Sequences in elementary and high school mathematics

U ovom radu analizirano je uvođenje i realizacija matematičkog pojma niza u osnovnoškolskoj i srednjoškolskoj matematici. Prvi dio rada nudi pregled ishoda učenja iz Predmetnog kurikuluma za matematičko područje vezanih za uzorke i nizove kroz osnovnu i srednju školu. Drugi dio je orijentiran na tipične zadatke kojima se obrađuje pojam niza i razvija kroz učenikovo obrazovanje te se nastavlja s opisom progresivne formalizacije Hansa Freudenthala na primjeru razvoja pojma niza. Na kraju rada analiziraju se kurikulumi Irske i Australije te se uspoređuju s hrvatskim kurikulumom.This thesis analyzes the introduction and realization of the mathematical concept of a sequence in primary and secondary mathematics. The first part of the thesis offers an overview of the learning outcomes from the Mathematics Curriculum related to patterns and sequences through primary and secondary school. The second part focuses on typical tasks that deal with the concept of a sequence and how the concept develops through the student’s education. It continues with a description of Hans Freudenthal’s progressive formalization on the example of the development of the concept of a sequence. At the end of the thesis, the curricula of Ireland and Australia are analyzed and compared with the Croatian curriculum