Representations play a key role in mathematical thinking: They offer "a medium" to express mathematical knowledge or organize mathematical information and to discern mathematical relationships (e.g., relative household expenditures on a pie chart) using text, symbols, or graphics. They also furnish "tools" for mathematical processes (e.g., use of a number line for addition). Thus, students' self-created representations give teachers "windows" into their mathematical thinking. The caveat is that these windows are affected by students' proficiency with representation and teachers' capacity to read (i.e., interpret) students' representations. In this article, the authors use a model to explore the role of representations in student thinking. They then discuss a set of student-created representations produced during an investigation and their implications for instruction. (Contains 6 figures.)