Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Curriculum and Instruction

Major Professor

Sarah van Ingen, Ph.D.

Committee Member

Jennifer Jacobs, Ph.D.

Committee Member

Eugenia Vomvoridi-Ivanovic, Ph.D.

Committee Member

Janet Richards, Ph.D.

Committee Member

Angela Hooser, Ph.D.


clinically rich teacher preparation, elementary mathematics education, Practice-based methods


The Common Core State Standards in Mathematics (CCSSM, 2010), refer to eight distinct Mathematical Practices describing what students should be doing for optimal learning during mathematics lessons. Specifically, Mathematical Practice 3 (MP3), “construct viable arguments and critique the reasoning of others” (CCSSM, 2010, para 4), posits students who are proficient in mathematics are able to compare different solutions, distinguish correct and logically sound answers from those that are incorrect and then explain why the solution is incorrect (CCSSM, 2010). MP3 requires teachers to provide opportunities for students to engage in discussions beyond just “show and tell” talk to develop a deeper knowledge (Stein, Engle, Smith, & Hughes, 2008). There is limited literature identifying teaching practices or behaviors for facilitating MP3 in the elementary classroom and how TCs learn to facilitate these practices. This study addresses the gap in the literature related to teacher preparation. It provides a proof-of-concept example of how method courses and field placement link theory to practice and outlines potential learning trajectories of TCs who engage in these practices.

I used an exploratory multiple case study to gain a better understanding of the ways three TCs learn to facilitate MP3, “construct viable arguments and critique the reasoning of others” (CCSSM, 2010) across math methods courses and accompanying clinical internships in elementary classrooms. I explored the similarities and differences in the ways each TC planned and enacted teaching behaviors for the facilitation of MP3. The following research questions helped me come to understand how TCs learn to facilitate MP3: Within the context of a practice-

based methods course and an accompanying clinical internship placement in an elementary classroom, how do three TCs learn to facilitate Common Core MP3? How does the TC plan to facilitate MP3 in their clinical internship classrooms? How does the TC enact teaching behaviors for facilitating MP3 in their clinical internship classrooms? In what ways do TCs perceive supports and tensions within a practice-based methods course and clinical internship classrooms when facilitating MP3?

First, I explored each case as a separate entity, attending to the configurations within the case, followed by a comparative analysis across cases attending to interpretive synthesis and common themes (Miles, Huberman, & Saldana, 2014). I used three rounds of coding during individual data analysis to assign categories and themes from the data sources. I focused on and described what behaviors and actions TCs exhibited (rather than behaviors not exhibited) and provided evidence for how each facilitated MP3. Finally, a cross-case analysis compared cases and made sense of the commonalities and differences in TCs’ facilitation.

I found the data supported a conceptual model, or trajectory, for understanding the ways TCs (and novice teachers) learn to facilitate MP3 and might apply to other Mathematical Practices or content areas.