The need to design teacher preparation programs to ensure that pre-service teachers (PSTs) are prepared and equipped with knowledge, skills and practices to increase the chances that they will become effective novice mathematics teachers is of prime importance. Teacher educators are facing lingering challenges, since teacher education is contextualized to specific institutions and the field of teacher education still lacks an identified common curriculum (Ball, Sleep, Boerst & Bass, 2009; Grossman & McDonald, 2008). Therefore, little is known about how PSTs acquire the knowledge, skills and practices that they need to become beginning teachers. Specifically, very little is known about how PSTs develop skills and practices needed to attend to children's strategies, interpret and respond based on children's mathematical understanding. This dissertation research addresses this gap by examining the extent to which a group of thirty PSTs enrolled in an elementary mathematics methods course attended to children's strategies, interpreted and responded based on children's mathematical understanding as they progressed in their methods course. The PSTs were provided with multiple scaffolds during the course of the semester. The scaffolds were purposefully designed to support PSTs' understanding of what it means to attend to children's strategies, interpret and respond based on children's mathematical understanding. The findings indicate that PSTs' capacity to attend to children's strategies and to interpret based on children's mathematical understanding grew over time. There was a shift from limited evidence that PSTs' interpretations were based on children's mathematical understanding to providing robust evidence across two assignments. However, the results also show that PSTs struggled with the component skill of responding based on children's mathematical understanding. The findings also indicate that PSTs' conceptions of productive tasks and tasks that engage children with high level thinking varied from tasks that "advance children's understanding, extend children's thinking to tasks that are based in real life connections." These two findings may have occurred, in part, because PSTs were "purposefully" scaffolded with activities that focused on developing the targeted skills and practices. The findings have theoretical implications for a hypothesized trajectory of professional noticing of children's mathematical understanding and the design of teacher preparation. [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://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]