There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’ mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity. The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning.

• The role of resources and technology in mathematics education, by Maria G. Bartolini Bussi and Marcelo C. Borba
• Historical comments on the use of technology and devices in ICMEs and ICMI, by Gert Schubring
• Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education, by Paulus Gerdes
• Concrete models and dynamic instruments as early technology tools in classrooms at the dawn of ICMI: from Felix Klein to present applications in mathematics classrooms in different parts of the world, by Maria G. Bartolini Bussi, Daina Taimina and Masami Isoda
• Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories, by Michela Maschietto and Luc Trouche
• Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI, by Mónica E. Villarreal and Marcelo C. Borba
• Charting the microworld territory over time: design and construction in mathematics education, by Lulu Healy and Chronis Kynigos
• Graphic calculators and connectivity software to be a community of mathematics practitioners, by Ornella Robutti
• A social perspective on technology-enhanced mathematical learning: from collaboration to performance, by George Gadanidis and Vince Geiger
• Integrating technology into mathematics teaching at the university level, by Zsolt Lavicza
• Place and use of new technology in the teaching of mathematics: ICMI activities in the past 25 years, by Colette Laborde and Rudolf Sträßer
• Clarkson, P., Presmeg, N. (eds) (2008): Critical Issues in Mathematics Education: Major Contributions of Alan Bishop, Springer, New York, 257 pp., ISBN 978-0-387-09672-8, by Irit Peled
• Acknowledgements to reviewers 2009, by Gabriele Kaiser
• Acknowledgments to the members of the Editorial Board, by Gabriele Kaiser
• Advances in mathematics education: new book series connected to ZDM—The International Journal on Mathematics Education, by Gabriele Kaiser and Bharath Sriraman

This case study deals with a solitary learner’s process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we have shown that the learner’s attempts at justification gave rise to several processes of knowledge construction, which develop in parallel and interact. In this paper, we analyze the interaction pattern of combining constructions and show that combining constructions indicate an enlightenment of the learner. This adds an analytic dimension to the nested epistemic actions model of abstraction in context.

In this article, we address online distance mathematics education research and practice in Brazil, which are relative newcomers to the educational scene. We present the national context of education in Brazil, highlighting the organization of the educational system, and also a summary of national legislation on distance education and an overview of digital inclusion in the country. We outline the potential and relevance of distance education for the Brazilian educational system and show how it could intervene in the system. With respect to research and practice in online mathematics education, we present support for research, examples of studies and highlight different aspects being addressed, including its essential components. In addition, we discuss the synergy between distance education and teacher education, and mathematics distance education and modeling, as well as other initiatives in the national scenario.

In this paper, we investigate the relationship between mathematics education and the notions of education for all/democracy. In order to proceed with our analysis, we present Marx’s concept of commodity and Jean Baudrillard’s concept of sign value as a theoretical reference in the discussion of how knowledge has become a universal need in today’s society and ideology. After, we engage in showing mathematics education’s historical and epistemological grip to this ideology. We claim that mathematics education appears in the time period that English becomes an international language and the notion of international seems to be a key constructor in the constitution of that ideology. Here, we draw from Derrida’s famous saying that “there is nothing beyond the text”. We conclude that a critique to modern society and education has been developed from an idealistic concept of democracy.

Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of “feeling number”, a phrase that we offer in a twofold sense—resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the quantities they represent. First, we distinguish between quantity sense and the relatively vague notion of number sense. Second, we consider the human capacity for quantity sense and place that in the context of related cultural issues, including verbal and symbolic representations of number. Third and more pragmatically, we offer teaching strategies that seem helpful in the development of quantity sense coupled with number sense. Finally, we argue that there is a moral imperative to connect number sense with such a quantity sense that allows students to feel the weight of numbers. It is important that learners develop a feeling for number, which includes a sense of what numbers are and what they can do.

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the “What If Not?” (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs’ portfolios reveals that they believe that engaging in the inquiry-based activity enhanced both their mathematical and meta-mathematical knowledge. As to the mathematical knowledge, they deepened their knowledge regarding the geometrical concepts and shapes involved, and during the process of creating the problem and checking its validity and its solution, they deepened their understanding of the interconnections among the concepts and shapes involved. As to meta-mathematical knowledge, the PTs refer to aspects such as the meaning of the givens and their relations, validity of an argument, the importance and usefulness of the definitions of concepts and objects, and the importance of providing a formal proof.