This chapter contributes to broader research on mathematical discourse and its multimodal forms that reveal how students interpret, make meanings in mathematics, and communicate their understandings. Central to this chapter is explanatory writing in mathematics, which targets a specified audience to explain and transmit mathematical ideas. In the context of a mathematics problem-solving course and focusing on contextual problem-solving situations, this chapter illustrates how explanatory writing in mathematics offers a window into prospective elementary school teachers' (PTs') reasoning and communication skills. The chapter highlights PTs' strategic reasoning and sense-making and describes how they communicate their problem solutions. It provides mathematics teacher educators with insights into how PTs think about contextual problem situations, offering directions for planning how to help PTs develop new ways of thinking. This chapter also includes suggestions for future research on PTs' learning to construct written mathematical explanations.