Abstract:

The article presents a qualitative analysis of special fraction test developed by Cypriot researches Marilena Pantziara and George Philippou. The test consists of 21 tasks in seven groups focus on part-whole and measure subconstructs of fractions together with the notions of equivalence, comparison and addition of fractions and in three columns which represents each level of Sfards´ theory of reification. We have translated, modified and adapted this test to the Slovak conditions. We focused on examination of statements of Kieren (1981), Smith (2002), Behr et al. (1983) that at first students need to master the notions of order and equivalence of fractions to fully understand to measure personality of fraction. And then they also need to master measure personality of fraction to master additive operations on fractions on each level of Sfards´ theory of reification. The part–whole subconstruct is considered fundamental for developing understanding of the other four subconstructs. For analysing of these statements we used the SIA (Statistical Implicative Analysis) method. Based on results of the SIA analysis we can conclude that the statements were confirmed for interiorization stage and partially for the other two stages. Our research sample consist of 113 first year Bachelor students of Teacher Training for Preschool and Elementary Education within the subject Relations and Operations with Numbers and 49 first year Master students of Teacher Training for Primary Education within the subject Didactics of Mathematics at Constantine the Philosopher University in Nitra. The data was collected in February and March 2016.

Keywords:

fractions, reification, measure, par-whole