Classroom Practice & PD1
Running Head: Classroom Practice & PD
The Interaction Between Classroom Practice & Professional Development
Elham Kazemi
University of Washington
122 Miller Box 353600
Seattle, WA98195-3600
Paper presented at the annual meeting of the American Education Research Association, (AERA), San Diego, CA, 2004
Abstract
A key component of professional development focused on student reasoning is teachers’ own reports of their efforts to elicit and build on children’s thinking in their own classroom. This paper focuses on the relationship between teachers’ engagement in professional development and their work in their own classrooms. The goal is to understand how teachers engage with new ideas about student reasoning during and after their professional development experiences and how their participation in the professional development and in their classrooms mutually influence each other.
The Interaction Between Classroom Practice and Professional Development
A key component of professional development focused on student reasoning is teachers’ own reports of their efforts to elicit and build on children’s thinking in their own classroom. This paper focuses on the relationship between teachers’ engagement in professional development (PD) and their work in their own classrooms. The goal is to understand how teachers engage with new ideas about student reasoning during and after theirPD experiences and how their participation in PD and in their classrooms mutually influence each other.
Theoretically, I draw on Rogoff’s (1997) notion of learning as transforming participation. I examine how different forms of participation across the PD and classroom setting account for different learning trajectories among teachers. I draw on my experiences with two professional development projects for elementary mathematics teachers to raise conceptual and design issues about the ways teachers draw on their experiences in the classroom as they engage in professional development.
Background
At the same time that researchers have been experimenting with designs for professional development, there has been an increasing demand for documenting what teachers gain from professional development (e.g., Wilson & Berne, 1999). Evidence of learning has often been conceptualized as assessing teachers’ implementation of new ideas into their classroom. One way of determiningimplementation is to design measures that show evidence of growth in knowledge after a PD experience is finished. This view typically defines implementation as something that happens after an experience. In this paper,I argue that analyzing the relationship between teachers’PD experience and their classroom participation is significant to understanding teacher learning. Since it is highly unlikely and unfavorable for teachers to end a PD experience with their learning complete, I contend that one way of examining how PD is influencing teacher learning is to go back and forth between the professional development setting and the classroom, to see how teachers’ participation in the classroom and PD communities are changing. This would indicate how teachers are developing knowledge, skills, and new ways of defining their work as teachers.
What I propose is that part of the design of PD experience is to be aware of and capitalize on how teachers are engaging in their classrooms. So rather than think of it as implementation issue, I suggest that professional educators think more about how teachers’ classroom work can enter into professional development. In the data I will present in this paper, I studied how teachers’classroom practice interacted with their PD experiences. In one case, I describe the different learning trajectories or forms of participations that teachers engaged in and use this evidence to evaluate what teachers gained from the PD design.In the second case, I draw on data gathered from classroom visits to teachers’ classrooms who had been participating in several years of professional development, which included as a main component participation in Developing Mathematical Ideas (DMI; Schifter, Bastable, Russell, 1999). I use illustrative cases from the data to raise questions about how classroom practice could be used in ongoing PD.
Theoretical Framework
Understanding learning, as it emerges in activity, guides the analytic framework for this paper(Greeno & Middle School Mathematics Through Applications Project, 1998). This situated perspective centers on how people engage in routine activity and the role that tools and participation structures, for example, play in the practices that evolve (Wertsch, 1998). I apply a transformation of participationview, as described by Rogoff (1997), Lave (1996) and Wenger (1998), to account for individual participation.
Rogoff (1997) explains a transformation of participation view of learning by contrasting it with two other models of learning: acquisition and transmission. Both models assume a boundary between the world and individual; the former posits that individuals receive information transmitted from their environment while the latter posits that the environment inserts information into the individual. The transformation of participation view takes neither the environment nor the individual as the unit of analysis. Instead, it holds activity as the primary unit of analysis and accounts for individual development by examining how individuals engage in interpersonal and cultural-historical activities. Rogoff (1997) provides the following explication:
…a person develops through participation in an activity, changing to be involved in the situation at hand in ways that contribute both to the ongoing event and to the person’s preparation for involvement in other similar events. Instead of studying a person’s possession or acquisition of a capacity or a bit of knowledge, the focus is on people’s active changes in understanding, facility, and motivation involved in an unfolding event or activity in which they participate (p. 271).
The shifts in participation do not merely mark changes in activity or behavior. Shifts in participation involve a transformation of roles and the crafting of new identities, identities that are linked to new knowledge and skill (Wenger, 1998). Lave (1996) states, “…crafting identities is a social process, and becoming more knowledgeably skilled is an aspect of participation in social practice, who you are becoming shapes crucially and fundamentally what you know” (p. 157).
Viewing learning as changing participation has several implications that relate both to the study of and design of professional development. Central to a transformation of participation perspective is that shifts in participation are in service of new roles and identities. If we want the work of teaching to involve collective inquiry and the development of a shared professional knowledge base (Hiebert, Gallimore, & Stigler, 2002), then attention to changing participation becomes important because of the kinds of practices that teachers will pursue with one another and with their students as their engagement in their work lives change.
Teachers’ Changing Participation:
The Relation Between Professional Development and the Classroom
In this section, I draw on my work with teachers in two professional programs to advance my argument about the need to examine how teachers’ classroom practices relate to their engagement in professional development.
Case One: Studying Student Work to Support Teacher Learning
The first examples come from a study of teachers using their own students’ work to learn about children’s thinking in number and operations based on a CGI model of professional development (Franke & Kazemi, 2001; Franke et al., in press; Kazemi & Franke, in press). In this case, teachers from one school met in monthly workgroups to analyze the student work. Each teacher had posed a similar problem to their students, and during meetings they compared and analyzed the student work those problems generated. Table 1 lists the problems that teachers were asked to try with their students. Over the course of several years, teachers in this school developed detailed understandings about the development of students’ computational fluency and collaborated to develop classroom practices and instructional goals to advance their students’ achievement (see Franke et al., in press). In my analysis of the professional development, I gathered data about how teachers engaged in the workgroups, how they adapted and experimented with workgroup problems, and how they engaged with their own students in the classroom. What emerged from this analysis weredifferent patterns of participation between the classroom and workgroup setting that enabled me as a researcher and professional educator to understand what teachers gained from the professional development. I focus here on the experiences of two teachers in particular.
Juan.
Use of workgroup problems
Juan faithfully posed the workgroup problemsto his first and second graders and brought student work to the meeting. In fact, Juan posed each workgroup problem multiple times and had typically tried the problem with numerous changes in number size before he came to the workgroup and continued to work with that problem type after the workgroup. Notably, he did not comment on why he was making those adaptationsin his written or participatory comments during workgroup discussions.
Workgroup participation
Juan typically shared at least one strategy during each workgroup he attended. Because of his use of the workgroup problem in his classroom, he was the first to share an important revelation with his colleagues. He noticed that when he showed his students a particular strategy, many were likely to use it. If he just posed the problem, he observed a much wider range of strategies in his students’ work. Juan wanted to make math more understandable. He wrote in January, “Our math program consists entirely of math word problems where they have to describe what strategy they used.” In May, he wrote, “We started studying base ten because I believe they (most) don’t have the ability to manipulate tens and ones.” He cared that his students learned. He was learning, through his participation in the workgroup that children’s understanding of the tens structure of numbers is important to their number and operation sense.
Classroom participation
At the beginning of the year, Juan, was already engaged in what he called the “problem solving” approach to mathematics. He established a routine for his math time. First, students solved a number sentence and wrote a story problem to accompany it. Then they worked in their math workbooks for 10 or 15 minutes choosing whichever pages they wanted to work on. Then Juan led a problem-solving oriented lesson. For example, one lesson involved students tallying data they had gathered at home. Juan wanted his students to be actively engaged during math time, often providing them with such opportunities for “hands-on math.” But Juan also participated in teaching math in ways that contradicted his hopes to develop student understanding. He focused only on addition during the first three months of school and was planning to then move to subtraction for the second trimester and finally onto measurement, geometry, and money, following a traditional curricular sequence. When he wrote computational problems on the board, he often chose numbers well into the hundreds, which was unusual for first and second grade in his school. Yet, he purposefully selected numbers that did not require regroupinjg. He often wrote the addition problems vertically, drawing a vertical line to separate the tens and the ones. He taught the students to add the ones first and then the tens.
Relation between workgroup and classroom practice
Because of his participation in the workgroup, Juan made adjustments to his math lessons. He used the workgroup problems for stretches of a week or more. He became convinced through our workgroup conversations that building understanding of tens and ones was important, especially after I pointed out that one of his students was using his knowledge of a numbers’ composition to generate his own efficient way to add numbers. In April, Juan found a series of lessons in the faculty resource room that focused on tens and ones. He began to use those daily in his classroom. One aspect of the relation between his workgroup and classroom participation stands out. As part of the design of our PD, I made classroom visits in between workgroup meetings. Throughout the year, when I visited Juan’s classroom, I did not observe him eliciting his students’ mathematical thinking. Instead, he monitored student activity and typically talked to his students about managerial or logistical aspects of their work. He did not typically ask them questions about their thinking or solutions. Occasionally, he would help a student who was having difficulty. If I asked him how hisstudents were doing, he pulled out their journals where they record most of their work and appeared to be looking at them for the first time. It did not appear that he was paying particularly close attention to his students’ problem solving activities, even though he provided many opportunities for them to solve problems. He confirmed this limited reflection during the final interview.
Lupe.
Use of workgroup problems
Lupe, like Juan, routinely incorporated “problem solving” into her fourth grade curriculum. She used the workgroup problems regularly in her classroom. But what made her use different from Juan’s is that she used number sizes that would help encourage children to generate their own algorithms or to think about breaking apart numbers by tens and hundreds. She was more purposeful in trying to support students’ understanding of the tens structure of the number system. For her, one adaptation would lead to another, each a means to gather information about student thinking.
Workgroup participation
Lupe began participation in the workgroup hoping to improve how she supported students to understand mathematics. She did not want to use the traditional math textbook that she had access to, but she did not know how to structure her curriculum without it. She was an active, vocal member of the workgroup discussions. Her participation in the workgroup changed along three dimensions: detailing students’ strategies, sharing her experimentation, and offering advice to other teachers. During the first meeting, Lupe, like most teachers at the meeting, were uncertain exactly how their students solved the problem. They expected that students’ written explanations would adequately convey their strategy. For the second meeting, she reported that many of her students had tried to use the standard algorithm for subtraction, often unsuccessfully. Over the course of the first three workgroup discussions in which the topic centered on students’ understanding and use of tens, Lupe began sharing how she was trying to support her students understanding of number. And by the third workgroup, she came to the workgroup with evidence of her students generating their own methods and her continued efforts to improve students’ number sense. She was clearly able to describe the methods her students were using and began to offer advice and respond to questions from other teachers about how to develop students’ place value understanding. Several of the student generated strategies that were discussed in the workgroup came from Lupe’s classroom. Mid year, Lupe was able to explain why she was using particular kinds of problems and number sizes. In the final meetings of the year, Lupe initiated other relevant issues that troubled her: how to coordinate her emerging mathematical curriculum with the demands of standardized testing, how to assess students’ mathematical thinking; and how to plan for the following year’s curriculum.
Classroom participation
At the beginning of the year, Lupe, as she recounted in the workgroup discussions was engaging her students in what she described as problem solving. For several weeks at the beginning of the year, her students has been engaged in counting activities, discussing what problem solving meant. They had worked in teams to solve problem from the children’s book, Math Curse. They played with logic games and tangrams. As soon as the workgroups began, Lupe was eager to try the workgroup problems numerous times with her students. The problems were not drastically different from the kinds of tasks she was already giving her students. What changed, however, was the way she engaged with her students. During the first visit to her classroom, I observed Lupe asking the students to explain their thinking in writing. She walked around the room helping students who were stuck but she was not paying attention to the details of the strategies students were using. As she reported in the workgroup, she had a difficult time figuring out how to keep track of students’ strategies. Because her fifth grade students had had more exposure to standard algorithms throughout their schooling, she also battled to push her students away from using it exclusively. She noticed a high number of buggy or incorrect algorithms.
In October, Lupe noticed strategies that she did not understand. She asked students several times to explain so that she could follow what they did. She began to have students share their strategies in whole class discussions and wrote their names next to each strategy so she could keep track of the range in her classroom. She began a unit of multiplication and wanted to help her students understand the idea of grouping. She found and provided a variety of manipulatives to her students to make use of as they chose. She probed for the details of students’ strategies. By January, she noticed that more students were trying strategies other than the standard algorithm. She began to think about how to help students move along in their thinking. In April, she noticed that students used the standard algorithm when she wrote computations vertically, but they used invented algorithms if the problems were written horizontally. She began to concentrate more on assessing and building students understanding of tens. Now, instead of posing word problems, she posed problems like 610 + 340 and pushed students to think about ways of combining hundreds and tens instead of adding up columns. She began to find ways for students not only to hear each other’s strategies but to compare them mathematically and try to use each other’s strategies. She started with round numbers and made the problems progressively difficult. She continued on that trajectory for the rest of the year, combining word problems and computation problems to develop students’ own algorithms and build their understanding of place value.