This qualitative research study investigates dialogic discourse (i.e., give-and-take communication where students actively construct meaning) aimed at supporting mathematical meaning making in linguistically diverse elementary classrooms. For this study, linguistically diverse classrooms refer to classrooms where Spanish is the home language of many of the students--both dual-language (Spanish and English) and English-only elementary classrooms that include English learners (ELs). Multiple classrooms in two schools in the western and eastern United States were observed. Data sources include field notes, audio and video recordings, transcriptions of dialogue, and translations of dialogue (as appropriate). Qualitative methods including constant comparative methods, thematic coding, and discourse analysis techniques are used to examine verbal moves, exchanges, sequences, and episodes of discourse from mathematics lessons. A first-grade dual-language classroom is highlighted to illustrate methods and findings. Analysis demonstrates that, similar to monolingual classrooms, specific verbal moves (e.g., exploratory talk, accountable talk, and generative assessment) may shift discourse toward dialogic. Other supporting moves and practices (e.g., think time, visuals, use of primary language, and code-switching) are identified. Models of teaching are built from examination of relationships among moves, exchanges, sequences, and episodes within mathematics lessons. The models of teaching demonstrate practices with potential for infusing dialogic discourse and mathematical meaning making in linguistically diverse mathematics classrooms.