Interweaving Pedagogies of Care and Inquiry: Tensions, dilemmas and possibilities

Abstract

This article reports a collaborative, participatory self-study designed to examine the practices and experiences of a teacher educator (Janice) and her students with the support of critical dialogue partners (Cynthia and Feda). We explore the tensions and possibilities that arise as a teacher educator attempts to foster both a pedagogy of care and a pedagogy of inquiry in a mathematics methods course. We share these tensions and possibilities from the perspective of the teacher educator and her students during the course, following seven students into the practicum field experience and one student (Sarah) into her first year of teaching.

Keywords:

• pedagogy of care
• pedagogy of inquiry
• mathematics education
• collaborative self-study
• teacher education
• teacher educators
• variation

We are members of a Teacher Educator Collaborative created to study and support each other in our self-studies of teacher education practices. As a self-study collaborative we have explored our commitments to fostering and sustaining both a pedagogy of care (Hackenberg, 2005; Noddings, 1984, 2002) and a pedagogy of inquiry (Nicol, 2006; Wells, 1999) in our mathematics methods courses. We engaged in self-study practices (Berry & Loughran, 2005; Nicol, 2006; Samaras, 2002) within our own classrooms and came together as teacher educators [TEs] to provide critical support, share insights and questions, and collectively analyze our developing understandings of our students and ourselves (Berry & Crowe, 2007). We wondered what a mathematics teacher education course inspired by an ethic of care and inquiry might look like. What are the tensions and the possibilities?

A number of studies report the challenges, limitations, or successes of particular mathematics teacher education courses or programs related to developing preservice teachers' mathematical understanding for teaching (Ball, 1990), beliefs about mathematics and teaching mathematics (Wilkins & Brand, 2004), and understandings developed through embedded field experiences (Moyer & Husman, 2006). Other studies focus more generally on the quality of the pedagogical relations developed between students and their teacher (Noddings, 1984, 2002; Lake, Jones, & Dagli, 2004). Our study brings these two fields together to help us understand the pedagogical practices of a mathematics teacher educator and the experiences of her students. We first draw upon the work of Noddings (1984, 2002), Hackenberg (2005, 2010), and Long (2010) to explore the nature of a pedagogy of care in mathematics teacher education for elementary preservice teachers.

Caring as Relations

Noddings (1984, 2002) argues for the importance of developing caring relations in working, living, and being with others. Caring, according to Noddings, is not only important, but is also an inclination or an obligation toward something we feel we must do. It is an ethic of care. It involves a deep moral obligation. Caring is not located in individuals, but rather in the relations with one another. Caring is an action; it is something that is done. Noddings (2002) distinguishes between natural caring and ethical caring. Natural caring occurs when we feel we must respond because we want to feel with and for the other, we feel we must, or have no tension or conflict not to care. The caring occurs and in return the cared for respond. In this case, Noddings states, “the relation, episode, or encounter is one of natural caring” (p. 13). In contrast, ethical caring involves some conflict or internal resistance. It could be that we feel too tired or unprepared to respond to our preservice teachers' questions; we may be aware of and recognize their needs and interests but for whatever reason we experience some resistance to responding with care. Ethical caring involves a belief that we should respond with care. Noddings suggests that in this case we turn to an ethical ideal, our memories of being cared for and caring, to help us in “establishing, restoring, or enhancing the kind of relation in which we respond freely because we want to do so” (2002, p. 14).

Caring and the ethic of care then, as Noddings describes it, is an interaction or relation between a person giving care and a person being cared for. In a caring encounter the carer meets the cared for with full awareness and attentiveness – what Noddings (1984) terms engrossment. It also involves the carer moving to a level of receptivity in a way that puts aside the carer's own motivations to, if even for a moment in a particular situation, place the needs and interests of the cared for first. This, Noddings refers to as motivational displacement. Noddings notes: “Caring involves stepping out of one's own personal frame of reference and into the other's” (1984, p. 24). A caring encounter implies reciprocity. And so it is not until the cared for responds with some form of acknowledgement that the caring encounter is said to be complete. Caring then involves the engagement of both the carer and the one being cared for.

Noddings' ethic of care is not without its critics. Davion (1993) argues that Noddings' theory is overly focused on relationships through one-way caring at the expense of self-development and autonomy. This is important to consider, especially in educational relationships between a teacher and student where there is often a power difference. Nonetheless, an ethic of care does provide a way of framing the educational encounter. Hackenberg (2005) draws upon Noddings' work to develop a model of mathematics learning and caring relations. She describes interactions between students and teachers as involving an interplay between stimulation (being excited, awakened, alive, and motivated) and depletion (less interested, less energized or having diminished well being). Hackenberg argues that social interactions involve each of these factors in different degrees. However, when students and teachers engage in mathematical interactions, depletion can often dominate over stimulation. Students may experience math anxiety, they may find mathematics difficult or teachers' instructional approaches ineffective, or they may find it disconnected to their lives. For Hackenberg, “caring is conceived of as work toward balancing the ongoing depletion and stimulation involved in student-teacher mathematical interaction” (2005, p. 45). How might a teacher educator maneuver this dance of attention to students' stimulation and depletion toward learning to teach mathematics?

Pedagogy of Inquiry

How does a pedagogy of care include a pedagogy of inquiry? A pedagogy of inquiry involves designing classroom relationships and activities that shift the emphasis of learning to teach from a focus on best teaching methods to an emphasis on discussion, critique, and investigation of pedagogical problems that arise in the context of practice. A pedagogy of inquiry provides occasions that provoke and support ongoing action. It involves creating conditions that are intentionally ambiguous, and considers prospective teachers as researchers, where the teacher and the taught become less distinguishable.

Opportunities to stand back and reflect on practice, to inquire with others, to prepare for teaching, to analyze curriculum texts, are all aspects of practice. Our role as teacher educators, then, is to consider ways in which we might engage our students in authentic aspects of practice so that they may learn to use teaching practice as a source of inquiry and continued professional learning. Ball and Cohen (1999) refer to this as developing a stance of inquiry in terms of learning both in and from teaching practices. Sherin (2001) refers to this as developing a professional vision of classroom events.

Mason (2002) conceptualizes noticing as an intentional stance of inquiry. Noticing as inquiry refers to a type of professional vision that is “sensitised to notice things” (p. 1). Learning to teach, then, according to Mason is about developing the sensitivity to notice. Expert teachers, for instance, notice and see aspects of classroom practice in ways that beginning teachers do not. Mason offers the idea of noticing as an intentional stance: “a collection of practices both for living in, and hence learning from, experience, and for informing future practice” (p. 30). The discipline of noticing is about making the effort to notice particular things, for instance, in classroom teaching or research, and being able to notice these things when needed or “when it would be useful to have noticed [them] (and not merely later, in retrospect)” (p. 31). And so learning to notice does not just involve noticing aspects of teaching that before went un-noticed but also includes the sensitivity and inclination to be aware.

What is the relationship between a pedagogy of inquiry and pedagogy of care? Does one necessarily imply the other? These questions arose as we studied our practice as teacher educators. Our desire to help our preservice teachers experience layers of inquiry toward developing a stance of inquiry (Jaworski, 2006; Mason, 2002; Sherin, 2001) framed our teacher education collaborative. We ask: How can we as teacher educators design a mathematics methods course with attention to care and inquiry? How is this possible when many elementary preservice teachers fear, loath and would rather avoid doing mathematics themselves or teaching it to their students?

Context of the Self-Study

The context for this study was a mathematics methods course for a teacher education cohort in a 12-month elementary education program for post-baccalaureate students at a large Canadian university. The course was scheduled over an eight-week period, with two two-hour classes each week. Janice was the instructor for the course and was an experienced mathematics teacher educator (TE) and elementary classroom teacher. At the time of the study, she was in her first year of doctoral studies in mathematics education. Cynthia, a university faculty member, was also an experienced TE with seven years of mathematics classroom teacher experience. Feda, with two years of classroom teaching experience, was beginning her doctoral program at the time of this study. As we began the study Cynthia and Feda were critical dialogue partners for Janice and all three were members of the self-study teacher education collaborative that met monthly to research their teaching.

Our self-study collaborative brought us together to study our practice as mathematics teacher educators. There are multiple models of collaborative self-study groups. One model involves teacher educators researching their own practices and regularly coming together to share their insights, questions and knowledge. Bodone, Gudjónsdóttir, and Dalmau (2004) refer to this form of collaborative self-study as cross-disciplinary or multi-party collaboration. Another model could involve teacher educators coming together to understand a particular event, concept or idea, moving into their respective classroom contexts to explore that idea and then returning to the group to share their experiences of self-study. We see this form of collaborative self-study sharing some aspects of the teacher-researcher learning study model developed by Marton and Tsui (2004) where teachers come together to study their teaching in relation to their students' learning. A third model of collaborative self-study could involve a group of educators working together in the same classroom, collaborating on teaching and/or researching practice (e.g., Trumbull & Fluet, 2007). Typically this form of collaborative self-study has involved two people researching together: one as the teacher and the other as a critical friend (e.g., Loughran & Northfield, 1996). We refer to this form of collaboration as critical collaborative self-study to emphasize the inclusion of critical friends. Our collaborative self-study was of this third type and involved three educators (Janice, Cynthia and Feda), and once the course was completed, involved a group of interested preservice teachers.

As a collaborative we met regularly during the eight-week course. We met before the course began to articulate assumptions that guided our practices as teacher educators and in particular to provide a space for Janice to explore her understandings of her own practice. We met before and after each two-hour class and audio recorded all our conversations. We invited preservice teachers in the course to participate as co-researchers. All 30 preservice teachers in the course volunteered to participate. Preservice teachers were from a range of backgrounds that included Caucasian, South Asian Indo-Canadian, and Chinese-Canadian and 40% of the class was male. No preservice teacher had undergraduate mathematics majors or minors and most expressed concern about their mathematical content knowledge and/or their anxiety about teaching mathematics at the beginning of the course. University behavioral research ethical review required that we wait until the end of the course to invite students to collaborate in the project. Sarah (co-author of this paper) along with six other preservice teachers accepted the invitation and presented their experiences in the course at a local conference with Cynthia, Janice and Feda, while a further four students presented at a conference the following year. Sarah was one of the students who maintained her connection with the collaborative upon graduation of the program and into her first year of teaching.

Data include audio records before and following the class, researcher field notes, journal notes, digital video records of class activities, copies of students' course work and students' notes for their conference presentations. Janice kept journal notes of the class sessions and of the collaborative self-study meetings, recording her course planning ideas, summaries of class events, and critical or memorable incidents or tensions (Berry, 2007). Seven preservice teachers volunteered to be interviewed following their 12-week teaching practicum. These interviews were semi-structured and were video recorded. Interview questions focused on what preservice teachers experienced in the mathematics methods course and how this may have impacted their own practicum teaching. One student (Sarah) provided written reflections of her experiences following the course and into her first year as a beginning teacher.

All video was compressed to QuickTime movie format and copied, along with audio files, to CDs. The task of transcribing and analyzing audio and video data was initially shared by Janice, Cynthia and Feda and then later involved Sarah. All participating preservice teachers viewed transcripts of their interviews, and analyzed course experiences in preparation for their conference presentations. Janice, Cynthia and Feda each analyzed the preservice teachers' interviews first individually and then collectively for themes that would describe these teachers' experiences in the course. Meeting to discuss our individual interpretations we found a number of common categories that could describe preservice teachers' experiences, including a focus on classroom diversity, a felt lack of time, students' requests and need for resources, and students' general fear of teaching mathematics. Across these categories we noticed a common finding focused on the theme of how care and caring was important for preservice teachers in learning to be mathematics teachers, while the theme of problem solving and inquiry was important to the teacher educator, Janice. We then re-analyzed the teacher educator's and preservice teachers' interview data, again first individually and then collectively, for evidence of a focus on caring relations, on inquiry and on how these ideas may have carried forward to the practicum setting. Three themes were developed that included a focus on caring for ideas and for people during the course, and caring for students in the practicum. In this article we focus attention on the parallels of desire for care and inquiry by Janice and her preservice teachers and extend these to include the relation between the researchers of the collaborative.

Results

Although preservice teachers were not explicitly asked questions about how the instructor's care was manifested in the classroom, results from this study reveal that a pedagogy of care was at the heart of their interaction with the instructor. We begin with an excerpt from Janice's teaching journal:

The content focus of this class is on algebraic thinking. I'm trying to help students [preservice teachers] see the big ideas by looking at experiences students might have from kindergarten to grade 7 and see how they are the same/different. I show some video excerpts of grade 6 students playing “Guess My Rule” where a student provides clues for a function rule and the other students have to guess what the rule is. At the break, a student approaches me with tears in her eyes.

I don't get the math. I don't get how those kids got those answers.

I know this student has “math anxiety.” She has been clear with me about this and has discussed it in front of her peers. How difficult it must be for her to watch a video showing 11-year-olds doing math that she can't follow herself. What is really happening here? … I don't know her well enough to know what to do. (Janice, journal, January class #3)

What courage it took for this student to come up and say, “I don't get it.” How might we as teacher educators respond? We might wonder how we can respond in ways that are respectful and continue building trusting relationships. But how can we balance preservice teachers' need to understand mathematics and at the same time learn ways to engage their own students in learning mathematics? (Janice, journal, March class #18)

These excerpts highlight the pedagogical decisions, questions and reflections made by a mathematics teacher educator. The excerpts provide early and later evidence of Janice's attention to care developed through what Hackenberg (2005) calls stimulation and depletion. For the teacher educator there is attention to her students' feelings of depletion. Knowing that mathematics itself is an area of concern for preservice teachers, Janice structured activities and tasks that were designed to help her students feel more confident and comfortable.

Preservice teachers recognized this attention to the support they needed as an outstanding quality of the teacher educator. In interviews, journal writing, and anonymous course evaluations, preservice teachers spoke highly about how Janice fostered the change in their views of mathematics and how such change could be taught. The following preservice teacher's comments are representative of others when she states:

I can't say enough about what that class did for me in terms of confidence … Janice gave me some really good ideas. I had lots of anxiety with the math thing, because just how would I teach it? I felt very empowered coming into the practicum because I felt I had a foundation to work with. I'm still rough around the edges, but the information that I've learned throughout the course was very helpful. (Mela, preservice teacher, interview)

Preservice teachers recognized their need to feel more comfortable with mathematics and part of addressing that need for comfort came from having access to course materials that they could use in their classrooms. As another preservice teacher stated:

The confidence that I built about math was due to the fact that I had resources. I had something in my back pocket that I could pull out. These were tangible things that I could try in my classroom [and] that I know that an amazing teacher has already tried them. (Chris, preservice teacher, interview)

When asked to describe memorable aspects of their mathematics education course, all preservice teachers who were interviewed spoke about the level of comfort and tone that the teacher educator had established in the classroom. They mentioned the teacher educator's approachability and warmth. This preservice teacher's comments are typical of others:

Janice created a very low risk environment, a very safe environment …, especially with sharing our answers. If your answers were wrong – first of all I don't think she really mentioned that your answer was wrong, she just asked of different ways of doing it and we found together that oh ok this is the answer so – it wasn't like you were singled out on your own for getting the wrong answer. A lot of things were done in a group so you're able to figure things out in groups first before you actually share them [with others]. So … you worked it out together so you weren't on your own that way. (Sasha, preservice teacher, interview)

Preservice teachers reported that participation in small group and whole class activities provided opportunities for them to build relations with each other and with their instructor. They made frequent comments that although they were self-conscious and questioned their ability to teach mathematics well, they felt safe to share their ideas with the whole class. Their confidence to make ideas public was related to the opportunities they had to first share their thinking during small group work. These opportunities helped support the development of preservice teachers' self-reliance and determination to teach mathematics well. However, it was not only opportunities for small and whole class interactions but also the nature of these interactions that was deemed significant.

Analysis of interviews and written feedback indicates that the nature and kind of interactions preservice teachers had during the class with the TE were important to preservice teachers. Comments focused not only on the mathematical and pedagogical productions produced in the class but also on the personal. Preservice teachers were aware of their instructor's interest in them as individuals, their emotional engagement with the course content, and their feelings about math and teaching math. Yet students also spoke about the care they felt their instructor took to prepare for their class, give feedback on their work, and respond to their questions. As one student stated:

Janice was aware that I had a fear of math. She was aware that coming over and checking on me once in a while made me feel that I was in a safe environment. She values everyone in the class. (Nikka, preservice teacher, interview)

This focus on students is also depicted in the teacher educator's reflections that involve both “reading” and listening to her students:

Decisions needed to be made about how long or how deep to go with a mathematical content area, how to structure classroom experiences so that different students can experience the mathematics at varying levels, when to create opportunities for individual thought and for group discussions and when to take time to discuss the more general pragmatics of teaching and learning. I believe that by creating opportunities for the pre-service teachers to feel confident, they will transfer this to their own teaching. (Janice, journal, January class #8)

The preservice teachers noticed, with appreciation, the teacher educator's attention to their feelings of stimulation and depletion. They commented on her awareness and attentiveness to their fears and concerns yet at the same time she designed class activities that were stimulating, challenging, and motivating. Students acknowledged and responded to that care through their enthusiasm and engagement, their risk-taking to share ideas, and overall positive change in their attitude toward the teaching of mathematics. Such attention in turn fueled preservice teachers' confidence and learning energy.

However, what is interesting is that although many explicitly mentioned the caring and safe environment created in the mathematics methods class, few preservice teachers mentioned a focus on mathematical problem solving or inquiry. They spoke about resources, making math fun and hands-on activities and games, yet did not refer to this in light of teaching through inquiry. Interestingly, although Janice offered time for preservice teachers to solve problems, she taught more about mathematical problem solving than through problem solving. That is, there was more class time spent discussing how to teach problem solving than there was engaging in or modeling teaching through problem solving. Janice acknowledged that unlike her own practice as an elementary teacher, her instruction as a teacher educator was more sharing/telling than problem-based. In wondering why there was more focus on sharing practical activities than teaching through a stance of inquiry, she considered how limited course time constrained pursuing a pedagogy of inquiry. “The issue of time was a consistent refrain … providing little time for thoughtful reflection” (Janice, journal, March class #20).

Discussion and Conclusion

The results of our study indicate that the process of mathematical caring relations involves the interplay or dance of attention to students' stimulation and depletion. We extend Hackenberg's caring relational framework to include not only mathematical caring but also pedagogical caring. When a teacher educator invites preservice teachers to work on and share their ideas on a mathematical or pedagogical problem in a caring relation they may feel valued, listened to, and recognized by the teacher educator. The mathematical and pedagogical caring relation may energize and excite preservice teachers. Although the problem may be challenging and perhaps unsolvable at the moment, preservice teachers may experience feelings of curiosity, strength, and stimulation. In a caring relation teacher educators recognize the need for care in the interaction of their preservice teachers. Some preservice teachers may feel mathematically and pedagogically cared for with frequent challenges and stimulation; for others it may be quite different. On the other hand, if over time preservice teachers experience more depletion than stimulation, they may not feel cared for.

Most preservice teachers in the course experienced more stimulation than depletion. It is notable that most preservice teachers in the course reported that the course changed their images about mathematics and how it might be taught. Overall, they were extremely grateful for their experiences in the course. Our results indicate that preservice teachers described the course as a caring place and the teacher educator as key to creating such a place. Although the course influence on students, as they began their first year of teaching, was not an explicit focus of this study, we do know that for at least one student, Sarah, the impact was significant. Sarah reflects upon her first year of teaching:

Josh is a grade 6 boy who excels at math but becomes increasingly anxious, and even aggressive, when faced with a problem requiring him to answer in multiple ways. I wanted Josh to continue to feel confident in math; however, I also wanted him to realize that understanding how to solve a mathematical problem is just as important, if not more so, than rapidly recalling basic facts from rote memory. (Sarah, as a beginning teacher)

It is hard to believe that Sarah was once that preservice teacher in tears described by Janice (see excerpt from January journal, class #3). From Sarah's comments we can see that she is engaged in a pedagogy of care with her students and that she is also striving to support students' inquiry and problem solving over rote learning.

Overall, however, preservice teachers' focus on care over inquiry was a surprise for us. As a group we have sought to develop pedagogical tasks in the spirit of inquiry and have designed mathematics education courses that are problem-based with the hope that experiencing a pedagogy of inquiry will challenge preservice teachers' images of teaching and learning mathematics (see Nicol, 2006). Results indicate that preservice teachers can experience a significant shift in their level of anxiety about teaching mathematics with a focus on developing mathematically and pedagogically caring relations. What more is it necessary to include to support their stance of mathematical and pedagogical inquiry?

One approach could involve offering the same kind of attention to stimulation and depletion for our students as we do for each other as researchers involved in critical collaborative self-study research. As Janice wrote:

Participating in a self-study caused disequilibrium in how I felt about myself as a teacher educator. Although generally a relatively self-confident person, self-doubt and a need for approval from my collaborators kept creeping into my journal entries and reflections. Although positive feedback from my students was regular and consistent, I began to think that I should be doing even more for them and began doubting what had been deemed to be successful practices for many years of teaching and with over 800 previous students. (Janice, journal entry one year later)

Our Mathematics Teacher Educator Collaborative played a role in fostering an interplay between stimulation and depletion that is often experienced in self-study research (Berry, 2007; Nicol, 2006). However, this is a delicate dance. It can challenge us to rethink our roles, assumptions and practices. It can take a confident and experienced educator such as Janice and move her to self-doubt and immobility. Critical collaborative self-study, then, is even more risky than individual self-study research or other forms of collaborative self-study. It might require, as Wilcox (2009, p. 126) notes, a kind of communication that is open and honest that: “demands a capacity for reflexivity … [with] the potential for miscommunication and misinterpretation among those with different values and backgrounds.” It not only requires a different kind of communication but also a different way of being with each other in collaboration. Thus, the stimulation and depletion that students might experience can also be experienced by us as collaborative self-study researchers. This does not directly answer the question of how we as teacher educators might move students toward a pedagogy of inquiry as well as a pedagogy of care within our courses. Nonetheless it does provide a strategy for beginning with ourselves to better understand the challenges and experiences of balancing care and inquiry toward living a kind of inquiry-oriented caring within our own practice. What is the relationship between care and inquiry for ourselves? Care needs to be offered, a relationship established, reciprocity acknowledged in order for transformative self-study research to occur. Taking the role of critical friend requires acknowledging times of stimulation and depletion. It also involves what Hackenberg (2005) conceptualizes as harmonizing and decentering. A critical friend might be in harmony with the teacher-researcher in ways that indicate willingness and attentiveness to the teacher's mathematical and pedagogical realities. By decentering and putting aside our own motivations, mathematical understandings and pedagogical values, the critical friend gives primacy to the teacher's ways of knowing and seeing. Just as a teacher may strive for harmony and decentering with her own students, so too can those working in a critical collaborative self-study context. However, this is not a straightforward linear task. As Cynthia learned, it was not easy to understand the teacher educator's (Janice's) ways of enacting her practice, where although teaching through inquiry was a goal of the course, it was not enacted to the same extent as the goal of developing caring relationships. This was a surprise to Cynthia and, as the critical friend, she struggled to find the appropriate questions to ask Janice about her teaching – questions that both acknowledged but also challenged what she saw in the classroom. Being a critical friend requires posing new challenges and problems to extend our understandings of practice in ways not previously imagined. It means being aware of and in tune to the flow of stimulation and depletion of ourselves as teachers. And it involves decentering ourselves by truly being with our collaborators rather than imposing ways in which we think things should be done. Participating in critical collaborative self-study is a way of being with each other's pedagogical worlds.

The depletion that Janice writes about stimulated her interest in more explicitly focusing on both care and inquiry in her practice. Janice is now restructuring her course assignments to be inquiry-based and is sharing these changes with the Collaborative. Cynthia continues to experiment with developing an open way of being that allows for difficult questions to be posed and explored. However, we wonder if perhaps there is no tension in creating both caring and inquiring environments. Perhaps, instead, we need to first create caring relationships so that preservice teachers are open to considering inquiry. Similarly, in critical collaborative self-study perhaps we need to create caring relationships within the collaborative before we can engage in transformative self-study. A mathematics teacher education course permeated with care and peppered with inquiry has the potential to build preservice teachers' confidence and empowerment as the course develops. This in turn may help our preservice teachers, such as Sarah, come to understand, through multiple experiences and layers, the possibilities for learning, teaching and inquiry. It may also help us, as collaborative self-study researchers, to live a practice that includes striving for harmony and decentering while attending to the flow of stimulation and depletion. This is compassionate and critical, caring and inquiry-based collaborative self-study, where we care for ourselves as well as each other.