Upotreba manipulativa u razvoju matematičkog mišljenja

Abstract

Manipulativi u nastavi matematike predstavljaju svojevrstan agens procesa razvoja matematičkog mišljenja. O ovome svedoče mnogobrojna teorijska i empirijska istraživanja koja su realizaovana u svetu, ali o tome se kod nas (u Srbiji) malo zna ili malo upotrebljava. Disertacija koristi sve najznačajnije, relevantne teorijske i empirijske nalaze iz oblasti upotrebe manipulativa u procesu nastave i učenja i sistematizuje ih, tako da uz empirijsko istraživanje stavova i mišljenja nastavnika o manipulativima, na uzorku u Srbiji daje jedinstvenu celinu. Dragocenost ove disertacije jeste u tome što predstavlja originalan prikaz okolnosti obrazovanja u svetu, filozofske i psihološke postavke pojma mišljenja, kao i alternativnih pristupa (lateralno razmišljanje). Nakon širokog pregleda i uvoda o pojmu mišljenja i konačno matematičkog mišljenja, disertacija se bavi manipulativima kao korisnim alatima nastave i učenja matematike i razvoja matematičkog mišljenja. Stvaranjem dualnih matematičkih reprezentacija, prevođenjem konkretnih okolnosti matematičke strukture u vizuelne reprezentacije, stvara se mentalna slika kojom se operiše na mentalnom planu i tako konkretno prelazi u formalno i apstraktno. Umešnost nastavnika da vodi ove procese u kojima se upotrebljavaju manipulativi, razlike i sličnosti između realnih ili fizičkih i virtuelnih manipulativa jeste jedna od podtema koje se izlažu u ovoj disertaciji. Prilozi za temu upotrebe manipulativa u funkciji razvoja matematičkog mišljenja imaju svrhu u približavanju objašnjenja nekog pojma ili fenomena koji se koristi tokom izlaganja u glavnom delu disertacije i od posebnog je značaja. Mnogi pojmovi su prava retkost/novost u polju metodike nastave matematike kod nas, tako da je u tom smislu ova disertacija od posebne važnosti. Obiman spisak referenci na koje se disertacija poziva, analiziran je i strukturisan i daje se kao prilog ovog rada.

Within the process of teaching mathematics manipulatives represent a kind of an agent in the process of developing mathematical thinking. A lot of theoretical and empirical research conducted around the world testifies to this fact, and yet here (in Serbia) this is little known or employed too little. This dissertation uses all the most significant and relevant theoretical and empirical findings from the area of using manipulatives in the process of teaching and learning and systematizes them, providing a unified whole together with the empirical research of the teachers’ attitudes and opinions on manipulatives sampled in Serbia. The value of this dissertation lies in the fact that it gives an original overview of the educational conditions throughout the world, philosophical and psychological bases for the notion of thinking, as well as some alternative approaches (such as lateral thinking). After a broad overview and introduction about the notion of thinking and eventually mathematical thinking, this dissertation deals with manipulatives as useful tools for teaching and learning mathematics and for the development of mathematical thinking. By creating dual mathe-matical representations, translating concrete conditions of a mathematical structure into visual representation, a mental image is formed which is then used on the mental level and in such way concrete is transformed into formal and abstract. The versatility of the teacher to lead these processes in which manipulatives are used as well as differences and similarities between real or physical and virtual manipulatives belong to one of the subthemes developed in this dissertation. These contributions to the theme of using manipulatives in the function of developing mathematical thinking have the purpose to facilitate a closer interpretation of notions or phenomena used within the main part of the dissertation and is of special significance. Some of the notions are true rarities/novelties in the field of methods of teaching mathematics in our country and that is why this dissertation holds special importance. Voluminous list of references cited in this dissertation is analyzed and structured, and given as an addendum to this thesis.