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Inovacije u nastavi - časopis za savremenu nastavu
2020, vol. 33, br. 1, str. 57-71
jezik rada: engleski
vrsta rada: pregledni članak
objavljeno: 26/07/2020
doi: 10.5937/inovacije2001057M
Creative Commons License 4.0
Abakus računaljka - od istorije do primene u matematičkom obrazovanju
aUniverzitet u Kragujevcu, Pedagoški fakultet, Užice
bUniverzitet u Novom Sadu, Učiteljski fakultet, Sombor

e-adresa: sanjamaricic10@gmail.com

Projekat

Nastava i učenje: problemi, ciljevi i perspektive (MPNTR - 179026)

Sažetak

Imajući u vidu da istorija matematike može imati značajnu ulogu u matematičkom obrazovanju danas, u radu skrećemo pažnju na drevnu računaljku - abakus. Abakus je najstarija poznata alatka za računanje koja je korišćena u Mesopotamiji, starom Egiptu, antičkoj Grčkoj i Rimu, a unapređeni model abakusa u upotrebi je i u današnje vreme. U radu predstavljamo različite verzije abakusa koje su se koristile tokom istorije (grčki, rimski, kineski, japanski, ruski i indijski abakus (mehanički i digitalni), a posebno se bavimo istraživanjem uticaja japanskog abakusa (Soroban) na sposobnost računanja, budući da se ovaj model računaljke smatra najefikasnijim, jer se bazira isključivo na decimalnom numeričkom sistemu. Cilj ovog rada je da primenom metode teorijske analize istražimo vrednost, mogućnosti i ulogu primene japanskog Sorobana u radu sa decom. Posebno skrećemo pažnju na upotrebu abakusa u matematičkom obrazovanju kroz sledeće aspekte: u učenju mentalne aritmetike, u shvatanju mesne vrednosti cifre, u mentalnom razvoju dece, u radu sa decom sa smetnjama u razvoju, naročito sa decom sa oštećenjem vida ili sluha, kao i pogledu svrsishodnosti abakusa kao sredstva za razvijanje veština za rešavanje problema. Smatramo da metodološki pristup koji treba da dovede do razumevanja pojma broja mora da bude zasnovan na konkretnim, aktuelnim i očiglednim faktorima koji omogućavaju jasno formulisanje pojma broja i vrednosti svake cifre, za šta abakus može biti dobra osnova. Upotrebom abakusa učenici upoznaju mesne vrednosti svake cifre u broju, a time stiču dublje razumevanje strukture broja uz pomoć kuglica na računaljki, jer im fizička i ne-simbolička predstava broja na abakusu pomaže da vizualizuju položaj mesta cifre, što doprinosi boljem razumevanju strukture broja. Učenici se obučavaju da koriste abakus za računanje prvenstveno kroz konkretne aktivnosti kroz koje uče kako da pomeraju kuglice na abakusu, čime se podstiču da stvaraju mentalne slike i tako bolje razvijaju mentalne strategije koje će im omogućiti lakši prelaz sa konkretnih aktivnosti na mentalni nivo računanja. Kroz ovaj proces deca bolje razumeju matematiku i mogu da rešavaju probleme i primenjuju matematiku, postaju fleksibilnija u rešavanju matematičkih problema, što su sve prednosti mentalnog računanja. Primenom abakusa u računanju sve aktivnosti učenja prelaze sa nivoa praktičnog-perceptivnog rezonovanja na nivo konceptualno-logičkog rezonovanja, zato što one od samog početka pružaju konkretnu vizuelnu i manipulativnu osnovu za učenje, što se direktno odražava na mentalni razvoj dece. Trenutno uspostavljanje veze između pokreta ruke i rada mozga doprinosi bržem i uravnoteženom ukupnom razvoju mozga. Mentalno računanje podstiče mentalnu aktivnost, koncentraciju, memoriju, analitičke veštine i strpljenje koji se razvijaju primenom abakusa u radu sa decom, dok vizuelizacija doprinosi razvoju neurona u mozgu. Pored toga, korist od upotrebe ovog sredstva za računanje naročito je vidljiva u radu sa decom sa oštećenim sluhom ili vidom, zato što im abakus olakšava da vizuelizuju mentalno računanje kroz kinestetičku aktivnost. Pomeranjem kuglica na računaljki ova deca mogu da vizuelizuju određene aktivnosti u okviru teme o brojevima, da ih prenesu na mentalni nivo i da razviju veštinu mentalnog računanja, čime se prevazilaze teškoće koje imaju u vezi sa jezikom, bilo govornim ili pisanim. Na osnovu brojnih istraživačkih radova i stavova autori ovog rada zaključuju da japanski abakus u radu sa decom u okviru matematičkog obrazovanja može ostvariti brojne dobrobiti, među kojima su svakako najznačajniji pojmovno razumevanje mentalne aritmetike i razvijanje sposobnosti mentalnog računanja i rešavanja problema, sticanje jasne mentalne predstave o strukturi brojeva, njihovoj veličini i odnosu, razumevanje mesne vrednosti cifre, ali i razvijanje motivacije i pozitivnih stavova prema matematici. U radu se bavimo samo nekim aspektima primene japanskog abakusa u radu sa decom, sa ciljem da skrenemo pažnju na ovo drevno sredstvo za računanje i na izuzetnu korist koju od njega možemo imati u učenju matematike.

Ključne reči

abakus; istorija matematike; soroban; mentalno računanje; matematičko obrazovanje

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