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This paper reflects on the use of didactic material in mathematics classes. It focuses on the mathematical activities of students and the didactical activities of teachers. Its point of departure is a critique of technical-managerial approaches to teaching, learning, and innovation. Based on this critique, fundamental tensions between the development of new didactic material and the cognitive style and daily routines of practising teachers are identified. In the last part of the paper, the concept of mathematical literacy is introduced in order to set the crucial relationship between didactic material for mathematics instruction and the ways in which it is used in the classroom on new and fertile grounds. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a theoretical model to analyze prospective teachers' reasoning and knowledge of real numbers, and to provide an empirical verification of it. The model is based on Sierpinska's theory of theoretical thinking. Data were collected from 59 prospective teachers through a written test and interviews. The data indicated that mathematical tasks on real numbers, based on Sierpinska's theory, could be categorized according to whether they require reflective, systemic or analytic thinking. Analysis of the data identified three different groups of prospective teachers reflecting different types of theoretical thinking about real numbers. The interviews confirmed the empirical data from the written test, and provided a better insight into the thinking and characteristic features of the prospective teachers in each group. The analysis also indicated that the participants were more successful in tasks requiring systemic and analytic thinking, and only when this was achieved were they able to solve problems which required reflective thinking. Implications for teaching related to the findings of the study are discussed. [ABSTRACT FROM AUTHOR]

This paper introduces the current situation of the popular Chinese university education, points out the impact of popularized Chinese higher education on its university mathematics education, and presents the actualities and existing problems of university mathematics education research in China. [ABSTRACT FROM AUTHOR]

This article deals with what it means to possess competence in mathematics. It takes its point of departure in the fact that the notions of mathematical competence and mathematical competencies have gained a foothold as well as momentum in mathematics education research, development and practice throughout the last two decades. The Danish so-called KOM Project (KOM: Competencies and the Learning of Mathematics), the report from which was published in 2002, has played an instrumental role in that development. Since then, a host of new developments has taken place, and we—as the authors of the original report—have felt the need to take stock of this development and revisit the conceptualisation of the basic notions in order to provide an updated version of the original conceptual framework and terminology. Whilst the fundamentals of this framework have been preserved in this article, the version presented here in addition to an up-to-date terminology offers greater clarity and sharpness and richer explanations than found in the original. [ABSTRACT FROM AUTHOR]