A design experiment in practice-based, technology mediated mathematics teacher education

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daniel chazan
8 November 2012

This position paper is situated in the context of mathematics teacher education as practiced in university settings. It involves the use of animations and slideshows that represent classroom interaction and an on-line platform--LessonSketch.org--in  which such rich media representations of practice can be discussed and created. The position paper provides context on video-based resources in teacher education and then provides a short description of the LessonSketch environment. It then provides an initial description of a plan for supporting groups of mathematics teacher educators in inquiry and design cycles that result in modules for use in teacher education. Finally, the paper sketches dimensions of a needed research design to study this process.


Contemporary developments in mathematics teacher education


University-based mathematics teacher education in the United States is at an important crossroads. The past decades have seen the development of important new representational tools for mathematics teacher educators. At the same time, there have been increasing criticisms of university-based teacher education in the United States and concomitant calls for changes in how it is done.


In terms of representational tools, as argued in Brophy (2004), there has been great enthusiasm for video in teacher education and professional development. The current ease in capturing video of classroom interaction and sharing it with others over time provides teacher educators with an important resource in preparing pre-service teachers.


Much more than other technologies, videos convey the complexity and immediacy of teaching with a richness that approximates that experienced by observers actually present in the classroom… It is as if one has been taken to the classroom of a particular teacher to observe a particular lesson. One can see students, hear their voices, look at their work, and even hear their teachers reflect on the lesson afterwards. The experience has been captured and can be replayed and transported to other locations. (Brophy, 2004, pp. 9-10)


The promise of video in teacher education plays out against the backdrop of long-term tensions around university-based preparation for professional practice. On the one hand, universities are seen as places where new developments in teaching might originate; on the other hand, universities do not seem well-suited to replication of existing practice (For a discussion of this issue, see Herbst, Chazan, Chen, Chieu, & Weiss, 2011).


For example, in the United States, the Common Core State Standards are an initiative (corestandards.org) of the states and their governors to move a decentralized system toward a common, national set of standards. With respect to mathematics, these standards include a set of standards for the nature of classroom mathematical practice. These standards envision a kind of classroom mathematical practice that is not common. In an effort to flesh out this vision, the Illustrative Mathematics Project (http://illustrativemathematics.org) is creating representations of teaching practice that represent the desired classroom practice, and the involvement higher education faculty has been actively sought.


At the same time, recently, under the banner of “practice-based teacher education” (see teachingworks.org, for example), there have been a number of calls to shift greater attention to the capacity for action of teacher education candidates when they leave their programs. Teacher education programs are criticized for focusing on foundational issues, rather than on providing candidates with methods that will serve candidates well in their initial years in teaching. With the increasing capacity to link teachers to learning gains of their students, it seems likely that in the future teacher education programs will examine program efficacy by judging relative impact on student achievement. And, if it turns out that professional education outside of the academy is more effective on this measure, then support for university-based teacher education may erode further. It is thus crucial for professional schools of education at universities to find ways of combining their academic customs with a focus on practice (Ball & Forzani, 2009).


Responding to this desire for practice-based teacher education, Grossman, Compton, Igra, Ronfeldt, Shahan, and Williamson (2009) undertook a cross-profession study of preparation for practice. Their study suggests that in preparation for practice pre-service professionals are engaged with practice in at least three ways. Their mentors use resources like video to represent practice as described by Brophy (2004). But, in addition, in preparation for practice, mentors break practice into smaller pieces creating decompositions of practice that help pre-service professionals observe particular aspects of practice. And, finally, mentors create approximations of practice that allow candidates to practice particular aspects of their profession in a sheltered context.


Related to these notions, we in the Thought Experiments in Mathematics Teaching project (ThEMaT) have explored technological developments related to the authoring of video. We have been exploring the affordances of animations of possible classroom interaction rather than video of actual classrooms. We believe that such animations can operate both as representations of practice and as decompositions of practice. In addition, we have been exploring an on-line environment for interaction between preservice candidates and these sorts of video-based artifacts of practice. The LessonSketch.org environment is a website within which teacher educators can ask preservice candidates to interact with animations and within which preservice candidates can be asked to create their own comic strip depictions of practice. Some early adopters across the United States have begun to explore the affordances of this environment and these representations for practice-based teacher education, particularly to support interaction outside of the classroom and in blended learning settings.


Modules for mathematics teacher education: Supporting inquiry and development


While the current resources in LessonSketch are of use to early adopters, for LessonSketch and its affordances to have a larger influence on teacher education, other teacher educators will need prepared materials that are prepared to help them meet their goals. The project we are contemplating proposes to energize a national network of teacher educators to develop and share curricular materials for teacher education.


Influenced by the experience of curriculum developers (e.g., the Connected Mathematics Project) in producing materials for middle grades classrooms, we are envisioning the creation of short modules of activity that might be used over 2-3 class sessions with outside of class assignments based on existing LessonSketch materials, instructor developed materials, and publicly available video. We would like to explore the use of these materials in a wide range of teacher preparation contexts: subject-matter content classes, instructional methods (or didactics) classes, adolescent development classes, content area reading courses, observation semester interactions with mentors, during student teaching (with support for interns, mentors, and field instructors).


Key to the proposed activity will be the support of teacher educators as they engage in an inquiry and design process to create these modules. We imagine supporting this process in three steps that involve: early adopters who design and create prototype modules, mathematics teacher education inquiry groups that develop and refine these modules, and then on-line groups of mathematics teacher educators who participate in further inquiry around the achievement of the goals of the modules.


The first step in the process will involve interaction between Thought Experiments in Mathematics Teaching Research group and a small group of initial collaborators excited about the potential of LessonSketch as a tool in teacher education. In concert with the ThEMaT research group, these early adopters will identify key mathematics teacher practices around which mathematics teacher education has important goals. They will design modules that involve both the use of animations and video, as well as including assignments that involve pre-service candidate created slideshows. The research group will support these early adopters with the development of additional materials in the LessonSketch environment. These materials will include a library of mathematics teaching practices, as well as a library of student mathematical conceptions.


At the next stage, each of the early adopters will recruit 6-7 colleagues to become a mathematics teacher education inquiry group. The focus of each group will be on the development in pre-service teachers of the mathematics teaching practices at the heart of the newly-designed module. Participants in the inquiry group will use the module in their program and adapt it to their contexts. The LessonSketch environment’s resources for sharing data from the use of the module and for sharing comments about the nature of the module will be used to support the work of these inquiry groups.


In the final stage, each of these inquiry groups will launch their module as a resource for mathematics educators more broadly. The inquiry groups will then operate as the authors of a set of materials for use by other teacher educators, as well as the convenors of on-line conversations and explorations about how to achieve the goals of their module more effectively.


Researching the development and use of a teacher education environment


LessonSketch provides a set of tools and resources for practice-based, media intensive, online interactions. Teacher educators come to it not only with their goals but also with a wealth of face-to-face activity structures and assessment ideas. Their mutual accommodation requires learning and design. Teacher educators need to learn how to use available tools and resources, while the LessonSketch design team will learn about the goals and expected practices of teacher educators. Teacher educators will design and create applications of LessonSketch tools, while the LessonSketch design team will improve user interface and functionalities to support better use and implementation. The process we anticipate is one of institutional design. Our research plan will investigate how this design proceeds. The idea is to do research around the interaction between teacher developers who use media and have a practice-based orientation and the designers of the LessonSketch environment as they attempt to incorporate some elements of a basic set of technology resources into teacher education. The research would include learning how they use those technological resources and determining how the system can better track that use so as to produce instructor and student feedback. The research would also include learning about other activity structures used that could be supported by technology and determining what kinds of technology supports could facilitate this work.


The data that we envision to be collected for this project is diverse. On the one hand, in depth interviews of teacher educators and observations of their work with teacher candidates could lead to case studies of needs, affordances, solutions, etc. On the other hand log data studies of what they do with their students could serve to evaluate features and discover errors.




Ball, D. L. and Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5):497-511.


Brophy, J. (2004). Introduction. In J. Brophy (Ed.), Using video in teacher education (pp. 1–27). New York, NY: Elsevier Science.


Chazan, D. and Herbst, P. (2012). Animations of classroom interaction: Expanding the boundaries of video records of practice. Teachers College Record, 114(3). 1-34.

Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.


Herbst, P., Chazan, D., Chen, C., Chieu, V.M., and Weiss, M. (2011). Using comics-based representations of teaching, and technology, to bring practice to university “methods” courses. ZDM—The International Journal of Mathematics Education, 43(1), 91-104.

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