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To characterize the actual political and social situation in mathematics education around the world, in particular in most of the rich countries, one could state that the commercial textbook 'business' community controls the materials available to teachers to an extent that teachers are rather slaves of the textbook than autonomous and enlightened users; and that assessment still is primarily and predominantly a mechanism for selecting the mathematical elite only instead to provide a profound mathematics education to all. The few promising developments in mathematics education could be seen in the increasing availability of personal technology, in the growth of the vocational education sector, in the growth of the informal sector through web- access, and – my big hope – in the increasing professionalization of mathematics teacher associations in many countries and the growth of equal and fair collaborative research within the mathematics education community.

Hans Freudenthal—in his capacity as a mathematician as well as a veryarticulate and thoughtful mathematics educator, as an international 'politician' ofmathematics education, as the founder ofEducational Studies in Mathematics,asa prolific writer, as an organiser of meetings and conferences—exerted quite aninfluence on Danish mathematics education from the late 1960s onwards. The Dutchmathematics education tradition thus founded always received close attention fromthe Danish mathematics education community. In this chapter, I outline and discussthe nature of this influence and I attempt to provide an explanation of why thistradition has resonated so well with implicit and explicit movements in Denmark.

International audience ; It can be said that mathematics education in Japan was started in 1872 when the school system was established. Since that establishment era, controversies have emerged time and again in mathematics education in Japan. Through these controversies, debates have been held on views on mathematics education such as how mathematics ought to be taught and what constitutes knowledge concerning numbers, quantities, and shapes that is desirable for students to acquire. In this paper, I shall look back at how views on mathematics education in Japan have developed since the Meiji era from the perspective of such controversies on mathematics education. As the controversies on mathematics education, the four phases are picked up. The first is Theoretical Mathematics and the Enumeration Principle. The second is Controversy over Formal Building. The third is Conventional Teaching of Mathematics and the Creation of Mathematics. The forth is Relationship between Daily Life and Mathematics. With regard to the conflict between theoretical arithmetic and the enumeration principle, debates were held over which policy to adopt in the process of editing the first government–designated textbook which was published in 1905. The conflict was ultimately settled when it was decided that the enumeration principle would be adopted. Attention must be paid to the fact that this conflict was taking place in an era when it was questioned what constitutes mathematics education in introducing the modern education system in Japan. In the controversy over formal building in 1920's , both the opponents and proponents based their arguments on overseas theories and survey results. The controversy was not settled in the form of one view being adopted while the other view was discarded in the education policy and the editorial policy concerning government-designated textbooks. Regarding formal building, assertions regarding the objectives of mathematics education and what is desirable for children to acquire are at the basis of ...

By a politics of meaning I refer to the social, economic, cultural and religious conditions for experiencing meaning. I refer as well to the layers of visons, assumptions, presumptions and preconceptions that might construct something as being meaningful. By addressing different politics of meaning in mathematics education, I want to show how meaning becomes formatted. In order to do this, I provide a foreground-interpretation of meaning. The basic idea is to relate meanings and foregrounds, acknowledging that foregrounds are formed bya range of factors, as well as by the person's experiences of such factors. Politics of meaning can be analysed with reference to sexism, racism, instrumentalism, the school mathematics tradition, critical mathematics education, and the banality of expertise. ; By a politics of meaning I refer to the social, economic, cultural and religious conditions for experiencing meaning. I refer as well to the layers of visons, assumptions, presumptions and preconceptions that might construct something as being meaningful. By addressing different politics of meaning in mathematics education, I want to show how meaning becomes formatted. In order to do this, I provide a foreground-interpretation of meaning. The basic idea is to relate meanings and foregrounds, acknowledging that foregrounds are formed bya range of factors, as well as by the person's experiences of such factors. Politics of meaning can be analysed with reference to sexism, racism, instrumentalism, the school mathematics tradition, critical mathematics education, and the banality of expertise.

International audience ; We describe ongoing work on the Culturally Responsive Elementary Mathematics Education (CREME) project, in which we work with teachers and students in two schools with contrasting student populations and communities. We present core principles of our emergent theoretical framework as we partner with the teachers and students to realize (in both senses of 'understand' and 'make happen') what culturally responsive elementary mathematics education might be. The backdrop for this activity is the educational/political arena within the United State, in particular in Oregon where we work, and in the schools themselves. We outline future development of CREME, and end with what we see as the implications of our experience with CREME for the ethical and political responsibilities of educational researchers.

An Invitation to Critical Mathematics Education deals with a range of crucial topics. Among these are students' foreground, landscapes of investigation, and mathematics in action. The book is intended for a broad audience: educators, students, teachers, policy makers, anybody interested in the further development of mathematics education. The book discusses concerns and preoccupation. This way it provides an invitation into critical mathematics education.

A radical form of postmodernity is presented with reference to Nietzsche's ideas with respect to truth, knowledge, sciences, progress, democracy, and ethical values in general. Thereafter is presented Foucault's archaeology of knowledge. This brings us forward to the notion of genealogy, which is a defining idea for the postmodern conception of critique. However, it is emphasised that a critique can address the generativity of mathematical rationality by considering mathematics-based fabrications. Finally, imagination is presented as yet another feature of a critical enterprise. It is illustrated how such a three dimensional critical enterprise is relevant for both mathematics and mathematics education. In this way the paper suggests moving beyond the postmodern outlook.

A well-informed and knowledgeable community is of vital importance for the economic and social development of a modem society. The knowledge and skills required for present day activities are much more complex than those required in the past. Today, many jobs require expert thinking and non-routine analytical skills, to identify and solve problems. Mathematics education focuses on developing a person's analytical and problem solving abilities. Thus a high quality mathematics education win ensure that students develop the skills that are essential not only in science and technology, but also in everyday life and the workplace. The government of Sri Lanka, recognizing the need for a high quality mathematics education has implemented several reforms in the recent past. Although the progress achieved is commendable, there is still room for improvement in certain important aspects of the learning teaching process. The main aim of the mathematics curriculum under these reforms is to create individuals who are able to think mathematically and apply mathematical knowledge effectively and responsibly in problem solving and decision making.

Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theory of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in the philosophy of mathematics and in mathematics education research in general, it is argued that it is necessary to give a relativist account mathematical reasoning. Hacking's framework of styles of reasoning is introduced as a possible solution. This framework distinguished between at least six different styles of reasoning, many of which are closely connected to mathematics, and argues that these frameworks define what we accept as decidable assertions, as justifications for such assertions, and as possible objects of such assertions. The articles end with a discussion of the implications of the framework for chosen fields of mathematics education research, which may motivate more focussed studies in the future.

The referential theory of meaning as well as the use-oriented theory of meaning have huge impacts on the discussion of meaning in mathematics education. Here, I present a third theory in terms of an intentionality interpretation of meaning, which provides an alternative departure for the discussion of meaning in mathematics education. The importance of intentionality for understanding human phenomena was emphasised by both Brentano and Husserl. They associated intentionality with a pure stream of consciousness, which constitutes an a priori to any human experience. I agree that the notion of intentionality is important; however, I find it crucial to provide a paradigmatic uprooting of this notion and to consider it as being structured by economic, political, cultural, and discursive factors. Such real-life intentionalities constitute the basis for an intentionality interpretation of meaning. I explore this interpretation with respect to mathematics education by addressing imaginations, possibilities, obstructions, hopes, fears, stereotypes and preconceptions. I relate meaning in mathematics education to far away horizons of students' life worlds, to negotiations, to political issues, to diversity and to instrumentalism.