Kritická místa matematiky na základní škole očima učitelů

Abstract

This book Critical places of primary mathematics through the eyes of teachers presents the results of research that was conducted under a GACR project in the years 2011 to 2013. The aim of the research was to collect and analyze teachers‘ experience with regards to so called critical places in primary and lower secondary school mathematics. These places are understood as areas that pupils often and repeatedly fail to master, in other words, they do not master them at a level necessary for the productive development and creative real-life application of their mathematical literacy. We have based our investigation on the premise that experienced teachers have already developed means for helping children in these difficult areas, ways to facilitate pupils‘ understanding of the mathematics at hand. Therefore, our secondary aim was to collect such practices and to compare them with results of mathematics education research.
In selecting the appropriate research method we chose to implement in-depth interviews with teachers. In-depth interviews are not uncommon in Czech educational research, however, a prior review of literature showed that no research of the kind and extent with Czech mathematics teachers had been reported.
There were a total of 60 participants in our study. All teachers were certified and showed sufficient confidence in their teaching of mathematics, offering their own professional expertise to researchers. We have a good reason to presume that they were teachers-experts. It is important in our study that participants come from a variety of schools in various districts of the Czech Republic. They are also of various age groups and the number of years they have been in service also varies. Further, they have different background in their teaching preparation and development and do not in general subscribe to one particular approach to teaching mathematics. Interviews reveal that the pupil population across the sample varies sufficiently in terms of socioeconomic background.
Quotations from interviews are used throughout the book and form an essential part of individual chapters. The quotations are chosen to illustrate and document important findings and propositions, and to demonstrate how our conclusions are grounded in data.
The book consists of eight chapters. The introductory chapter describes methods of data collection and analysis. It also informs the reader how data and results are presented in the text. The succeeding two chapters present the core mathematics-didactic view of the issue — the chapters identify critical places in mathematics of primary and lower secondary school, respectively, and present ways in which teachers strive to remediate the situation. The practices are compared with findings from international research in mathematics
education. The preliminary stage of interview analysis brought out the fact that when speaking about difficult areas of mathematics, teachers are likely to expand on a much wider variety of contextual issues than those concerning pure field didactical perspectives. Later chapters in the book focus on this context, this range of non-didactical aspects. Authors analyze how they are reflected in teachers‘ discourse, what views teachers hold about them and how these views compare in the context of relevant research literature.
The themes of each of the chapters are as follows: learning processes (Chapter 4), motivation to learn (Chapter 5), teachers‘ typologies of pupils and the differences between primary and secondary school teachers (Chapter 6), teachers‘ conception of success in mathematics and the sources of this success as well as the role division of family and school in relationship to pupils‘ success (Chapter 7). The final chapter titled Historical aspects of teaching and learning algebra is unique in the way that it does not directly work
with teachers‘ proposition. Its contribution lies in relating the results from Chapters 2 and 3 to the development of mathematics as a domain.
Even though each chapter can be read alone, the book as a whole presents a more complete picture of how experienced practising teachers reason about different aspects of their teaching practice and how this reasoning is (or is not) in view with current research results.
The book is intended for the use of mathematics didacticians, mathematics and primary school teacher educators, and of post-graduate students, as well as both in- and pre-service teachers of mathematics.