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ARTICULATING THE RELATION BETWEEN TEACHERS’ LEARNING IN PROFESSIONAL DEVELOPMENT AND THEIR PRACTICE IN THE CLASSROOM: IMPLICATIONS FOR DESIGN RESEARCH Qing Zhao Vanderbilt University
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Paul Cobb Vanderbilt University
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In this paper, our goal is to address a conceptual challenge that arises as researchers conduct design experiments to support and understand teachers’ learning. This challenge centers on articulating the relations between teachers’ learning in professional development and their practice in the classroom. In our view, designs for supporting teachers’ learning necessarily involve suppositions and assumptions about such relations. These suppositions and assumptions shape not merely the goals for teachers’ learning but the actual process of their learning and the means of supporting and organizing it. By drawing on our own design research experience we propose a bi-directional conceptualization that, in our view, profoundly influences all three phases in a design experiment. The design research methodology has become increasingly prominent in mathematics education and related fields in recent years. A program of design research that is aimed at supporting teacher learning involves engineering the process of supporting teacher change through iterative cycles of design and research (Brown, 1992). In this process, conjectures about the trajectory of the teachers’ learning and the means of supporting it are continually tested and revised in the course of the experiment. In this highly interventionist activity, decisions about how to proceed are informed by ongoing analyses of the participating teachers’ activity. As noted by Wilson and Berne (1999), design research is an appropriate methodology to investigate teacher professional development as little is known about systematically designing professional development to support teacher learning and as a result, teacher educators are “researching a phenomenon while they are trying to build it” (p. 197). Research of this type involves a “bifocal” attention encompassing both “designing meaningful professional development and conducting rigorous research” at the same time (Wilson & Berne, 1999, p.197). This interdependence between design and research is reflected in all three phases of a design experiment: preparing for the experiment, experimenting to support learning, and conducting retrospective analyses of the data generated in the course of the experiment (cf. Cobb, Confrey, diSessa, Lehrer & Schauble, 2003). In this paper, our goal is to address a conceptual challenge that arises as researchers conduct design experiments to support and understand teachers’ learning. This challenge is inherent to teacher development experiment as the primary intent is to engage teachers in activities in professional development sessions with the goal of supporting the reorganization of their activity in another setting, the classroom. Thus, the coordination of teachers’ learning across two differing settings is an distinctive characteristic of teacher development experiments that distinguishes them from classroom based design experiments aimed at supporting students’ learning of mathematics. The conceptual challenge that we address in this paper therefore centers on articulating the relations between teachers’ learning in professional development and their practice in the classroom. _____________________________ Alatorre, S., Cortina, J.L., Sáiz, M., and Méndez, A.(Eds) (2006). Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Mérida, México: Universidad Pedagógica Nacional.
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In the following sections, we first clarify the implications of a conceptualization as such for all three phases in a design research. We then draw on our own design research experience with a group of middle-school mathematics teachers to illustrate how our own conceptualization of this relation evolved as a result of our ongoing effort to support the teachers’ learning. We conclude by discussing the specific implications that the resulting conceptualization carries for more effective design. Implications for the Three Phases in a Design Research A research team’s conceptualization of the relations between teachers’ activities in these two settings profoundly shapes all three phases of an experiment even in cases where the nature of these relations is implicitly assumed rather than explicitly articulately. The design conjectures formulated in the preparation phase of a design research necessarily involves assumptions about the specific ways in which teachers’ learning in professional development sessions might influence their classroom practices and vise versa. It is possible to infer how these relations are conceptualized in various designs for supporting teachers’ learning even when underlying assumptions are not made explicit. In most cases, the relations are conceptualized in unidirectional terms (Borko, 2004; Clarke & Hollingsworth, 2002). It is assumed that teachers will develop insights into their instructional practices and their students’ learning in professional development sessions and then apply them in their classrooms. Designs for supporting teachers’ learning that reflect such a conceptualization typically focus on equipping teachers with forms of expertise that researchers believe are important their development of effective instructional practices. A number of researchers have challenged this uni-directional conceptualization by arguing that teacher professional development should be situated in the context of teaching. For example, Ball and Cohen (Ball & Cohen, 1999) call for teacher development activities to be centered on the use of artifacts and practices that are directly relevant to teachers’ daily practices. This proposal is underpinned by the claim that teachers’ classroom practices constitute a valuable resource on which researchers can draw as they formulate design conjectures. In this conceptualization, what counts as an effective design for supporting teachers’ learning depends on how closely it is tied to teachers’ classroom experiences, needs, and practices (Ball & Cohen, 1999; Franke, Carpenter, Fennema, Ansell, & Behrend, 1998; Nelson, 1997; Borko, 2000). The second phase of an experiment, experimenting to support learning, involves testing and revising design conjectures about both the learning of a group of teachers and the specific means of supporting that learning. In this phase, the research team’s assumptions about the relationship between teachers’ learning in the professional development sessions and their classroom practices circumscribe the ongoing design decisions to a considerable extent. For example, when this relationship is conceptualized in uni-directional terms, the revisions made to design conjectures are likely focus on 1) additional skills or insights that researchers think are crucial for effective instructional practice, 2) new tools or technologies that can be used to support teachers’ development of these skills or insights, and 3) the specific activities in which teachers should engage in professional development sessions in order to develop these skills or insights. In such cases, the iterative design cycles focus primarily on what can be accomplished in the professional development setting, and the teachers’ classrooms are viewed as settings in which the consequences of their learning in the professional sessions can be assessed. A research team might scrutinize its assumptions about the relations between teachers’ learning in professional development sessions and their classroom practices as it tests and revises design conjectures in the second phase of an experiment. However, it is unlikely that this will
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occur unless the research team has explicated its assumptions about these relations and is aware of how they shape design conjectures. In cases where the assumed relations have not been articulated or are not considered central to the design process, it is doubtful that they will be implicated in the success or failure of the design conjectures. The last phase of a design experiment involves conducting retrospective analyses. One of the goals of this phase should, in our view, be to contribute to the development of a domain-specific teacher development theory (cf. Cobb & Greveimeijer, in press; Cobb et al, 2004). Assumptions about the relations between teachers’ participation in professional development sessions and their classroom practices will be inherent in the retrospective account of the teachers’ learning and thus in the resulting teacher development theory. Our Evolving Conceptualization Having clarified the importance of explicating assumptions about relations between teachers’ activity in professional development session and the classroom, we now illustrate how our conceptualization of these relations evolved in the course of a five-year collaboration with a group of middle-school teachers. The school district in which the collaborating teachers worked is a large urban district located in a state with a high-stakes accountability program. Our longterm goal in working with the teachers was to support their development of instructional practices that place students’ reasoning at the center of their instructional decision making. To this end, we engaged the teachers in activities from a statistical data analysis instructional sequence that was designed, tested, and revised during prior NSF funded classroom design experiments conducted with middle grades students (Cobb, 1999; McClain & Cobb, 2001). During the five years of our collaboration with the teachers, we conducted six one-day work sessions each school year and three-day sessions each summer. About 18 months into the collaboration the group evolved into a genuine professional teaching community that satisfies Wenger’s (1998) criteria for a community of practice indicated by joint enterprise, mutual engagement, and a shared repertoire. As we have documented elsewhere (Cobb, McClain, Lamberg & Dean, 2003; Dean, 2005), the activities during the first two years supported the deprivatization of the teachers’ instructional practices and the evolution of the teacher group into a community. Against this background, we engaged the teachers in activities in which they analyzed their students’ work. At the outset of our collaboration with the teachers, our conceptualization of the relation between their activity in the two settings was consistent with Ball and Cohen’s (1999) view that professional development should involve the use of artifacts or practices that originate in the teachers’ classrooms. More specifically, this design decision was based on three rationales. We conjectured that because students’ work is an indispensable aspect of teachers’ instructional practices, making it a focus of activity would enhance the pragmatic value of the professional development sessions in relation to the teachers’ classroom practices. In addition, we conjectured that the teachers would openly critique and challenge each other’s interpretations of student work because teaching was now deprivatized. Finally, we conjectured that open discussions of this type would give rise to opportunities for the teachers to gain insight into the diversity of their students’ reasoning that would be useful when they attempted to build on their students’ solutions while conducting whole class discussions. These interrelated rationales reflect our conscious effort to build on the teachers’ classroom practices and indicate our conceptualization of the relations between the teachers’ activity in professional development sessions and their classrooms at that time. The specific questions that we posed in order to orient the teachers’ analysis of their students’ work were as follows:
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What are the different solutions that you can identify from your students’ work? How would you categorize students' solutions according to their level of sophistication? How would you, as a teacher, build on these different solutions? Which solutions would you choose to focus on in class and why? Our design conjectures proved to be unviable despite our detailed preparations. The teachers seemed to find the activity engaging and discussed their interpretations of the student work openly. Furthermore, most were able to discriminate between students’ solutions in terms of levels of sophistication. However, it became apparent that they did not view this activity as relevant to their classroom instruction. The teachers’ primary orientation was evaluative in that they assessed whether the instructional activity had been successful or not. Students’ work, for these teachers, was an assessment tool rather than a resource for instructional planning. The orientation that teachers took towards students’ work was particularly evident when our question of “how are you going to build on students’ different solutions” received puzzled looks and almost no response from the teachers. The conversation within the work group came to a halt at this point. The teachers’ orientation towards students’ work indicated that there was something about the teachers’ classroom practices that we had yet understood. This realization in turn led us to reexamine our assumptions about the relations between teachers’ activity in the professional development sessions and their classroom practices. We generated data to that might enable us to address these issues by conducting an unscheduled series of modified teaching sets (Simon & Tzur, 1999) with all the participating teachers. These modified teaching sets involve observing one or more lessons and then conducting an interview in which questions are grounded in specific activities and events that occurred during the observed lessons. A central principle that guided our analysis of these and other teaching sets was that the teachers’ instructional practices were reasonable and coherent within their landscape of teaching and learning. The analysis of the modified teaching sets revealed that the process of students’ learning and what supported their learning was, for the teachers, a black box. We conjectured that their repeated observation that students’ engagement in the same classroom activity typically resulted in different learning outcomes for different students only served to mystify the process of students’ learning. The teachers indicated that they had a limited sense of control in how they could influence their students’ learning and identified two ways in which they believed they could support student learning. The first was to ensure that students had sufficient opportunities to engage in instructional activities as intended. The common strategies that the teaches employed included using different forms of presentation (e.g. different visual supports or manipulatives), breaking mathematics problems down into smaller steps, and providing students with sufficient time and enough problems of a similar type. The second way that the teachers believed they could influence student learning was to make sure that the students attended to the learning opportunities that would arise if they engaging in tasks as intended. All the teachers valued students’ engagement highly and, for many, staying on task was synonymous with learning. The teachers typically accounted for students’ failure to learn in terms of their lack of focused attention or, sometimes, their unwillingness to concentrate on the mathematical intent of tasks. As a result, the overriding challenge that the teachers attempted to address in their instruction was that of ensuring that students were on task. This analysis of the teaching sets suggested that the teachers’ classroom practices might have been influenced by the institutional settings in which they worked more deeply than we had initially assumed. Their orientation to teaching was largely shaped by the fact that the school
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leaders assessed the quality of their instruction in terms of content coverage and the extent to which students were on task. The teaching sets also revealed that students’ reasoning was largely invisible to the teachers as they engaged in classroom instruction. This finding explained why the analysis student work was irrelevant to the teachers’ classroom practices. From the teachers’ perspective, the diversity in their students’ solutions served to confirm that learning was an elusive phenomenon. For most of the teachers, students’ work was a product of learning rather than a record of students’ reasoning and indicated whether the instructional activity was successful or not. In other words, the teachers viewed students’ work as a tool for retrospective assessment rather than as a resource for prospective planning. Our analysis of the teaching sets resulted in two important insights. First, it enabled us to understand why the teachers took an evaluative orientation towards the use of students’ work in the sessions. Second, we came to realize that the ways in which we assumed student work would be used in the sessions did not fit with how the teachers used student work in their classrooms. In Wenger’s (1998) terms, student work was a reification of students’ reasoning within the context of our practices as researchers and teacher educators. In contrast, student work was a reification of the outcome of instruction for the teachers within the context of their classroom practices. These insights led us to explicate and question our assumption that teachers’ learning in professional development sessions and in their classrooms could be related by focusing professional development activities on artifacts that originated in their classrooms. We found Beach’s (1999) notion of consequential transitions particularly useful as we attempted to rethink the relations between teachers’ activity in professional development sessions and their classroom practices. In Beach’s terms, transitions between settings occur when teachers shift from engaging in classroom teaching to participating in professional development activities, and vice versa. For Beach, these transitions are consequential if and only if teachers’ participation in professional development sessions is oriented towards reworking their classroom practices, and if their classroom teaching constitutes the context in which they make sense of their engagement in professional development activities. This perspective gives rise to two implications for professional development. The first implication is that professional development activities should be designed so that teachers can relate their participation in sessions to their classroom practices. In the case of the teachers with whom we worked, our design conjectures implicitly assumed that the teachers used student work as a reification of student reasoning in their classrooms. As we have illustrated, this assumption was unviable. The second related implication of Beach’s perspective on people’s activity in different settings is that teachers’ activity in professional development sessions should be interpreted against the background of their classroom practices. This implication clarifies that when the same artifact is used in activities in different settings (e.g., students’ work is used both in professional development activities and the classroom), its constitution in one setting needs to be understood in relation to how it is used in the other setting. In the case of student work, the questions that might be addressed when conducting an analysis of this type include: How do the participating teachers typically use students’ work in their classroom practices? What pedagogical value do they attribute to students’ work in the context of those practices? Are there significant differences between the teachers’ use of student work in their classrooms and the ways in which the researchers envision it being used in professional development sessions? Answers to these questions clarify whether the planned use of an artifact such as student work constitutes a viable means of supporting the teachers’ learning across the settings of the professional development session and their classrooms.
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In summary, when we began the teacher development experiment, we assumed that the twoway movement of artifacts between the professional development sessions and the teachers’ classrooms would support their learning across the two settings. In attempting to understand why design conjectures based on this assumption were unviable, we came to conceptualize the relations between the teachers’ activity in the two settings as involving a bi-directional interplay. This conceptualization focuses not on the movement of artifacts per se, but on the relations between teachers’ use of artifacts in professional development sessions and the classroom. Implications of the Bi-directional Conceptualization This bi-directional conceptualization is consequential for all three phases of a teacher development experiment. In preparing for an experiment, it indicates the importance of developing relatively detailed accounts of the collaborating teachers’ instructional practices and thus of the ways in which they use key artifacts. In our view, two aspects of teachers’ classroom practices are particularly worthy of attention. The first concerns the extent to which students’ reasoning is visible in teachers’ classroom practices whereas the second involves identifying issues that are pragmatically relevant to the teachers in the context of their instructional practices and that can be leveraged to achieve the professional development agenda of supporting their learning across the two settings. The bi-directional conceptualization implies that during the second phase of experimenting to support learning, the ongoing process of testing and revising the design conjectures should be informed by analyses of the collaborating teachers’ developing classroom practices as well as by analyses of their activity in the professional development sessions. Recall again that our design conjectures for analyzing student work proved to be unviable. We would not have understood why the teachers took an evaluative stance towards student work and thus did not view the activity as relevant to their classroom practices had we not conducted an additional round of data collection in order to analyze those practices. In the final phase of conducting retrospective analyses, the bi-directional conceptualization shapes the explanation of the teacher groups’ learning and also results in credible accounts for why particular design decisions did not work as expected. For example, to account for why students’ work did not support the learning of the teachers with whom we collaborated, we focused on the lack of alignment between how we envisioned student work might be used in the professional development sessions and how it was constituted in teachers’ classroom practices. This type of explanation is potentially generalizable to other cases in which there is a similar lack of alignments between the use of artifacts in professional development sessions and the classroom. In this regard, the bi-directional conceptualization structures the aspects of a design that are viewed as necessary and as contingent in supporting a group of teachers’ learning, and thus what is potentially generalizable and replicable. Conclusion Designs for supporting teachers’ learning necessarily involve suppositions and assumptions about the relations between teachers’ activity in the setting of professional development and the classroom. These suppositions and assumptions shape not merely the goals for teachers’ learning but the actual process of their learning and the means of supporting and organizing it. In our view, it is therefore crucial for researchers to scrutinize their assumptions and to be explicit about how they conceptualize the relations between teachers’ activities in the professional development sessions and their classroom instructional practices. In this paper, the bi-directional conceptualization that we have proposed to guide teacher development experiments reflects the
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view of these relations that we developed while collaborating with a group of teachers to support their learning. References Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes & L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey Bass. Beach, K.D. (1999). Consequential transitions: A sociocultural expedition beyond transfer in education. Review of Research in Education, 24, 101- 139. Borko, H.(2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33 (8), 3-15. Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. Journal of the Learning Sciences, 2, 141-178. Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18, 947-967. Cobb, P. (2001). Supporting the Improvement of learning and teaching in social and institutional context. In S. Carver & D. Klahr (Eds.), Cognition and instruction: Twenty-five years of progress (pp. 455-478). Mahwah, NJ: Erlbaum. Cobb, P., Confrey, J., diSessa, A. A., Lehrer, R., & Schauble, L. (2003). Design experiments in education research. Educational Researcher, 32(1), 9-13. Cobb, P., & Gravemeijer, K. (in press). Experimenting to support and understand learning processes. In A. E. Kelly (Ed.), Handbook of design research. Mahwah, NJ: Lawrence Erlbaum Associates. Cobb, P., McClain, K., Lamberg, T., & Dean, C. (2003). Situating teachers’ instructional practices in the institutional setting of the school and school district. Educational Researcher, 32(6), 13-24 Dean, C. (2005). Supporting the learning and development of a professional mathematics teaching community. Unpublished Dissertation, Vanderbilt University, Nashville, TN. Franke, M. L., Carpenter, T., Fennema, E., Ansell, E., & Behrend, J. (1998). Understanding teachers' self-sustaining, generative change in the context of professional development. Teaching and Teacher Education, 14, 67-80. Nelson, B. (1997) Learning about teacher change in the context of mathematics education reform: where have we come from. In E. Fennema & B. Scott Nelson (Eds.), Mathematics teachers in transition (pp. 3 –19). Mahwah, NJ: Lawrence Erlbaum Associates. Simon, M. A., & Tzur, R. (1999). Explicating the teacher’s perspective from the researchers’ perspective: Generating accounts of mathematics teachers’ practice. Journal for Research in Mathematics Education, 30, 252-264 Wilson, S.M. & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge; An examination of research on contemporary professional development. In Iran-Nejad & P.D. Pearson (Eds.), Review of Research in Education (pp. 173 - 209). Washington, DC: American Educational Research Association.
