Cross-analysis as a tool to forge connections amongst theoretical frames in using digital technologies in mathematical learning Chronis Kynigos & Jean-Baptiste Lagrange Published online: 12 November 2013 # Springer Science+Business Media Dordrecht 2013 Abstract This is the introductory paper of this special issue which contains a description of and reactions to a sample of cross–case analyses of empirical studies carried out by a group of six European research teams. The cross–case analysis, along with cross-experimentation was a key element of the teams' strategy for integrating theoretical frameworks with a view to also acquiring better focus on context and on the role and uses of the diverse representations afforded by the digital media developed within the project. Keywords Cross-experimentation . Cross–case analysis . Digital technologies . Representations . Context . Networking of theoretical frames In recent years, researchers in mathematics education have been increasingly concerned with realizations that the growth of our knowledge in the field seems to be slowing down due to the fragmented way in which a wealth of theoretical frameworks and constructs seem to be developing. The dual challenge of maintaining the richness of the many emergent theories while developing strategies and methods to forge connections and integrations amongst them is gaining attention and has become the object of study in recent works emerging for example from the CERME and PME conferences and related special issues (Prediger et al., 2008; Lester, 2007). One of the exciting features of these efforts is that they have generated a more succinct focus on the status, nature, growth mechanisms, and functions of theories in math- ematics education (Cobb, 2007). Within this context, this special issue is based upon a sample of the works of six European research teams. This group of research teams got together in the frame of a large-scale European Network of Excellence titled “Kaleidoscope” (http://www.noe-kaleidoscope.org/ telearc/) created in 2004 to “explore the future of learning with digital technologies.” A prime preoccupation within Kaleidoscope was the strategic and scientific integration of Educ Stud Math (2014) 85:321–327 DOI 10.1007/s10649-013-9521-3 C. Kynigos (*) Educational Technology Lab, N.K. University of Athens, Athens, Greece e-mail: kynigos@ppp.uoa.gr J.<B. Lagrange University Paris 7 DIDEROT, Paris, France J.<B. Lagrange University of Reims, Reims, France e-mail: jean-baptiste.lagrange@univ-reims.fr