Lesson study is a form of professional development for teachers adopted in recent years from Japan. Introducing lesson study to U.S. teachers and researchers has been the focus of most of the literature on this subject. Much of the literature outlines how lesson study works and describes its essential features. One of the features of lesson study is anticipating student responses, also known as anticipating student thinking. Anticipating student responses is passingly described in lesson study literature. This research was conducted to understand what it means to anticipate student responses for preservice mathematics teachers in a lesson study group. Lesson study literature indicates that anticipating student responses is to anticipate conceptual development from the students' perspective, and the purpose is to be prepared to have meaningful discussions and questions to enable students to develop the understanding. Anticipating student responses is highly related to the hypothetical learning trajectory described by Simon (1995), the self directed anticipative learning model described by Christensen and Hooker (2000) and the expert blind spot discussed by Nathan and Petrosino (2003). While their work does not stem from lesson study, they add theoretical perspective to the idea of anticipating student responses. Their work indicates that anticipating student responses is difficult, valuable, that one gets better at it through experience, and that it is very useful in refining lessons. Participants were enrolled in the mathematics education methods class of a large private university in the U.S. A characterization of anticipating student responses was developed as the participants met in group meetings to create a lesson. They anticipated student responses in ways that facilitated lesson planning and task design. Participants did not anticipate student responses toward students' conceptual development. This research reports five particular ways that anticipating student responses was used as a tool to define and refine the lesson so that it ran smoothly toward lesson goals. These ways are related to: goals, tasks and materials, procedural mathematical reasoning, successful student efforts, and emotional responses. It is believed that anticipating student responses towards task design is a necessary precursor to anticipating student responses toward students' conceptual development.

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