MATHEMATICS TEACHERS REFLECTING ON STUDENT'S NONSTANDARD REASONING ABOUT DIVIDING THE FRACTIONS

摘要

The national curriculum of the Slovak republic in mathematics suggests teaching in an inquiry way, which is the mathematically demanding way of teaching. Therefore, we ask whether Slovak mathematics teachers are ready to teach in this way. Our research question concerns teachers' knowledge of practices in mathematics (KPM) and focuses on fraction division. Data from 46 middle school mathematics teachers were analysed. Different levels of KPM were revealed, from simple inductive reasoning to regular correct proof. Our research revealed that among Slovak teachers, there is a group that uses inductive reasoning in order to verify the general applicability of the non-standard algorithm. Moreover, part of the teachers showed up problems with the conceptual understanding of the fractions division. This result indicated the need to strengthen further teacher education with an emphasis on mathematical knowledge.