Razvoj pojma površine u osnovnoj i srednjoj školi

master's thesis

• Title (english): Development of the concept of area in primary and secondary school
• Author: Eva Weitzer
• Mentor: Eva Špalj (mentor)
• Committee member: Eva Špalj (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Vedran Krčadinac (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

Jedan od najvažnijih geometrijskih pojmova koji se obrađuje u osnovnoj i srednjoj školi je pojam površine, jer ima veliki značaj u primjeni u svakodnevnom životu. U ovom radu prvo su dane aksiomatske definicije pojma mjere i površine te dokazi formula za izračunavanje površine pravokutnika, paralelograma i trokuta. Nadalje, opisani su ishodi učenja nacionalnog matematičkog kurikuluma vezanih za koncept površine. Posljednje su izložene razne praktične aktivnosti koje trebaju pridonijeti konceptualnom razumijevanju pojma površine likova s naglaskom na gradivo osnovnoškolskih razreda te integrala koji se obrađuju u četvrtom razredu srednje škole.

Abstract (english)

One of the most important geometrical concepts taught in elementary school is the concept of the area, which is important for its use in everyday life. In the first part of this diploma thesis, the concepts of measure and area are axiomatically defined with proofs of formulas for areas of rectangles, parallelograms, and triangles. Furthermore, the learning outcomes of the national mathematics curriculum related to the concept of surface area are described. Lastly, various practical activities for students to introduce the concept of the surface area and formulas for calculating the surface area of different geometrical figures with emphasis on the teaching content of elementary school and integrals introduced in the fourth year of high school are described.

• Keywords: aksiomatske definicije pojma mjere i površine; površine pravokutnika; površine paralelograma; površine trokuta; nacionalni matematički kurikulum
• Language: croatian
• URN:NBN: urn:nbn:hr:217:088842
• 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: 2024-02-13 09:32:36