This dissertation comprises two articles. In the first article, I review and synthesize literature on how prospective teachers (PTs) might evaluate students' mathematical thinking as manifested in written work. After defining evaluation, I argue that evaluating students' thinking in productive ways is both necessary and desirable within the context of responsive teaching. I then describe potential uses for evaluation in helping teachers respond productively to student thinking or in the enactment of responsive teaching moves. I synthesize findings of previous studies on evaluating student work into a framework of seven evaluation criteria. I then combine this framework with research on teachers' diagnostic processes to create an elaborated process for evaluating student work. Excerpts from interviews with PTs demonstrate the utility of these products. In the second article, I describe an empirical interview study conducted with 15 elementary PTs enrolled in their first mathematics content course to ascertain the extent to which their evaluations aligned with components of the elaborated process and how their evaluations changed over time. Key findings include: (1) strategic competence was consistently the evaluation criterion PTs used most frequently, but the depth of evaluations using this criterion was inconsistent; (2) criteria PTs used for evaluation were inconsistent among solutions and appeared to reflect PTs' perceptions of weaknesses; (3) PTs' use of the personal preference criterion decreased significantly throughout the course; and (4) some PTs exhibited a common and productive trajectory in their evaluations on the clarity criterion. Implications for future research and teacher preparation programs are shared. [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.]