Teachers are expected today to assess student understanding as an integral part of instruction, using a combination of various assessment methods and tools, among which are observing students solve problems in class and listening to their mathematical discussions. The aim of our study is to explore what it might mean for a teacher to hear students and to interpret their talk and actions. Analysis of an interview with Ruth--an experienced elementary school teacher--after she observed two of her students solve a mathematics problem, suggests four types of her interpretation: describing, explaining, assessing and justifying. This analysis illustrates the complexity of the way Ruth hears her students, as is indicated even in the relatively simple case of describing. Using various sources of data we also analyze different characteristics of Ruth's hearing for the describing and explaining types of interpretation and examine possible resources for her over-hearing, compatible-hearing, under-hearing, non-hearing and biased-hearing.