Razumijevanje vektora kod učenika i studenata

master's thesis

• Author: Damjan Klemenčić
• Mentor: Ana Sušac (mentor)
• Committee member: Ana Sušac (predsjednik povjerenstva)
• Committee member: Željka Milin-Šipuš (član povjerenstva)
• Committee member: Darko Androić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2017-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom diplomskom radu napravljena su dva istraživanja o razumijevanju vektora kod učenika i studenata u kojem je sudjelovalo 776 ispitanika. Cilj prvog istraživanja bio je ispitati konceptualno i proceduralno razumijevanje vektora kod studenata, a obuhvaćena su područja duljine i smjera vektora, zbrajanja i oduzimanja vektora, skalarnog produkta, vektorskog produkta te rastavljanje vektora na komponente. U drugom istraživanju ispitano je kako učenici i studenti rješavaju paralelne zadatke iz matematike i fizike koji su identični što se tiče ideja vezanih uz vektore, ali stavljeni u različite kontekste. Zadaci iz fizike obuhvaćali su pojmove sile, brzine i rada. Ispitanici su trebali na svakom pitanju izabrati jedan od pet ponuđenih odgovora. Testiranja su pokazala s kojim konceptima i procedurama učenici i studenti imaju najviše poteškoća, ali i koji su najčešći krivi odgovori. Osim toga, uočene su razlike u postotku točnih odgovora s obzirom na kontekst zadatka. Rezultati ovog istraživanja mogu pomoći nastavnicima da bolje razumiju poteškoće učenika i studenata s vektorima te da bolje i učinkovitije planiraju nastavu. Na kraju, ovaj rad sugerira da je potrebna jača integracija matematike i fizike u osnovnoj i srednjoj školi, ali i u visokoškolskom obrazovanju.

Abstract (english)

In this diploma thesis, two research studies on high school and university students’ understanding of vectors were conducted on 776 participants. The goal of the first research study was to investigate conceptual and procedural student understanding of vectors; the included conceptual areas were length and direction of vectors, addition and subtraction of vectors, dot product and cross product, and vector resolution to its components. In the second research study, we explored how high school and university students solve parallel math and physics test items that were identical in the ideas related to vectors but they were set in different contexts. The physics test items were about force, velocity, and work. On each test item, the participants had to choose one from five possible answers. The test results have shown which concepts and procedures are the most challenging for high school and university students and what were the most common mistakes. Besides, the differences in the percentages of correct answers depending on the context of the test item were found. The research results can help teachers to better understand the difficulties of high school and university student with vectors and can also help them to organize better and more effective lessons. Finally, this thesis suggests the need for stronger connections between mathematics and physics in elementary and high schools but also in universities.

• Keywords: razumijevanje vektora; nastava matematike; nastava fizike; srednja škola
• Keywords (english): understanding vectors; teaching mathematics; teaching physics; high school; middle school
• Language: croatian
• URN:NBN: urn:nbn:hr:217:154846
• Study programme: Title: Mathematics and Physics Education; specializations in: Mathematics and Physics Education; Course: Mathematics and Physics Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra edukacije matematike i fizike (magistar/magistra edukacije matematike i fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-01-31 13:31:29