Learning Translation in Geometric Transformations Through Digital and Manipulative Artefacts in Synergy Antonella Montone 1 , Michele Giuliano Fiorentino 2(&) , and Maria Alessandra Mariotti 2 1 Department of Mathematics, University of Bari Aldo Moro, Bari, Italy Antonella.montone@uniba.it 2 Department of Information Engineering and Mathematics Science, University of Siena, Siena, Italy michele.fiorentino@uniba.it, mariotti21@unisi.it Abstract. In this paper we report a study that aims to highlight the potential- ities of the combined use of both digital and manipulative artefacts to construct and conceptualize mathematical meanings related to the notion of translation. The research hypothesis of our study is that, the alternating use of a digital and a manipulative artefact foster synergically the construction of mathematical meanings. Both the design and the analysis of data is framed by the Theory of Semiotic Mediation in a Vygotskijan perspective. The study involved a class of 20 students, aged 13–14, of a secondary school in the Apulia Region, Italy. Data collection of the study is based on student interaction transcriptions during experimental task execution, written answers to given questions, and finally the transcripts and video analysis of the collective discussions concluding each experimental cycle. Keywords: Semiotic mediation Á Digital artefact Á Translation Á Interaction Á Synergy 1 Introduction and Rationale Technology is almost everywhere in our lives and there is no process, even educational, that does not deal with it. Moreover, technological resources have been combined with already existing instrumental resources and used in didactic practices supporting the construction of mathematical meanings. In recent years, a considerable corpus of research has focused on the ways in which technologies can influence mathematics learning, in particular how technology could offer new ways to interact with mathe- matical thinking and generate new kinds of mathematical experiences for students [1– 3]. However, the digital technologies do not eliminate the need of a synergic rela- tionship between all the educational artefacts, each of them bringing different possi- bilities and supporting the process of incorporation and conceptualization in a different way [4–8]. Moreover, one of the mathematical topics that need to be supported by artefact is the geometric transformation. In Italy, as in other countries, geometric transformations © Springer Nature Switzerland AG 2019 P. Zaphiris and A. Ioannou (Eds.): HCII 2019, LNCS 11590, pp. 191–205, 2019. https://doi.org/10.1007/978-3-030-21814-0_15