Matematička statistika u nastavi matematike

master's thesis

• Title (english): Mathematical statistics in mathematics teaching
• Author: Anja Stanković
• Mentor: Matija Bašić (mentor)
• Committee member: Matija Bašić (predsjednik povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U diplomskom radu "Matematička statistika u nastavi matematike" cilj je bio dati pregled Statistike prema "novom" kurikulumu u osnovnim i srednjim školama. Fokus rada bio je na davanju ideja za dublje razumijevanje koncepata i povezivanje sa svakodnevnim životom. Prvenstveno je bit uvidjeti primjenu znanja statistike u aktualnim zanimanjima, ali i osvijestiti zašto je znanje statistike bitno za budućnost. U prvom dijelu rada čitatelj može pročitati koji se statistički koncepti uče u obrazovnim sistemima drugih zemljama te su detaljno analizirani ishodi kurikuluma iz statistike po razredima. U drugom dijelu rada tema je deskriptivna statistika. Mjere srednjih vrijednosti i mjere raspršenosti obrađene su tako da su uz definicije prezentirane aktivnosti kroz koje će učenici primjenjivati koncepte te uvidjeti primjenu znanja u ekonomiji, trgovanju dionicama i trgovanju nekretninama. Posebno se obrađuje histogram. U trećem dijelu rada postupno je prezentirano kako na metodički način učenicima definirati pojam slučajne varijable. U radu su detaljno obrađene diskretne i kontinuirane slučajne varijable te su dani prijedlozi aktivnosti za primjenu koncepata. Dani su primjeri u kojima je prikazano kako se računaju očekivanje, varijanca i standardna devijacija za neprekidnu i kontinuiranu slučajnu varijablu. Posebno je obrađena najpoznatija razdioba podataka - normalna razdioba: od povijesnog pregleda preko uvođenja normalne razdiobe u nastavi, formalne definicije i svojstava sve do primjene. Rad završava Centralnim graničnim teoremom, jednim od najvažnijih teorema iz statistike, kojim se tvrdi da razdioba slučajne varijable s n mjerenja teži normalnoj razdiobi ako \( n \) teži u beskonačnost. Nadamo se da se čitanjem ovog diplomskog rada čitatelji mogu upoznati s osnovnim statističkim pojmovima potrebnim za dublju analizu podataka te dobiti motivaciju za daljnje istraživanje i proučavanje statistike u svakodnevnom životu.

Abstract (english)

In graduate thesis "Matematiˇcka statistika u nastavi matematike" the goal was to give an overview of statistics by the new curriculum in elementary and high schools. Focus was on giving ideas for deeper understanding of concepts and linkage with everyday life. Primarily the goal is to see application of statistics knowledge in different professions, but also to become aware why statistics knowledge is important for the future. In first part of the thesis the reader can see which statistical concepts are studied in educational systems in other countries where outcomes of curriculum by each class is analyzed in detail. In the second part of the thesis descriptive statistics can be found. Measures of mean values and measures of dispersion are done in a way that activities are presented along the definitions, where students can apply concepts and see application in economy, stock trading and real estate. Special focus is on histogram. In the third part of the thesis students are gradually presented how to methodically define random variables. In thesis discrete and continuous random variables are discussed in most detail, as well as suggestions of activities are given to apply concepts. Examples are given how to calculate expectation, variance and standard deviation for nonstop and continuous random variable. Special focus is on the most famous data distribution - normal distribution: from historical overview to the introduction of normal distribution in class teaching, formal definitions and properties to the application. Thesis ends with The Central Limit Theorem, one of the most important theorems of statistics, which claims that distribution of random variables with n measurement tends to normal distribution if \( n \) tends to infinity. We hope that by reading this graduate thesis readers can familiarize with basic statistic terms required for deeper analysis and find motivation for further research and study of statistics in everyday life.

• Keywords: kurikulum iz statistike; deskriptivna statistika; ekonomija; histogram; pojam slučajne varijable; normalna razdioba
• Keywords (english): curriculum; descriptive statistics; economy; histogram; random variable; normal distribution
• Language: croatian
• URN:NBN: urn:nbn:hr:217:289816
• 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: 2021-11-08 10:27:31