Synergies between theoretical approaches to mathematics education with technology: A case study through a cross-analysis methodology

Mathematics education as a research domain is characterized by a plurality of theoretical approaches. Acknowledging the existence of such diversity and the risks of an excessive theoretical fragmentation does not mean to search for a unifying theory but to urge the community to develop strategies for coping with this diversity. This article is meant to show the potential of a “cross-analysis” methodology for establishing connections between different theoretical approaches to mathematics education with technology. Within the frame of the ReMath European Project, two Teaching Experiments were realized, centred on the use of a same ICT tool—Casyopée. Two distinct theoretical approaches shaped both the Teaching Experiments design and their enactments: the Theory of Didactical Situations and the Theory of Semiotic Mediation. The two Teaching Experiments have then been analysed from both theoretical points of view. In this article we will provide some examples drawn from this cross-analysis that show the synergy which can be established between the aforementioned theoretical approaches. Beyond contributing to a deeper understanding of the observed “didactical phenomena”, that synergy allows establishing connections between the two approaches that lead to their reciprocal enrichment.