Diseño y estudio de situaciones didácticas que favorecen el trabajo con registros semióticos

What’s behind the mistakes and difficulties that appear on the students to understand and study mathematics?are only related to the cognitive complexity of the content or such difficulties are also related to the possible ways to access the different mathematical objects? The mathematical activity generated in many students learning difficulties that are not manifested in cognitive processes related to other areas of knowledge. If something characterizes the processes of teaching and learning of mathematics is that, unlike what happens with the objects of study in the experimental sciences, the only way to access to them is through its different semiotic representations. The coordination among the different systems of representation that refer to the same mathematical concept, needs to move from one register to another (D’Amore, 1998, 2001, 2003, 2004, 2006; Duval, 1993, 1994, 1995, 1996, 2000, 2003, 2004, 2005, 2007, 2008, 2011, 2012; Godino, 2002, 2003, 2012, 2014; Kaput, 1989a, 1989b,1992, 1998; Radford, 1998, 2004a, 2004b, 2004c, 2006a, 2008,2009, 2011, 2013, 2014a). Therefore, the treatments that can be realized within a given register and the conversion of one register into another, play an essential role in the grasp of the object and mathematical concepts. Through this work with representations, students give meanings to the objects of study and are able to understand the underlying mathematical structures, which is the main educational interest of this issue...

El aprendizaje en una comunidad en internet de profesores de español como segunda lengua: estudio etnográfico virtual de la comunidad Todoele

In the digital era the availability of resources for online learning has multiplied along with personal learning environments. Proof of this is the proliferation of phenomena in the internet like Open Educational Resources or the Massive Open Online Course (MOOC) and the vast diversity of Online Communities of Practice (OCoP). The former is the object of study in the present Thesis. As Juan Freire (2012: 71) wrote: “The education is already happening, specially outside of educational institutions and formal process of education.” The OCoP garnered attention in the research community during the last few years. And, according to published research, online communities are turning into an emerging phenomena not only for “digital natives” (White, 2011) but also for lifelong learning (Wenger et al, 2002; Dubé et al, 2006; Lai et al, 2006) and specially as a tool for teacher training (Garrido, 2003; Murua, 2015). Teachers develop, through these tools, networks of self support, share didactic material, and look for solutions to common problems while undertaking initiatives towards even more collaboration. The present thesis is a study of Comunidad Todoele (CT) one of the most reputable networks for Spanish as a Foreign Language Teachers (ELE, from it’s Spanish acronym). Currently the community has near 11,000 members and it’s main purpose is researching, describing, and theorising the formative processes that happen inside the network from the perspective of those experiencing it. Debate is centred on the questions: What relevant knowledge do the teachers get from the community? In which way are these processes of learning developed? In other words, How, and what, do teachers learn in these environment?..