Problematika ekvipotentnosti skupova u školskoj matematici

master's thesis

• Author: Marija Marijić
• Mentor: Dora Pokaz (mentor)
• Committee member: Dora Pokaz (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu proučavamo problematiku ekvipotentnosti skupova u srednjoškolskoj matematici. Prvo prikazujemo koliko se o skupovima uči kroz osnovnu i srednju školu te dajemo prikaz kako se ekvipotentnost skupova uvodi u udžbeniku za četvrti razred prirodoslovno-matematičke gimnazije. Nakon toga slijedi pregled osnovnih pojmova, relacija i metoda teorije skupova te prebrojivost racionalnih brojeva dokazujemo pomoću dijagonalnog postupka, Calkin-Wilfova stabla i Stern-Brocotova stabla. Konačno, dajemo i nekoliko primjera ekvipotentnih skupova.

Abstract (english)

In this paper we study the issue of equipotent sets in high school mathematics. Firstly, we show what are students learning about sets in primary school and high school and how equipotent sets are introduced in the last grade of mathematical gymnasium. Further, we give the basic terms, properties and methods of set theory. We give proof that rational numbers are countable using diagonal argument, Calkin-Wilf tree and Stern-Brocot tree. Lastly, we give several examples of equipotent sets.

• Keywords: ekvipotentnost skupova; nastava matematike; srednja škola; Calkin-Wilfova stabla; Stern-Brocotova stabla
• Keywords (english): equipotent sets; teaching mathematics; high school; middle school; Calkin-Wilf tree; Stern-Brocot tree
• Language: croatian
• URN:NBN: urn:nbn:hr:217:032086
• 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: 2019-06-06 11:01:51