maSin moswavles rigrigobiT TiTo-TiTo davalebis Ses-ruleba uwevs. roca erT davalebas gaumklavdeba, miRweulis gamo mas kmayofilebis grZnoba eufleba da amis Semdeg morig davalebaze gadadis.

• davalebis baraTebis Sedgena SeiZleba specifi-kuri saswavlo miznebis gansaxorcieleblad. Tu Tqveni moswavleebi ama Tu im specifikur sfero-Si moikoWleben, SegiZliaT SeadginoT davaleba an gamoiyenoT zemoT moyvanili romelime nimuSi specifikuri unaris ganviTarebaze fokusirebuli swavlebis dros. amis gamo davalebis baraTebi Ses-aniSnavi saSualebaa testisTvis mosamzadebladac!

• davalebis baraTebi swavlebis diferencirebas aadvileben. sakoreqcio swavlebis saWiroebis mqone moswavleebs SeiZleba mieceT specifikuri davalebebi, romlebic maT Znelad gasagebi cnebis gagebaSi daexmareba. moswavleebs, romlebsac ukve

11

kargad esmiT esa Tu is cneba, SeiZleba mieceT dam-atebiTi davalebebi, romlebic maT am cnebis ufro Rrmad gaazrebis saSualebas miscems.

• davalebis baraTebi sxvadasxvagvaria. davalebis baraTebis erTi kompleqti SeiZleba bevrnairad iqnas gamoyenebuli: individualurad, e. w. maTema-tikis kuTxeebSi, wyvilebSi an mcire jgufebSi da mTel klasTan erToblivadac ki. baraTebi SegiZli-aT gamoiyenoT Tqveni yoveldRiuri rutinis gas-amravalferovneblad, TamaSebis an saSinao dava-lebis Sesrulebis dros. garda amisa, maTi gamoy-eneba yvela klasSi SeiZleba.

baraTebis gamoyenebis xerxebi

davalebis baraTebis erTerTi yvelaze Zlieri mxare isaa, rom maTi gamoyeneba mravalgvarad SeiZleba. maswav-leblebs SeuZliaT baraTebis gamoyeneba moswavleebisT-vis Cveulebrivi saswavlo dRis nawilad aqcion: gamoiy-enon im moswavleebis damatebiTi mecadineobisTvis, rom-lebic ama Tu im cnebas Znelad iTviseben, an gamoiyenon im moswavleebis codnis gasamdidreblad, romlebic, ro-gorc wesi, sxvebze adre asruleben davalebas.

dawyebiTi klasebis zogierTi maswavlebeli maTema-tikaSi mecadineobis dawyebamde 10 wuTis ganmavlobaSi amuSavebs bavSvebs davalebis baraTebze. davalebis ba-raTebi, romlebzedac maswavlebeli maT amuSavebs, im wlis masalis, zogierT SemTxvevaSi gasul wels SeZenili unarebis gameorebasac ki exeba. maswavleblebi moswav-leebs konkretuli davalebis baraTebis iseT kompleqts urigeben, romelTa saSualebiT moswavleebs swored im unarebze amuSeveben, romelTa gameoreba an gamdidrebac sWirdebaT. bavSvebs uyvarT davalebis baraTebis gamoy-eneba da am dros swavlis procesSi CarTuli arian.

davalebis baraTebi mSvenieri saSualebaa swavlebis gamravalferovnebisa da diferencirebisTvisac!

12

mas wavleblebi adgenen baraTebis or TiTqmis erTnair kompleqts, Tumca erT kompleqtSi damatebiT safex-urebs amateben. maswavleblebi adgenen moswavlis Sesa-bamisi klasis programaze ufro maRali donis baraTebis kompleqtebsac, romlebiTac mocemul masalaSi gawa-ful moswavleebs SeuZliaT muSaoba. baraTebis nawili iseTi davalebebs moicavs, romlebiTac kritikuli az-rovneba mowmdeba. moswavleebs uxariaT, roca aseT ba-raTebze muSaobis SesaZlebloba eZlevaT!

davaleba momzadebis dabali donis moswavleebisaTvis naSTian gayofaze:

maTematikuri davalebis baraTidawereT 4 iseTi ricxvi, romelTa 7-ze

gayofiT miiReba naSTi 2.

davaleba momzadebis saSualo donis moswavleebisaTvis naSTian gayofaze:

maTematikuri davalebis baraTirisi tolia naSTi?

(5X6X7X8X9+4):7

davaleba momzadebis maRali donis moswavleebisaTvis naSTian gayofaze:

maTematikuri davalebis baraTidaasaxeleT umciresi ricxvi, romlis 5-ze,

6-ze an 7-ze gayofiT naSTSi miiReba 2?

13

baraTebis individualuri gamoyeneba

Tu maswavlebeli baraTebis kompleqts moswavleebs rigrigobiT miscems gamosayeneblad, man garkveuli meTodiT unda ixelmZRvanelos, raTa Tvalyuri adev-nos, Tu vin daasrula baraTebis kompleqtze muSaoba. maswavleblebs SeuZliaT TviT moswavleebs mianiWon TavianTi samuSaos dasrulebaze meTvalyureTa fun-qcia da gaakeTebinon CaniSvna specialur furcelze, maswavleblis JurnalSi, gancxadebebis dafaze an var-sklavebian cxrilze. maswavlebels aseve SeuZlia sa-muSaos dasrulebis Semdeg moswavleebs aCvenos swori pasuxebi, raTa maT TviTon SeZlon TavianTi naSromis Semowmeba. davalebis baraTis individualuri gamoy-enebisaTvis gTavazobT ramdenime ideas:

• maswavleblebs SeuZliaT Seqmnan maTematikis “kuTxe” specialurad garkveuli tipis baraTebi-sTvis an davalebis baraTebi maTematikuri “kuTx-is” Semadgenel nawilad gaxadon. moswavleebs Seu-ZliaT am baraTebiT imuSaon “maTematikis kuTxisT-vis” gankuTvnil dros an maSin, roca Tavisufali dro rCebaT.

• moswavleebs SeuZliaT davalebis baraTebi aiRon da TavianT adgilebze Seavson.

• Tu klasSi romelime moswavles Zalian uWirs garkveuli koncefciis gageba, maswavlebels Seu-Zlia saxlSi gaatanos davalebis baraTebis komple-qti, romelic konkretuli unaris gasaviTareblad gamoiyeneba. amgvarad moswavles ara mxolod dam-atebiTi dro miecema misTvis rTul unarze koncen-trirebisaTvis, aramed aseve uxerxulobis grZno-bac moexsneba, romelic SeiZleba daufleboda im SemTxvevaSi, Tu Tanaklaselebis Tvalwin mouwev-da Tavisi sisustis gamosworebaze muSaoba. meore mxriv, Tu romelime moswavlis mSoblebi maswavleb-

14

els Txoven, maT Svils damatebiTi davaleba misces, maswavlebels SeuZlia davalebis gasamdidreblad moswavles ramdenime Ria SekiTxvis Semcveli bara-Ti gaatanos.

• miuxedavad imisa, rom davalebis baraTebi ar aRiqmeba, rogorc testi, sulac ar iqneba urigo, Tu baraTebis nakrebi testis magivrobas gawevs. maswavlebels SeuZlia gamoiyenos mTeli kompleq-ti an ramodenime baraTi imisTvis, rom darwmundes, Tu rogor gaigo bavSvma esa Tu is cneba.

wyvilebSi an mcire jgufebSi

zogierTi baraTi advili gamosayenebelia wyvilebSi an mcire jgufebSi. gTavazobT ramdenime ideas:

moswavleebi wyvilebad iyofian, erTmaneTs rigri-gobiT ukiTxaven baraTebs da maTze pasuxoben. moswav-les SeuZlia gamoiyenos swori pasuxebis furceli im-isTvis, rom Seamowmos, sworad gasca Tu ara pasuxi mew-yvilem.

mcire jgufebis SemTxvevaSi jgufis lideri kiTxu-lobs baraTs, jgufis danarCeni wevrebi ki pasuxebs weren TavianT patara dafebze, romlebsac isini aravis aCveneben, sanam lideri ar gascems brZanebas: “pasuxebi maCveneT!” jgufs SeiZleba mTeli aqtivobis ganmav-lobaSi erTi an monacvleobiT ramdenime lideri uZRve-bodes.

ar aris aucilebeli, rom moswavleebma baraTebs rig-rigobiT upasuxon. specialurad mowyobil kuTxeSi ramodemine moswavles erT kompleqtze erTad SeuZlia muSaoba da baraTebis gaziareba.

davalebis baraTebi SeiZleba sxvadasxva saxis Tama-SebisTvis iqnas gamoyenebuli.

15

mTel klasTan erTad

maswavleblebs SeuZliaT ar dayon saklaso oTaxi kuTxeebad da davalebis baraTebi mTel klasTan samuSa-od gamoiyenon. gTavazobT ramdenime ideas:

• SegiZliaT gamoiyenoT baraTebi, rogorc gakveTi-lis Sesavali aqtivoba. rogorc ki moswavleebi sak-laso oTaxSi Semovlen, maswavlebeli maRla awevs da aCvenebs Ria SekiTxvis mqone baraTs.

• SegiZliaT gamoiyenoT baraTebi imisTvis, rom iTamaSoT `gadaadgileba~. amisTvis maswavlebeli yvels moswavles daurigebs TiTo baraTs da dan-omril furcels masze pasuxebis dasawerad. mo-swavleebi waRma piriT alageben baraTebs TavianT merxebze. yvela moswavle Tavis merxTan dgeba da baraTze mocemuli kiTxvis pasuxs wers pasuxebis furcelze, amisTvis specialurad gankuTvnil adgilas. ramdenime wuTSi maswavlebeli gascems brZanebas: “gadaadgildiT!” am dros yvela bavSvi gadaadgildeba momdevno merxTan da Semdeg kiTx-vas pasuxobs. moswavleebi ganagrZoben saklaso oTaxSi siaruls maswavlebelis brZanebiT manamde, sanam yvela moswavle daasrulebs yvela baraTze muSaobas.

davalebis baraTebis tipebi

davalebis baraTebi SeiZleba nebismier maTematikur sakiTxs exebodes. igi unda Seesabamebodes mocemuli klasis dones, saswavlo mizans da aqtivobas. davalebis baraTebis klasifikacia xdeba sxvadasxva klasis donee-bisa da Tematikis mixedviT. amas garda, isini erTmane-Tisgan formatiTac gansxvavdeba. baraTis Sedgenisas gasaTvaliswinebelia is, Tu ra tipis pasuxs saWiroebs igi. sxvadasxva tipis pasuxi sxvadasxva aqtivobis Cat-arebis saSualebas iZleva.

16

asarCevi pasuxebi

asarCevi pasuxebis mqone davalebis baraTebi albaT yvelaze advili gamosayenebelia. moswavleebs Sedare-biT swrafad SeuZliaT maTi amoxsna. garda amisa, vinaid-an aseTi baraTebis formati standartuli testebis mravali tipis msgavsia, maTi gamoyeneba idealuria tes-tebisaTvis mosamzadeblad. baraTebze pasuxis gacema swrafad da martivad xerxdeba, radganac moswavlem masSi sul raRac erTi aso unda Caweros an Semoxazos. Tu xelT gvaqvs swori pasuxebis furceli, moswavlee-bs SeuZliaT advilad Seamowmon sakuTari namuSevari. asarCevi pasuxebis mqone baraTi zedgamoWrilia aseve mTel klasTan samuSaod “gadaadgilebis” msgavsi tipis TamaSebisTvis, an moswavleebis individualur dafebT-an pasuxis dros.

mokle pasuxi

mokle pasuxis mqone davalebis baraTebis mTavari up-iratesobaa imaSi mdgomareobs, rom isini moswavles met gamowvevas sTavazobs, vidre asarCevi pasuxis mqone ba-raTebi. aseTi baraTebis gamoyenebisas diferencirebis erTerTi xerxia Tanabari gamowvevis mqone baraTebis ori kompleqtis qona, romelTagan erTerTi Seicavs mokle pasuxebis mqone baraTebs SedarebiT Zlieri mo-swavleebisTvis. mokle pasuxebis mqone baraTebze pa-suxis gacema Cveulebriv ufro xangrZlivi procesia, vinaidan am SemTxvevaSi moswavlem erT asoze meti unda daweros. swori pasuxebis furclis qonis SemTxveva-Si moswavleebs aqac SeuZliaT sakuTari namuSevrebis Semowmeba.

Ria kiTxvebi

Ria SekiTxvebze erTaderTi swori pasuxi ar arse-bobs. SeiZleba ramdenime pasuxi iyos misaRebi, an sulac SesaZlebelia, SekiTxva sruliad Riad darCes da masze

17

yvela moswavles unikaluri pasuxi gaaCndes. aseTi ti-pis baraTi met sivrces tovebs kreatiulobisaTvis, ris gamoc igi xSir SemTxvevaSi moswavleTa sayvareli bara-Tis tipicaa.

aqtivobis baraTebi

aqtivobis baraTebSi Cveulebriv araa dasmuli SekiTxva. maTSi mocemulia moswavlis mier Sesasrule-beli davaleba. aseT baraTze mocemuli davalebis Ses-ruleba, Cveulebriv, erTbaSad ver moxerxdeba. erT baraTze mocemuli davalebis Sesasruleblad moswav-leebs SeiZleba saaTebi dasWirdeT. aseT baraTs ideal-urad moergeboda saSinao davalebis roli.

sxva gasaTvaliswinebeli sakiTxebi

umetes SemTxvevaSi maswavleblebi TviTon beWdaven, Wrian da alaminireben baraTebs. imisda miuxedavad, yidu-loben Tu qmnian isini baraTebs, maT unda gaiTvaliswinon dro da masalebi, romlebic ixarjeba baraTebis dasamza-deblad da is, Tu rogor apireben maT gamoyenebas.

• baraTebis zoma: didi zomis baraTebi mSvenivrad gamoiyeneba patara asakis moswavleebTan samuSaod da maTze Tvalyuris devnebac ufro advilia. meore mxriv, mcire zomis baraTebis gamoyenebiT Segvi-Zlia qaRaldis ekonomia.

• rogor gamoiyeneba ferebi: zogierT davalebis baraTs Wreli foni aqvs. amis gamo baraTebi Sei-Zleba ufro lamazi gamovides, magram maT beWdvaSi maswavlebelma SeiZleba printeris bevri saRebavi daxarjos.

• saerTo xarisxi: maswavleblebi unda darwmundnen, rom baraTebs, romelTa gamoyenebasac isini mo-swavleebTan muSaobis dros apireben, kargi dizaini aqvs da lamazad gamoiyureba.

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baraTebi gavlili masalis gansamtkiceblad

davalebis baraTebis gamoyeneba SesaniSnavi ideaa im moswavleTa SemTxvevaSi, romelTac ama Tu im sferoSi cotaodeni gavarjiSeba sWirdebaT. moswavleebs ba-raTebi xSirad savarjiSoebis furcels urCevniaT, vi-naidan baraTze mxolod erTi davalebaa mocemuli, rac moswavles gadaRlisgan icavs. moswavleebs SeuZliaT amoxsnan zustad imdeni davalebis baraTi, ramdenic maT konkretul unarSi gawafvisaTvis esaWiroebaT. mo-swavles SeuZlia imuSavos davalebis baraTebze maSinac ki, roca maswavlebeli jgufTan erTad muSaobs. aseve SegviZlia baraTebis kompleqtebi momdevno dRisaTvis saSinao davalebad gavatanoT garkveul moswavleebs, romelTac damatebiTi samuSao waadgebodaT.

gamocdilebis gamravalferovneba

Zlieri moswavleebisaTvis gamowvevis Semcveli dava-lebis baraTebis micema SesaniSnavi ideaa. idealur Sem-TxvevaSi baraTebze mocemuli davalebebiT moswavlem ufro Rrmad unda gamoikvlios Sesaswavli sakiTxi an daamyaros kavSiri momijnave sakiTxebTan. ar Rirs brwy-invale moswavlis drois fuWi xarjva erTferovan dava-lebebze.

jgufebSi muSaoba

mcire jgufebSi davalebis baraTebi SegviZlia ram-denimenairad gamoviyenoT. individualuri dafebis gamoyenebiT yvelas SeuZlia imuSavos erTsa da imave baraTze da momdevno baraTze gadasvlamde erTmane-Tis pasuxebi Seadaron. aseve SegviZlia yvela moswavles sxvadasxva baraTi davurigoT, mivceT garkveuli dro davalebis Sesasruleblad da vTxovoT, gadaawodos Ta-visi baraTi mis gverdze mjdom moswavles da axla ukve axali davaleba SevasrulebinoT.

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progresisTvis Tvalyuris devneba

pasuxebis Caweris xerxi damokidebulia imaze, Tu ra tipis baraTebs iyenebs maswavlebeli. moklepasuxebi-ani baraTebis SemTxvevaSi sruliad misaRebia pasuxebis furceli. moswavleebs SeuZliaT Caiweron TavianTi pa-suxebi pasuxebis furcelSi da Caabaron is maswavleb-els an Seamowmon TavianTi pasuxebi swori pasuxebis furclis meSveobiT, romelsac maT maswavlebeli dau-rigebs.

zogierTi davalebis baraTis amosaxsnelad saWiroa SedarebiT vrceli, Ria pasuxebi. maswavlebels SeuZlia daawerinos moswavles pasuxi rveulis furcelze an davalebis baraTis kiTxvebze pasuxisaTvis gankuTvnil dRiurSi. moswavles SeiZleba erTi kompleqtiT gaT-valiswinebuli davalebebis Sesasruleblad ramdenime dRe dasWirdes. sxva SemTxvevaSi maswavlebels SeuZlia moswavleebs amoarCevinos garkveuli raodenobis ba-raTebi. moswavleebs amoxsnil baraTebze Tvalyuris sadevnelad SeiZleba gamoadgeT sakontrolo furceli.

Tu maswavlebels surs, qaRaldi saerTod ar gamoiye-nos, mas SeuZlia moswavleebi kompiuterebTan amuSavos da pasuxebi eleqtronuli formiT Caawerinos. moklepa-suxebiani baraTebis SemTxvevaSi qaRaldis gareSe muS-aobis kidev erTi varianti aris moswavleebis mier Tavi-anTi pasuxebis individualur dafebze Cawera da Tavi-anTi namuSevrebis Sesamowmeblad swori pasuxebis fur-clis gamoyeneba.

dawyebiti klasebis matematikis davalebis...

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