Given the prevalence and academic impact of technology in mathematics education, increasing attention has been paid to the role of digital artifacts in promoting productive classroom discourse. This study investigates the association between the qualities of mathematics discussion and artifacts generated by individual teachers, individual students, and jointly by multiple students. We also examine the influence of pedagogical moves on artifact mediation and discourse. Drawing on video data from the mathematics classroom of five pre-service teachers, we found that discourse based upon student ideas occurred most frequently with reference to student-generated artifacts, and dialogic discourse occurred almost exclusively with reference to jointly constructed artifacts. With six episodes mediated by three types of artifacts, we provide descriptive empirical evidence to illustrate the complex interplay of artifact construction, student ownership, teacher pedagogical moves, and artifact mediation for mathematical discourse and meaning-making. We also provide an Artifact Mediated Discourse Matrix with examples as a framework for examining artifact-supported discourse in mathematics classrooms. We discuss implications related to teacher pedagogical moves, a classroom culture discourse, and the role of mediation embedded in the digital artifact.