Abstract
The book describes results of research carried out in 2012-2014 within the project GAČR Critical areas of primary school mathematics. One of the goals of the project was to collect and analyse pupils' strategies for solving problems from so called critical areas of primary school mathematics.
These are the areas in which pupils often and repeatedly fail, in other words, which they do not master on such a level that their mathematical literacy develops productively and can be used creatively in everyday life. When determining which topics can be considered critical, we based our considerations on (1) results of secondary analyses of results of TIMSS 2007, (2) teachers' experience as expressed in clinical interviews which had been carried out in the previous stage of our research and (3) results of an on-line questionnaire for teachers which aimed at validating some observations from the interviews on a bigger sample.
The book consists of seven chapters. The introductory chapter is devoted mainly to the methods of data gathering and their elaboration and describes a way in which the results are presented in chapters.
The chapters are devoted to individual critical areas given above and have a similar structure. First, the theoretical background of the interviews and their analysis is presented.
Next, the selected research, both local and international, which is related to our research is summarised. We mainly selected research (both from mathematics education and psychology) which aims at pupils and their thinking processes when solving mathematical problems which are similar to ours in their structure, context, etc.
In the discussion section of the chapters, we revisit some of this research as a background for the presentation of our own research results. The chapters also touch on possible causes of the problematic nature of critical areas for pupils and sometimes also on possible didactic implications.
The final chapter strives to present a more general view of some phenomena identified in several critical areas in our research, for which it was possible to find a common denominator. Namely, we deal with the identified problems of pupils when grasping the text of word problems and when formulating mathematical models.
We highlight that some difficulties which we identified in pupils in geometry, arithmetic and algebra can also be interpreted on a more general level as difficulties of the transfer from concrete representations to the abstract ones. Additionally, we focus on difficulties the pupils had with short records of word problem assignments or drawings and diagrams across the investigated topics.
Finally, we suggest possible continuation of our research which is by no means complete.