The Effects of Coaching
On One Teacher’s Classroom Discourse
Lawrence Linnen
University of Colorado at Denver
Douglas County School District
Colorado, USA
Paper presented at the British Educational Research Association Annual Conference, Institute of Education, University of London, 5-8 September 2007
The discourse in most United States classrooms has long been little more than a speech on topics by teachers and one-sided at that. Student to student discourse has long been minimal. This study examined effects of my coaching on the teacher’s communication with her students. The specific research question addressed in this study was, “How does instructional coaching influence the teacher being coached, her students, and the coach?” The theoretical framework for this study used activity-reflective cycles, which included analyses of classroom interactions followed by adapting learning trajectories, creating new learning activities, and observing the interactions between students, the teacher, and the coach. Although student presentations were initially procedural in nature, their discourse changed over time. Presentations that had initially been characterized by merely the reading of the written procedural steps now took the form of questioning and wondering about the procedures and mathematics. The study results, analyzed through a multi-level framework, found that the teacher used traditional materials in innovative ways by promoting classroom discourse and modeling a classroom based on mathematical inquiry.
My experiences as a classroom teacher, a university professor, an educational consultant, and a district-level mathematics coordinator, spread over thirty-seven years, have provided me with opportunities to view mathematics instruction from several perspectives. I have viewed my own teaching of mathematics, the teaching of others, and how these endeavors fit into the systems determined by schools and the districts in which they reside. As part of a collaborative project between a university and a middle school, I was invited into one teacher’s classroom to act as a coach to help the teacher improve her teaching.
Many of us have strong beliefs about how school mathematics should look and how it should be taught (Aichele & Coxford, 1994; Andrews & Hatch, 1999; Archer, 1999; Bauch, 1984; Nathan & Koedinger, 2000; Stigler & Hiebert, 1999; Varrella & Burry-Stock, 1996; Weissglass, 1994). Many mathematics teachers, parents, and administrators hold the belief that school mathematics should be taught just like it was taught for them and that not everyone needs the same mathematics to be successful (Gage, 1963; Noddings, 1994). After all, it worked for them. Why shouldn’t it work now for their children? This belief suggests that the primary purpose of schools is to provide students with knowledge, in other words fill their heads with knowledge. Others feel this traditional approach does not provide opportunities for students to grow as thinkers and learners (Brooks & Brooks, 1993; Cangelosi 2003; Stigler & Hiebert, 1999). Ritchhart (2002) summarized his thoughts clearly when he stated,
Rather than working to change who students are as thinkers and learners, schools for the most part work merely to fill them up with knowledge. Although some may see intelligence as a natural by-product of schooling, in reality the curriculum, instruction, and structure of schools do little to promote intelligence and may even impede it in some cases. (p. 7)
Clearly, teachers’ instruction is strongly influenced by their beliefs in how school, and particularly school mathematics, should look, and it often looks quite similar to instruction the teachers got when they were students (Stigler & Hiebert, 1999). Freire (2003) claimed the teachers doing the telling and the students listening fundamentally characterized the teacher-student relationship, either in or out of school. Freire (2003) warned of the risk of such instruction, saying, “Narration (with the teacher as narrator) leads the students to memorize mechanically the narrated content” (pp. 71-72). Simon, Tzur, Heinz, Kinzel, and Smith (2000) questioned,
What pedagogical approaches are teachers of mathematics developing to meet the challenges posed by current mathematics education reforms, particularly the challenges of adapting their teaching to perceived mandates to reduce the role of teachers’ showing and telling? What are the perspectives (meaning-making systems) that underlie such adaptations of teaching practice? An understanding of the perspectives teachers hold while they struggle to participate effectively in reforming mathematics teaching can contribute to mathematics educators’ efforts to work more effectively with teachers in transition. (p. 579)
It should come as no surprise that recent research (Schmidt & Kennedy, 1990) has also suggested that teachers' beliefs about subject matter influence what they choose to teach and how they choose to teach it. Cooney, Shealy, and Arvold (1998) suggested that understanding the structure of teachers’ beliefs, as systems of beliefs, would provide a “certain dimensionality to what people believe” (p. 331). Teachers likely did not need research to tell them that their beliefs would influence the scope and structure of their instruction or that understanding these beliefs would likely lead to improved instruction. Nonetheless, research has revealed much about what teachers believe and conceive about mathematics and its instruction. For instance, Archer (2000) found that primary teachers tended to see mathematics as linked to students' everyday lives, while secondary teachers tend to see mathematics as self-contained, and their role is to guide students through its structure. Raymond (1997) suggested that although her study suggested, “beliefs about the nature of mathematics were more strongly linked to actual teacher practice than were pedagogical beliefs, there was not sufficient evidence to confirm or refute this assertion” (p. 573). However, Raymond (1997), in her discussion about a particular teacher said, “Thus, her traditional practices were more heavily influenced by her deeply held beliefs about mathematics content than her surface beliefs about mathematics teaching and learning” (p. 573).
As mathematics teachers seek to improve their instructional practices, they naturally choose or discard ideas based upon what they believe is best for their students. These beliefs may or may not be consistent with their students’ beliefs about mathematics and its instruction, e.g., a teacher’s belief may be that mathematics is largely the study of patterns, but his or her students may believe mathematics is largely a set of rules to master. In light of my background as a classroom teacher, coach of teachers, and district mathematics coordinator, this study offered a rich source of insights into the system comprising teacher, students, coach, and school culture.
Theoretical Orientation
The theoretical framework for this study was based on activity-reflective cycles as used by Tzur and Simon (1999), and by Olson and Barrett (2004), described below and depicted in Figure 1:
In an activity-reflective cycle, the professional developer (a) assesses the teacher’s current knowledge, (b) describes a conceptual advance, (c) creates a learning trajectory, (d) selects activities, and (e) supports the teacher’s reflection. Key to advancing teacher’s learning is their reflection on the activity or activities that cause perturbation (Olson & Barrett, 2004, pp. 2-3)
Observations of class lessons were followed by debriefing that included analyses of the lessons and suggestions for learning trajectories, or strategies for curricular or pedagogical adjustments, for subsequent lessons. Future activities were selected based on the teacher’s reflections and the coach’s recommendations. The cycle was repeated for each observed lesson and data were collected on evidence of change,
Figure 1: Activity Reflective Cycle
The activity-reflective cycles included analyses followed by adapting the learning trajectory theory, creating new learning activities, and observing the interactions between students and teachers (Olson & Barrett, 2004). In this study, the teacher, her students, and the coach gradually evolved into a learning community (Lave & Wenger, 1991), and the observations revealed changes in the classroom discussions of mathematical ideas. This report focuses on those changes.
Method
The teacher, Jane, a pseudonym, and I identified the improvement of student engagement in learning mathematics as an overarching goal for her classroom. This issue of student engagement presented an opportunity for me to use activity reflective cycles to examine and reflect upon specific teaching and learning by Jane, her students, and myself, the coach. I chose to conduct a multi-level action research study of this teacher. Audio and video recordings of class sessions and discussions between the teacher and myself were transcribed and analyzed from a systems perspective, (e.g., Jenlink (1995) and Clarke (2003b)), by examining patterns of activity through various lenses. Clarke (2003) stated, “Because the problems we are interested in are complex and manifest themselves in many contexts, we believe it is necessary to work simultaneously at different levels of scale; hence the addition of the phrase ‘multi-level’” (p. 4).
Clarke (2001) confirmed that a systems approach necessarily involved levels of scale that needed consideration. He asserted, “Teaching results in change, not only in individuals, but also in organizations and, ultimately, in society” (Clarke, 2001, p.12). Thus it makes sense to pay attention to the components of a system that are directly and indirectly affected by change. Clarke (2003a) warned us though that, “Things are the way they are because living systems tend to function toward stability; they resist change” (p. 11). Bateson (2000) pointed out that, “Epistemological error is often reinforced and therefore self-validating. You can get along all right in spite of the fact that you entertain at rather deep levels of the mind premises which are simply false” (p. 488). For example, many schools, instead of improving teaching (Stigler & Hiebert, 1999), typically try to fix underachievement by implementing a new curriculum, buying software purported to improve student achievement, or changing graduation requirements to include more academic credits, and so putting increased pressure on students, parents, and communities. All of these perceived fixes for underachievement allow teachers to perpetuate their ingrained beliefs without considering change.
Clarke (2003b) stated, “Action research is an approach to inquiry that provides a theoretical umbrella and an action agenda for community and organizational development and individual change” (p. 5). All of these definitions and clarifications of action research point to the need for a systemic and collaborative approach for conducting studies of human beings. But essential to the present study is the examination not only of the interactions between the teacher and her students, but also of the emerging changes in my own knowledge and understanding of my practice. Argyris, Putnam and Smith (1985) argued,
To put it most succinctly, action scientists engage with participants in a collaborative process of critical inquiry into problems of social practice in a learning context. The core feature of this context is that it is expressly designed to foster learning about one's practice and about alternative ways of constructing it. (p. 237)
My role as participant and researcher in the present study thus became an important factor in addressing the issues of interactions, because these interactions impacted the teacher’s thinking and behaviors, her students’ learning, and my work as a district leader dealing with the complexities of adult learning. Schön (1983) emphasized,
The inquirer's relation to this situation is transactional. He shapes the situation, but in conversation with it, so that his own models and appreciations are also shaped by the situation. The phenomena that he seeks to understand are partly of his own making; he is in the situation that he seeks to understand. (pp. 150-151)
The teacher and I engaged in examination of both her practice and mine. Action research thus surfaced as a logical and valid approach for such an examination.
Participants
This investigation was conducted at Makefield Middle School. Negotiating entry to this site was enhanced by several factors. A partnership between my university and Makefield had existed for over two years. In fact two of my university advisors were already working with Jane and the technology teacher at Makefield. These two professors were also in the second year of a three-year grant investigating ways to improve the academic engagement of African American and Latino students.
Data Collection and Analysis
Study participants included one teacher and two classes of her students. One class agreed to be videotaped and the other class agreed only to be taped only by audio means, because three students declined to be taped at all. These three students agreed, however, to participate in the study. Norms for all participants were identified for behavior, participation, sharing information, talking to others about study events, and withdrawal from participation. Expectations for these norms included preserving confidentiality and safety as primary goals. Data were recorded from 3/31/03 to 5/22/03 using observations of classroom events and interviews with Jane, field notes, audiotapes, and videotapes. Data were not collected from the three students who declined to be taped, and, in fact, one of the three was never present in class when I observed. In situations where the other two students were speaking, the tape recorder was turned off. This was significant, because otherwise the study would not have been possible. Observations were focused on what students and teachers said, and how they responded to comments or observations of others. Interviews included questions about the observations that emerged from the observations.
Demographics
Makefield is a Rocky Mountain region urban public middle school for students in grades six through eight. Most students at the school are African American or Hispanic. Most of the homes in the neighborhood were built in the early twentieth century. The houses are being remodeled and wealthier residents are solicited and encouraged to move into the neighborhood. Almost 75% of the neighborhood students qualify for free or reduced school lunches. The majority of Makefield’s students were from low-income families, as evidenced by the fact that in fall 2002, 76% of the total number of students qualified for free or reduced school lunches during the 2002-2003 school year. There were 493 students who were enrolled at Makefield Middle School in 2002-2003, and the average daily attendance was 462. During the school year there were six incidents of substance abuse involving drugs, two incidences of substance abuse involving tobacco, no incidences of substance abuse involving alcohol, and 209 other minor violations of Code of Conduct. Student dropouts, calculated for the 2002-2003 school year, were at 1.5%. I cite these data to provide a small snapshot of the milieu that many Makefield students brought to the classroom.
Results and Analyses
Presentations by students and much of Jane’s dialogue were initially characterized by merely the reading of the written procedural steps of solving equations or problems. Early in the study, in one observation of the algebra class, Louise, an algebra student, demonstrated her views of mathematics that I interpreted as symbolic-procedural: