This report is a summary of the questions, comments and issues brought up in the ETC4 panel of three expert researchers on mathematics and language. The purpose of this panel was to discuss: (1) What do we mean by the language of the learner, of the teacher and of mathematics? (2) What are today the opportunities and challenges of classroom-based research on mathematics and language? The major recommendations and position statements included: (i) Develop more nuanced theoretical frameworks for the understanding of the politics of language use in the mathematics classroom (ii) Re-evaluate conceptualizations of languages and speakers in terms of distinctions, differences, dichotomies and difficulties (iii) Conduct more language-related design research for teaching and learning of specific mathematical content areas.