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

Abstract

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

Didactic Situations and Didactical Engineering in university mathematics: cases from the study of Calculus and proof

“…Cazes et al, 2006). Other recent uses of TDS to analyse the use of technology, in this case studying the synergy between TDS and the Theory of Semiotic Mediation, have been shown in Maracci, Cazes, Vandebrouck & Mariotti (2013).…”

Networking theoretical frames: the ReMath enterprise

“…Building up from these answers a general answer to the CRQ was finally attempted (Artigue, 2009c). Certainly, the coordination of the answers and the coordination of the different teaching experiment contributions was not completely satisfactory, nevertheless possible paths emerging constituted an important direction for further investigations that in some cases led to interesting results (Maracci, Cazes, Vandebrouck, & Mariotti, 2009;2013).…”

“…The ReMath crossexperimentation of the Casyopée DDA by the UNISI and DIDIREM teams offered new possibilities for deepening the potential of theoretical connections between the TDS and the TSM, by making these an explicit object of study. Moreover the work was pursued beyond the official end of the ReMath project (Maracci & al., 2009(Maracci & al., , 2013. In this paragraph, we synthesize its main results.…”

“…The cross-analysis made it possible to contrast these institutionalization phases with the collective phases in the UNISI experimentation. A first analysis of these phases by DIDIREM researchers also identified Topaze effects in that case, but a second analysis jointly performed by the DIDIREM and UNISI researchers, using the tools provided by the TSM and especially the notion of semiotic chain, convinced researchers that such an interpretation was not appropriate for the Italian collective phases (Maracci & al., 2013). It is interesting to notice that, in the first analysis, episodes in the transcripts had been determined by looking at changes in the questions at stake or in the distribution of responsibilities between teacher and students (that is to say in accordance with a transcript analysis informed by TDS).…”

“…Conversely, they also showed that the vision of semiotic mediation and the associated constructs, carried by the TSM, if appropriately integrated in the design could increase the design strength of the TDS, and limit the risks linked to paradoxes of the didactic contract such as the Topaze effect in actual realizations, providing powerful tools for ameliorating the design and the management of the collective phase of Institutionalization and stressing the importance of installing an appropriate didactic contract in the classroom for the success of the didactical engineering hinged upon the process of semiotic mediation. All this makes the concept of didactical contract an interesting object for evidencing complementarities between the two theories (Maracci & al., 2013).…”