Title Učeničko razumijevanje vektora u različitim kontekstima
Title (english) Student understanding of vectors in different contexts
Author Filip Tušek
Mentor Ana Sušac (mentor)
Committee member Ana Sušac (predsjednik povjerenstva)
Committee member Maja Planinić (član povjerenstva)
Committee member Željka Milin Šipuš (član povjerenstva)
Committee member Emil Tafra (član povjerenstva)
Committee member Rudi Mrazović (član povjerenstva)
Granter University of Zagreb Faculty of Science (Department of Mathematics) Zagreb
Defense date and country 2020-09-30, Croatia
Scientific / art field, discipline and subdiscipline NATURAL SCIENCES Mathematics
Scientific / art field, discipline and subdiscipline NATURAL SCIENCES Physics
Abstract Brojna istraživanja su pokazala da učenici i studenti imaju poteškoća u prijenosu konceptualnih i proceduralnih matematičkih znanja u kontekst fizike. Vektori su važna tema u nastavi matematike, a nužni su za razumijevanje mnogih fizikalnih koncepata. U ovom diplomskom radu napravljeno je istraživanje razumijevanja vektora kod učenika četvrtih razreda općih i prirodoslovno-matematičkih gimnazija. Mjereni pokreti očiju učenika dok su rješavali test koji se sastojao od 12 izomorfnih zadataka iz matematike i fizike u kojima se ispitivao isti vektorski koncept. Zadaci su ispitivali sljedeće vektorske koncepte: smjer i duljinu vektora, komponente vektora, zbrajanje, oduzimanje, množenje skalarom i skalarni umnožak vektora. Rezultati su pokazali da su učenici slično riješili zadatke iz matematike i fizike te su često birali isti odgovor u paralelnim zadacima. Moglo bi se reći da su učenici uspješno primijenili znanja o vektorima u oba konteksta, vjerojatno zbog toga što su u zadacima iz fizike jasno bili naznačeni vektorski koncepti koji su se ispitivali. Mjerenje pokreta očiju omogućilo je dodatni uvid u pažnju učenika dok su rješavali zadatke koji su ispitivali razumijevanje vektora. Pokazalo se da su učenici dulje rješavali zadatke iz fizike jer je tekst bio dulji, a i neki grafički prikazi kompleksniji. Analiza pojedinačnih zadataka pokazala je da su učenici najviše poteškoća imali s računanjem skalarnog umnoška vektora u ortonormiranoj bazi, razumijevanjem geometrijske interpretacije skalarnog umnoška i oduzimanjem vektora u 1D i 2D. Razmatrane su implikacije dobivenih rezultata za nastavu matematike i fizike.
Abstract (english) Numerous studies have shown that pupils and students have difficulties transferring conceptual and procedural mathematical knowledge into the context of physics. Vectors are an important topic in mathematics instruction and are necessary for understanding many physical concepts. In this diploma thesis, understanding of vectors in fourth-grade students of general and science high schools was investigated. Students’ eye movements were measured while they solved a test consisting of 12 isomorphic mathematics and physics items in which the same vector concept was examined. The items examined the following vector concepts: direction and length of vectors, vector components, addition, subtraction, scalar multiplication, and scalar product of vectors. The results showed that students solved mathematics and physics items similarly and often chose the same answer in parallel items. It could be said that the students successfully applied the knowledge of vectors in both contexts, probably because in the physics items the vector concepts to be examined were clearly indicated. Measurement of eye movements provided additional insight into students’ attention as they solved items that examined vector understanding. It turned out that students took longer to solve physics items because the text was longer, and some graphical representations were more complex. The analysis of individual items showed that students had the most difficulties with calculating the scalar product of vectors in the orthonormal base, understanding the geometric interpretation of the scalar product, and subtracting vectors in one and two dimensions. The implications of the obtained results for the teaching of mathematics and physics are discussed.
Keywords
nastava matematike
izomorfni zadataci iz matematike i fizike
skalarni umnožaka vektora u ortonormiranoj bazi
Keywords (english)
teaching mathematics
isomorphic problems in mathematics and physics
scalar product of vectors in orthonormal base
Language croatian
URN:NBN urn:nbn:hr:217:270081
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
Terms of use
Created on 2021-03-08 10:36:06