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Vizualne reprezentacije omogočajo osmišljanje pomena matematičnih pojmov, odnosov in procesov, zato imajo pomembno vlogo pri pouku matematike. V predstavljeni raziskavi smo pri udeležencih preučevali razumevanje osnovnih matematičnih pojmov s pomočjo risb. Pojem je bil podan v simbolni obliki (npr. 17 - 9), udeleženci pa so ga morali prikazati z risbo. Zanimalo nas je, ali dijaki oz. študenti in bodoči učitelji (N=345) ustrezno (v skladu z matematično definicijo) narišejo podani matematični pojem. Podatke smo obdelali s kombinacijo kvantitativne in kvalitativne metodologije. Rezultati so pokazali, da udeleženci zahtevane pojme z risbo ustrezno prikazujejo, pri čemer je delež ustreznosti risb v povezavi z abstraktnostjo prikazanega pojma. Ugotovili smo tudi, da študenti 4. letnikov, ki se izobražujejo za poučevanje na razredni stopnji, pozitivno izstopajo. Po pregledu vzorca risb smo na osnovi vsebinske analize oblikovali dve temi, ki prikazujeta dva načina matematičnega razumevanja (instrumentalno in relacijsko) oz. dva tipa matematičnega znanja (proceduralni in pojmovni). Izsledki raziskave lahko služijo raziskovalcem pri oblikovanju novih raziskovalnih instrumentov za merjenje matematičnega razumevanja in učiteljem pri izbirah načina vpogleda v učenčevo razumevanje. Visual representations allow us to interpret the meanings of mathematical concepts, relationships and processes, therefore they play an important role in mathematics education. In the present study, we analysed participants' understanding of basic mathematical concepts through drawings. Symbolic representation of mathematical concept was provided (e.g., 17-9) to participants and they were asked to represent the given concept through a picture. We were interested if high school students and future tea chers (N=345) adequately (in accordance with mathematical definition) depicted given mathematical concept. The data were analysed using a combination of qualitative and quantitative analyses. The results show that participants quite adequately depicted basic mathematical concepts. Less abstract concepts were depicted more accurately. It was also noted, that 4th year students, studying to teach at primary level, have performed better than others. In qualitative content analysis two themes emerged. Those themes illustrate two ways of mathematical understanding (instrumental and relational) and two types of mathematical knowledge (procedural and conceptual). The research results can serve researchers in the creation of new research instruments for measuring mathematical understanding and help teachers to find new approaches that will offer them an insight into students' mathematical understanding. |
