Algebra u nastavi matematike

master's thesis

• Title (english): Algebra in teaching of mathematics
• Author: Ana Blazinarić
• Mentor: Matija Bašić (mentor)
• Committee member: Matija Bašić (predsjednik povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-11-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Algebra i funkcije jedna je od pet matematičkih domena koje se spominju u hrvatskom kurikulumu. Neophodno je da učenici izgrade temelje dovoljno rano u obrazovanju kako bi im kasnije bilo lakše razumjeti algebru. Što je to algebra i algebarsko mišljenje? Koji nam sve alati pomažu u razvoju algebarskog mišljenja kod učenika? Kako prijeći s induktivnog načina razmišljanja za konkretne primjere do apstraktnog? Ovo su samo neka od pitanja na koja ćemo se osvrnuti u ovom radu. Proučit ćemo elemente algebarskog mišljenja, te ih razjasniti i potkrijepiti primjerima. Čitateljima ćemo približiti sličnosti i razlike hrvatskog i finskog matematičkog kurikuluma s naglaskom na algebru. Također, spomenuti ćemo i primjenu tehnologije i CAS sustava u nastavi matematike te njihovu ulogu kod rješavanja različitih problema. U nastavku ćemo istaknuti razne nejednakosti i sredine te njihovu primjenu kroz zadatke s natjecanja, a spomenuti ćemo i Cauchy-Schwarz-Bunjakovski nejednakost. Za kraj, promotrit ćemo optimizaciju kvadratnom funkcijom i općenite primjere zadataka vezane uz minimizaciju ili maksimizaciju funkcije.

Abstract (english)

Algebra and functions are one of the five mathematical domains important for a student’s education mentioned in the Croatian curriculum. It is of utmost importance for students to build a foundation early enough in their education to understand algebra better in the later parts of education. What is algebra and algebraic thinking? Which tools can help teachers encourage algebraic thinking among students? How do students switch from inductive reasoning to abstract thinking? Those are some questions that we will discuss in this paper. We will analyze elements of algebraic thinking, explain them and support them with examples. We will talk about similarities and differences between Croatian and Finnish mathematical curriculum, mostly focusing on algebra. We will also briefly mention the use of technology and CAS systems in teaching of mathematics and their application on solving different problems. Continuing on, our focus will be on different types of inequalities and means and their use in competitions. There will be a brief mention of Cauchy-Schwartz- Bunjakovski inequality. In the end, we will take a look at optimization using quadratic function and general examples of minimization or maximization of a function.

• Keywords: hrvatski kurikulum; algebarsko mišljenje; finski matematički kurikulum; CAS sustav; Cauchy-Schwarz-Bunjakovski nejednakost; optimizacija kvadratnom funkcijom
• Keywords (english): Croatian curriculum; algebraic thinking; Finnish mathematics curriculum; CAS systems; Cauchy-Schwartz- Bunjakovski inequality; optimization using quadratic function
• Language: croatian
• URN:NBN: urn:nbn:hr:217:031480
• 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: 2023-01-02 12:11:14