Didactical Phenomena of Unusual Geometry Tasks in Teaching of Stereometry

The National Program of Education Mathematics - ISCED 3A specifies the mathematical standards at Slovak secondary schools. In the curriculum of stereometry, the topic of the planar sections of solids is included due to the development of the spatial imagination of students. For this purpose, the students solve the selected types of tasks by using special methods and strategies. Obvious different forms of visualisations are used, though the results are not satisfactory. The cause of this phenomenon seems to be insufficient training of the future teachers of mathematics due to different reasons. It appears the first one is the problematic usage of different didactical software for the transformation of the educational process. The second one is the impact of motivational factors of non-standard tasks and their solutions. In our paper we continue the research which was already carried out. We analyse in detail the conclusions of Slovak and Czech mathematics experts and university teachers whose research field is focused on the development of spatial and geometric imagination. Based on the findings that the subject area is developed mainly through planar sections of solids, we propose a new inspirational type of task on sections of cube building special solids constructed from multiple cubes. We aim to show the possibilities of using geometric software Cabri 3D to attain the problems' solutions, and we also analyse various aspects of the educational process in regard to the implementation of using appropriate geometry software in teaching support. (C) 2015 The Authors. Published by Elsevier Ltd.