UC Santa Barbara

Preservice mathematics teachers today are charged with the challenging yet vital task of learning how to authentically engage their future students in the Standards for Mathematical Practice. These eight practices specify the various levels of competence that mathematics teachers of all levels should explore to see their students flourish. While they are a critical component of the Common Core State Standards for Mathematics and are based on longstanding processes and mathematical proficiencies established in mathematics education, there is little research to date that has looked at how preservice mathematics teachers understand, implement, and engage their students in these practices. This dissertation sought to understand how preservice mathematics teachers conceptualized the Standards for Mathematical Practice throughout their teacher education. Data collection consisted of initial and follow-up interviews and completed edTPA portfolios from 47 preservice mathematics teachers from three separate cohorts across four different university teacher education programs in California. I analyzed the data for this dissertation in three separate ways. First, I looked at which of the Standards for Mathematical Practice preservice mathematics teachers reported in interviews as the most important to teach, as well as which ones they needed further help in understanding (Chapter 2). I looked to see how their responses compared across initial and follow-up interviews, as well across the four universities participants were from. Participants overwhelmingly considered Practices 1 and 3 to be the most important to teach regardless of pre- or post-interview and which university they attended. The same applied to which practices preservice mathematics teachers reported needing further support in understanding, which were Practices 4 and 8. Next, I investigated how the participants in this study incorporated the Standards for Mathematical Practice in their edTPA (Chapter 3). By coding preservice mathematics teachers’ edTPA video clips according to the MCOP2, I was able to create a correlation coefficient between participants’ MCOP2 scores with their edTPA instructional commentary and overall edTPA score, therefore understanding the extent to which preservice mathematics teachers incorporated the practices in their edTPA. Finally, I looked at how a subset of preservice mathematics teachers drew on the Standards for Mathematical Practice through the use of cognitively demanding tasks in their edTPA (Chapter 4). Through the correlation I created in Chapter 3, I selected six participants, three of who scored high and three low, and investigated the levels of cognitive demand of the tasks they incorporated into their edTPA planning section, as well as which Standards for Mathematical Practice these tasks incorporated. Participants who received high edTPA scores tended to include tasks that were of higher demand, which not only reflected a higher number of the practices, but also engaged students in Practices 1 and 3. Those who received low scores had a higher frequency of low demand tasks, which included less practices overall, with Practices 1 and 3 frequently absent. My work extends the literature on preservice mathematics teachers’ understanding of the Standards for Mathematical Practice and supports the need for future research that will continue to support the successful education of our preservice mathematics teachers.