The Zen concept of beginner's mind describes how one's level of awareness can open one's mind to growth and possibilities, an attitude that would be beneficial for many mathematics students. In this naturalistic case study, two small groups of middle years students engage in the same mathematical task, one group demonstrating the characteristics of beginner's mind and the other not. One group focuses on making sure that all its members can follow the steps of one member's proposed solution. The other group, which displays characteristics of beginner's mind, explores the task thoroughly, and in its openness to ideas it notices mathematically salient details in the task that the first group overlooks completely. This paper suggests that through beginner's mind, students may develop habits of mind that enable them to attend to and think about mathematical possibilities deeply.