Abstract:

Fractions are among the most complex mathematical concepts that children encounter in their years in primary education. One of the resources of misunderstanding to fractions may be the fact that the fractions can be interpreted in different ways – as a ratio, an operator, a quotient, a measure and a part-whole subconstruct. In our research we have analyzed students’ solutions of the tasks in special fraction test developed by Cypriot researches Marilena Pantziara and George Philippou which is connected to Sfards´ theory of reification. Our research sample consist of 113 first year Bachelor students of Teacher Training for Preschool and Elementary Education (PEE students) and 49 first year Master students of Teacher Training for Primary Education (PE students) at Constantine the Philosopher University in Nitra. We have expected that the all of students had fractions in the same extent in their primary schools. But these students were taking part at different high schools so the time allowance of mathematics and the curriculum of mathematics could be different. We have identified the main misconceptions of subconstructs of fractions and analyzed the reason. The fraction as a part of whole and the fraction as a measure were in the center of our attention. In Kieren’s theoretical model of he fraction concept the part–whole subconstruct is considered fundamental for developing understanding of the other four subconstructs. In this model, the measurement subconstruct is considered necessary for developing proficiency in additive operations on fractions (Charalambous & Pitta-Pantazi, 2007). Our findings are presented in the paper.

Keywords:

Fractions, misconceptions, higher education.