DESIGN AND IMPLEMENTATION OF DIGITAL MATHEMATICAL DISCUSSION: FOCUS ON STUDENTS¿ COLLABORATIVE PROCESSES AND THE DEVELOPMENT OF COLLECTIVE ALGEBRAIC THINKING

The integration of digital technologies into education provides significant opportunities to enhance mathematics teaching and learning, particularly by fostering collaboration and communication beyond traditional classroom settings. The research presented in this thesis contributes to the ongoing investigation on the role of digital technologies to support mathematical discussion, which is a didactic methodology designed to actively involve students in constructing mathematical knowledge through interaction with peers and experts. While existing research has already started addressing the support digital technologies can give to the design and unfolding of synchronous mathematical discussions, taking place in classrooms or through conferencing platforms, this thesis focuses on asynchronous mathematical discussions. In fact, asynchrony allows participants to engage with the discussion at their own pace, encouraging thoughtful reflections and giving time to process information. Written communication, in turn, encourages participants to make their reasoning more explicit, making their thinking visible. Research on asynchronous mathematical discussion remains an understudied emerging area, especially in high school contexts. Thus, we aim to contribute to this research gap introducing and investigating the design and implementation of Digital Mathematical Discussion. Digital Mathematical Discussion is a didactic methodology stemming from both mathematical and asynchronous discussions. It comprises three phases: group-work within chats to solve a mathematical problem; whole-class balance discussion within Padlet to compare solutions; and wrap-up classroom discussion. For the scopes of this research, we focus on the first two phases, as we intend to deepen the investigation on asynchronous mathematical discussions. We answer the questions of what kind of students’ collaborative processes are fostered in the digital environments facilitating a Digital Mathematical Discussion and how they intertwine with the development of collective algebraic thinking. To investigate the collaborative processes we refer to the dimension of social modes of co-construction, while for the use of algebra as a thinking tool we focus on conceptual frames and anticipating thoughts. To address the research questions, we adopt a design-based research methodology, including a pilot study with university students familiar with traditional mathematical discussion, and two cycles of experimentations with grade 9 classes. The tasks proposed within the experimentations highlight the use of algebra as a thinking tool and enable students to explore numerical situations, formulate conjectures, and construct proofs through the use of algebraic language. Our findings reveal different outcomes on the intertwining between social modes of co-construction and the development of collective algebraic thinking by students within the different digital environments facilitating Digital Mathematical Discussion. Within the chats, we identify varying collaboration processes, more or less effective in actively considering and building on each other’s proposals and for the development of a shared understanding and collective algebraic thinking. Within Padlet, there is a flattening of the social modes of co-construction and a prevalence of individual algebraic thinking. Moreover, the research provides insights for the design of a platform to facilitate Digital Mathematical Discussions, which have informed the development of a prototype.