Lesson Study is rapidly becoming one of the most adopted models of teacher professional development worldwide. In this paper, we examine the teachers' discussions that are an integral part of the Lesson Study research cycle. In particular, we investigate the "dialogic mechanisms" that enable teachers' pedagogical intentions to be developed within the context of discussions that stem from observations of students as they address mathematical problems. In so doing we hypothesize about the nature of the "dialogic space" that is created and how this allows teachers to move from the collaborative analysis of student outcomes to an enhanced understanding of pedagogical intentions in mathematics. Data for this paper derive from a large research project taking place in Camden, London. This project aims to implement Lesson Study in the context of the introduction of a New National Curriculum for Mathematics in England. It involves a large cohort of mathematics teachers across primary and secondary schools. Quantitative analysis of video-recorded Lesson Study discussions is reviewed and one illustrative case study is included to contextualise the quantitative data. Findings suggest that a focus on student outcomes enables teachers to collaborate effectively on developing pedagogical intentions to directly address student need. Further, it seems that particular features of dialogue are evident where teachers move to an agreed perspective on pedagogic change; and evidence of 'supportive moves' in interactions suggest that a form of dialogic space is necessary if all teachers in a Lesson Study group are to learn from shared understandings about future teaching and learning needs.