While conducting this self-study, the integrated instructional third space was an
interwoven path for me to support culturally responsive teaching in elementary mathematics with my preservice teachers. The research questions that guided this study included: (1) In the
context of the self-study, to what extent do I enact my espoused teacher education platform in the integrated instructional third space that exists at the intersection of an undergraduate elementary field experience and an undergraduate elementary mathematics methods course in relation to culturally responsive teaching and mathematics? (a) What facilitators and challenges do I face as I try to enact my espoused platform within this third space?; (2) In the context of the self-study, how do I transform as a teacher educator while engaging in the process of framing and reframing my platform within this integrated instructional third space? I conducted a self-study within the context of an integrated instructional third space within a clinically rich teacher education program where I served as both a field supervisor as well as a mathematics course instructor concurrently to the same group of preservice teachers. Data collection included a series of three phenomenological interviews, observation notes from pre and post conferences with my
preservice teachers, documents and artifacts from my own teaching practice, transcripts of pre and post conferences, and a researcher’s journal. I analyzed the data for each semester and made assertions across the two semesters of data collection.
In chapter four I discussed specific routines of practice I uncovered that helped me enact all of the aspects of my platform. These routines of practice include: supervision practices, culturally responsive teaching, and mathematics knowledge for teaching. The five routines of practice I uncovered were: probing questions, utilizing personal connections, offering
suggestions modeling, and targeted activities. Additionally, I outlined how each routine of practice connected to my platform and the specific pedagogies I used to help foster the routines of practice. I found I used whole group discussions and pre and post conferences conversations in order to engage in probing questions. I used hands on mathematics activities and whole group discussions to utilize personal connections with my preservice teachers. Pre- and post-
conference conversations allowed me to offer suggestions to my preservice teachers. I engaged in the routine of practice of modeling through hands on mathematics activities and meta
cognition. Finally, online supplemental mathematics content lessons, in class readings, and micro teach lessons allowed me to provide targeted activities for my preservice teachers.
In chapter five, I shared facilitators and barriers I encountered while working with my preservice teachers in the integrated instructional space. I discussed how relationships with preservice teachers and relationships with collaborating teachers were key in allowing me to facilitate preservice teachers’ learning about culturally responsive teaching and mathematics knowledge for teaching. Additionally, I presented challenges in relation to facilitating difficult conversations with my preservice teachers about culturally responsive teaching and mathematics knowledge for teaching. Specifically, I addressed challenges in facilitating theory to practice connections, promoting sociocultural consciousness, and promoting an affirming attitude
towards diverse students with my preservice teacher. Finally, I presented concluding thoughts on the three iterations of my platform.
Discussion
Two powerful calls drove this self-study. First the call from the Blue Ribbon Panel Report titled Transforming Teacher Education Through Clinical Practice: A National Strategy
to Prepare Effective Teachers (NCATE, 2010). In this call the panel argued that teacher
educators who support preservice teacher learning during clinical experiences must be able to integrate coursework and fieldwork in order to develop preservice teachers’ abilities to meet the needs of diverse students. In this self-study I was teaching in a unique version of a third space. As a teacher educator, I was both the mathematics instructor and the field supervisor for the same cohort of preservice teachers within a clinically rich teacher education program. While many teacher educators have the opportunity to work with preservice teachers in clinically rich spaces, this space was unique in that I served this dual role and was able to help my preservice teachers make theory to practice connections from our shared experiences in both the
mathematics methods course and the field experience.
A second important call for teacher educators, made by the National Council for Teachers of Mathematics (NCTM) in their book Principles to Action in the equity strand, stated, “An excellent mathematics program requires that all students have access to a high-quality
mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential” (2014, p. 5). The important call made by NCTM and the research conducted by others, as seen in chapter two (Aguirre & Zavala, 2013; Castro, 2010; Gay, 2000, Gutierrez, 2013; Presmeg, 1998; Sleeter, 2001; Villegas & Lucas, 2002; White, 2002) illustrated the need for preservice teachers to be exposed to culturally responsive teaching in mathematics early on in their teacher education programs. The findings from this study addressed these calls by looking at how a teacher educator in a clinically rich
teacher education program could support preservice teacher learning about mathematics knowledge for teaching and culturally responsive teaching.
In addition to the calls from NCATE (2010) and NCTM (2014) for the inclusion of equity in mathematics, Villegas and Lucas’ (2002) proposed six salient characteristics to engage preservice teachers in culturally responsive teaching. This is particularly important in
mathematics because we know that mathematics tends to be a subject that is seen, “more than any other, that [is] considered to be value- and culture-free; hence the view of many educators that mathematics education [has] no need to take the growing diversity of student populations into account” (Presmeg, 1998, p. 317). This view that mathematics is culturally neutral can be difficult to overcome; however, a framework including routines of practice, and the specific pedagogies to enact these routines, could help to guide teacher educators to think about how to facilitate preservice teacher learning in relation to culturally responsive teaching and elementary mathematics in both coursework and field experiences.
In this self-study I positioned myself as a teacher educator, but also as a learner of pedagogy in relation to integrating culturally responsive teaching and mathematics knowledge for teaching. While I had previous experiences attempting to facilitate preservice teachers’ learning about culturally responsive teaching and mathematics knowledge for teaching I was still a novice throughout this self-study. It was my hope during the self-study to learn better ways to facilitate my preservice teachers’ learning about the integration of culturally responsive teaching and mathematics knowledge for teaching. For this reason, I extensively documented my practice and reflections on my practice in order to study my own enactment of pedagogy with my
preservice teachers. Throughout this self-study I positioned myself as a constructivist. While working with my preservice teachers I attempted to model constructivist pedagogies to them and
enact constructivist practices with them. However, as seen in chapter four I did not always enact my platform using constructivist pedagogies. For example, I found the routine of practice of offering suggestions to my preservice teachers, which does not align with my constructivist lens. In regards to the mathematics knowledge for teaching throughout this study, I believe the
mathematics and its interconnectedness with culturally responsive teaching could potentially have been replaced with other content areas. My focus and passion was mathematics; however, due to my novice status facilitating culturally responsive teaching with the mathematics
knowledge for teaching I believe this foundational learning has the potential to apply to any content area.
Finally, I recognize there were some issues of power with my position as a teacher educator working with my preservice teachers. I tried to mitigate any perceived or real power struggles between my preservice teachers and me through relationship building. I recognized that as their instructor and supervisor I was giving my preservice teachers grades throughout this process and this could have impacted our relationships. I also recognized that there was a perceived power struggle between my preservice teachers and their collaborating teachers. This power struggle led to the preservice teachers not having full control over what types of lessons they planned for and enacted in their internship classrooms. Additionally, it could have impacted how my preservice teachers thought about culturally responsive teaching and mathematics
knowledge for teaching in their internship classrooms, depending on the stance of their collaborating teachers.
Routines of Practice
As seen in chapter four, the findings from this self-study showed routines of practice and specific pedagogies that helped me, as a teacher educator, facilitate the learning of my preservice
teachers in relation to mathematics knowledge for teaching and culturally responsive teaching. The routines of practice I found build off of the framework from Burns and Jacobs (in press) and interweave tasks related to culturally responsive teaching and elementary mathematics
knowledge needed in order to teach (Villegas & Lucas, 2002; Ball, Thames, & Phelps, 2008). Grossman, Hammerness, and McDonald (2009) called for teacher educators to shift away from teacher education programs that have curricula organized by knowledge domains to one
organized around practices of the profession. They called for teacher educators to first “work to develop programs that undo the historical separation between foundation and methods courses; second, teacher educators must focus upon helping novices develop and refine a set of core practices for teaching” (Grossman et al., 2009, p. 276). In the field of elementary mathematics, teacher educators are beginning to develop a framework for instructional practices that can be used in mathematics methods courses with preservice teachers called routines of practice (Kazemi, Lampert, & Ghousseini, 2007). The routines of practice I found built on this research yet are unique in that they focused on the core practices I used to facilitate preservice teacher learning in relation to culturally responsive teaching and mathematics knowledge for teaching as a teacher educator in the integrated instructional space. In order to support preservice teacher learning in relation to mathematics knowledge for teaching and culturally responsive teaching I found I used a combination of the routines of practice.
One of the factors that required a combination of routines of practice was the structure of the integrated instructional third space. In the clinically rich teacher education program I served as both the mathematics methods course instructor as well as the field experience supervisor for the same cohort of preservice teachers. Early on in the self-study I noticed that I planned activities with relative ease in relation to culturally responsive teaching and mathematics in the
mathematics methods courses; however, when the environment was less structured, such as in spur of the moment conversations during the field experience, I had trouble finding ways to facilitate conversations about culturally responsive teaching and mathematics knowledge for teaching. When I used probing questions with my preservice teachers in order to hold
conversations about culturally responsive teaching and mathematics knowledge for teaching it occurred during an opportunity that arose as a ‘teachable moment.’ However, by utilizing a variety of routines of practice I was able to move beyond the ‘teachable moments’ when working with my preservice teachers. For example, I used the routine of practice of offering suggestions while in the field with my preservice teachers in order to help focus and facilitate their learning in the field in relation to culturally responsive teaching and mathematics knowledge for teaching.
Additionally, within each routine of practice I found I used different specific pedagogies depending on the needs of my individual preservice teachers. For example, I found I used online supplemental mathematics content lessons, in class readings, and mathematics micro teach lessons in the mathematics methods course to facilitate my preservice teachers’ learning. These specific pedagogies allowed me to purposefully plan targeted activities that facilitated my preservice teachers’ learning about culturally responsive teaching and mathematics knowledge for teaching. In the mathematics methods course I facilitated many activities and discussions surrounding the preservice teachers’ mathematics knowledge for teaching. However, when the preservice teachers attempted to utilize this knowledge in both the methods class, through assignments, and the field experience, through teaching, they still needed support. Therefore, mathematics knowledge for teaching needs to be illuminated for preservice teachers and woven into the field experience, not addressed in isolation in the mathematics methods course(s).
Relationships
As seen in chapter two, Nolan and Hoover (2011) encouraged teachers to articulate their belief system with other stakeholders as a source dialogue, as well as to build relationships and trust among stakeholders. Bowers and Flinders (1991) discussed the implications a supervisor's personal beliefs and values can have on the task of working in field experience classrooms with preservice teachers. This connected with other researchers’ suggestions of uncovering one's platform (Bates, Drits, & Ramirez, 2011; Bullock, 2012; Glickman, Gordon, & Ross-Gordon, 2014; Nolan & Hoover, 2011; Sergiovanni & Starratt, 2002). Taking the time to write out a platform and share it with others allows for a more open and trustful relationship. This was also apparent in the platform reflections found in chapter five.
In the self-study I found building and maintaining relationships with preservice teachers was key in allowing me to facilitate my preservice teachers’ learning about culturally responsive teaching and mathematics knowledge for teaching. As seen in chapter five, when I built and maintained relationships with my preservice teachers I found that I more closely followed the goals and beliefs in my platform: to build relationships with my preservice teachers, to foster my preservice teachers’ construction of knowledge, to use that knowledge to plan for instruction, to understand their knowledge of content and students, and to utilize targeted instructional feedback with my preservice teachers in their field experience classrooms.
Through the process of building relationships with my preservice teachers I learned more about them personally and professionally, which built trust and allowed me to use the knowledge about my preservice teachers to facilitate their learning about mathematics knowledge for
teaching and culturally responsive teaching. I learned where my preservice teachers were most comfortable in terms of their enactment of elementary mathematics lessons and how they were
able to incorporate culturally responsive teaching practices into their elementary mathematics field experience classrooms. However, many of my preservice teachers were not comfortable teaching mathematics, and were more hesitant to engage in mathematically focused
conversations. I found that when my preservice teachers were more comfortable in our
relationship I was better able to facilitate conversations about culturally responsive teaching and mathematics knowledge for teaching, and they were more comfortable telling me what they struggled with in relation to mathematics content. I learned that when I lacked knowledge about my preservice experiences, it influenced my ability to support them, both in relation to
mathematics and culture.
I also learned from the self-study that I should have used the collaborating teachers’ knowledge and experience more in my facilitation of my preservice teachers’ learning. As seen in chapter two, many researchers have studied the struggle teacher educators have feeling like an outsider when working with collaborating teachers and preservice teachers in the field
experiences (Basmadjian, 2011; Cuenca, Schmeichel, Butler, Dinkelman, & Nichols Jr., 2011; Slick, 1998a, Slick, 1998b). I too felt a bit like an outsider and hesitated to use the collaborating teachers more at times because I did not want to overwhelm them since they volunteered to host a preservice teacher. Another hesitation was my lack of experience in facilitating their
knowledge and experience about mathematics to help my preservice teachers grow into using more culturally responsive practices in their elementary mathematics classrooms.
Another aspect of facilitating preservice teachers’ learning about mathematics knowledge for teaching and culturally responsive teaching that I learned was the lack of knowledge I had about the elementary students, culturally and mathematically. I believe that I would have been better able to facilitate my preservice teachers’ learning if I knew their elementary school
students on a deeper level. From the self-study I reflected about the difference in my facilitation of the group of preservice teachers I had in both the mathematics methods course and the field experience, versus the group I only saw in the methods course. It was easier for me to talk to the group I saw in the field because I could picture their mathematics environment, including the classroom and the students. I was able to pull from my own experiences of seeing their elementary students and used what I knew about their teaching to provide more in depth
opportunities for reflection about mathematics knowledge for teaching and culturally responsive teaching.
Critical Conversations
Villegas and Lucas (2000) argue that sociocultural consciousness, “the recognition that there are multiple ways of perceiving reality and that these ways are influenced by one’s location in the social order”, cannot be learned in one course or even in multiple courses in one semester (p. 21). This was true not only for my preservice teachers, but also for me as a teacher educator. Through the reflections on my practice I found a challenge I faced as a teacher educator was realizing that I did not always have enough knowledge and experience to support my preservice teachers’ needs. Personally, I found that I struggled at times to make connections between the elementary mathematics content and how I could embed culturally responsive teaching practices in the mathematics methods course, as well as when attempting to facilitate theory to practice connections with my preservice teachers. I found that I struggled with promoting critical reflection with my preservice teachers during our conversations, especially impromptu conversations. I tended to fall back to teaching practices that were comfortable for me, being direct in conversations with my preservice teachers through giving them suggestions or feedback, rather than follow my platform beliefs of constructivist learning. These types of
conversations sometimes hindered my preservice teachers’ ability to construct their own knowledge about culturally responsive teaching and mathematics knowledge for teaching. Furthermore, my own experience and knowledge about how to facilitate conversations centered on mathematics knowledge for teaching and culturally responsive teaching impacted my
preservice teachers’ learning.
I realized in order to facilitate my preservice teachers’ learning I needed to provide them with more open-ended questions during our conversations. I also needed to create a more
structured environment for myself as a supervisor by more thoroughly planning for conversations with my preservice teachers. The field experience is a much less structured environment than the mathematics methods course, and through reflecting on my practice I saw when I did not plan for