Primjena naprednih opcija GeoGebre u nastavi matematike

master's thesis

• Author: Karolina Rastić
• Mentor: Maja Starčević (mentor)
• Committee member: Maja Starčević (predsjednik povjerenstva)
• Committee member: Goran Igaly (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-07-16, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Kao što znamo, program GeoGebra nudi niz mogućnosti pri rješavanju matematičkih problema. Zbog prevelikog obujma gradiva koje pokriva i naredbi koje sadrži, u ovom radu odabrali smo tipične primjere koji prezentiraju neke od tih naredbi. Najprije smo razmotrili naredbe koje se odnose na gradivo geometrije, a potom naredbe za algebru, analizu i vjerojatnost. U poglavlju Geometrija pokazali smo kako se izrađuje alat s kojim dalje jednostavno možemo konstruirati likove, tj. popločavati. Zgodan dio koji je idealan za nastavu matematike svakako je prikaz rotacijskog tijela. Učenicima često nije jasno koje tijelo nastaje vrtnjom oko osi pa im to možemo prikazati pomoću GeoGebre. Problem tangente, kod određivanja derivacije funkcije, učenicima možemo vizualno prikazati što smo i pokazali u poglavlju Algebra kao i kako računamo određeni integral. Posljednje poglavlje, Vjerojatnost, odnosilo se na gradivo koje nas možda odmah ne asocira na GeoGebru, ali kao što smo mogli vidjeti, i ono se može prikazati u ovom programu. GeoGebra nudi proračunsku tablicu nalik onoj u Excelu u kojoj možemo izvoditi iste jednostavne račune kao i u Excelu. Također, na konkretnim primjerima pokazali smo kako se koristi kalkulator vjerojatnosti. Možda najzanimljiviji dio poglavlja Vjerojatnost jest dio koji se odnosi na geometrijsku vjerojatnost. Objasnimo li učenicima na satu te zadatke koristeći se GeoGebrom, oni lakše vizualiziraju problem i dolaze do rješenja. Ovaj rad presjek je nekih naredbi GeoGebre. Ostale naredbe i mogućnosti koje nudi GeoGebra lako pronađemo na službenim stranicama ovog programa (https://www.geogebra.org/materials) gdje se nalaze neki već gotovi uradci koji se slobodno mogu koristiti na satu.

Abstract (english)

As we know, the GeoGebra application offers a lot of options for solving mathematical problems. Due to the overflow of materials that GeoGebra covers and the commands it contains, in this paper we have chosen typical examples that present some of those commands. First, we reviewed the commands related to geometry, and then those related to algebra and analysis, and at the end to probability. In the chapter Geometry we have shown how to create a tool with which we can further easily construct shapes. A part that is ideal for the teaching of mathematics is certainly a representation of a rotating shape. It is often unclear to students which shape is created when a polygon rotates around an axis, so to clarify that to them we can show the rotation of the polygon with GeoGebra. The problem of tangent, when determining the derivation of a function, can be visualized to students as we have shown in the chapter Algebra and analysis, as well as how to calculate a definite integral. The last chapter, Probability, refers to the material that we may not immediately associate with GeoGebra, but it can be displayed in this program. GeoGebra offers a spreadsheet similar to the one in Excel in which we can run the same simple problems. Also, we have shown in concrete examples how the probability calculator is used. Perhaps the most interesting part of the chapter Probability is the part that refers to the geometric probability. If we explain lessons of the geometric probability to students by using GeoGebra, they can easily visualize the problem and come up with solutions. This paper is a cross section of some GeoGebra commands. Other commands and features offered by GeoGebra can be easily found on the official pages of this program ( https://www.geogebra.org/materials) where some of the already finished works are available and can be used freely in the class.

• Keywords: GeoGebra; rješavanje matematičkih problema; prikaz rotacijskog tijela; proračunska tablica; kalkulator vjerojatnosti
• Keywords (english): GeoGebra; solving mathematical problems; representation of a rotating shape; spreadsheet; probability calculator
• Language: croatian
• URN:NBN: urn:nbn:hr:217:231934
• 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: 2019-12-02 14:29:20