Vjerojatnost i statistika u nastavi matematike

master's thesis

• Title (english): Probability and statistics in teaching mathematics
• Author: Ana Barać
• Mentor: Matija Bašić (mentor)
• Committee member: Matija Bašić (predsjednik povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Marko Radulović (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 diplomski rad istražuje temeljne aspekte vjerojatnosti i statistike kroz analizu osnovnih pojmova, teorijskih koncepata i njihovih primjena u obrazovanju. U prvom poglavlju razmatramo definicije vjerojatnosti, uključujući skupove elementarnih događaja te osnovna svojstva vjerojatnosnog prostora. Posebna pažnja posvećena je razumijevanju i formaliziranju vjerojatnosti kao matematičkog koncepta, što stvara čvrst temelj za daljnju analizu. Drugo poglavlje fokusira se na slučajne varijable,... More razlikujući diskretne i neprekidne slučajne varijable te naglašavajući njihove karakteristike, distribucije i primjene. Također, razmatra se povezivanje ovih varijabli na primjeru bacanja kockice, čime se ilustriraju njihove zajedničke i specifične aspekte. Centralni granični teorem, kao ključni koncept u statistici, omogućuje razumijevanje ponašanja sumiranih slučajnih varijabli i aproksimaciju normalnih distribucija. Na kraju, istražuje se primjena vjerojatnosti i statistike u hrvatskom obrazovnom kurikulumu te predlažemo aktivnosti za unapređenje nastave matematike. Ovaj rad pruža sveobuhvatan pregled ključnih koncepata vjerojatnosti i statistike, s naglaskom na njihovu primjenu u obrazovanju, čime doprinosi boljem razumijevanju i primjeni statističkih metoda u različitim kontekstima. Less

Abstract (english)

This thesis explores the fundamental aspects of probability and statistics through the analysis of basic concepts, theoretical principles, and their applications in education. The first chapter examines definitions of probability, including the sets of elementary events and the basic properties of probability spaces. Special attention is given to understanding and formalizing probability as a mathematical concept, providing a solid foundation for further analysis. The second chapter focuses... More on random variables, distinguishing between discrete and continuous random variables while emphasizing their characteristics, distributions, and applications. Additionally, it explores the connection between these variables using the example of rolling a die, illustrating their common and specific aspects. The Central Limit Theorem, as a key concept in statistics, facilitates the understanding of the behavior of summed random variables and the approximation of normal distributions. Finally, the application of probability and statistics in the Croatian educational curriculum is examined, and activities are proposed to enhance mathematics teaching. This thesis offers a comprehensive overview of key probability and statistics concepts, with an emphasis on their application in education, contributing to a better understanding and application of statistical methods in various contexts. Less

• Keywords: nastava matematike; vjerojatnost; slučajne varijable; centralni granični teorem
• Keywords (english): teaching mathematics; probability; random variables; Central limit theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:553784
• 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 13:20:50