Razvoj geometrijskog mišljenja u nastavi matematike u osnovnoj školi

master's thesis

• Author: Petra Kovačević
• Mentor: Aleksandra Čižmešija (mentor)
• Committee member: Aleksandra Čižmešija (predsjednik povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-12, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Geometrija je grana matematike koja ima primjenu u brojnim područjima. Zato je važno kod učenika razvijati geometrijsko mišljenje. Nastavnik u tome ima veliku ulogu jer je kreator nastavnih sati koji će, nizom učeničkih aktivnosti, tome i doprinijeti. Nakon uvoda, u prvom poglavlju ovog diplomskog rada je opisana van Hiele teorija geometrijskog mišljenja, najprije teorijski pristup, a zatim primjerene učeničke aktivnosti vezane za pojedinu van Hiele razinu geometrijskog mišljenja. U drugom su poglavlju opisane brojne aktivnosti koje se izvode korištenjem geoploče, u čemu se vidi efikasnost primjene didaktičkih pomagala i konkretnih materijala u učeničkom radu i napretku. Napredovanjem kroz razine geometrijskog mišljenja, učenici postaju sposobni razumjeti, a zatim i sami napisati konkretan matematički dokaz neke tvrdnje. U tome je od velike pomoći alat dinamične geometrije, stoga je treće poglavlje posvećeno upravo ulogama dokaza te učeničkim aktivnostima koje se provode koristeći neki od alata dinamične geometrije. Nerijetko učenici imaju problema pri usvajanju geometrijskih sadržaja, a pogotovo pisanju dokaza. Posljednje, četvrto poglavlje se bavi opisom projekta čiji je cilj bio utvrditi razinu geometrijskog znanja te razinu geometrijskog mišljenja na kojoj se pojedini učenik nalazi. Osim toga, jedan testni instrument ispitivao je sposobnost učenika u razumijevanju i samostalnom izvođenju dokaza.

Abstract (english)

Geometry is a branch of mathematics applicable to many areas. This explains the importance of developing geometric thought of scholars. The teacher plays a big role as he or she will contribute to this aspect of development by creating lessons and a series of activities intended for pupils. After introduction, the first chapter of this thesis describes Van Hiele model of geometric thought. First the theoretical approach and afterwards the congruent student activities related to specific levels of van Hiele geometrical thought. Second chapter defines numerous activities performed by using geoboards, which shows the efficiency of implementing didactic apparatus and specific materials in student's work and progress. By advancing the thought levels of geometric thought, pupils become more able to understand and thence produce a specific mathematical argument of a certain theorem. The tool of dynamic geometry can be of a great assistance, therefore the third chapter is dedicated to proving the argument and conducting student activities using some of the tools of dynamic geometry. Not infrequently scholars confront problems using some of the tools of dynamic geometry, especially proving theorems. The last, fourth chapter deals with describing the project whose goal was to determine the level of geometrical knowledge and the level of geometrical thought in which certain pupil is situated. Besides, one of the test instruments has reviewed the student's ability of understanding and independent proving of arguments.

• Keywords: nastava matematike; osnovna škola; geometrijsko mišljenje; van Hiele teorija geometrijskog mišljenja; geoploča; alati dinamične geometrije
• Keywords (english): teaching mathematics; elementary school; primary school; geometric thought; van Hiele geometrical thought; geoboard; tools of dynamic geometry
• Language: croatian
• URN:NBN: urn:nbn:hr:217:716643
• 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: Closed access
• Created on: 2019-02-19 10:43:37