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Індивідуалізація навчально-пізнавальної діяльності учнів початкової школи в процесі засвоєння математичних знань: Автореф. дис… канд. пед. наук / Л.

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?INOEOOO IAAeAAIA?EE AII OE?A?IE

OAeE 37.372.2

EIEII?E*AIEI E?e?y Aai?a??aia

?IAeEA?AeOAE?CAOe?ss IAA*AEUeII-I?CIAAAEUeII? Ae?ssEUeIINO? O*I?A
II*AOEIAI? OEIEE A I?IOeAN? CANAI?IIss IAOAIAOE*IEO CIAIUe

13.00.01 – oai??y oa ?noi??y iaaeaaia?ee

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa iaaeaaia?/ieo iaoe

Ee?a – 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia o I?aaeaiiioe?a?inueeiio aea?aeaaiiio iaaeaaia?/iiio
oi?aa?neoao? ?i. E.Ae.Ooeinueeiai

Iaoeiaee ea??aiee – aeieoi? iaaeaaia?/ieo iaoe, i?ioani?

Oiaethe ?a?na ?ee?aia, eaoaae?a iaaeaaia?ee I?aaeaiiioe?a?inueeiai
aea?aeaaiiai iaaeaaia?/iiai oi?aa?neoaoo ?i. E.Ae.Ooeinueeiai, i?ioani?

Io?oe?ei? iiiiaioe – aeieoi? iaaeaaia?/ieo iaoe, i?ioani?, aeaaeai?e
AII Oe?a?ie

Aii/a?aiei Naiai Onoeiiae/, ?inoeooo iaaeaaia?ee ? ineoieia??

i?ioan?eii? ina?oe AII Oe?a?ie, aieiaiee iaoeiaee ni?a?ia?oiee

– eaiaeeaeao iaaeaaia?/ieo iaoe, noa?oee iaoeiaee ni?a?ia?oiee

Aaaea?aa Iaae?y ?aai?aia, noa?oee iaoeiaee ni?a?ia?oiee eaai?aoi???
aeioe?eueiiai aeoiaaiiy ?inoeoooo i?iaeai aeoiaaiiyAII Oe?a?ie,

I?ia?aeia onoaiiaa – E??iaia?aaenueeee iaaeaaia?/iee oi?aa?neoao ?i.
Aieiaeeie?a Aeiie/aiea, I?i?noa?noai ina?oe Oe?a?ie, i. E??iaia?aae

Caoeno a?aeaoaeaoueny “ 26 ” aa?aniy 1999 ?. i 14 aiae. ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.452.01 a ?inoeooo? iaaeaaia?ee AII
Oe?a?ie (252053, Ee?a, aoe.A?oaia, 52a)

C aeena?oaoe??th iiaeia iciaeiieoenue o iaoeia?e /anoei? ?inoeoooo
iaaeaaia?ee AII Oe?a?ie

Aaoi?aoa?ao ?ic?neaiee “ 26 ” ethoiai 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee i?io. Eaaeee I.I. CAAAEUeIA OA?AEOA?ENOEEA
?IAIOE

Aeooaeuei?noue oaie. ?aeay ?iaeea?aeoaeueiiai i?aeoiaeo aei o/i?a o
i?ioean? iaa/aiiy iaeaaeeoue aei a?/ieo i?iaeai oeiee ? ? iaeaaaeeea?oei
?c caeueiiaeeaeaeoe/ieo i?eioeei?a, iaiao?aei?noue ?aae?caoe?? yeiai a
oe?euei?e i?aeoeoe? coiiaeaia oei, ui caaacia/eoe oi?ioaaiiy iniaenoino?
aeeoeie, canai?iiy iath ciaiue c on?o iaa/aeueieo aeenoeeie?i oa
ae?iaeaiiy a ia? i?aeoe/ieo oi?iue ? iaae/ie, ?icaeoie ?? cae?aiinoae oa
iaaea?oaaiue iiaeia eeoa oeyoii ?iaeea?aeoae?caoe?? iaa/aiiy. Oiio
iniaeeaiai cia/aiiy iaaoaa? ?iaeea?aeoae?caoe?y iaa/aeueii-aeoiaiiai
i?ioeano a ii/aoeia?e oeie?, ai inoaiiy ? ooiaeaiaioii ia yeiio
aoaeo?oueny iiaeaeueoa iaa/aiiy oa aeoiaaiiy.

I?iaeaia ?iaeea?aeoae?caoe?? iaa/aiiy aeine?aeaeoaaeany o a?o/eciyi?e ?
ca?oa?aei?e ineoieiai-iaaeaaia?/i?e iaooe? a ??cieo aniaeoao: ye can?a
i?aeaeuaiiy aoaeoeaiino? iaa/aiiy (A.A.Aooe?i, A.?.Aeaaeeeo, ?.?.Oio oa
?i.), i?ciaaaeueii? aeoeaiino? ? naiino?eiino? (A.?.Eiaa?i?e,
?.N.?aaoinueeee, ?.A.*o??eia, O.?.Oaiiaa oa ?i.), niiniae i?aai?caoe??
o?iioaeueii?, a?oiiai? oa ?iaeea?aeoaeueii? ?iaioe o/i?a (A.I.Aeo?ou,
I.N.Eaeoan, E.O.Eeeiaon, O.I.I?eiea?aa), ye can?a ?icaeoeo niaoeeo?/ieo
cae?aiinoae (E.?.Aiaeiae/, A.I.E?ooaoeueeee, I.N.Eaeoan, I.I.Eaiioue?a,
I.A.Ii?iciaa, ?.A.Nenaoeueeee, A.I.Nooiieeinueeee, A.I.Oaieia,
A.O.Oaaei?eoei, I.I.sseianii), iiia?aaeaeaiiy ? onoiaiiy iaoni?oiino?
(A.?.Cyaayc?inueeee, I.?.Iaoiooia, I.I.Iai/einueea, E.N.Neaa?ia,
A.O.Oa?e?anueea), iioeae, ye? niiioeathoue o/i?a aei iaa/aiiy, oa ye
i?iaeaio oi?ioaaiiy i?ciaaaeueieo ?ioa?an?a (E.?.Aiaeiae/, I.A.Ii?iciaa,
A.?.Uoe?ia oa ?i.), ye aecia/aiiy ??ai?a, oi?i ? aeae?a aeeoa?aioe?aoe??
oa ?? iaa/aeueii-iaoiaee/ia caaacia/aiiy (TH.E.Aaaainueeee,
TH.C.A?eueaoo, TH.?.Iaeueiaaiee, A.I.Iieuoe, A.O. Iaeaia?/oe,
I.ss.Naa/aiei, ?.A.Nenaoeueeee oa ?i.).

Iaeiae, iacaaaeath/e ia oa, ui i?iaeai? ?iaeea?aeoae?caoe?? iaa/aiiy a
ineoieiai-iaaeaaia?/i?e iaooe? i?eae?ey?oueny aaeeea oaaaa, a oe?euei?e
i?aeoeoe? a i?ioean? iaa/aiiy caeeoa?oueny iaeaea iacaeieaiiith
oaiaeaioe?y aei ona?aaeiaiiy, oiio ui a oiiaao eeanii-o?i/ii? nenoaie
iaa/aiiy i???iooaaoeny ia ?iaeea?aeoaeueii-ineoieia?/i? iniaeeaino?
eiaeiiai o/iy iaaecae/aeii neeaaeii.

Iaaeaaia?/ia i?aeoeea na?ae/eoue, ui ona?aaeiaiiy i?ecaiaeeoue aei oiai,
ui iaa?oue iieaaoai? caaaeaiiy /anoi aeyaeythoueny iaiineeueieie aeey
o/i?a c iecueeei ??aiai iao/oaaiino?, ?icaeoie ?ioaeaeooaeueii
iaaea?iaaieo ae?oae aaeueio?oueny, ona?aaeiaiiy ia aeicaiey? ?i
?aae?coaaoe nai? iioaioe?ei? iiaeeeaino?. A oea a naith /a?ao iiaea
i?ecaanoe aei iaiii?aaieo iane?aee?a, ai eoeueoo?a noni?euenoaa, yea
noaea ia oeyo oi?o?eaoe?? (ona?aaeiaiiy), on?/aiiy nai?o “cae?aiinoae”,
i?e?a/aia ia aaiethoe?eiee ?aa?an (I.A.Aniieia).

Inoaii?i /anii, ye iieacaee aeine?aeaeaiiy, ?aae?co?oueny
aeeoa?aioe?aoe?y iaa/aiiy, ai aeeoa?aioe?eiaai? caaaeaiiy a i?aai?caoe??
iaa/aeueii? ae?yeueiino? o/i?a o ianiaiio iaaeaaia?/iiio aeina?ae?
aeei?enoiaothoueny ia/anoi (I.ss.Naa/aiei). I?ioa ?iaeea?aeoae?caoe?y ?
aeeoa?aioe?aoe?y aeaeaei ia iaeia ? oa ae. ?iaeea?aeoae?caoe?y – oea
?aae?caoe?y i?eioeeio ?iaeea?aeoaeueiiai i?aeoiaeo aei o/i?a, yeee
ia?aaeaa/a? a?aooaaiiy ?iaeea?aeoaeueiino? eiaeii? aeeoeie ye aeyaeaiiy
iniaeeainoae ineoi-o?c?ieia?/ii? i?aai?caoe?? a ?? iaiiaoi?iino?,
nai???aeiino?, oi?eaeueiino?.

Aeeoa?aioe?aoe?y – oea ?aae?caoe?y i?eioeeio aeeoa?aioe?eiaaiiai
i?aeoiaeo, yeee ia?aaeaa/a? a?aooaaiiy a?aei?iiinoae i?ae a?oiaie o/i?a
ca ?oi?ie ?ioa?anaie, ??aiai ciaiue, iao/oaaiino?, oiui.

Neacaia aeua ? na?ae/aiiyi oiai, ui i?iaeaia ?iaeea?aeoaeueiiai
i?aeoiaeo i?iaeiaaeo? caeeoaoeny aeooaeueiith, aeooaeuei?noue yei?
i?aeneeth?oueny iaaeinoaoiueith oai?aoe/iith ? iaoiaee/iith
?ic?iaeai?noth, nioe?aeueiith ? iaaeaaia?/iith cia/ou?noth i?iaeaie,
iio?aaith a i?e oe?eueii? i?aeoeee.

I?e aeai?? oaie ie coieieeeny ia oi?ioethaaii? “?iaeea?aeoae?caoe?y
iaa/aeueii-i?ciaaaeueii? ae?yeueiino? iieiaeoeo oeiey??a a i?ioean?
canai?iiy iaoaiaoe/ieo ciaiue”, oiio ui iniiae iaoaiaoe/ieo ciaiue
caeeaaeathoueny a ii/aoeia?e oeie? ? aoaeue-yea oiouaiiy ia oeueiio
aoai? iiaea aeeeeeaoe aaeee? ao?aoe, ia eeoa iaa/aeuei?, a e ii?aeuei?,
ye? eiiiainoaaoe iio?i iaeaea iaiiaeeeai, a oaeiae oiio, ui i???ioaoe?y
iaa/aiiy iaoaiaoeee ia iniaeno?noue o/iy oaeiae i?iaeiaaeo? caeeoaoeny
iaaeinoaoiuei ?ic?iaeaiith.

Ana neacaia iineoaeeei iniiaith i?e aecia/aii? ia’?eoa, i?aaeiaoa, iaoe,
?iai/i? a?iioace ? caaaeaiue aeine?aeaeaiiy.

Ia’?eoii aeine?aeaeaiiy ? ?iaeea?aeoae?caoe?y iaa/aeueii-i?ciaaaeueii?
ae?yeueiino? o/i?a ii/aoeiaeo eean?a.

I?aaeiao aeine?aeaeaiiy – ?iaeea?aeoaeueiee i?aeo?ae aei iieiaeeo
oeiey??a i?e canai?ii? ieie iaoaiaoe/ieo ciaiue.

Iaoa aeine?aeaeaiiy – aeyaeoe i?e/eie, ye? ia aeicaieythoue ?aae?coaaoe
i?eioeei ?iaeea?aeoaeueiiai i?aeoiaeo, oeyoii aeine?aeaeaiiy i?iaeaie a
?? ?noi?e/iiio ?icaeoeo; aeyaeoe ineoieiai-iaaeaaia?/i? oiiae
cae?eniaiiy ?iaeea?aeoaeueiiai i?aeoiaeo; ?ic?iaeoe oaeo iiaeaeue
iaa/aiiy oa caniae ?iaeea?aeoae?caoe??, ye? aeicaieyee a ?aae?coaaoe
iacaaiee i?eioeei i?e canai?iiy iieiaeoeie oeiey?aie iaoaiaoe/ieo ciaiue
? aenia?eiaioaeueii ia?aa??eoe ?o aoaeoeai?noue.

A?iioaca aeine?aeaeaiiy: ?iaeea?aeoae?caoe?y iaa/aeueii-i?ciaaaeueii?
ae?yeueiino? o/i?a ii/aoeiaeo eean?a o i?ioean? canai?iiy iaoaiaoe/ieo
ciaiue aoaea cae?enithaaoeny oni?oii ? ?acii c oei i?aeaeueoueny ye?noue
iaa/aiiy, yeui a iniiao iiaeae? iaa/aeueiiai i?ioeano iieeanoe ?aea?
iniaeno?nii-i???ioiaaiiai iaa/aiiy (?.N.sseeiainueea), iiaoaiiiai
oi?ioaaiiy ?icoiiaeo ae?e, iiiyoue (I.ss.Aaeueia??i, I.O.Oaeec?ia),
i?aeoeeoaaoe ia?i?, a?oiia? oa eieaeoeai? oi?ie iaa/aiiy.

Caaaeaiiy aeine?aeaeaiiy:

1. Aea/eoe noai aeine?aeaeoaaii? i?iaeaie a oai??? ? oe?euei?e i?aeoeoe?
a ?? ?noi?e/iiio ?icaeoeo c iaoith aeyaeoe i?e/eie, ye? ia aeicaieythoue
i?eioeei ?iaeea?aeoaeueiiai i?aeoiaeo aei o/i?a.

2. Ia iniia? aiae?co ineoieiai-iaaeaaia?/ii? ? iaoiaee/ii? e?oa?aoo?e oa
oe?eueii? i?aeoeee aeyaeoe ineoieiai-iaaeaaia?/i? oiiae, ye?
caaacia/othoue o i?ioean? iaa/aiiy ?iaeea?aeoaeueiee i?aeo?ae aei o/i?a,
? ia ?o iniia? aeaanoe i?eioeeie ?iaeea?aeoae?caoe??.

3. Ia iniia? ?aeae iniaeno?nii-i???ioiaiiai iaa/aiiy, eiioeaioe??
iiaoaiiiai oi?ioaaiiy ?icoiiaeo ae?e, aeei?enoaiiy ia?ieo a?oiiaeo ?
eieaeoeaieo oi?i iaa/aiiy noai?eoe oaeo iiaeaeue iaa/aiiy ? ?ic?iaeoe
caniae ?iaeea?aeoae?caoe?? – i???iooth/? ea?oee (IE), ye? caaacia/othoue
?iaeea?aeoae?caoe?th iaa/aeueii-i?ciaaaeueii? ae?yeueiino? oeiey??a o
i?ioean? canai?iiy ieie iaoaiaoe/ieo ciaiue ? iiceoeaii aieeaathoue ia
ye?noue iaa/aiiy.

4. Aenia?eiaioaeueii ia?aa??eoe aoaeoeai?noue ?ic?iaeaii? ae?yeuei?nii?
iiaeae? iaa/aiiy oa IE i?e iaa/aii? o/i?a ii/aoeiai? oeiee iaoaiaoeee,
iaa?oiooaaoe aeniiaee i?i aeioe?euei?noue ai?iaaaeaeaiiy ?o o oe?eueio
i?aeoeeo.

5. ?ic?iaeoe aeey a/eoae?a ii/aoeiaeo eean?a iaoiaee/i? ?aeiiaiaeaoe?? c
aeine?aeaeoaaii? i?iaeaie.

Iaoiaeieia?/ieie canaaeaie aeine?aeaeaiiy ?: oai??y i?ciaiiy
(aca?iica’ycie oai??? ? i?aeoeee, aenie?eaoe?y aii??e/ieo ? oai?aoe/ieo
??ai?a i?ciaiiy, i?ciaiiy ye aeoeaia ia?aoai?thaaeueia e
a?aeia?aaeoaaeueia ae?yeuei?noue); eiioeaioe?y iiaoaiiiai oi?ioaaiiy
?icoiiaeo ae?e; eiioeaioe?y ?icaoaeiae ia?iaeii? ina?oe ia iniia?
?icaeoeo ?iaeea?aeoae?caoe??, aoiai?caoe?? e aeaiie?aoecaoe??,
?ioaineo?eaoe?? iaa/aiiy, oai??y iniaeno?nii-i???ioiaaiiai iaa/aiiy.

Iaoiaee aeine?aeaeaiiy:

– aea/aiiy e aiae?c ineoieiai-iaaeaaia?/ii? e iaoiaee/ii? e?oa?aoo?e c
aeine?aeaeoaaii? oaie;

– aii??e/i? iaoiaee: oe?eani?yiiaaia niinoa?aaeaiiy ca
iaa/aeueii-aeoiaiei i?ioeanii (aea??eiaa e nenoaiaoe/ia), aieaooaaiiy oa
?ioa?a’thaaiiy, ii??aiyiiy;

– aea/aiiy ci?noo iaoa??aeueieo iin??a ?ioi?iaoe?? (iaaeaaia?/ii?
aeieoiaioaoe??, ieai?a-eiiniaeo?a o?ie?a o/eoae?a ii/aoeiaeo eean?a,
o/i?anueeeo cioeo?a);

– iaaeaaia?/iee aenia?eiaio (eiinoaooth/ee, oi?ioth/ee ? eiio?ieueiee);

– iaoaiaoeei-noaoenoe/i? aeine?aeaeaiiy (ia?iaea aenia?eiaioaeueieo
aeaieo).

Ia’?eoeai?noue ? a??ia?aei?noue iaea?aeaieo ?acoeueoao?a oa aeniiae?a
aeine?aeaeaiiy caaacia/ai? iaoiaeieia?/iith iaa?oioiaai?noth eiai
aeo?aeieo iiceoe?e, aaeaeaaoi?noth iaoiae?a aeine?aeaeaiiy eiai iao? e
caaaeaiiyi, aeinoaoi?i ianeaii ?aniiiaeaio?a, aeei?enoaiiyi eiiieaeno
aca?iiaeiiiaithth/eo iaoiae?a ye?niiai ? e?euee?niiai aiae?co
aenia?eiaioaeueieo aeaieo.

Aaca aeine?aeaeaiiy. Iniiaiith aeine?aeieoeueei-aenia?eiaioaeueiith
aacith aeine?aeaeaiiy aoee caaaeueiiina?oi? NO ??4,25, 60 i. Iaeane,
Ethaao?anuee? NO ??1,2 Iaeanueei? iaeano? oa NO ?174 i. Ee?aa.
Eiinoaooth/ee aenia?eiaio i?iaiaeeany oaeiae a Iaeanueeeo NO
??29,72,121, Eiaeeinuee?e NO ?1, Iao?iaeieeinuee?e NO
Ia?ae?iiieuenueeiai ?aeiio oa A?ey?anuee?e NO ?2 Iaeanueei? iaeano?.

Aeine?aeaeaiiy cae?enithaaeiny c 1992 ii 1998 ?. o /ioe?e aoaie.

Ia ia?oiio aoai? (1992-1993) aea/aeanue i?iaeaia ?iaeea?aeoae?caoe?? a
ineoieiai-iaaeaaia?/i?e oa iaoiaee/i?e e?oa?aoo?? a ?? ?noi?e/iiio
?icaeoeo. Aeine?aeaeoaaany noai cae?eniaiiy ?iaeea?aeoaeueiiai i?aeoiaeo
aei o/i?a o oe?euei?e i?aeoeoe? ?, cie?aia, ia o?ieao iaoaiaoeee a
ii/aoeiaeo eeanao. Aeyaeai? i?e/eie, ye? ia aeicaieythoue
?iaeea?aeoae?coaaoe iaa/aiiy, oa aecia/aii? ineoieiai-iaaeaaia?/i?
oiiae, ye? caaacia/othoue ?iaeea?aeoae?caoe?th. Ia oeueiio aoai? aoei
noi?ioeueiaaii ia’?eo, i?aaeiao ? caaaeaiiy aeine?aeaeaiiy, ?iai/a
a?iioaca, ?ic?iaeaia aenia?eiaioaeueia iaoiaeeea, neeaaeaia i?ia?aia
eiinoaooth/iai aenia?eiaioo.

Ia ae?oaiio aoai? /1993-1994 ??./ cae?eniaii eiinoaooth/ee aenia?eiaio:
aea/aeeny iaoiaee iaa/aiiy iaoaiaoeee a ii/aoeiaeo eeanao, aiae?coaaeeny
iio?i/i? ieaie-eiiniaeoe a/eoae?a ii/aoeiaeo eean?a, aea/aeeny a?eia? oa
?iaeea?aeoaeuei? iniaeeaino? iieiaeoeo oeiey??a, a oaeiae oni?oi?noue c
iaoaiaoeee o/i?a ia?oeo eean?a aenia?eiaioaeueieo ? eiio?ieueieo eean?a,
?ic?iaeaia i?ia?aia Oi?ioth/iai aenia?eiaioo, IE.

Ia o?aoueiio aoai? /1994-1997 ??./ iiaoaiii ai?iaeiaae o?ueio ?ie?a
i?iaaaeaii oi?ioth/ee aenia?eiaio a 1-3 eeanao, o oiae? yeiai
ia?aa??yeeny ?iai/a a?iioaca oa aoaeoeai?noue aenia?eiaioaeueii?
iaoiaeeee, aiineeeny a?aeiia?aei? aeiiiaiaiiy a ?iai/o a?iioaco oa
ei?aeoe?? a ae?yeuei?nio iiaeaeue iaa/aiiy. Ia caaa?oaeueiiio aoai?
i?iaaaeaii eiio?ieueiee aenia?eiaio, ?acoeueoaoe yeiai ii??aithaaeeny c
?acoeueoaoaie eiio?ieueieo eean?a, oae ? c iiia?aaei?ie ?acoeueoaoaie.

Ia /aoaa?oiio aoai? /1998 ?./ cae?enithaaeany ia?iaea iaea?aeaieo
aeaieo, ocaaaeueithaaeeny noaoenoe/i? aeai?, oi?ioethaaeeny e oai?aoe/ii
ia??oioiaoaaeeny aeniiaee, i?eioeeie ?iaeea?aeoae?caoe??, ?ic?iaeyeeny
iaoiaee/i? ?aeiiaiaeaoe??, cae?enithaaeiny ai?iaaaeaeaiiy ?acoeueoao?a
aeine?aeaeaiiy a oe?eueio i?aeoeeo.

Iaoeiaa iiaecia e oai?aoe/ia cia/ou?noue aeine?aeaeaiiy iieyaathoue o
aecia/aii? ineoieiai-iaaeaaia?/ieo oiia, ye? caaacia/othoue ?aae?caoe?th
i?eioeeio ?iaeea?aeoaeueiiai i?aeoiaeo a oe?euei?e i?aeoeoe?,
noi?ioeueiaaieo i?eioeeiao ?iaeea?aeoae?caoe?? oai?aoe/ii e
aenia?eiaioaeueii iaa?oioiaai?e ae?yeuei?nii? iiaeae? iaa/aiiy e cania?a
?iaeea?aeoae?caoe?? -IE (ia iniia? ?aeae iniaeno?nii-i???ioiaaiiai
iaa/aiiy, eiioeaioe?? iiaoaiiiai oi?ioaaiiy ?icoiiaeo ae?e, canoinoaaiiy
ia?ieo, a?oiiaeo ? eieaeoeaieo oi?i iaa/aiiy). ?ic?iaeaia iaoiaeeea
oi?ioaaiiy iaae/ie canoinoaaiiy iaoaiaoe/ieo ciaiue iieiaeoeie oeiey?aie
ia oai?/iio ??ai?.

Iniaenoee aianie caeiaoaa/a. Ia iniia? aeine?aeaeaiiy i?iaeaie
?iaeea?aeoaeueiiai i?aeoiaeo aei o/i?a o iaaeaaia?/i?e oai??? ?
i?aeoeoe? a ?? ?noi?e/iiio ?icaeoeo aaoi?ii: ?)aeyaeaii i?e/eie, ye?
no?eiothoue ?iaeea?aeoae?caoe?th; 2) aecia/aii oiiae a?aooaaiiy
?iaeea?aeoaeueieo iniaeeainoae o/i?a o i?ioean? iaa/aiiy; 3)
noi?ioeueiaaii i?eioeeie ?iaeea?aeoae?caoe??; 4) oai?aoe/ii e
aenia?eiaioaeueii iaa?oioiaaia ae?yeuei?nia iiaeaeue iaa/aiiy; 5)
?ic?iaeaii caniae ?iaeea?aeoae?caoe?? iaa/aeueii-i?ciaaaeueii?
ae?yeueiino? iieiaeoeo oeiey??a i?e canai?ii? iaoaiaoe/ieo ciaiue – IE ?
6) ?ic?iaeaii iaoiaeeeo oi?ioaaiiy iaae/ie canoinoaaiiy o/iyie
ii/aoeiaeo eean?a iaoaiaoe/ieo ciaiue ia oai?/iio ??ai?.

I?aeoe/ia cia/ou?noue iieyaa? a ?ic?iaoe? iaoiaee/ieo ?aeiiaiaeaoe?e
aeey a/eoae? ii/aoeiaeo eean?a, ye? aeicaieythoue ?aae?coaaoe i?eioeei
a?aooaaiiy ?iaeea?aeoaeueieo iniaeeainoae o/i?a o i?ioean? aea/aiiy
iaoaiaoeee a ii/aoeiaeo eeanao. Iaoa??aee aeine?aeaeaiiy iiaeooue aooe
aeei?enoai? aaoi?aie i?ae?o/iee?a iaaeaaia?ee, aeeeaaea/aie iaaeaoc?a oa
iaaeo/eeeu, ye? aeeeaaeathoue iaaeaaia?eo, a oaeiae iaoiaeeeo
aeeeaaeaiiy iaoaiaoeee a ii/aoeiaeo eeanao, ia eo?nao i?neyaeeieiiii?
ina?oe ? a oe?euei?e i?aeoeoe? a/eoaeyie ii/aoeiaeo eean?a.

Ai?iaaoe?y ?acoeueoao?a aeine?aeaeaiiy. Iniiai? ?acoeueoaoe
aeine?aeaeaiiy aena?oethaaeeny a ioae?eaoe?yo, aeiiia?aeaeeny e
iaaiai?thaaeeny ia ani??aionueeeo nai?ia?ao oa can?aeaiiyo eaoaae?
iaaeaaia?ee e ineoieia?? I?aaeaiiioe?a?inueeiai aea?aeaaiiai
iaaeaaia?/iiai oi?aa?neoaoo ?i. E.Ae.Ooeinueeiai oa iaoeiai-i?aeoe/ieo
eiioa?aioe?yo i?ioani?nueei-aeeeaaeaoeueeiai neeaaeo iacaaiiai
oi?aa?neoaoo (Iaeana, 1993, 1994, 1995, 1996, 1997), i?aeaoc?anuee?e
iaoeiai-i?aeoe/i?e eiioa?aioe?? “Ii/aoeiaa oeiea: i?iaeaie, aeina?ae,
ae??oaiiy” (?cia?e, 1993), i?aeia?iaei?e eiioa?aioe?? c ieoaiue o?ce/ii?
eoeueoo?e ? oe?eueii? a?a??ie (Iaeana, 1993).

No?oeoo?a ?iaioe. Aeena?oaoe?y neeaaea?oueny c? anooio, aeaio ?icae?e?a,
aeniiae?a aei eiaeiiai ?icae?eo, caaaeueieo aeniiae?a, nieneo
aeei?enoaieo aeaea?ae (256 iaca). ?iaioa i?noeoue 154 noi??iee,
?ethno?iaaia 4 noaiaie, 5 oaaeeoeyie ? 2 iaethieaie.

INIIAIEE CI?NO ?IAIOE

O anooi? aeena?oaoe?? iaa?oioiaaia ?? aeooaeuei?noue, aecia/ai? ia’?eo,
i?aaeiao, iaoa, ?iai/a a?iioaca ? caaaeaiiy aeine?aeaeaiiy, iiaeaii
ia?ae?e aeei?enoaieo iaoiae?a, aeacaia eiai iaoiaeieia?/ia iniiaa,
noi?ioeueiaaia iaoeiaa iiaecia, oai?aoe/ia ? i?aeoe/ia cia/ou?noue
aeine?aeaeaiiy, iaa?oioiaaia a??ia?aei?noue ?acoeueoao?a aeine?aeaeaiiy,
aeacaii iniaenoee aianie caeiaoaa/a, iaaaaeaii aeai? ai?iaaoe??
?acoeueoao?a aeine?aeaeaiiy.

O ia?oiio ?icae?e? – “?iaeea?aeoae?caoe?y ye iaaeaaia?/ia i?iaeaia”
i?eaaaeai? ?acoeueoaoe aiae?co ?noi??? aeieeiaiiy i?iaeaie
?iaeea?aeoaeueieo iniaeeainoae oeiey??a, i?ieaeai? iath aoaie ?icaeoeo,
ii/eiath/e c aeieeiaiiy ? aei iaoeo aei?a, ?icaeyiooi ?aea?, ye?
i?iiiioaaeeny aeey ?? ?ica’ycaiiy, a oaeiae aeacaii ia aaeuei?ai?
oaeoi?e, ye? no?eioaaee e no?eiothoue ?iaeea?aeoae?caoe?th. E??i oiai,
i?iaaaeaii aiae?c iaoeiaeo aeine?aeaeaiue c ieoaiue ?iaeea?aeoae?caoe??,
ye? cae?enithaaeeny a inoaii? ?iee, a ?acoeueoao? /iai c?iaeaii aeniiaie
i?i oa, ui a iaaeaaia?/i?e iaooe? ? aaea aaeee? iai?aoethaaiiy uiaei
iiaeo i?aeoiae?a aei ?aae?caoe?? i?eioeeio a?aooaaiiy ?iaeea?aeoaeueieo
iniaeeainoae o/i?a, iaeiae ua a?aenooiy ioi?ieaia o oe?e?nio iaoeiai
iaa?oioiaaio oai??th ?iaeea?aeoae?caoe??.

O iania?e oe?euei?e i?aeoeoe?, ye iieacaa aiae?c ?acoeueoao?a
aeine?aeaeaiiy /eiinoaooth/ee aenia?eiaio/ ? nueiaiaei? cae?enithaaoe
?iaeea?aeoaeueiee i?aeo?ae iaaecae/aeii neeaaeii, ai an? ?nioth/?
iaoiaee ? niiniae i?aai?caoe?? iaa/aiiy, o?aaeeoe?ei? e iao?aaeeoe?ei?,
iacaaaeath/e ia ciai?oith ??ciiiai?oi?noue ii noo? aeyaeeeny aa??aioaie
iaeiiai e oiai naiiai iaoiaeo, i?e yeiio nai i?ioean canai?iiy ciaiue
a?aeaoaa?oueny aac iaeaaeiiai ea??aieoeoaa, eiio?ieth?oueny aieiaiei
/eiii ca e?ioeaaei ?acoeueoaoii, aei yeiai i?eoiaeyoue iaine?i
(I.ss.Aaeueia??i) Oaeee noai ?a/ae iiynith?oueny ianaiia?aae oei, ui
o/aiue i?iaeiaaeo? caeeoaoeny ia’?eoii iaa/aeueii-aeoiaiiai i?ioeano.

?iaeea?aeoae?caoe?y iiaea cae?enithaaoeny eeoa ca oiiae, eiee o/aiue c
naiiai ii/aoeo aoaea noa’?eoii, a ia eeoa ia’?eoii iaa/aeueii-aeoiaiiai
i?ioeano (?.N.sseeiainueea). Aeey oeueiai a ci?no iaa/aiiy iathoue
aeeth/aoeny ia eeoa iaoeia? ciaiiy, a e iaoaciaiiy, ye? caaacia/othoue
iaeii/ania canai?iiy oai?aoe/ieo ciaiue e oi?ioaaiiy i?aeoe/ieo oi?iue ?
iaae/ie aac iiia?aaeiueiai cao/oaaiiy iaa/aeueiiai iaoa??aeo
(I.ss.Aaeueia??i) ? aeicaieythoue cae?enithaaoe cai?ioi?e ca’ycie, oiaoi
eiio?iethaaoe canai?iiy a ?iaeea?aeoaeueiiio oaii?, ae?iaeaiiy
i?aeoe/ieo oi?iue oa iaae/ie ? oi?aaeyoe iaa/aeueiei i?ioeanii, oiaoi ia
oiio /e ?ioiio aoai? canai?iiy nai?/anii aiineoe iaiao?aei? ei?aeoeae a
?iaioo ie?aieo o/i?a, ye? iio?aaothoue aeiiiiiae e i?aeo?eiee.

Ae?oaee ?icae?e – “Cae?eniaiiy ?iaeea?aeoae?caoe??
iaa/aeueii-i?ciaaaeueii? ae?yeueiino? o/i?a ii/aoeiai? oeiee i?e
canai?ii? iaoaiaoe/ieo ciaiue” – i?enay/aiee iaoeiaiio iaa?oiooaaiith
noai?aii? ae?yeuei?nii? iiaeae? iaa/aiiy oa cania?a ?iaeea?aeoae?caoe??
– IE oa aenia?eiaioaeuei?e ?o ia?aa??oe?. Iayai?noue IE aeicaiey? a
i?ioean? iaa/aiiy ?iaeoe iaa/aeueiee i?ioean ea?iaaiei ?
eiio?ieueiaaiei c aieo a/eoaey, a o/aiue, ei?enooth/enue IE, “io?eio?
cia?yaeaey o aeani? ?oee” ? noa? ainiiaea?ai noaiiaeua, oiae? ye i?e
a?aenooiino? ?? a?i caeeoa?oueny ianeaiei aeeiiaaoeai /oaeeo aeac?aie
(I.ss.Aaeueia??i). ?ioeie neiaaie ei?enooth/enue IE, ia ye?e
cao?eniaaiee o noene?e oi?i?, i?enoiniaai?e aei iiia?aaei?o ciaiue,
oi?iue ? iaae/ie, iaa/aeueiee iaoa??ae ? ii?yaeie ae?e c oeei
iaoa??aeii, o/aiue i?ney iiia?aaeiueiai “i???iooaaiiy” ia? iiaeeea?noue
i?enooieoe aei aaeaeaaoii? ?iaioe aac iiia?aaeiueiai, ye oaea
cacia/aeiny, cao/oaaiiy oai?aoe/iiai iaoa??aeo. A ?acoeueoao? oaei?
i?aai?caoe??, caaaa/aiiy oaeoe/ieie ciaiiyie, ai?iiyie e iaae/eaie
a?aeaoaa?oueny iaeii/anii c iaieiae?iiyi i?eeiiaie ieneaiiy , oiaoi
eiaeai o/aiue iaa/a?oueny ieneeoe i?aaeeueii, aac “ni?ia” ? “iiieeie”.

Caaaeath/e ia oa, ui a iniiao ae?yeuei?nii? iiaeae? iieeaaeaia oaeiae
nenoaia aaoi?nueei? oeiee I.I.Aoceea, a oeueiio ?icae?e? i?aaenoaaeaia,
e??i noaie e aiae?co ae?yeuei?niiai iaoiaeo, a?aeiia?aeii noaia oa
aiae?c i?aai?caoe?? iaa/aiiy iacaaii? aaoi?nueei? oeiee, a ye?e aaeeea
oaaaa i?eae?ey?oueny ?iaeea?aeoaeuei?e i?i?iaoe? iaa/aeueiiai iaoa??aeo.
Iaeiae oey nenoaia aeei?enoaia aaoi?ii aeine?aeaeaiiy eeoa /anoeiai, ai
aiia ?ic?aoiaaia ia aiiiaaii?, a ia ia aaoa?iaaii? eeane /e a?oie..

Aeae? iiaea?oueny noaia noai?aii? ae?yeuei?nii? iiaeae? iaa/aiiy oa ??
iaoeiaa iaa?oiooaaiiy.

Noaia 2.4. No?oeoo?a ae?yeuei?nii? iiaeae? iaa/aiiy.

1. Aecia/aiiy iaa/aeueiiai caaaeaiiy. Iioeaaoe?y. ?icaeyae iaoa??aeo
iaa/aeueiiai aeieo. O?iioaeueia ii?aoethaaiiy c aeei?enoaiiyi IE.

2. ?iaeea?aeoaeueia ii?aoethaaiiy iaa/aeueiiai iaoa??aeo aeieo c
aeei?enoaiiyi IE ? ia?iiai eiio?ieth.

3. ?iaeea?aeoaeueia ii?aoethaaiiy iaa/aeueiiai iaoa??aeo c iii?ith (/e
aac iii?e) ia IE o ?aieao naiieiio?ieth ? c aeei?enoaiiyi
aca?iiia?aa??ee.

4. Ocaaaeueiaiiy e nenoaiaoecaoe?y oi?iue ? iaae/ie ia oai?/iio ??ai? c
aeei?enoaiiyi a?oiiaeo ? eieaeoeaieo oi?i iaa/aiiy.

5. Oaiaoe/iee cae?e: o?ie ni?eeoaaiiy ? o?iioaeueia ia?aa??ea ciaiue
(onii).

6. ?iaeea?aeoaeueiee cae?e: ienueiiaa eiio?ieueia ?iaioa.

7. Aiae?c eiio?ieueii? ?iaioe.

Ae?yeuei?nia iiaeaeue, ye ? ae?yeuei?niee iaoiae, iaceaa?oueny oae oiio,
ui a ?? iniia? eaaeeoue ia iaa/aiiy, a ae?yeuei?noue naiiai o/iy, oiaoi
a?i aenooia? noa’?eoii, a ia o?eueee ia’?eoii iaa/aeueii-aeoiaiiai
i?ioeano, ui aeicaiey? ?aae?coaaoe i?eioeei ?iaeea?aeoaeueiiai
i?aeoiaeo.

06ia’yceiaei eiiiiiaioii ae?yeuei?nii? iiaeae? ? iioeaaoe?y, ai aac ia?
i?aaeiaoi? ae?? ia iathoue naino.

Aei/ia ii?aoethaaiiy iaa/aeueiiai iaoa??aeo aeicaiey? noi?ioaaoe a o/i?a
oe?e?nia oyaeaiiy i?i iueiai, ui a naith /a?ao aeicaiey? caiia?aoe
?ioa?oa?aioe?? iaae/ie ? ni?ey? ?o ?aii?e aeeoa?aioe?aoe??.

Ae?yeuei?niith iiaeaeeth iaa/aiiy ia?aaeaa/aii ia ia?oiio o?ioe?
ii?aoethaaiiy iaa/aeueiiai iaoa??aeo aeieo ?icii/eiaoe c aiae?co eiai
a/eoaeai, iiynithaaeueii-?ethno?aoeaiei iaoiaeii c aeei?enoaiiyi
aa?enoe/ii? aan?aee /e i?iaeaiiiai iaa/aiiy, aea a/eoaeue ia iiaeiai
oe?iei caeo/aoe aei ?ica’ycaiiy i?iaeaiieo ieoaiue o/i?a, oiio ui aeey
iaeieo c ieo i?iaeaia aeyaeoueny iioeiaeueii? o?oaeiino?, aeeee/a a ieo
aiioe?eia i?aeianaiiy, aeoea?co? ?oith ?icoiiao ae?yeuei?noue ? ?acii c
oei iiceoeaii aieeia ia ?oi?e ?icoiiaee ?icaeoie. Oa ae naia i?iaeaia
aeey ?ioeo oeiey??a iiaea aooe iaaecae/aeii neeaaeiith, oiio ui ia
a?aeiia?aea? ?oiueiio noa’?eoeaiiio aeina?aeo, ciaiiyi aiane?aeie /iai
i?ciaaaeueia aeoeai?noue o ieo ia aeieea?. Oiio ii/oaaoe aiie naaa
aoaeooue aeeneiioi?oii: ia?aaeeaathoue naith iaiiaiioe?ii?noue, ?iiae?
ia?aaoaathoue o noai? aeai?an??, oiio iaa?oue ia ?iaeyoue ni?iae
aeeth/eoenue a ?ica’ycaiiy i?iaeaie, aiy/enue iani?oie ? iaaaea/.

Oiio c iaoith a?aooaaiiy ?iaeea?aeoaeueieo iniaeeainoae o/i?a ?
aeoea?caoe?? ?o iaa/aeueii-i?ciaaaeueii? ae?yeueiino? aeioe?eueii, uia
o/eoaeue, iiynithth/e iiaee iaoa??ae, nai noaaea i?iaeaio ? nai ??
?ica’ycoaaa; iieacoaaa oeyoe ?? ?ica’ycaiiy, a o/i? iiaeoiee
ne?aeeothoue ca eiai eia?eith, canaithth/e aoaie ?ica’ycaiiy. Cai?noue
o?aaeeoe?eiiai cae??ieaiiy c o??? naii? i?e/eie aeioe?eueii
aeei?enoiaoaaoe iiaoi?ia iiyniaiiy a/eoaeai aeo/oaaiiai iaoa??aeo, ui
ni?ey? e?auiio canai?iith iaoa??aeo an?ia o/iyie ? aeicaiey? ia
o?aaioaaoe ineo?eo iaio cae?aieo ae?oae.

O?iioaeueia ii?aoethaaiiy iaoa??aeo iaa/aeueiiai aeieo cae?enith?oueny c
iii?ith ia NE. Ia aoai? ?iaeea?aeoaeueiiai ii?aoethaaiiy iaoa??aeo c
iii?ith ia IE ? aeei?enoaiiyi ia?iiai eiio?ieth, eiio?ieue
cae?enith?oueny aaea ia o/eoaeai, ye oea aoei ia iiia?aaeiueiio aoai?,
eiee ae?oe aaiein oi?ii eiiaiooaaee eiaeio iia?aoe?th, a non?aeii ii
ia?o?: iaeei o/aiue, aeeiioth/e caaaeaiiy, iioaiee eiiaioo? nai? ae??, a
?ioee – eiio?ieth?, iio?i ae?oe i?iythoueny ?ieyie. Nii/aoeo ia?iee
eiio?ieue aoa aaaaeaiee oiio, ui a/eoaeue ia a ciic? i?ieiio?iethaaoe
eiaeiiai o/iy, a iio?i aeyaeeiny, ui ia?iee eiio?ieue ? aaaeeeaei
noeioethth/ei caniaii aeoea?caoe?? iaa/aeueii-i?ciaaaeueii? ae?yeueiino?
o/i?a, caaaeyee eiio a eean? noai?th?oueny aoiinoa?a caoe?eaaeaiino? a
iaa/aeuei?e ae?yeueiino? ? ciaiiy canaiththoueny ia ciainiaeaii, aiie
noathoue iniaeno?nii-cia/eieie.

Ia ianooiiiio aoai? ia?iee eiio?ieue cai?ith?oueny aca?iieiio?ieai, oiio
ui o/i? aaea ia iiia?aaeiueiio aoai? a?ae i?aeeiio?ieueiiai iia?oaaiiy
ia?aoiaeyoue aei naiieiio?ieth ? iaiao?aei?noue eiio?iethaaoe eiaeio
iia?aoe?th aaea iaia iaiao?aeiino?.

C iaoith a?aooaaiiy ?iaeea?aeoaeueieo iniaeeainoae o/i?a ia oeeo o?ieao,
oae naii ye ? ia ianooiieo, ia?aaeaa/ai?, e??i caaaeueieo, iaia’yceiaeo
aeey an?o caaaeaiue, ua e aeiaeaoeia?, aeeiiaiiy yeeo an?ia o/iyie
iaiaia’yceiaa.

I?ney aeeiiaiiy an?o iaia’yceiaeo caaaeaiue iaiia o/iyie, ye? neaeyoue
ca iaei??th ia?oith cae?enith?oueny aca?iiia?aa??ea oaeei /eiii: o/aiue
A aa?a cioeo o/iy A, ?, /eoath/e iioaiee, ia?aa??y? aeeiiaia caaaeaiiy,
a o/aiue A oaaaeii ne?aeeo? ca eiai ia?aa??eith. Aeyaeaio iiieeeo ii
iiaeeeaino? aei?aaey? o/aiue A nai aai ae A, oiaoi oie, ooi ia?aa??y?.
Iio?i o oaeee naiee niin?a o/aiue A ia?aa??y? aeeiiaia caaaeaiiy o/iai
A.

Aeiaeaoeia? caaaeaiiy ia ia?aa??ythoueny non?aeii ii ia?o?, ai aiie
iiaeooue aooe aeey iueiai neeaaeieie. Aeeiiaiiy aeiaeaoeiaeo caaaeaiue
iiynith? nai aeeiiaaaoeue, a eiai non?ae ii ia?o? oaaaeii neooa?, a
iio?i ? nai aeeiio? aiaeia?/i? caaaeaiiy.

Ia o?ieao ocaaaeueiaiiy e nenoaiaoecaoe?? ciaiue ia oai?/iio ??ai? c
aeei?enoaiiyi a?oiiaeo ? eieaeoeaieo oi?i iaa/aiiy eiaeia a?oia o/i?a
aeae?a? iaeio ?c i?ia?ai “A”, “A” /e “A”. I?ney aeeiiaiiy an?ia /eaiaie
a?oie ia?oiai caaaeaiiy iaeei ?c o/i?a iia?aeiiey? na?e ?acoeueoao.
sseui a?i iaeiaeiaee o an?o, oi a?oia i?enooia? aei aeeiiaiiy
ianooiiiai. sseui ae aeyaeoueny, ui ooinue ?c o/i?a iaea?aeaa ?ioee
?acoeueoao, a?i iiynith? an?e a?oi?, ye a?i eiai aeeiioaaa. sseui ae
i?ney iiyniaiiy a?i nai ia ci?a ciaeoe iiieeeo, oiaa?eo? aeiiiiaaathoue
eiio.

I?ae /an ?iaioe o/i?a a?oiaie a/eoaeue oiaeeoue ii eeano, coieiyth/enue
oi a?ey iaei???, oi a?ey ?ioi? a?oie, noaaeeoue ca ?o ?iaioith. Eiee o
yei?nue ?c a?oi aeieea? oo?oaeiaiiy, a/eoaeue aeeth/a?oueny a ?? ?iaioo
e ea?o? iaaiai?aiiyi. Oaeei /eiii, a?i ia? iiaeeea?noue i?eae?eyoe
a?eueoa oaaae oei o/iyi, ye? iio?aaothoue aeiiiiiae.

I?ney aeeiiaiiy iaei??? c i?ia?ai a?oie iai?iththoueny i?ia?aiaie ? ii
/a?c? aeeiiothoue caaaeaiiy aeaio ?ioeo i?ia?ai, i?e oeueiio
cae?enith?oueny e?oaiaee eiioaeo i?ae o/iyie, oiaoi a?oiiaa oi?ia ?iaioe
cai?ith?oueny eieaeoeaiith. I?e oae?e i?aai?caoe?? iaa/aiiy
caaacia/o?oueny iiaia ??aiii?aai?noue an?o ?? o/aniee?a, ui iniaeeaa
aeaaioai?ii iicia/a?oueny ia iiaaae?ioe? o/i?a c iecueeei ??aiai
i?ciaaaeueii? aeoeaiino?, oiio ui aiie c iii?ith ia IE iaa/athoueny
i?aaeeueii canoiniaoaaoe iaaoo? ciaiiy ia i?aeoeoe?, a i?e aeeiiaii?
caaaeaiue oai?/iai oa?aeoa?o, ciath/e, ui ?i aeiiiiiaeooue ? ?o
i?aeo?eiothoue, oaeiae ii/oaathoue naaa aiaaiaii, o ieo oi?io?oueny
a?aeiia?aeaeueia noaaeaiiy aei iaa/aiiy.

Ia o?ioe? ni?eeoaaiiy non?aee ii ia?o? ?iciia?aeathoue iaeei iaeiiio
iniiaiee ci?no iaoa??aeo iaa/aeueiiai aeieo Uia iieaaoeoe ?iciia?aeue,
a/eoaeue aea? o/iyi ieoaiiy cacaeaeaa?aeue. I?ney ni?eeoaaiiy
i?iaiaeeoueny oaiaoe/iee cae?e o oi?i? o?iioaeueii? ia?aa??ee ciaiue
onii. Ia caaa?oaeueiiio aoai? o/i? aeeiiothoue eiio?ieueio ?iaioo, yea ?
iaeii/anii ? ?iaeea?aeoaeueiei cae?eii. I?ney eiio?ieueii? ?iaioe
i?iaiaeeoueny ?? aiae?c. Ia oeueiio cae?i/o?oueny ?iaioa iaae eiie?aoiei
aeieii aeo/oaaiiai iaoa??aeo. Ca iei ?aea aea/aiiy iiaiai aeieo ca
oaeith naiith oaoiieia??th.

A inoaii?o aeaio ia?aa?aoao eaeaoueny i?i aenia?eiaioaeueio ia?aa??eo
ae?yeuei?nii? iiaeae? oa cania?a ?iaeea?aeoae?caoe?? – IE a i?ioean?
aea/aiiy iaoaiaoeee a ii/aoeiaeo (?-C) eeanao oi?iaeiaae o?ueio ?ie?a oa
ii??aiththoueny ?acoeueoaoe aenia?eiaioo.

sse iieacaea aenia?eiaioaeueia ia?aa??ea, noai?aia ae?yeuei?nia iiaeaeue
? ?ic?iaeai? IE aeicaieythoue iaeneiaeueii ?iaeea?aeoae?coaaoe
iaa/aeueii-i?ciaaaeueio ae?yeuei?noue o/i?a ii/aoeiaeo eean?a a i?ioean?
canai?iiy ieie iaoaiaoe/ieo ciaiue ? cia/ii i?aeaeueoe ?o ye?noue.

Iaeiae oaea ia ia?oiio aoai? oi?ioth/iai aenia?eiaioo aoei aeyaeaii, ui
oae aeia?a “ni?aoeueiao?” ae?yeuei?nia iiaeaeue ?acii ?c caniaaie
?iaeea?aeoae?caoe?? i?e canai?ii? iaia’yceiaeo, oeiiaeo (noaiaea?oieo)
ciaiue (i?i ui na?ae/aoue i?ioieiee oa i?ioieieuei? caiene, a oaeiae
eiio?ieueiee c??c), iaeiae ia ni?aoeueiao? oae, ye o?aaa, i?e aeeiiaii?
oai?/eo caaaeaiue, ai iiieeee a o/i?a aenia?eiaioaeueieo eean?a aoee
cao?eniaai? naia a caaaeaiiyo oai?/iai oa?aeoa?o.

Oaeee noai ?a/ae iiynith?oueny ianaiia?aae oei, ui ia ia?oiio aoai?
Oi?ioth/iai aenia?eiaioo aaeeea oaaaa i?eae?eyeany ?iaeea?aeoae?caoe??
iaa/aeueii-i?ciaaaeueii? ae?yeueiino? o/i?a o i?ioean? canai?iiy iiaeo
ciaiue. Ae?iaeaiiy ae iaae/ie canoinoaaiiy ciaiue ia oai?/iio ??ai?
caeeoaeiny, ye ? ca cae/aeiith i?aai?caoe??th iaa/aiiy, o?iioaeueiei.
Uia ?iaeea?aeoae?coaaoe iaa/aeueiee i?ioean ? ia oeueiio aoai?, iaie
aoea aenoiooa a?iioaca i?i aeei?enoaiiy ?ioaeaeooaeueiiai oiio eeano
(A.I.Nooiieeinueeee) oeyoii aaaaeaiiy a ?ic?iaeaio iiaeaeue (yea
oi?iaeiaae o?ueio ?ie?a oaeineiiaethaaeany), a?oiiaeo ? eieaeoeaieo oi?i
iaa/aiiy, ine?eueee ia ia?oiio aoai? iaa/aiiy a aenia?eiaioaeueieo
eeanao i?iaiaeeeiny aac ieo. Ioaea, ia ae?oaiio aoai? oi?ioth/iai
aenia?eiaioo aoee aaaaeai? a?oiia? ? eieaeoeai? oi?ie iaa/aiiy. I?ioa ?
oeueiai aeyaeeiny iaaeinoaoiuei, oiio ui i?yea oai?/?noue (a iaoaiaoe/ia
oei a?eueoa) ia iiaea ii/aoeny ia ionoiio i?noe?, aeoiaey/e eeoa c
?ioo?oeaieo ?aaeoe?e.

C iaoith i?aeaioiaee o/i?a aei aeeiiaiiy oai?/eo caaaeaiue ia ae?oaiio
aoai? oi?ioth/iai aenia?eiaioo iaie aoea aenoiooa ua iaeia a?iioaca:
aeey oi?ioaaiiy a o/i?a oi?iue i?aaeeueii aeeiioaaoe oai?/? caaaeaiiy
iaiao?aeii i?e ?ica’ycoaaii? oeiiaeo caaea/ aeei?enoiaoaaoe oai?aoe/i?
a?aeiiino?, ye? ia?aaeaa/athoue i?aeaaaeaiiy aei iaaiiai niiniao ae??.

Oai?aoe/i? aeia?aeee nii/aoeo i?e ?icaeyae? iaoa??aeo iaa/aeueiiai aeieo
aeaaaa nai o/eoaeue, iio?i aiie aeei?enoiaoaaeeny o/iyie i?ney
?ica’ycaiiy eiaeii? caaea/?, ii noo?, aoee caeeth/ieie aeniiaeaie. A ia
i?inoiooiio aoai?, ?ica’ycoth/e iaa?oue caaea/? ia aea? e o?e ae??
ae?oe iiae?eyee ?o ia i?ino? ? aecia/aee niin?a eiaeii? ae??,
iineeath/enue ia oai?aoe/i? a?aeiiino?. Ai?iiy canoiniaoaaoe oai?aoe/i?
a?aeiiino? i?e ?ica’ycaii? oeiiaeo caaea/ ni?eyee aeoea?caoe?? ?icoiiai?
ae?yeueiino? o/i?a ? i?e aeeiiaii? caaaeaiue oai?/iai oa?aeoa?o.

Iaeiae, ye iieacaee niinoa?aaeaiiy ? aenia?eiaioaeueia ia?aa??ea, aeaye?
o/i? (ia?aaaaeii c iecueeei ??aiai iao/oaaiino?) i?e aeeiiaii? oai?/eo
caaaeaiue, cie?aia, i?e neeaaeaii? aiaeia?/ieo caaea/ /e ca ae?acii
a?ae/oaathoue aeao?oeeo ne?a. O iaeieo aeiaaeeao iaai?iiy aeiae?aoe
iio??ai? neiaa i?e aeeiiaii? oai?/eo caaaeaiue oiia?eueithaaei oai?/ee
i?ioean, a a ?ioeo – ci?no neeaaeaieo caaea/ aoa iaeiiiai?oiee. Oiio
aeieeea ua iaeia i?iaeaia: ye aeoea?coaaoe neiaieeiaee caian o/i?a i?e
neeaaeaii? caaea/. Aeey ?? ?ica’ycaiiy iaie aoea aenoiooa ua iaeia
a?iioaca: a ?ic?iaeaio iaoiaeeeo, e??i oai?aoe/ieo a?aeiiinoae,
iaiao?aeii aaanoe oaaeeoe? c iii?ieie neiaaie aeey eiaeiiai oeio i?inoeo
caaea/.

Aeoiaey/e c oiai, ui any iaoa ?iaioa aoaeoaaeany ia aa?aaeiiio noaaeaii?
aei aeeoeie, oaaeeoe? c iii?ieie neiaaie aeey neeaaeaiiy oaeno?a caaea/
iaie i?iiiioaaeeny ia eeoa o/iyi c iecueeei ??aiai iao/oaaiino? (oi/ ie
e ciaee, ui aiie iio??ai? ianaiia?aae ?i, a, iiaeeeai, ? o?eueee ?i), a
an?i aaaeath/ei.

E??i oiai, oni?oe eiaeiiai o/iy ii??aithaaeeny o?eueee c eiai
iiia?aaei?i ??aiai oni?oiino?, oiio eiioe?eo?a i?ae ae?oueie, iia’ycaieo
c i?ea?eaeiaaiei noaiiaeuai iaeieo ? i?eieceeaei ?ioeo, ye? iaee i?noea
a eiio?ieueieo eeanao, a aenia?eiaioaeueieo ia niinoa??aaeiny.

A aenia?eiaioaeueieo eeanao iino?eii caioi/oaaeeny aeia?ice/eea?
noinoiee i?ae o/iyie, ai iaeaeeneo/?oa oaoiieia?y o a?ae?ea? a?ae
ii?aeueieo aeaiaio?a iaieio/a aaaea aei oi?iae?cio e aei ?ioeo
iaaeaaia?/ieo i?i?aooie?a (O??aeiai E.I.).

Ia o?aoueiio aoai? oi?ioth/iai aenia?eiaioo iaoiaeeea ae?iaeaiiy iaae/ie
canoiniaoaaoe iaaoo? ciaiiy ia oai?/iio ??ai? aoea aeiiiaiaia c iaoith
?icaeoeo oai?/iai ieneaiiy o/i?a niaoe?aeueieie ai?aaaie, – ye? ie
iacaaee o?ai?iaaie ieneaiiy. O?ai?iae ieneaiiy ia o?aoueiio aoai?
oi?ioth/iai aenia?eiaioo aoee iaia’yceiaeie eiiiiiaioaie eiaeiiai o?ieo,
ui ni?eyei aeoea?caoe?? ?icoiiai? ae?yeueiino? an?o o/i?a ? ?icaeoeo
?oiueiai ieneaiiy. E??i oiai, ia iueiio aoai? o/i? iaee iiaeeea?noue
ei?enooaaoeny i?e iio?aa? noaiaie-nii?aie.

Oaeei /eiii, e??i IE, aoea ?ic?iaeaia aeiaeaoeiai iaoiaeeea oi?ioaaiiy
iaae/ie canoinoaaiiy iaaooeo ciaiue ia oai?/iio ??ai?a, ui cia/ii
i?aeaeueei aoaeoeai?noue ae?yeuei?nii? iiaeae? iaa/aiiy.

Aeey aecia/aiiy aoaeoeaiino? ?ic?iaeaii? iaoiaeeee a 1-3 eeanao aoee
i?iaaaeai? eiio?ieuei? c??ce ciaiue, ?acoeueoaoe yeeo iiaeai? a
oaaeeoeyo, iaaaaeaii iaeio c ieo, yea aeicaiey? i?inoaaeeoe aeeiai?eo
??ai?a ciaiue c iaoaiaoeee o/i?a 1 – 3 eean?a.

Oaaeeoey 2.5

Aeeiai?ea ??ai?a ciaiue c iaoaiaoeee o/i?a 1-3 eean?a

C aeaieo oaaeeoe? aeieeaa?, ui ?ic?iaeaia iaoiaeeea aoaeoeaia, oiio ui
aenieiai ??aiy ciaiue c iaoaiaoeee aeinyaee 29% o/i?a o?ao?o
aenia?eiaioaeueieo eean?a ? eeoa 7% – eiio?ieueieo eean?a, ia
eiinoaooth/iio aoai? oe? iieacieee neeaee ii 3% ? a aenia?eiaioaeueieo,
? a eiio?ieueieo ia?oeo eeanao. Ae?oe, ye? aeinyaee aenieiai ??aiy
ciaiue, eaaei e oaeaeei aeeiioaaee caaaeaiiy aoaeue-yei? neeaaeiino?, a
oiio /ene? e ia oai?/iio ??ai?, i?iyaeyee ?i?oe?aoeao, naiino?ei?noue ?
aaeeeee ?ioa?an aei ciaiue.

Aeinoaoiueiai ??aiy aeinyaee 44% aenia?eiaioaeueieo eean?a ? 14 %
eiio?ieueieo, a aei oi?ioth/iai aenia?eiaioo oeae iieaciee a o/i?a
aenia?eiaioaeueieo eean?a noaiiaea ?C%, a a eiio?ieueieo – 17%. O/i?,
ye? aeinyaee oeueiai ??aiy, aoee aeoeai?, i?iyaeyee oai?/o ?i?oe?aoeao,
aiie oaeiae aeeiioaaee caaaeaiiy ??cii? neeaaeiino?, aea i?e oeueiio
niinoa??aaeeny aeaye? ia??oe.

Na?aaei?e ??aaiue aoei aeyaeaii o 24 % o/i?a aenia?eiaioaeueieo ? 59 % –
eiio?ieueieo eean?a. (Ia eiinoaooth/iio aoai? ?o e?euee?noue aoea
i?eaeecii iaeiaeiaa ? neeaaeaea 57% oa 56%). O/i? aenia?eiaioaeueieo
eean?a aeineoue eaaei ni?aaeyeeny c caaaeaiiyie oeiiaeie, a oai?/?
aeeeeeaee iaai? oo?oaeiaiiy, oiae? ye o/i? eiio?ieueieo eean?a ?ieiee ia
ni?aaeyeeny ia eeoa c oai?/eie, a e c cae/aeieie caaaeaiiyie.

Ia ei?enoue aoaeoeaiino? ae?yeueiino? na?ae/eoue ? oie oaeo, ui a
na?aaeiueiio eeoa aeey 3% o/i?a aenia?eiaioaeueieo eean?a aiia aeyaeeany
ia?acoeueoaoeaiith, oiaoi aiie neeaee iecueeee ??aaiue ciaiue (aei
oi?ioth/iai aenia?eiaioo ?o aoei 27%).

Aeieacii aoaeoeaiino? ?ic?iaeaii? iaaeaaia?/ii? ae?yeuei?nii? iiaeae? ?
ii??aiyiiy ?acoeueoao?a o aeeiai?oe?, yeo eaaei i?inoaaeeoe ca iiaeaiith
oaaeeoeath, a oaeiae ii??aiyiiy eiao?oe??ioa oni?oiino? (Eo) yeee oaeiae
iiaeaiee o oaaeeoe?. Eo a aenia?eiaioaeueieo eeanao i?aeaeueany ia I,3
(a?ae 0,5 aei 0,8) ii a?aeiioaiith aei eiinoaooth/iai aenia?eiaioo. O
eiio?ieueieo eeanao a?i iaeaea ia ci?ieany, oiio ui i?aeaeueany anueiai
ia 0,01 (a?ae 0,6 aei 0,6?).

Aeua cacia/aia, a oaeiae ?acoeueoaoe ia?aa??ee ?ic?iaeaii? iiaeae?
iaa/aiiy ? cania?a ?iaeea?aeoae?caoe?? a?aeia?aaeai? a caaaeueieo
aeniiaeao aeena?oaoe?eiiai aeine?aeaeaiiy, iaeaaaeeea?oeie c yeeo ?:

1. I?e/eia “a?/iino?” i?iaeaie ?iaeea?aeoae?caoe?? iieyaa? ianaiia?aae a
oiio, ui aaeoi? ?icaeoeo cae?aiinoae o/i?a o iaaeaaia?oe? caeeoa?oueny
iaeei ? oie aea: aoaeo?oueny a?i a?ae iaa/aiiy aei o/?iiy, a ia,
iaaiaee, a?ae o/?iiy aei iaaieo iaaeaaia?/ieo ae?e. Oiaoi o?aaeeoe?eia
iaa/aiiy caaea? aaeoi? ?icaeoeo, cai?noue oiai, uia noai?thaaoe aeey
iueiai iaiao?aei? oiiae ae. ?ioeie neiaaie, a ?acoeueoao? aeine?aeaeaiiy
iacaaii? i?iaeaie a ?? ?noi?e/iiio ?icaeoeo ie ae?eoee aeniiaeo: aee oeo
i??, iiee o/aiue aoaea ia’?eoii iaa/aiiy, ?aae?coaaoe i?eioeei
?iaeea?aeoaeueiiai i?aeoiaeo a oe?euei?e i?aeoeoe? ia iiaeia.

2. A ?acoeueoao? aiae?co e?oa?aoo?ieo aeaea?ae ? aeaniiai aii??e/iiai
aeine?aeaeaiiy iaie aecia/ai? ineoieiai-iaaeaaia?/i? oiiae
?iaeea?aeoae?caoe??, ia iniia? yeeo aeaaaeai? i?eioeeie
?iaeea?aeoae?caoe??:

– ciaiiy iiaeii? canaithaaoeny /a?ac aeanio ae?yeuei?noue o/i?a, yea
cae?enith?oueny a ?iaeea?aeoaeueiiio oaii?;

– ae?yeuei?noue o/iy iiaeiia aooe ea?iaaia ? eiio?ieueiaaia c aieo
a/eoaey;

– a iaa/aeueiee ci?no i?ia?aiiaiai iaoa??aeo iiaeii? aeeth/aoeny ?
iaoaciaiiy, uia o/aiue ?acii ?c canai?iiyi ciaiue a/eany i?aaeeueii
ieneeoe;

– o i?ioean? iaa/aiiy ia? cae?enithaaoeny iino?eiee cai?ioi?e ca’ycie;

– caaaeaiiy iaa/aiiy iiaeii? aooe iaeneiaeueii eiie?aoeciaai?, a nai
i?ioean canai?iiy ciaiue iioeaiaaiei;

– eiaeai o/aiue iiaeiai ii/oaaoe naaa eiioi?oii a on?o a?aeiioaiiyo.

3. sse iieacaea aenia?eiaioaeueia ia?aa??ea, cacia/ai? i?eioeeie
?iaeea?aeoae?caoe?? aeicaiey? ?aae?coaaoe ?ic?iaeaia iaie ae?yeuei?nia
iiaeaeue iaa/aiiy oa caniae ?iaeea?aeoae?caoe??, oiio oaeo i?aai?caoe?th
iaa/aiiy, ia iao iiaeyae, iiaeia iacaaoe o??th “iaaeaaia?/iith i?/eith”
(TH.E. Aaaainueeee) a?ae yei? a/eoaeaa? c?o/ii oaioethaaoe i?e
?aae?caoe?? i?eioeeio ?iaeea?aeoaeueiiai i?aeoiaeo aei o/i?a o oe?euei?e
i?aeoeoe?.

Ia?niaeoeae iiaeaeueoiai aeine?aeaeaiiy i?iaeaie ?iaeea?aeoae?caoe??
iaa/aeueii-aeoiaiiai i?ioeano, ia iaoo aeoieo, iiaeooue aooe a
aeno?aiieyoe?? i?eioeei?a ?iaeea?aeoae?caoe?? oa ae?yeuei?nii? iiaeae?
ia ?io? i?aaeiaoe ye ii/aoeiai?, oae ? na?aaeiuei? oeiee aai ae o
aeei?enoaii? aeey ?iaeea?aeoae?caoe?? iaa/aiiy eiii’thoa?a i?e aea/aii?
iaoaiaoeee /e ?ioeo i?aaeiao?a o ii/aoeia?e ? na?aaei?e oeie?.

Iniiaiee ci?no aeena?oaoe?? a?aeia?aaeaiee o oaeeo ioae?eaoe?yo:

1. Iao/oaai?noue ye ineoieiai-iaaeaaia?/ia i?iaeaia// A?niee Iaeanueeiai
?inoeoooo aioo??oi?o ni?aa.-1998.- ?1.-N.116-119.

2. Aca?iiae?y i?ae o/eoaeai ? o/iyie ye oaeoi? aieeao ia ye?noue
iao/oaaiino? //Iaoa oeiea. – 1998.- ?3.- N.26-29.

3. I?aai?caoe?y aeeoa?aioe?eiaaieo oi?i ?iaioe c o/iyie ye oiiaa
i?aeaeuaiiy aoaeoeaiino? iaa/aiiy //Iaoeiaee a?niee I?aaeaiiioe?.
aea?ae. iaae. oi?a-oo.- Iaeana.- 1998.- Aei. 2-3.- N.144-148.

4. E aii?ino ia eiaeeaeaeoaeecaoeee o/aaiiai i?ioeanna //Iaaeaaiae/aneay
eoeueoo?a o/eoaey.- 1995.- N. 26-27.

5. Ia eiaeeaeaeoaeecaoeee iao/aiey //Oacenu iao/ii-i?aeo. eiio.
“Ia/aeueiay oeiea: i?iaeaiu, iiuo, ?aoaiey”. – Eciaee, 1992.- N. 52-53.
/a niaaoi?noaa/.

6. Aeaye? ieoaiiy ?icaoaeiae iaaeaaia?/ii? iaoee //Oace iaoeiai-i?.
eiioa?. “Eeane/ia iaaeaaia?ea ? o?eieia?y a na?oe? no/anieo caaaeaiue
oe?eueii? ? aoc?anueei? neiaaniino?”. – Iaeana, 1993- N. 7-8.

7. Eiaeeaeaeoaeecaoeey iao/aiey eae i?aaeiinueea niyoey aeeneiioi?oiiai
ninoiyiey iiae?inoea // Oacenu iao/ii-i?aeo. eiio. ii oece/aneie
eoeueoo?a e oeieueiie aeaeaia.-Iaeanna, 1993.- N. 105-106.

Eieii?e/aiei E.A. ?iaeea?aeoae?caoe?y iaa/aeueii-i?ciaaaeueii?
ae?yeueiino? o/i?a ii/aoeiai? oeiee a i?ioean? canai?iiy iaoaiaoe/ieo
ciaiue.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa iaaeaaia?/ieo
iaoe c? niaoe?aeueiino? 13.00.01 – oai??y oa ?noi??y iaaeaaia?ee.

I?aaeaiiioe?a?inueeee aea?aeaaiee iaaeaaia?/iee oi?aa?neoao, Iaeana,
1999.

Caoeuathoueny ae?yeuei?nia iiaeaeue iaa/aiiy, caniae
?iaeea?aeoae?caoe??, ye? caaacia/othoue ?aae?caoe?th a oe?euei?e
i?aeoeoe? i?eioeeio ?iaeea?aeoaeueiiai i?aeoiaeo aei iieiaeoeo oeiey??a
a i?ioean? canai?iiy iaoaiaoe/ieo ciaiue oeyoii ci?ie iai?yieo “aaeoi?a”
a iaaeaaia?oe? a?ae iaa/aiiy aei o/?iiy, oa i?eioeeie
?iaeea?aeoae?caoe??.

Eeth/ia? neiaa: noa’?eo iaa/aeueii-aeoiaiiai i?ioeano, ae?yeuei?niee
iaoiae, ae?yeuei?nia iiaeaeue iaa/aiiy, i???iooth/a ea?oea, noaie-iii?e,
o?ai?ia ieneaiiy,

Eieiiee/aiei E.A.

Eiaeeaeaeoaeecaoeey o/aaii-iiciaaaoaeueiie aeayoaeueiinoe o/aueony
ia/aeueiie oeieu i?e onaiaiee iaoaiaoe/aneeo ciaiee.

Aeenna?oaoeey ia nieneaiea iao/iie noaiaie eaiaeeaeaoa iaaeaaiae/aneeo
iaoe ii niaoeeaeueiinoe 13.00.01 – oai?ey e enoi?ey iaaeaaiaeee.

THaeii-Oe?aeineee ainoaea?noaaiiue iaaeaaiae/aneee oieaa?neoao, Iaeanna,
1998.

Caueuaaony aeayoaeueiinoiay iiaeaeue iao/aiey, n?aaenoaa
eiaeeaeaeoaeecaoeee, iaania/eaathuea ?aaeecaoeeth a oeieueiie i?aeoeea
i?eioeeia eiaeeaeaeoaeueiiai iiaeoiaea e ieaaeoei oeieueieeai i?e
onaiaiee iaoaiaoe/aneeo ciaiee iooai niaiu iai?aaeaiey “aaeoi?a” a
iaaeaaiaeea io iao/aiey e o/aieth, e i?eioeeiu eiaeeaeaeoaeecaoeee.

Eeth/aaua neiaa: noauaeo o/aaii-ainieoaoaeueiiai i?ioeanna,
aeayoaeueiinoiue iaoiae, aeayeueiinoiay iiaeaeue iao/aiey,
i?eaioe?iaaiiay ea?oi/ea, noaiu-iii?u, o?aioeia iuoeaiey.

Kolomiychenko L.G.

Individualization of educationally – cognitive activity of primary
school pupils when mathematical knowledges are acquired.

Submitted dissertation for a candidate of pedagogical science degree on
the specialty 13.00.01 – Theory and History of Pedagogic.

South-Ukrainian State Pedagogical University, Odessa, 1998.

An actioning model of education, means of individualization that secure
realization of the individual approach to younger pupils in the school
practice of principle when mathematical knowledge’s are acquired by the
” vector ” trand change from teaching to learning, and in pedagogics and
principles of individualization are defended.

Key words: type of educational process, actioning model of education,
actioning methods reference card, stand-by scheme, tranning of
mentality.

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