Cijeli brojevi i algebra u nastavi matematike

master's thesis

• Title (english): Integers and algebra in teaching mathematics
• Author: Karla Ban
• Mentor: Matija Bašić (mentor)
• Committee member: Matija Bašić (predsjednik povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Franka Miriam Brückler (član povjerenstva)
• Committee member: Nina Kamčev (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad opisuje ključne aspekte poučavanja cijelih brojeva i algebarskih izraza u nastavi matematike s naglaskom na prevladavanje uobičajenih poteškoća i miskoncepcija koje učenici susreću pri učenju ovih temeljnih koncepata. Algebarsko mišljenje, koje se uvodi postupno, često zahtijeva od učenika da savladaju apstraktne koncepte poput negativnih brojeva i nepoznanica, što može dovesti do različitih miskoncepcija i poteškoća u razumijevanju. Rad obuhvaća metode i didaktičke pristupe za uvođenje cijelih brojeva, poput modela toplih i hladnih žetona te upotrebu algebarskih pločica za vizualizaciju algebarskih izraza. Također se opisuje kako uravnotežen pristup konceptualnom i proceduralnom znanju može doprinijeti učinkovitijem učenju matematike te pruža pregled aktivnosti kojima se ove miskoncepcije mogu adresirati.

Abstract (english)

In this thesis, key aspects of teaching integers and algebraic expressions in mathematics education are described, with a focus on overcoming common difficulties and misconceptions that students encounter when learning these fundamental concepts. Algebraic thinking, which is introduced gradually, often requires students to master abstract concepts such as negative numbers and variables, which can lead to various misconceptions and difficulties in understanding. The thesis covers methods and didactic approaches for introducing integers, such as the use of the neutralisation model, as well as the use of algebra tiles for visualizing algebraic expressions. It also describes how a balanced approach to conceptual and procedural knowledge can contribute to more effective learning of mathematics and provides an overview of activities that can address these misconceptions.

• Keywords: nastava matematike; cijeli brojevi; algebarski izrazi; algebarsko mišljenje
• Keywords (english): teaching mathematics; integers; algebraic expressions; algebraic thinking
• Language: croatian
• URN:NBN: urn:nbn:hr:217:711807
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2025-02-05 13:01:59