This paper reports on a study of the process of professional development for mathematics teachers. The analysis connects two theoretical frameworks: the Meta-Didactical Transposition model developed by Arzarello et al. (2014), which describes the macro level, and, at the micro level, the idea of emergence, which has been around since at least the time of Aristotle and has been defined by Mill (1843), Lewes (1875), Blitz (1992), Huxley and Huxley (1947) and many others. The meta-didactical transposition model considers the evolution of teachers' practices as part of a community process, while the notion of emergence helps us to gain better insights into the details of the practices of individual teachers. This paper focuses on secondary school teachers' learning of new digital technologies to illuminate this theoretical framework.