Kombinatorika u nastavi matematike

master's thesis

• Title (english): Combinatorics in mathematics teaching
• Author: Ana Martinović
• Mentor: Vedran Krčadinac (mentor)
• Committee member: Vedran Krčadinac (predsjednik povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-11-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U diplomskom radu je izložen povijesni pregled razvoja kombinatorike u granu matematike. Povijesna i kulturna vrijednost matematike jedan je od odgojno-obrazovnih ciljeva navedenih u kurikulumu. Navedeni su ishodi učenja koji se ostvaruju usvajanjem nastavnih sadržaja iz područja kombinatorike. Principi prebrojavanja prvi su nastavni sadržaj koji je analiziran. Opisani su princip umnoška, princip zbroja, princip razlike i princip kvocijenta te su za svaki od navedenih principa dani primjeri zadataka iz udžbenika srednjih škola. Definirani su pojmovi permutacije, varijacije i kombinacije s ponavljanjima i bez uz primjere zadataka koji zorno predočuju pojmove. Osim zadataka iz udžbenika navedeni su i primjeri zadataka s nacionalnih matematičkih natjecanja. Na kraju su dani primjeri nastavnih aktivnosti. Prva nastavna aktivnost vizualnim materijalima je prilagođena osnovnoškolskom uzrastu te je cilj aktivnosti opisati princip produkta. Zadatak sa županijske razine nacionalnog matematičkog natjecanja odabran je za nastavnu aktivnost u srednjoj školi. Cilj nastavne aktivnosti je prepoznati različite metode rješavanja zadatka i riješiti ga na četiri različita načina.

Abstract (english)

This thesis presents a comprehensive overview of the historical evolution of combinatorics into a separate branch of mathematics. Within the educational framework, the appreciation for the historical and cultural dimensions of mathematics stands as a prominent goal. Listed within are also the learning outcomes derived from the integration of combinatorial principles into teaching methodologies. The initial focus centers on the foundational topic of counting principles, with subsequent analyses delving into the principles of multiplication, sum, difference, and quotient. Each principle is explicated through illustrative problems sourced from high school textbooks, enhancing clarity and comprehension. Extending beyond the basics, the thesis defines the concepts of permutations, variations, and combinations, considering both repetitions and non-repetitions. Accompanying these definitions are practical examples showcasing the application of these concepts. Additionally, a compilation of problems from national mathematics competitions enriches the illustrative repertoire. Towards the conclusion, the thesis provides examples of teaching activities. The first activity, tailored for elementary school students and employing visual aids, aims to describe the multiplication principle. For high school students, a challenging problem from the county level of the national mathematics competition is incorporated into one of the teaching activities, fostering the recognition and application of diverse problem-solving methodologies through four distinct approaches

• Keywords: kombinatorika; princip umnoška; princip zbroja; princip razlike; princip kvocijenta
• Keywords (english): combinatorics; principles of multiplication; sum; difference; quotient
• Language: croatian
• URN:NBN: urn:nbn:hr:217:492959
• 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: 2024-02-12 13:22:09