This study investigates how Japanese mathematics classroom discourse is socially constituted. The investigation focuses on the ways that teacher and students coordinate their purposes and maintain a predictable sense of the ongoing discourse. The discussion consists of two parts. The first part introduces the theoretical framework. Grounded on the Bakhtinian perspective, this framework is applied to the study of classroom discourse in which the concept of “voice” plays a significant role. The second part involves analysis of discourse structure in public and private interaction and description interpretation of students’ voice. Utterances which the teacher and students addressed in public and private interaction, as well as post lesson interviews, illuminate sharp discrepancy in discourse structure. The discrepancy suggests under-represented voices in public and private classroom discourse. Analysis of voice shows that classroom mathematical interaction is characterized by a monologic suppression by authoritarian voice, rather than by a dialogicality of voices. The analysis of the teacher's utterances suggests that he sends implicit message that homogeneity among students activity should be attained. Students are constrained to expression through the monologic voice which assumes that there is only one true formulation of a mathematical task and solution.