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The aim of the paper is to show whether the systems of mathematics teacher education in two countries whose historical development may seem quite similar (the Czech Republic and Hungary were parts of the Habsburg Monarchy, and they were part of the Eastern European communist block) are also very similar, or whether each country follows its own, unique path. In this paper we build on the general need for more international comparative studies in the area of teacher education. We present a historical review of development of mathematics teacher education in both countries and analyse and compare current teacher education programs, their structure and organization, the demands on mathematics teachers and their qualifications for teaching at various levels. In the paper we pinpoint a number of aspects resulting in differences in the two systems, including historical development and traditions, (de)-centralization, globalization and international cooperation, etc. The comparison based on these aspects shows that the systems in both countries are very different. The analysis described in this paper could become the starting point for further research using the data from international surveys (e.g. PISA). Such research would enable us to make conjectures about the effects of various ways of organizing teacher education.

Teachers’ understanding of formative assessment is quite essential for its implementation in everyday classroom practices [Heritage, M. (2007). Formative assessment: What do teachers need to know a...

The book introduces the issue of productive culture of teaching and learning in broader didactical context. In the first part of the book, three areas of productive culture of teaching and learning are as theoretical framework presented: 1. clarity, structure, coherence, 2. cognitive activation, instrumentalization, semantization, 3. Supportive learning environment. The second part of the book presents 17 didactic case studies that have been developed by teams that consisted of researchers and teachers from schools. The aim of didactic case studies is to highlight key areas of productive culture of teaching and learning.

Education has always played an important role in the history of the region of the current Czech Republic. Five phases of development after 1989 can be differentiated: (a) deconstruction (1990–1991)—characterized by opposition against the current state; (b) partial stabilization (1991–2000)—decision-making based on what needed to be addressed and analysis of the state of education; (c) system reconstruction (2001–2004)—the beginning of the National Program for the Development of Education (2001) and subsequent Educational Framework Programs; (d) implementation (2005–2015)—elaboration of school education programs, and (e) the current period. This chapter describes the characteristics of these phases, legislative documents, and the development of approaches to the concept of mathematics education, mathematics teacher education, textbooks, and forms of assessment. This chapter concludes with a reflection on the problems with mathematical education in the Czech Republic and the outlook for the future.

Inquiry-based education means that the teacher in the classroom creates the conditions for pupils to inquire independently a part of knowledge which they are supposed to learn. This study is based on an analysis of several lessons of inquiry based mathematics education in primary classrooms, and its aim is to identify phenomena which characterize this culture of education and cause difficulties in its implementation. Problems used in our experiments had the character of (a) reviving the preconceptions of mathematical concepts that students know from everyday life, (b) using the already learned knowledge in new contexts. As an incentive for pupils’ inquiry was also used simulated incorrect solution. The process of inquiry in the classroom hinted at problems (a) with the formulation of learning objectives relevant to the valid curriculum, (b) with the management of pupils’ experiments designed to accomplish these objectives, (c) with respecting the individual differences of pupils. Implementation differed mainly according the level of autonomy the teacher allowed students, the teacher’s ability to cope with ambiguity and uncertainty, which appeared in a dialogue with the pupils, and a deeper insight into the structure of mathematics.

International audience; This chapter reports the results of three research studies on peer assessment carried out in different countries where it is an unusual practice (France, Switzerland, and the Czech Republic). The three research studies focus on different competences and different disciplines (sciences and mathematics), but they all involve inquiry-based approaches at primary and secondary school level. In the French study, the data reported in this chapter explore relationships between success in task processing and the ability to mark a peer’s written artefact on the same task. The Swiss research study examines the type of peer feedback students offer their peers while assessing their models, based on a fine-grained analysis of peer feedback comments. In the Czech Republic, the study focuses on students’ reflection on peer assessment in inquiry lessons. The three studies conclude the necessity of allowing the sharing of “knowledge authority” in the classroom to evolve and to be integrated into usual classroom practice. However, researchers have a divergent view on the sharing of responsibility for validation of knowledge between the student and the teacher. Moreover, we can conclude that peer assessment can be a way to trigger metacognitive work on knowledge and competences in science and on assessment criteria and teacher expectations, at a class level and individual student level.

The chapter presents findings related to Czech teachers’ and pupils’ difficulties with, opinions on, and needs associated with formative assessment, namely, peer assessment, in inquiry-based lessons. The research was conducted within the EU-funded Assess Inquiry in Science, Technology, and Mathematics Education project (ASSIST-ME). Six teachers of primary mathematics worked with researchers on inquiry tasks and methods of peer assessment and implemented them in their classrooms. The paper focuses mainly on (a) the interplay of teachers’ intentions, subject matter, and learners in inquiry; (b) the teachers’ role in supporting learning via (formative) assessment; and (c) the pupils’ role in their own learning and the learning of peers. Significant phenomena in implementation of assessment were identified, namely, the importance of formulation of learning objectives; pupils’ ability to decide about the correctness, identify the mistakes, and give supporting feedback to their peers; possible (and needed) support; and institutionalization of knowledge.

This chapter examines three different classroom teacher perspectives when using ASSIST-ME project formative assessment methods as described in the introductory chapter. The first ‘teacher perspective’ is about changes in teacher self-efficacies while using formative assessment methods as monitored by a pre- and post-teacher questionnaire. Teachers who tried the unfamiliar formative methods of assessment (see introductory book chapter for these methods) as well as their colleagues who did not were surveyed. The second ‘teacher perspective’ examines changes in teachers’ subjective theories while trying project-specific formative assessment methods in Czech Republic. Analyses are done through case studies and interviews. The final part of the chapter looks at teacher perspectives while using an Internet-based application to facilitate formative assessment. The teacher use of the application and their feedback about its utility are discussed.

Problem posing (not only in lesson planning but also directly in teaching whenever needed) is one of the attributes of a teacher’s subject didactic competence. In this paper, problem posing in teacher education is understood as an educational and a diagnostic tool. The results of the study were gained in pre-service primary school teacher education. Students were asked to pose problems containing some given data (namely fractions). The subsequent analysis of the problems posed by the students revealed shortcomings in their conceptual understanding of fractions. Classroom-based joint reflection became the means of reeducation.

The chapter reports results of a survey whose aim was to contribute to research in the area of problem posing in teacher training. The core of the research project was empirical survey with qualitative design. Preservice and in-service teachers were posing problems in the environment of fractions and reflected on this activity in writing. Analysis of the posed problems and participants’ reflections were to answer the following questions: (a) What shortcomings can be identified in the posed problems? (b) How are the posed problems perceived by preservice and in-service teachers? (c) What relations are there between quality of the posed problems and perception of this activity by their authors?

All changes of the character of education and improvement of its quality depend, in our view, particularly on the teacher. To be able to do their work efficiently, teachers have to be equipped with professional skills and dispositions, with “teachers’ competence”. For their professional growth, we consider indispensable competence in reflection, which is aimed at the teacher’s activities with regard to aspects of pedagogy and/or subject-didactics. From the point of view of the goals and content of their teaching and the methods of work (and their realisation), the development of teachers’ conscious self-reflection on their own teaching and systematic pursuance of joint reflection with other teachers and/or researchers can promote the teacher’s professional growth. In this paper, we show how a selected group of elementary school teachers reflected on their competence in the course of preparing, carrying out and analysing several instruction experiments. The paper is based on samples of teachers’ reflections and their gradual development from mere simple conversations based on intuitive perceptions, through searching for effective teaching approaches, to the deep assessment of mathematics teaching from the point of view of topics and their didactic elaboration and to suggestions for the teachers’ own experiments.

Van Ameron (2002, p. 3) stated that “Algebra is known to be a major stumbling block in school mathematics, both in the past and present. Historical studies on the developments of algebra education in the twentieth century show that the algebra studied in secondary school has not changed much over the years”. Sutherland (2000) presented a comparative study of algebra curricula in twelve countries all over the world.

Giving students the space to actively participate in the introduction of new knowledge through their own independent discovery is one of the demands of pedagogical theory and curricular documents. For example, Czech official pedagogical documents demand that pupils develop their problem solving competence by “making use of the acquired knowledge to discover/identify various ways of a problem solution” (Framework Education Programme for Basic Education, 2007, p. 12).

Článek seznamuje čtenáře s International Group for the Psychology of Mathematics Education (PME). Jsou charakterizovány cíle PME, historie jejího vzniku a její současné aktivity.