Research on preservice teacher learning has often focused on coursework and course related field experiences, and not as much on the learning that takes place during student teaching field experiences. Since preservice student teachers are engaged with children on a daily basis, attention to their own students' thinking should be viewed as a means of development. Jacobs, Lamb, and Philipp (2010) proposed a construct of professional noticing of children's mathematical thinking that can be used to evaluate teachers' decision-making processes when analyzing students' verbal and/or written responses. Analysis of student work has a strong potential benefit for preservice student teachers. This design research study focuses on preservice student teachers' learning to professionally notice their students' mathematical thinking through analysis of their students' multi-digit addition and subtraction work samples. Four preservice student teachers placed in first grade and three preservice student teachers placed in second grade participated in this study. A sequence of three professional learning tasks (PLTs) focused on preservice student teacher analysis of student work was developed. Data analysis led to an extension of the professional noticing framework proposed by Jacobs and colleagues to the field of preservice teacher education (2010). Results show specialized content knowledge, a subset of mathematical knowledge for teaching, as an integral part of the professional noticing framework components. The results suggest that preservice student teachers can be taught how to professionally notice their students' mathematical thinking during their preservice student teaching field experience. [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/en-US/products/dissertations/individuals.shtml.]