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The article contributes to the ongoing discussion on ways to deal with the diversity of theories in mathematics education research. It introduces and systematizes a collection of case studies using different strategies and methods for networking theoretical approaches which all frame (qualitative) empirical research. The term 'networking strategies' is used to conceptualize those connecting strategies, which aim at reducing the number of unconnected theoretical approaches while respecting their specificity. The article starts with some clarifications on the character and role of theories in general, before proposing first steps towards a conceptual framework for networking strategies. Their application by different methods as well as their contribution to the development of theories in mathematics education are discussed with respect to the case studies in the ZDM-issue.

In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching-learning. To analyze them, we introduce a suitable model, the semiotic bundle. It allows focusing on the relationships of gestures with the other semiotic resources within a multimodal approach. It also enables framing the mediating action of the teacher in the classroom: in this respect, we introduce the notion of semiotic game where gestures are one of the major ingredients.

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We present a model to analyze the students' activities of argumentation and proof in the graphical context of Elementary Calculus. The theoretical background is provided by the integration of Toulmin's structural description of arguments, Peirce's notions of sign, diagrammatic reasoning and abduction, and Habermas' model for rational behavior. Based on empirical qualitative analysis we identify three different kinds of semiotic actions featuring the organization of the argumentations, and related to different epistemological status of the arguments. In such semiotic actions, the students' argumentation and proof activities are managed and guided according to two intertwined modalities of control, which we call semiotic and theoretic control. The former refers to decisions concerning the selection and implementation of semiotic resources; the latter refers to decisions concerning the selection and implementation of a more or less explicit theory or parts of it. The structure of the model allows us to pinpoint a dialectical dynamics between the two.

In Plato's famous dialogue Phaedo, Simmias is asked to determine who, amongst all sorts of men, is able to attain true knowledge. Is it not he, Socrates asks, who pursues the truth by applying his pure and unadulterated thought to the pure and unadulterated object, cutting himself off as much as possible from his eyes and ears and virtually all the rest of his body, as an impediment which by its presence prevents the soul from attaining to truth and clear thinking? (Plato, 1961, 65e-66a, p. 48) He then continues: "we are in fact convinced that if we are ever to have pure knowledge of anything, we must get rid of the body and contemplate things by themselves with the soul by itself" (Plato, 1961, 66b-67b, p. 49). In tune with Plato's ideas, Descartes maintained that the objects of the external world are known "by the intellect alone," for things "are not perceived because they are seen and touched, but only because they are rightly comprehended by the mind" (Descartes, 1651, II.16).The belief in a dualism that separates the mind from the body has had a strong influence on both mathematics and mathematics education for some time. The purpose of this Special Issue is not only to bring the body fully into our attempts to understand mathematical thinking but also to explore the range of specific ways that embodiment is enacted in mathematical situations. We will examine the construction of mathematical meaning from the perspective of multimodality, that is, taking into account the range of cognitive, physical, and perceptual resources that people utilize when working with mathematical ideas. These resources or modalities include both oral and written symbolic communication Educ Stud Math (2009) 70:91-95

We use eye-tracking as a method to examine how different mathematical representations of the same mathematical object are attended to by students. The results show that there is a meaningful difference in the eye movements between formulas and graphs. This difference can be understood in terms of the cultural and social shaping of human perception, as well as in terms of differences between the symbolic and the graphical registers, as they have been examined in literature. The results are also discussed in terms of didactic implications to support teachers in helping students to both deal with and to integrate multiple mathematical representations as well as acknowledge their own specificity.

We present a new measure for evaluating focused versus overview eye movement behavior in a stimulus divided by areas of interest. The measure can be used for overall data, as well as data over time. Using data from an ongoing project with mathematical problem solving, we describe how to calculate the measure and how to carry out a statistical evaluation of the results.