New ZDM-articles

Four new articles has been published online in ZDM recently:

• Strategies to foster students’ competencies in constructing multi-steps geometric proofs: teaching experiments in Taiwan and Germany by Aiso Heinze, Ying-Hao Cheng, Stefan Ufer, Fou-Lai Lin and Kristina Reiss. Abstract: In this article, we discuss the complexity of geometric proofs with respect to a theoretical analysis and empirical results from studies in Taiwan and Germany. Based on these findings in both countries, specific teachings experiments with junior high school students were developed, conducted, and evaluated. According to the different classroom and learning culture in East Asia and Western Europe, the interventions differed in their way of organizing the learning activities during regular mathematics lessons. The statistical analysis of the pre–post-test data indicated that both interventions were successful in fostering students’ proof competence.
• Connecting theories in mathematics education: challenges and possibilities by Luis Radford. Abstract: This paper is a commentary on the problem of networking theories. My commentary draws on the papers contained in this ZDM issue and is divided into three parts. In the first part, following semiotician Yuri Lotman, I suggest that a network of theories can be conceived of as a semiosphere, i.e., a space of encounter of various languages and intellectual traditions. I argue that such a networking space revolves around two different and complementary “themes”—integration and differentiation. In the second part, I advocate conceptualizing theories in mathematics education as triplets formed by a system of theoretical principles, a methodology, and templates of research questions, and attempt to show that this tripartite view of theories provides us with a morphology of theories for investigating differences and potential connections. In the third part of the article, I discuss some examples of networking theories. The investigation of limits of connectivity leads me to talk about the boundary of a theory, which I suggest defining as the “limit” of what a theory can legitimately predicate about its objects of discourse; beyond such an edge, the theory conflicts with its own principles. I conclude with some implications of networking theories for the advancement of mathematics education.
• A networking method to compare theories: metacognition in problem solving reformulated within the Anthropological Theory of the Didactic by Esther Rodríguez, Marianna Bosch and Josep Gascón. Abstract: An important role of theory in research is to provide new ways of conceptualizing practical questions, essentially by transforming them into scientific problems that can be more easily delimited, typified and approached. In mathematics education, theoretical developments around ‘metacognition’ initially appeared in the research domain of Problem Solving closely related to the practical question of how to learn (and teach) to solve non-routine problems. This paper presents a networking method to approach a notion as ‘metacognition’ within a different theoretical perspective, as the one provided by the Anthropological Theory of the Didactic. Instead of trying to directly ‘translate’ this notion from one perspective to another, the strategy used consists in going back to the practical question that is at the origin of ‘metacognition’ and show how the new perspective relates this initial question to a very different kind of phenomena. The analysis is supported by an empirical study focused on a teaching proposal in grade 10 concerning the problem of comparing mobile phone tariffs.
• Comparing, combining, coordinating-networking strategies for connecting theoretical approaches by Susanne Prediger, Ferdinando Arzarello, Marianna Bosch and Agnès Lenfant. This is the editorial for the next issue, and it does not have an abstract.