Razvoj algebarskog mišljenja u osnovnoj i srednjoj školi: algebarski izrazi i identiteti

master's thesis

• Title (english): Development of algebraic thinking in primary and secondary school: algebraic expressions and identities
• Author: Matija Kujundžić
• Mentor: Aleksandra Čižmešija (mentor)
• Committee member: Aleksandra Čižmešija (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Matko Ljulj (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog rada jest detaljno opisati proces razvoja algebarskog mišljenja kod učenika te opisati učinkovite metode i aktivnosti koje doprinose tom razvoju u nastavi matematike. U uvodnom dijelu rada analizira se sam koncept algebarskog mišljenja kroz njegove različite aspekte, s naglaskom na osnovne elemente nužne za pravilno usvajanje algebarskih izraza. Poseban naglasak stavlja se na aktivnosti usmjerene na razvoj ključnih koncepata poput jednakosti i varijable. Rad sadrži i aktivnosti usmjerene na uvođenje algebarskih izraza, pri čemu se koristi model novca i površine. Opisane su aktivnosti koje uključuju upotrebu algebarskih pločica u nastavi kao alata za vizualizaciju i aktivno sudjelovanje učenika u procesu otkrivanja osnova računanja s algebarskim izrazima. Algebarske pločice koriste se kako bi učenici stekli vizualno iskustvo i bolje usvojili osnove računanja s algebarskim izrazima. Aktivnosti namijenjene za otkrivanje osnovnih algebarskih identiteta služe kako bi se učenike potaklo na otkrivanje osnovnih algebarskih identiteta pomoću modela površine i volumena, što omogućuje razvoj njihove sposobnosti povezivanja geometrijskih i algebarskih koncepata. Opisanim aktivnostima rad pridonosi razumijevanju razvoja algebarskog mišljenja kod učenika te opisuje pristupe koji potiču dublje razumijevanje i usvajanje ključnih algebarskih koncepata.

Abstract (english)

The aim of this paper is to comprehensively describe the process of developing algebraic thinking in students and to outline effective methods and activities that contribute to this development in mathematics education. In the introductory part, the concept of algebraic thinking is analyzed through its various aspects, with a focus on fundamental elements necessary for the proper acquisition of algebraic expressions. Special emphasis is placed on activities directed towards the development of key concepts such as equality and variables. The paper includes activities aimed at introducing algebraic expressions, utilizing models such as money and surface area. There is a description of activities that involve the use of algebraic tiles as tools for visualization and active student participation in the process of discovering the basics of computing with algebraic expressions. Algebraic tiles are employed to provide students with a visual experience and enhance their understanding of the fundamentals of computing with algebraic expressions. Activities designed to explore basic algebraic identities are intended to encourage students to discover fundamental algebraic identities using surface and volume models, facilitating the development of their ability to connect geometric and algebraic concepts. Through the described activities, the paper contributes to understanding the development of algebraic thinking in students and outlines approaches that promote deeper comprehension and adoption of key algebraic concepts.

• Keywords: algebarske pločice; jednakost; varijable; algebarski identiteti
• Language: croatian
• URN:NBN: urn:nbn:hr:217:000568
• 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: 2024-03-13 11:40:00