Teachers are often faced with the difficulty of deciding exactly what problems the students are experiencing, and the extent to which students might understand "some of it". The one-on-one approach to helping students is most common, but very time consuming, and is an approach that may only serve to fix an immediate difficulty, perhaps by addressing procedural aspects rather than the concepts. One reason for this may be the very real difficulty both parties have in identifying exactly what the problem(s) could be. Teachers questioning students about their mathematical understanding often results in a conversation with the teacher leading in ways that he or she feels appropriate and the student responding in the accepted form. However, as Barnes (1999) reveals in the recorded observations of student talk in small groups, student-student talk is much freer. The tenor of the talk changes when the teacher is present but it also appears to remain more free-ranging than would appear to be the case in other classroom situations. It is this free-ranging nature of student-student conversations that can reveal much about students' understandings. The model described in this paper utilises a situation where students can engage in a conversation with each other, with the teacher present. The teacher partly "eavesdrops" and partly guides the conversation. The guidance is not directed towards some goal determined by the teacher (such as having the students solve a problem), but towards the teacher finding out what is going on in the students' thinking. The underlying premise for the model is that mathematics is a language (e.g., Pimm, 1987). Techniques of language-arts teaching together with non-routine tasks generate student conversations, which provide linguistic clues to student understanding. In this article, the theoretical bases for the model are briefly outlined and two snapshots of a discussion in a class conducted with a small group of students are presented as examples.