Izinhlobo zama-abacuses: umhlahlandlela ophelele wamamodeli, ukusetshenziswa, nomlando

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Ama-Abacuse abelokhu ekhona amakhulu eminyaka, kodwa ayaqhubeka nokumangala ngobulula bawo namandla awo. Angamathuluzi okubala okusebenza ngomshini avumela ukubala okusheshayo futhi ayinsiza enhle kakhulu yokufundisa yokuqonda inani lendawo kanye nokwenza izibalo zengqondo.

Ngale kwe-abacus yesikole evamile, kukhona umhlaba wezinhlobonhlobo zamasiko anemiklamo nokusetshenziswa okuhlukile. Ama-Suanpan (isiShayina), ama-Soroban (isiJapane), ama-Schoty (isiRashiya), nama-abacus anezinsika eziyishumi ahambisana namabhodi okubala asendulo kanye nezinguqulo ezenzelwe izimpumputhe noma ukufundisa esikoleni samabanga aphansi kanye nesikole samabanga aphansi. Ake siwahlole ngokucophelela, ngezibonelo namathiphu okukhetha.

Iyini i-abacus futhi isetshenziselwa ini?

I-abacus empeleni iyithuluzi elinezinduku noma izintambo ezithwala ubuhlalu obushelelayo . Ngokuhambisa lobu buhlalu ngokwemithetho ethile (ama-algorithms), imisebenzi yezibalo ingenziwa: ukuhlanganisa, ukususa, ukuphindaphinda, ukuhlukanisa, kanye nokubala okuthuthukile kakhulu njengokukhipha izimpande.

Kumamodeli avamile kakhulu ekilasini (okuthiwa i -abacus enama-bead ayishumi ), umugqa ngamunye noma "umugqa" umele amandla ayishumi. Ngakho-ke, umugqa owodwa umele amayunithi, amashumi alandelayo, bese kuba amakhulu, njalo njalo. Leli nani lesikhundla livumela ukumelwa okusheshayo nokucacile kwezinombolo ezivamile.

Isihluthulelo se-abacus akusikho nje ukusebenza kwayo kodwa futhi nenani layo lemfundo. Iguqula izinto ezingabonakali (izinombolo) zibe yinto ephathekayo : ubuhlalu bungathinteka, bubonwe, futhi buzwiwe njengoba bushelela. Lokhu okuhlangenwe nakho okunezinzwa eziningi kwenza kube lula ukufunda kwezingane ezincane futhi kunikeza nokuqeqeshwa kwengqondo kubantu abadala.

Umlando omfushane we-abacus

Imvelaphi eqondile ye-abacus ayikaziwa kahle, yize iShayina ibhekwa njengesikhungo esiyinhloko sokulinganisa kwayo komlando . Kunobufakazi bezinsimbi zokubala ezifanayo emasikweni asendulo njengeBabiloni neGrisi (amaGreki ayesebenzisa "i-abakion," ibhodi elinemigqa), futhi amaRoma avumelanisa imodeli yawo ngemifantu namatshe amancane.

Kusukela ngekhulu le-12 AD kuqhubeke, i-abacus yabekwa ezingeni elifanayo eShayina , isiko elihlala likhona e-Asia (eShayina naseJapan). EYurophu, phakathi neNkathi Ephakathi, i-abacus yaqhubeka isetshenziswa njalo, kodwa ukusetshenziswa kwayo kwehla njengoba uhlelo lwezinombolo lwesiHindu-Arabhu kanye nezibalo ezibhaliwe kwanda kakhulu.

Ezikoleni zaseYurophu zekhulu le-19, ama-abacuse ayevame ukusetshenziswa ngawodwana nangokubambisene. Namuhla, iminyuziyamu namaqoqo emfundo agcina izibonelo eziningi zokuvela kwawo, izinto zokwakha, kanye nokusetshenziswa kwawo. Lokhu kuqhubeka komlando kuchaza ukuthi kungani ehlala eyinsiza yemfundo eyigugu kangaka.

Isetshenziswa kanjani i-Abacus: Umbono Ojwayelekile kanye Nenani Lendawo

Umqondo we-abacus yesimanje usekelwe enanini lendawo lamadijithi . Ngokunikeza amandla ayishumi emgqeni ngamunye (noma ikholomu, kuye ngohlobo), ubuhlalu obushintshiwe bumelela amayunithi, amashumi, amakhulu, njalo njalo. Lokhu kumelwa okubonakalayo kusiza ukuqonda ukuthi kungani u-507 engafani no-57: ku-abacus, ukubala "amakhulu" kwenza umehluko ucace kakhulu.

Ku -abacus yesikole enama-bead ayishumi ngenduku ngayinye , mane ushelele eceleni ama-bead amaningi njengenani lamayunithi ofuna ukuwaqopha. Uma ufika eshumini, "ukhuphukela phezulu" i-bead eyodwa emgqeni wamashumi bese "uhlehla" lawo ayishumi emgqeni wamayunithi (njengokubhaliwe kokuhlanganisa nokuthwala). Le ndlela efanayo isebenza kweminye imisebenzi.

Ukuze wengeze futhi ususe, ubuhlalu buhanjiswa ngokunyuka noma ngokunciphisa, kunakekelwe ngokuboleka nangokuthwala. Ukuze kuphindaphindwe futhi kwahlukaniswe, kusetshenziswa ama-algorithm athile asebenzisa isakhiwo sethuluzi kanye nokufunda kwesimo salo. Ngokuzijwayeza, kungenzeka nokubala izimpande zesikwele usebenzisa izindlela zendabuko.

Izinhlobo ze-abacus: ukusuka eMpumalanga ukuya eNtshonalanga

Umhlaba we-abacus uhlukahlukene futhi uyathakazelisa. Kunemiklamo enezigaba ezihlukile , eminye enokuqondiswa okuvundlile, kanye namabhodi okubala andulela izinduku ezinobuhlalu. Lawa amamodeli amele kakhulu.

I-Chinese abacus (Suanpan)

I-Suanpan ihlukaniswa ngokuhlukanisa induku ngayinye ibe yizingxenye ezimbili : ingxenye ephezulu (ngezinye izikhathi ebizwa ngokuthi "iZulu") kanye nengxenye engezansi ("uMhlaba"). Enguqulweni yayo yakudala, ingxenye ephezulu inamabhere amabili kanti ingxenye engezansi inamahlanu. Amabhere aphezulu anenani lamayunithi amahlanu ngalinye; amabhere aphansi, iyunithi elilodwa.

Eminye imithombo yanamuhla ichaza i-Suanpan ngokuthi “yakhelwe ukubalwa kwesisekelo-16.” Empeleni, i-Suanpan isetshenziswa ngama-algorithms edesimali , futhi ukuhlelwa kwayo kwama-bead angu-2/5 ngenduku kuye kwasebenza ngokomlando ukusebenza ngezisekelo ezahlukene nama-engeli okusebenza. Iyithuluzi eliguquguqukayo kakhulu nelisheshayo, elihlobene eduze nesiko lokuhweba laseShayina.

I-Japanese abacus (Soroban)

I-Soroban iyinguquko ye-Suanpan, futhi ukwakheka kwayo kwamanje, enobuhlalu obubodwa engxenyeni ephezulu kanye no-4 engxenyeni engezansi, kwathandwa kakhulu . Lokhu kulula kuhambisana kahle nohlelo lwedesimali futhi kuholele ekuthuthukisweni kwezikole eziphelele zokubala ngengqondo kusetshenziswa i-abacus eJapane.

I-Soroban isebenzisa ama-algorithms athuthukisiwe ukwengeza, ukususa, ukuphindaphinda, nokuhlukanisa ngempumelelo emangalisayo. Ochwepheshe abaningi bagcina "bebona ngeso lengqondo" i-abacus ezingqondweni zabo, okubavumela ukubala ngaphandle kokuba nethuluzi elibonakalayo phambi kwabo (elaziwa ngokuthi i-mental abacus).

I-Russian abacus (Schoty)

I-Schoty ayifaki isihlukanisi esiphakathi bese ihlela ubuhlalu ngokuvundlile , okwenza kube lula ukufundwa okuqondile kwamanani. Ngokuvamile inebuhlalu obuyishumi ngenduku kanye nenani lezinduku ezilungiselelwe ubude bezinombolo ezisetshenziswayo.

Lo mklamo, osakazeke kabanzi eRussia nakwamanye amazwe angomakhelwane, uphumelela kakhulu ekuthengiselaneni kwansuku zonke kanye nemali. Ukungabikho kwemikhakha ephezulu nephansi kwenza kube lula ukuqonda kwabanye abasebenzisi, yize kudinga ama-algorithm athile ahlukile kwalawo e-Suanpan noma e-Soroban.

I-abacus yobuhlalu obuyishumi (isikole)

Lolu uhlobo lwephazili esivame ukulibona emakilasini ezingane zabantwana abancane kanye nezikole zamabanga aphansi emazweni amaningi. Luqukethe uhlaka olunezinduku noma izintambo eziyishumi kanye nama-bead ayishumi ku- . Imigqa imelela amandla e-10; ngokuhambisa ama-bead, izingane ziqonda ngokuqonda inani lendawo kanye nokwakheka kanye nokuhlukana kwezinombolo.

Ngokombono wokufundisa, le fomethi isiza abafundi ukuthi bashintshele kokubonakalayo baye kokungacacile. Ikhuthaza ukubala ngengqondo kanye nokuqonda ukuthwala nokuboleka , amakhono asetshenziswa kamuva ekubaleni okubhaliwe kanye ne-algebra yokuqala.

I-abacus yokubala yangaphandle namabhodi okubala

Ngaphambi kokuba kusetshenziswe izinduku ezinezinhlayiya ezishelelayo, kwakusetshenziswa amabhodi noma amatafula anemigqa lapho kwakubekwa khona amatshe amancane noma amathokheni: yingakho kwabizwa ngokuthi "ama-abacuses angaphandle e-bead." Umsebenzisi wayehambisa izingcezu ezindaweni eziphawuliwe, ikhambi lasendulo kakhulu elase lisetshenziswa amaGreki namaRoma.

Lawa mabhodi abalulekile ekuqondeni uhlu lozalo lwe-abacus. Ngokusebenza kahle, asebenza ngenhloso efanayo : ukumela izinombolo nokusebenza nazo ngendlela ehlelekile, ethembele enanini lesikhundla kanye nokuphathwa okungokoqobo kwezibali.

I-abacus yaseRoma

I-abacus yamaRoma iyindlela ewusizo yokuguqula enezikhala noma imigodi yezinhlamvu zemali nezingxenyana . Kweminye imiklamo yanamuhla, ukucabanga kwayo kuqhathaniswa nokwaseSoroban, yize inezici zayo zokumelela ukwahlukaniswa kwemali.

Ngokomlando, lawa mamodeli abhekane nezidingo zezentengiselwano kanye nezokubalwa kwezimali. Umqondo wawo oyinhloko ukuhlukaniswa ngenani , okulindeleke ukuthi kube nomqondo wemikhakha noma imigqa enesisindo esihlukene sokulinganisa esizobona sithuthukiswa kabanzi eMpumalanga.

I-abacus emfundweni yesimanje

Kungase kubukeke “njengenye nje indlela yokubala,” kodwa akunjalo: i-abacus iyithuluzi lokufundisa elinamandla anganikezwa yizibali ze-elekthronikhi. Ngokusebenzisa ubuhlalu, umfundi ubamba ukubona, ukuthinta, nokuzwa, futhi kumele agcine izinyathelo eziphakathi enkumbulweni yakhe yokusebenza.

Lokhu kuhlanganiswa kokuhlangenwe nakho kwezinzwa kanye nenkumbulo yokusebenza kukhuthaza ukunaka, ukugxila, kanye nokubona ngeso lengqondo . Yingakho kusetshenziswa kabanzi ezinhlelweni zezibalo zengqondo kanye nasekwethuleni inani lendawo ezinganeni ezincane.

Esikoleni sabantwana abancane kanye nesikole samabanga aphansi, i-abacus ivumela abafundi ukuthi "babone" ukuthi inombolo ishintsha kanjani lapho kwakhiwa amashumi anamayunithi ayishumi noma kuhlanganiswa ikhulu . Lokhu kuqonda okunembile kusheshisa izibalo futhi kulungiselela isisekelo sokuqukethwe kwezinga eliphezulu.

Kukhona futhi inguqulo eguquliwe yabantu abanenkinga yokubona. Lokho okubizwa ngokuthi "i-abacus for the blind" kufaka izindlela zokubopha ubuhlalu endaweni, ukuqinisekisa ukuzinza ngokuthinta. Kuyithuluzi eliwusizo lokubala okuzimele kanye nemfundo ehlanganisa bonke.

Okokugcina, uma ukhetha ukungasebenzisi ithuluzi elingokoqobo, kulezi zinsuku kunezinhlelo zokusebenza nezinsizakusebenza ezibonakalayo ezilingisa ukunyakaza kwama-bead. Lokhu kuwusizo kakhulu ekuzijwayezeni usohambeni noma ekuboniseni ekilasini, yize ulwazi oluthintayo lwe-abacus yangempela luhlala luhlukile.

Imisebenzi engenziwa

Ngokuqonda kahle ama-algorithms aleli thuluzi , ukuhlanganisa, ukususa, ukuphindaphinda, kanye nokuhlukanisa kungenziwa ngesivinini esimangalisayo. Isihluthulelo ukwazi imithetho yokuguqula (isibonelo, ukuthi kufanele "wehlise" noma "wenyuse" ubuhlalu phakathi kwemigqa) bese ubenza.

Ngaphandle kwemisebenzi emine eyisisekelo, isiko likaSoroban nelikaSuanpan lihlanganisa izinqubo zezimpande namandla , yize ukuzifunda kudinga umzamo oqhubekayo. Ekilasini elijwayelekile, isici esibalulekile ukusebenzisa inani lazo ekubaleni ngengqondo nasekuqiniseni inani lendawo.

Inzuzo eyengeziwe ukuthi konke kubonakala ngaphakathi kohlaka : umfundi angabona ngokushesha ukuthi yini eshintshile nokuthi kungani. Lokhu kusabela okusheshayo kusiza ukulungisa amaphutha, ukuthuthukisa ukunemba, nokuthuthukisa amasu okuziqapha enqubo.

Ungayikhetha kanjani i-abacus yakho (ngokusebenzisa nephrofayili)

Uma umgomo uwukufundisa izingane ezincane, i -abacus enama-bead ayishumi enemibala egqamile kanye nama-beads anobukhulu obuhle iyafaneleka. Into ebalulekile ukuthi imigqa nama-beads kuhlukaniswe ngokucacile, ukuze inani lendawo libonakale.

Ukuze kuqeqeshwe ukubala ngengqondo komuntu ngamunye kubantu abasha kanye nabantu abadala, i -Soroban yesimanje (1–4) ivame ukunconywa ngenxa yokuhambisana kwayo nesistimu yamadesimali kanye nengcebo yayo yezinsiza zokufunda. I-Suanpan nayo inhle kakhulu uma ukhangwa isiko layo kanye nokuguquguquka kwayo.

Labo abenza ukuthengiselana kwemali kwansuku zonke noma ukwengezwa okusheshayo bathola i -Schoty (isiRashiya) eqondiswe ngokuvundlile ilula . Iqinile, ilula, futhi isebenza kahle kakhulu emisebenzini ephindaphindwayo.

Ngokuphathelene nezinto zokwakha, ukhuni lunikeza umuzwa omnandi nokuqina, kuyilapho ipulasitiki ilula futhi iyonga kakhulu. Usayizi wohlaka kanye nenani lezinduku kufanele kulungiswe kuye ngezinombolo ozosebenza ngazo; ekilasini eliyisisekelo, ithuluzi elikhulu kakhulu alidingeki.

Uma uzokuhlanganisa nezikrini, ungasebenzisa i- abacus ebonakalayo ukuze uzijwayeze noma uchaze, ngaphandle kokuyeka ukukhohlisa ngokomzimba lapho ufuna ukuqinisa ukufunda kokuthinta.

Ilukuluku namanothi awusizo

Kuvamile ukudida i-abacus "ngozimele bokubala" ezilula. I-abacus yangempela ilawulwa yimithetho yenani lesimo ; akukhona nje ukushelela ubuhlalu ukuze kubalwe, kodwa mayelana nokumelela izinombolo nokusebenza nazo ngokwe-algorithms.

Umniningwane owodwa omangalisayo: ezikhathini zasendulo nangaphambi komlando wokubala, umqondo wokubala izikhundla kanye nezimo waphefumulela amathuluzi okusebenza afana nomqondo we-abacus. Akukhona ukweqisa ukusho ukuthi, ngandlela thile, i-abacus yavula indlela yokubala okuhlelekile.

Izinguqulo zekilasi ngalinye neleqembu zigcinwa emaqoqweni emfundo naseminyuziyamu . Njengensiza yokufundisa, ayizange isetshenziswe amashumi eminyaka, kodwa isibuye ngamandla ngenxa yokubaluleka kwayo ekuthuthukiseni ukuqonda okujulile kwezinombolo nokubala ngengqondo.

Uma ulingeka ukuthi uyithenge, manje sekunamamodeli enziwe ngokhuni, ipulasitiki, iSoroban, neSuanpan ngamanani aphansi kakhulu. Okokuqala, awudingi ithuluzi elibizayo: ukucaca komklamo kanye nokulula kokusetshenziswa kubaluleke kakhulu.

Kuyafaneleka ukugcizelela ukuthi kungani i-abacus ihlala ibalulekile kangaka: yenza izinombolo zibonakale, idinga ukunakwa nenkumbulo, futhi ikhuthaza amasu engqondo . Lokhu kuhlanganiswa kuyenza ibe ithuluzi eliwusizo lokufunda, ukufundisa, nokugcina amakhono ezinombolo kunoma yimuphi ubudala.