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Ikonične reprezentacije so reprezentacije, ki predstavljajo prehod med enaktivnimi in simbolnimi reprezentacijami. Ikonične reprezentacije matematičnih pojmov na razredni stopnji so v veliki večini primerov grafične. V magistrski nalogi smo s pomočjo preizkusa znanja želeli ugotoviti, na kakšen način učenci od 5. do 8. razreda osnovne šole grafično ponazarjajo vnaprej podane matematične pojme (odštevanje s prehodom, številski izraz z oklepaji, izraz dela celote in potenca). Zanimalo nas je tudi, ali učenci ob reprezentiranju dobijo pravilen rezultat ter ali lokacija šole učenca vpliva na podano rešitev. V raziskavo je bilo vključenih 1595 osnovnošolcev. Metodološko smo se odločili za v podatkih utemeljeno teorijo. Podatki so bili obdelani s kombinacijo kvalitativnih in kvantitativnih metod pedagoškega raziskovanja. Rezultati kažejo, da učenci podane pojme grafično ponazarjajo na 3 različne načine kot ilustracijo, rezultat ali koncept. Pri vseh podanih matematičnih pojmih je koncept tisti, preko katerega učenci najpogosteje reprezentirajo matematične pojme. Glede same pravilnosti rezultata ugotavljamo, da je le-ta najvišja pri reprezentiranju odštevanja s prehodom, najnižja pa pri izrazu dela celote. Rezultati kažejo tudi, da učenci mestnih šol v večini izmerjenih postavk ustrezneje ponazarjajo podane matematične pojme. Če pogledamo celostno, ugotovimo, da učenci v splošnem najustrezneje reprezentirajo računsko operacijo odštevanja s prehodom, najbolj problematičen z vidika pravilnosti rezultata reprezentiranja je izraz dela celote, z vidika načina reprezentiranja pa je najmanj ustrezno reprezentiran številski izraz z oklepaji. Iconic representations are representations that present the transition between enactive and symbolic representations. Iconic representations of elementary level mathematical concepts are in most cases graphical. In this Master’s Thesis we wanted to determine in what way pupils from 5th to 8th grade of primary school graphically depict mathematical concepts that were given in advance (subtraction with regrouping, numerical expression with brackets, expression for parts of a whole and exponent). In our interest it was also whether the pupils while representing get the correct result, and whether the pupils school location has influence on their solution. The survey involved 1,595 primary school pupils. Methodologically we have decided on a theory grounded in data. The data were analyzed with a combination of qualitative and quantitative methods of pedagogical research. The results show that the given concepts were graphically depicted by the students in 3 different ways as an illustration, result or concept. In all given mathematical concepts, pupils most frequently represent mathematical concepts by means of a concept. Regarding the correctness of the result we found that it is highest in representing subtraction with regrouping and lowest in expression for parts of a whole. Results also have shown that pupils in urban schools in most measured items depict given mathematical concepts more appropriately. Looking at it as a whole, we found that pupils are most accurate in representing the mathematical operation subtraction with regrouping. Most problematic in terms of correctness of the representation result is the expression for parts of a whole, while the least adequately represented in relation to the manner of representation is the numeric expression with brackets. |
