Professional Development1
Running Head: PROFESSIONAL DEVELOPMENT
Relating professional development to the classroom
Elham Kazemi
Anita Lenges
University of Washington
Correspondence to:
Elham Kazemi
Assistant Professor, Mathematics Education
University of Washington
122 Miller
Box 353600
Seattle, WA 98195-3600
Office: (206)221-4793
Fax: (206)543-1237
Anita Lenges
Doctoral Student, Mathematics Education
University of Washington
Abstract
Much professional education with elementary teachers is designed to support them to recognize the mathematical ideas inherent in students’ work and use the diversity of mathematical thinking in the classroom to advance students’ understanding and reasoning. In this study, we present classroom episodes that characterize the diversity of instruction we observed in the classrooms of six teachers who had participated in a substantial amount of professional learning focused on understanding children’s mathematical thinking. We explain the diversity in classroom practice theoretically by viewing the professional development seminars and the classroom as forming distinct communities with their own norms, practices, and tools. Teachers may become full participants in a professional development community in which they have a high degree of support to puzzle over and deliberate students’ mathematical thinking. Yet the classroom, responding to both external and internal goals, with its own practices and tools, may offer different resources for learning and being. What teachers do in any given day in their classroom is a result of heeding many—sometimes contrasting or competing—images of what it means to teach mathematics. The episodes we present in this paper raise a number of questions about characterizing the coherence of instruction and understanding the complex relationship between professional development experiences and classroom practice.
Key Words: professional development, classroom instruction, using children’s thinking in the classroom, instructional coherence
Relating Professional Development in Mathematics to the Classroom
Much of mathematics professional education with elementary school teachers focuses on examining children’s mathematical reasoning (e.g., Carpenter et al., 1996; Saxe et al., 2001; Schifter et al., 1999; Stein et al., 2000). This emphasis is designed to help teachers recognize the mathematical ideas inherent in students’ work and use the diversity of mathematical thinking in the classroom to advance students’ understanding and reasoning (Driscoll, 1999; Fennema et al., 1998; Lampert & Ball, 1998; Stein et al., 2000). A focus on children’s thinking can also deepen teachers’ understanding of mathematics (Ball & Cohen, 1999; Schifter, 1998). Even when teachers find their experiences in such professional development to be transformative, they may not consistently engage in practices in their own classrooms that elicit and build children’s reasoning. To explore the questions raised by this issue, we describe the variations in instruction we saw in the classrooms of six teachers who had participated in 120 hours1 of professional education focused on understanding children’s thinking. The diversity in lessons suggests that students and teachers have varied experiences with what it means to learn and know mathematics. These findings underscore the need to understand the complex relationship between professional development experiences and classroom practice.
Literature on Professional Development
Current curricular goals for teaching mathematics are commonly viewed as ambitious—enacting them in classrooms is anything but simple. In the research literature there are at least three different kinds of studies that have examined the connection between professional development and classroom practice. Each of these bodies of literature rests on the assumption that professional development experiences enable teachers to develop new skills, knowledge, and dispositions, which can lead to instructional change. We review these literatures briefly in order to frame our approach to understanding the relationship between professional development on classroom practice.
One set of studies focuses on describing the change individual teachers undergo over time as they learn to understand children’s reasoning processes (Fennema et al., 1993; Fennema et al., 1996; Heaton & Lampert, 1993; Lampert, 1984; Schifter, 1998; Wood et al., 1991). Changes in teacher beliefs and knowledge accompanied by changes in teaching practice are central to these studies. This body of work has shown that teachers’ beliefs about the role of a teacher shifted from one who demonstrates procedures to one who actively supports children to build mathematical knowledge through engagement in mathematical argumentation and problem solving (Ball & Bass, 2000). More recently, studies of individual teacher change have addressed the situated nature of teachers’ learning trajectories by emphasizing how the development of new knowledge and skills is necessarily linked to the nature of teachers’ participation in professional development and to their evolving intellectual and professional identities (e.g. Franke et al., 2001; Franke & Kazemi, 2001; Hammer & Schifter, 2001; Rosebery & Puttick, 1998). Importantly, these studies have primarily focused on the nature of individual change and have not addressed the institutional or sociopolitical forces that impact teachers’ instruction.
A second set of studies, in contrast, has been concerned with the relationship between policy and practice, documenting how policy environments influence teacher practice. Such policy initiatives are often accompanied with professional training linked to new curriculum adoptions. Such research has emphasized how teachers’ own conceptions and interpretations of the goals embodied in new policies or standards documents impact their classroom practice (Ball, 1990; Cohen, 1990; Grant et al., 1996; Heaton, 1993; Spillane, 2000; Spillane & Zeuli, 1999). This work has helped us understand that the connection between new policies and classroom instruction is not seamless. Teachers filter and adapt their professional development experiences through their own experiences. The tenor of much of this work has been that teachers have different visions of what the discourse about mathematics reforms mean in their classrooms, and these visions may not coincide with the intents of policymakers and standards documents. Researchers have argued that this misalignment is not surprising given that teachers are being asked to create forms of instruction that they themselves did not experience as students (Little, 1989; Little, 1993). McLaughlin (1990) has described this as a process of mutual adaptation—policy may change teachers’ practices, but teachers, through the ways they enact policy, in fact change policy.
A third set of studies has focused on evaluating the merits of particular forms of professional development in mathematics on teacher learning from intensive institutes focused on content to Lesson Study and study groups (e.g., Crockett, 2002; Lewis,2000; Saxe et al., 2001; Simon & Schifter, 1991; Simon & Schifter, 1993). From these studies, we have learned that professional development efforts that have a clear focus, are ongoing and more closely tied to teachers’ own classrooms have a stronger impact on classroom practices than either one-shot workshops or collegial meetings where teachers share new ideas but do not necessarily work towards achieving a particular goal (Cohen & Hill, 1998; Garet et al., 2001). Recent studies have also begun to explore what teachers gain from professional development that is centered on the study of artifacts of practices, such as written or video cases and student work. (e.g., Barnett, 1998; Franke & Kazemi, 2001; Sherin, 2002; Smith et al., 2001)
Our study contributes to these bodies of work because it too is concerned with the relationship between teachers’ professional development experiences and their classroom practices. We aim to contribute to understanding the relationship between professional development and classroom life as issues of understanding connections between two distinct communities of practices (cf., Wenger, 1998). Viewed in this way, the problem of assessing the impact of professional development on classroom practice means not only attending to teachers’ knowledge, skills, and beliefs but also to the varying values, tools, practices, and sociopolitical goals of each community.
This Study
Developing Mathematical Ideas(DMI, Schifter et al., 1999) is an example of professional development curricula that heeds many of the current calls to engage teachers in long-term experiences that develop their knowledge of children’s mathematics by situating discussions in real episodes of classroom instruction. In each of five published seminars, teachers discuss written and video cases, engage in doing mathematics together, and have opportunities to explore student reasoning in their own classrooms. Each seminar focuses on a different mathematical domain: place value, operations, measurement, geometry, and statistics.
Participation in DMI encourages teachers to discuss many vivid examples of classroom discourse that productively elicit student thinking. The seminar materials are meant to achieve several goals with teachers, including (a) developing teachers’ mathematical knowledge, (b) supporting teachers to make sense of children’s thinking and connect those understandings to instructional goals, and (c) encouraging teachers to engage their own students in discussions so that they can analyze and support their mathematical ideas. In this study, we asked how teachers who had experience with DMI and summer content institutes enacted principles of eliciting and building on children’s thinking in their own classrooms. We collected classroom data from six teacher leaders who spoke positively and confidently about their participation in DMI to see how they interacted with students and facilitated mathematics lessons.
We characterize all of the study participants as skilled teachers who have learned how to help children articulate, deliberate, and extend their mathematical understandings. We have evidence of each teacher’s ability to interact with children in those ways. And we also found that the teachers did not always facilitate lessons in which they actively attempted to elicit and build on children’s thinking. The mathematics instruction tended to vary within classrooms. We will present five vignettes to represent these varied enactments in the classrooms that we visited and explain from the teachers’ perspective why they were engaging in those particular forms of instruction. The lessons varied in the cognitive demand of the mathematical tasks (Stein, Grover, & Henningsen, 1996) and the nature of the mathematical discourse.
We interpret the findings of our study in light of the settings in which these teachers work. We have evidence that the teachers in this study have learned about children’s reasoning because of their experiences in DMI. In fact, as mathematics leaders in their district, the teachers in this study committed much of their time to learn how to help other teachers learn about students’ reasoning. We view DMI as a tool that has helped teachers learn about student thinking and raise questions about classroom practice. We interpret teachers’ choices about how to teach and what to teach, during the lessons we observed, not just a matter of their own personal preferences or a direct result of their experiences in professional development. Put simply, we do not view the variation within classrooms as a classic issue of “transfer.” Rather, we recognize that these teachers work in a particular historical moment in a particular place. State and district policies, curricular resources, and the particular school and district cultures in which they work interact with their own personal commitments to create varied forms of teaching mathematics.
Theoretically, we understand these experiences by viewing the contexts in which teachers work as forming distinct communities of practice with their own norms, practices, and tools. Teachers may become full participants in a professional development community in which they have a high degree of support to puzzle over and deliberate students’ mathematical thinking (cf., Wenger, 1998). But what does it mean for teachers to draw on that participation in their classrooms in which the resources for learning and being, in terms of practices and tools, are not always the same? We argue that what teachers do in their classrooms is a result of heeding many—sometimes competing—voices of what it means to teach mathematics. The vignettes we present in this paper raise a number of questions for us about characterizing the coherence of instruction as well as both students’ and teachers’ experiences during mathematics lessons. Further, we suggest implications for the way we design continued professional development if our goal is to produce coherent mathematical experiences in classrooms where teachers work to advance children’s thinking.
Method
Participants and Data Collection
The participants in this study included six teachers who were among the first tier of “volunteers” in a multi-district five-year project aimed at enhancing teachers’ professional development in mathematics and developing leadership capacity within each district. The teachers in this study taught in different schools in the same district that had adopted Everyday Mathematics (EM; Bell et al., 1999) several years prior to the study. As a central part of the leadership project, teachers first participated in DMI seminars and were later given opportunities to develop the knowledge and skills needed to facilitate seminars for other teachers. At the time of the study, the six teachers had participated in two number sense modules (Building a System of Tens, Making Meaning for Operations) and were participating in their third module, Statistics: Working with Data. They had also attended two week-long summer institutes designed to extend their experiences with the content of the number sense modules and their skills in facilitating them. All of the teachers in this study reported their experiences in DMI to be both positive and powerful, characterizing DMI as some of the best professional development they had experienced in their careers. At the time of the study, their teaching experience ranged from 5 to 27 years. One teacher taught first grade, the other teachers taught third or fourth grade.
During the 2000-2001 academic year, four classrooms were observed by a member of the research team at least three times, but scheduling problems allowed only two visits to the two remaining classrooms. The researcher stayed for the entire duration of the mathematics lesson, which typically ranged from 60 to 90 minutes. During each visit, the researcher took detailed fieldnotes of classroom instruction and collected artifacts from the lesson. After each observation, the researcher reviewed the fieldnotes, filling in any additional details not captured in the moment of observation. During whole group discussions, the researcher scripted the talk as closely as possible, reproducing any representations drawn on the board or overhead. During small group or independent work time, the researcher noted the teacher’s movement and interactions with students around the room. When students worked independently, the researcher also talked to individual students about their problem solving efforts on the assigned task. At the end of the year, each teacher was interviewed about her experience in the professional development and leadership project (see interview protocol in appendix). The authors of this article also interacted regularly with the participating teachers during DMI seminars and other activities related to the larger leadership project.
Data Analysis
Fieldnotes and transcribed interviews were entered into a qualitative data analysis software package for easy retrieval and coding. We reviewed the fieldnotes for each observation several times. We discussed the nature of classroom lessons for each teacher. For each lesson, we noted the nature of the task, the role of the teacher in eliciting student thinking, the mathematical goal for the lesson, and the nature of discourse during the lesson. When teachers used the EM curriculum, we compared the way the lesson was enacted to the directions in the teacher’s manual for the lesson, noting deviations from the instructional guidelines. In the process of our analyses of each lesson, we found that we could characterize lessons into three macro categories: (a) Lessons that focused on the teacher presenting students with a particular approach to solving a problem that could then be practiced by all; (b) Lessons that focused on eliciting student reasoning and facilitating discussions so that students could compare their approaches; and (c) Lessons that involved an indirect method (i.e., computer programs) for students to practice particular mathematics skills. We noticed that while we made few visits to the classrooms, we saw evidence of these various types of lessons across the teachers. We made a matrix to look at which of these kinds of lessons we observed for which teachers. We further noted that the type of lesson was linked to the use of particular materials. Lessons that focused on presenting students with a particular approach were drawn rather faithfully from a set of problem-solving steps (see Figure 1) used widely in the district or from the EM curriculum. Lessons that elicited and focused on student reasoning either stemmed from tasks teachers were posing as “homework” for a DMI seminar or modifications to the EM curriculum or another curricular resource. The third kind of lesson was linked to the use of a computer program called Accelerated Mathematics in which students practice skill and fact-based multiple choice problems (see Table 1). In the findings below, we will present vignettes of each kind of lesson, showing variations we saw across teachers and provide our analytic commentary to describe differences in the nature of the task and the classroom discourse that each kind of lesson generated.
Findings
Based on our analysis of the classroom data, characterizing each teacher’s instruction globally became a difficult task. We found instead that mathematics instruction differed according to how the teachers used particular materials to frame the task. We draw on our fieldnotes and interviews with teachers to characterize these different lessons. The findings are organized around five main vignettes; together they represent the range of kinds of lessons we observed in teachers’ classrooms (refer to Table 2 to see in which teachers’ classrooms each type of lesson was observed).