There is a plethora of research in learning theories (e.g., in cognitive psychology, sociology of education, pedagogy, etc.) highlighting the role of language (talk) as a means that mediates learning (Cazden, 2001; Diez-Palomar & Cabré, 2015; Mercer & Sams, 2006). Mehan (1979) and many others focused their attention on the I-R-E pattern (initiation-response-evaluation) to analyse what happens within instructional talk, when the teacher poses a task, and then children solve the task producing responses which are evaluated by the teacher again (Hall & Walsh, 2002). Cazden and her colleagues have criticised this pattern on the grounds that it acts to prevent students developing autonomous thinking and understanding. Recently, Clarke and his colleagues (Kaur, Anthony, Ohtani, & Clarke, 2013) analysed student voice in the Learner’s Perspective Study demonstrating that students are co-constructors of mathematical knowledge together with the teachers. This is consistent with the socio-cultural proposition claiming that children learn with the guidance of adults or other more capable peers (Vygotsky, 1978). In this paper, I describe a methodological tool used to analyse the type of mathematical talk produced within a peer group-based problem-solving experimental environment, with no intervention from the teacher. I used video data from the project Social Unit of Learning directed by David Clarke at the University of Melbourne to analyse episodes of interaction. Data were collected by Clarke’s research team at the International Centre for Classroom Research, in a room equipped with 10 cameras and up to 32 audio channels to comprehensively document all social interactions. My approach was to identify what Cazden calls “real discussion” rather than just recitation or non-instructional talk (Cazden, 2001), using a communicative methodological approach (Gómez, Racionero, & Sordé, 2010). I looked for utterances (characterising the negotiation events embedded in each episode of interaction), where students used validity claims (in Habermasian terms) to justify, explain, describe, convince, persuade, or alternatively, make power claims to impose, annoy, insult, or disregard. My main aim was to identify successful learning trajectories through this discourse analysis. I conclude that distinguishing between dialogic and non-dialogic talk (talk based on validity claims versus talk based on power claims) allows us (as researchers), and teachers as well, to identify successful ways for children to develop mathematical understanding when solving problems. I use some cases drawn from the data to illustrate this claim.