A central aspect of reform-minded mathematical teaching is training and developing teachers' ability to notice vital aspects in the classroom and more specifically, students' mathematical thinking. As there is an abundance of evidence and research that support the benefits for teachers to elicit and use students' ideas and thinking during instruction, there are just as many challenges associated with developing and mastering this skill. Specially, teachers must learn to attend to important details of students' thinking, interpret the meaning and understanding of students' thinking, and finally, teachers must decide how to purposefully respond to the student in a manner that extends the students' understanding. This process happens continually throughout the day but teachers must react quickly in specific moments. This in-the-moment attending, interpreting, and decision-making is called "professional noticing of students' mathematical thinking" (Jacobs et al., 2010). The purpose of my study is to examine preservice teachers' noticing of students' mathematical thinking (van Es, 2011) through three planned, taught, and reflected teaching cycles. Specifically, I hope to gain insight into what preservice teachers notice through the cycles while enrolled and completing an undergraduate Mathematics and Science method course. I hope to add to the growing research which focuses on that of preservice teachers noticing but also, I hope to help bridge the gap between novice and expert noticing of students' mathematical thinking. [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.]