The authors of the four papers defining this symposium invite us to discuss about the role that interactions among students, teachers and other members of the community (families, etc.) play in the learning of mathematics.

Research in education has highlighted the central role of interactions in learning; a role that classic authors had already highlighted in their research. These authors suggest that dialogue is a key tool of learning; although not any type of dialogue, but the kind of dialogue that is based on verifiable arguments. The work of Flecha (2000) and his collaborators (Elboj & Niemelä, 2010; Valls & Kyriakides, 2013) substantially improved our comprehension of interactions in learning mathematics (or any other subject). Their research suggest that the more diverse are the interactions, the best is the learning already achieved. According to them, it is crucial that other members of the community, not only teachers, participate within the teaching process, because children learn from a huge variety of interactions (not just academic ones).

Dialogue is crucial for learning mathematics. In the moment that one student explains how he or she has solved a mathematical task, then is when he or she is learning, as a result of the effort to find arguments that validate his or her assertions. Research like the one of Forman, Larreamendy-Joerns, Stein and Brown (1998) illustrates that mathematics teachers not only have to guide students facilitating them new concepts and explanations on the mathematical objects; but they also have to encourage students to explain themselves how they solved the task, orchestrating their discussions on mathematical concepts.

Classic research in mathematics education (Lampert, 1990) suggest that the use of logical argumentation “should augment or even replace the (often meaningless) manipulation of symbols and algorithms in classrooms.” (Forman et al., 1998, p. 528) This trend has transformed the way of teaching mathematics (NCTM, 2000). A number of studies have examined the discursive practices occurring within the classroom, when students and teachers interact around mathematics tasks. Elbers and Streefland (2000) in a study conducted with 8^thgraders in a Dutch primary school conclude that students use argumentation to disseminate and expand knowledge. As they claim “[t]hese argumentation cycles were used as a tool that allowed students to propose ideas, repeat them, explore and evaluate them, and in such a form that many pupils could contribute.” (Elbers & Streefland, 2000, p. 487) Drawing on Vygotsky’s and Bakhtin’s previous works, Zack and Graves (2001) claim that although dialogue has become a metaphor for knowledge “nevertheless spoken words do not equal thoughts in the mind.” (Zack & Graves, 2001, p. 265) It entails a more complex process of individuals re-constituting the words into mathematics knowledge. This process is social in essence, since it involves different individuals sharing their thoughts through (dialogic) argumentation.

Papers presented within this symposium introduce four different study cases to expand how this process of argumentation works to lead students to learn mathematics successfully. Drawing on qualitative data analysis, papers examine how group work, mathematical discussions, and dialogic talk involving teachers, students (children and adult learners as well), and other members of the community, may led us to clarify the role that those different interactions play to encourage successful learning. The conclusions of this symposium may have impact on future teachers’ training guidelines.

Elbers, E., & Streefland, L. (2000). Collaborative learning and the construction of common knowledge. European Journal of Psychology of Education, 15(4), 479-490. Elboj, C., & Niemelä, R. (2010). Sub-communities of Mutual Learners in the Classroom: The case of Interactive groups. Revista dePsicodidáctica, 15(2), 177-189. Flecha, R. (2000). Sharing words: Theory and practice of dialogic learning. Rowman & Littlefield. Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998). “You're going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and instruction, 8(6), 527-548. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: mathematical knowing and teaching. American Educational Research Journal, 27, 29–63. Valls, R., & Kyriakides, L. (2013). The power of Interactive Groups: how diversity of adults volunteering in classroom groups can promote inclusion and success for children of vulnerable minority ethnic populations. Cambridge Journal of Education, 43(1), 17-33. Zack, V. & Graves, B. (2001). Making mathematical meaning through dialogue: “Once you think of it, the Z minus three seems pretty weird.” Educational Studies in Mathematics, 46, 229-271.