Abstract
This book is intended for university students who are training to become mathematics teachers in lower and upper secondary schools, or for practising mathematics teachers. It is devoted to one of the critical areas of primary school mathematics (Rendl, Vondrová et al., 2013) - the issue of measure in geometry.
Our aim is for the reader to gradually build up not only an understanding of what measure in geometry is, but also what difficulties pupils have in this area, how teachers deal with them and how they approach teaching measure in geometry. An important part of the book, in which we summarize the results of research (especially international), is the chapter devoted to conceptual processes that enable pupils to grasp the concepts of surface area and volume.
Understanding these conceptual processes will help the future teacher understand how pupils think about geometry and how s/he could tailor his or her teaching methods in a way that enables the pupils to gain an insight into these problematic concepts. It is this insight into the whole process that we believe will also be useful for teaching practitioners.
As we have noted, our goal is for the reader to gradually make his or her own idea of the issue in its entirety, which is why the book is not written in an interpretative way. The reader is led through specific tasks to deeply reflect on the situation based on his or her experience from the time s/he learned mathematics or from the time when s/he began to teach (or tutor) others.
The tasks relate to curriculum, pupil difficulties and teaching practice. For this purpose, we also make extensive use of the various "stories" of mathematics lessons, either in the form of video recordings of the mathematics lessons and their summaries (if a video is not publicly available) or through written reflections from the mathematics lessons we have collected.
The theoretical grasp of the issue is presented later. In this way, we hope that the reader will have enough experience and information to be aware of the complexity of the issue and thus be able to relate the theoretical knowledge to their own experience.