Vizualizacija i istraživanje pomoću računala u nastavi matematike

master's thesis

• Author: Ida Balković
• Mentor: Maja Starčević (mentor)
• Committee member: Maja Starčević (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ideja istraživanja u nastavi matematike je da učenici vlastitom aktivnošću istražuju odgovor na postavljeno pitanje. Na taj način im se približava proces znanstvenog istraživanja. U nastavi matematike se to ostvaruje i korištenjem računala. Cilj ovog rada je pokazati da se različiti matematički pojmovi u nastavi matematike mogu obraditi pomoću računala. Pomoću alata dinamične geometrije obrađuju se osnovni geometrijski pojmovi. Učenici samostalno ili u paru istražuju dane pojmove uz pomoć takvih alata i istraživanjem dolaze do željenih zaključaka. Osim alata dinamične geometrije, u nastavi se mogu koristiti i različiti alati za izradu proračunskih tablica. Kombiniranjem tih alata ispituju se funkcije (linearna i kvadratna funkcija, te funkcija apsolutne vrijednosti) i limes nizova. Nedostatku vizualizacije problema se može doskočiti grafičkim alatima koji učenicima mogu omogućiti i razvijanje vlastitog prostornog zora. Vizualizacija problema pomaže pri obradi osnovnih pojmova, ali i pri rješavanju složenijih problema, kao što je prikazano u zadnjem poglavlju rada.

Abstract (english)

The basic idea behind using investigation and discovery techniques in the mathematics education is to encourage students to find the answer to the asked question by themselves. In this way, students are becoming familiar with all phases of the scientific research. In the mathematics education this can be accomplished by using computer technology as well. The main goal of this thesis is to show that different mathematical concepts can be introduced to students by using computer technology. Using dynamic geometry software, basic geometrical concepts are thought. Students, working alone or in pairs, by means of dynamic geometry software, explore given concepts and come to desired conclusions on their own. Apart from dynamic geometry software, spreadsheet tools can be used. By combining aforementioned tools, functions (affine functions, quadratic functions and absolute value functions) and limit of a sequence are tested. If students cannot visualize particular mathematical problem, they can use different graphical tools. If so, students can visualize problems and develop their own “spatial hut”. The last chapter of the thesis demonstrates that the visualization helps when basic mathematical concepts are thought, but also when more advanced mathematical problems are being solved.

• Keywords: nastava matematike; istraživanje; znanstveno istraživanje; alati dinamične geometrije; vizualizacija problema; grafički alati
• Keywords (english): mathematics education; investigation and discovery techniques; scientific research; dynamic geometry software; visualization of problems; graphical tools; teaching mathematics
• Language: croatian
• URN:NBN: urn:nbn:hr:217:589686
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-05-10 11:51:22