Introduction: the transformative nature of “dynamic” educational technology

The presence and intelligent use of digital technologies in mathematics education has awakened an interest in understanding new ways of conceiving mathematics and mathematical cognition. Cognition, especially mathematical cognition, can be understood in terms of the emergence of successive and evolving representational systems (Kaput, 1991). As a consequence, the presence of digital technologies in education calls us to address this fundamental issue that curricular structures eventually will be inhabited by these technologies. It has already happened in the past: the technology of writing and the technology of positional notation of numbers are two of the milestones in the history of semiotic representations with a living impact on education. However, we cannot forget that a school culture always leaves significant marks on students’ and teachers’ values. Artigue (2005, p. 246) states that ‘‘these [previous] values were established, through history, in environments poor in technology, and they have only slowly come to terms with the evolution of mathematical practice linked to technological evolution.’’ Thus, the school culture requires the gradual re-orientation of its practices to gain access to new habits of mind and to the new environments resulting from a serious presence of digital technologies. Consequently, this issue will offer a new perspective with examples from our research to approach the new problematique made tangible by digital technologies. We particularly focus on the role of ‘‘dynamic mathematics’’ as an umbrella description of a certain technology (both software and integrated hardware) that opens up a new exploration space for learners. We present data and analyses of students working with dynamic geometry environments and software that links multiple representations of function in interactive ways across networks. We refer to these more globally as Dynamic Technological Environments or simply DTE(s). Within such environments, students are capable of exhibiting new forms of expressivity associated with their explorations and new forms of understanding based upon the capacity of the environment to react to the actions proposed by the students. This special issue aims to analyze the impact of dynamic mathematics technologies on learning, didactics and curriculum development from multiple perspectives. Particularly, it will examine the differences between the phenomenological aspects of dynamism in the use of technology more generally—contrasting the use of technology as a temporary, engaging activity (the ‘‘field trip’’ syndrome) with more fundamental theoretical and epistemological dimensions of sustained uses of certain technologies. These focus on increasing accessibility of conceptually difficult mathematics through the transformation of mathematical ideas and experiences. A specific contribution of all articles in this special issue is the presentation of the paucity of research in the field from an interdisciplinary perspective, especially with respect to particular mathematical topics, and suggestions for programs of research that might attend to these issues. When we thought about a title for this issue, the word transforming became our main focus of attention. Given the challenges of education globally, we prefer to think about ‘‘transforming’’ the very socio-cultural system within S. J. Hegedus (&) L. Moreno-Armella James J. Kaput Center for Research and Innovation in Mathematics Education, University of Massachusetts Dartmouth, Dartmouth, MA, USA e-mail: shegedus@umassd.edu