In the past two decades, research on learning has focused on understanding how students think and how that thinking becomes more sophisticated over time. Some researchers have verified sufficient consistency and robustness in their findings relating to these constructs, which they have articulated in the form of learning trajectories. While an articulation of such constructs has contributed greatly to the knowledge base of how students learn, the field has just begun to explore the extent to which learning trajectories can be integrated into the practice of teaching. Though useful at the level of curriculum, assessment, and standards development, it remains to be shown that learning trajectories can be incorporated into teachers' practice and become a tool to understand students' thinking, for planning instructional activities, for interacting with students during instruction, and for assessing students' understandings. Thus, bringing learning trajectories into the classroom through teacher education is one critical area of knowledge that needs to be investigated. This study addresses to what extent and in what ways can pre-service elementary teachers use a learning trajectory for equipartitioning to build models of student thinking. Over an eight-week period, within an elementary mathematics methods course, 56 pre-service teachers (PSTs) participated in this design study. Data included the following: video & audio recordings of class meetings, researcher's notes of class meetings and school-based experiences, pre- and post-test data, clinical interviews and analysis of interviews, and other artifacts. Findings from this study indicate that PSTs used an equipartitioning learning trajectory to (1) deepen their understanding of mathematics and knowledge for teaching mathematics; (2) build more precise and adequate models of student thinking; and (3) incorporate models of student thinking into instructional practices. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]