In our field, there is a tradition of using representations of teaching in the form of written cases and video-cases in teacher education and in research (Jacobs & Morita, 2002; Nemirovsky, Dimattia, Ribeiro, & Lara-Meloy, 2005; Stein, Smith, Henningsen, & Silver, 2000).  Most recently, the use of animations has opened novel possibilities for illustrating specific problems of practice.  Nevertheless, issues pertaining to the design of representations of teaching continue to be a challenge, especially, when considering various dimensions of a representation.  For example, researchers must make important questions regarding the extent to which representations depict the individualities of people and settings from real events, reproduce the passing of time of real events, and incorporate the audience in the events represented.  Therefore, an examination of design decisions is important for increasing teacher educators’ and researchers’ control of the process of creating representations of teaching.

The papers in this session focus on design principles to be considered when creating representations of teaching.  The papers include discussions about theoretical considerations such as models for developing stories, the relationship between the representations and the practices that are the target of the representations, and the generalities that could be represented through the creation of particular cases.  The papers also discuss practical issues such as decision-making processes around editing stories, choices of media to showcase the representations, and the use of visual displays.  Altogether, the papers discuss how the interplay between theoretical and practical matters frames the creation of representations of teaching.  In addition, the papers ponder how other elements such as the audience for the representations of teaching (e.g., teacher candidates, in-service teachers, and students) and the goals of the representations of teaching (e.g., research, professional development, methods courses, etc.) shape decisions about the design.  The proposed session will be helpful for researchers to broaden their repertoire of choices when designing new representations of teaching according to their particular needs.

The session is structured around four papers (40 minutes), with a brief introduction at the beginning (6 minutes) and a response by a discussant (14 minutes).  The five central questions to focus the audience participation during the discussion (30 minutes) are the following:

1. What theoretical frameworks support the design of representations of teaching?
2. What are some relationships between design principles and specific mathematics teaching practices that want to be represented?
3. What design principles are connected with specific types of representations of teaching?
4. What are affordances and constraints of available technologies that aid the creation of representations of teaching?
5. How do the audience and the goals of the representation shape design decisions?

The papers include examples of the application of design principles according to the use of different media (e.g., video cases and animations) with different constituencies—pre-service teachers, in-service teacher, and mentor teachers—in different environments—online discussion boards, focus groups, and interviews.

1.  Design considerations in creating story-based, multimedia surveys
This presentation discusses the design of cartoon-based representations of teaching to be included in online survey-like instruments. We show examples of instruments that assess decision-making as well as teachers’ recognition of classroom norms. We describe the process followed to eventually create and validate these items--from the hypotheses that the items attempted to confirm, to their instantiation in stories, their representation in cartoon-based slideshows, and their embedding in online questionnaires.  

2.  Truth, Lies, and Videotapes: Composing Multiple Video Representations of the Same Lesson
This presentation considers a different approach to making and using video representations of mathematics teaching for teacher development.  Setting aside typical concerns with such representations of teaching— authenticity, context, and focus on either exemplars or dilemmas of practice (Sherin et al., 2009)—this presenter embraces the impossibility of representing a teachers’ full repertoire of mathematics teaching. Instead this presentation considers the affordances of composing multiple (rather than single) video representations of a mathematics lesson to illustrate contraries (i.e., idyllic/flawed, extreme/mundane, comedic/drama) that exist within everyday mathematics teaching. Consider, for example, how it is possible to compose (edit) both a Ms. Jekyll and a Ms. Hyde from the video footage of a single math lesson. This approach takes the perspective that “everything is said from an observer,” (Maturana, 1987) and that examining events from multiple vantage points can lead to a much richer and nuanced understanding (Goldman-Segall, 1994, 1998).

3.  From Videos to Animations: Designing Animated Vignettes about Problem-Based Instruction
This presentation discusses design principles used when creating animated vignettes based upon videos of classroom instruction for the purpose of conducting focus group sessions with mathematics teachers.  In contrast with the videos, the animated vignettes showed snapshots of a teacher’s work during different moments in the lesson.  In addition, the animated vignettes showed variations in the division of labor between the teacher and the students and in the timeliness of teaching actions.  The paper argues that the “incompleteness” of the vignettes can be useful for researchers to elicit from practitioners their perspectives about specific teaching actions.

4.  Representing Students’ Reasoning Using Slide Shows: Designing Multiple Layers of Meaning
This presentation reports on theoretical and practical considerations related to the design of slide-show representations of students’ mathematical reasoning. Theoretical considerations address: What does it mean to represent students’ reasoning? How can students’ work on a particular task be used to represent a more general way of reasoning? Practical considerations address: What kind of interplay is involved in the layered artifacts, speech, and gestures? What are affordances and constraints of including commentary within the representations? Slide show representations of students’ reasoning provide a sequence of snapshots of students’ work on a mathematical task. Users interacting with slide show representations can view the snapshots individually or in an entire sequence as a comic strip. Selected examples of empirically based slide show representations of students’ reasoning about rate of change highlight theoretical and practical considerations. By foregrounding students’ reasoning as a viable way of making mathematical sense of a situation, slide show representations could foster practitioners’ making inferences about students’ mathematics and developing descriptions of students’ ways of reasoning.

References

Goldman-Segall, R. (1998). Points of viewing children’s thinking: A digital ethnographer’s journey. Mahwah, NJ: Lawrence Erlbaum Associates.

Goldman-Segall, R. (1995). Deconstructing the Humpty-Dumpty myth: Putting it together to create cultural meaning. In E. Barrett & M. Redmon (Eds). Contextual Media: Multimedia and Interpretation. Boston, Mass: MIT Press.

Jacobs, J. K., & Morita, E. (2002). Japanese and American teachers' evaluations of videotaped mathematics lessons. Journal for Research in Mathematics Education, 33(3), 154-175.

Maturana, H. R. (1987). Everything is said by an observer. In I. Thompson (Ed.) Gaia, a way of Knowing. Political implications of the New Biology. NY: Lindsfarne Press.

Nemirovsky, R., Dimattia, C., Ribeiro, B., & Lara-Meloy, T.  (2005).  Talking about teaching episodes.  Journal of Mathematics Teacher Education, 8, 363-392.

Sherin, M. G., Linsenmeier, K., & van Es., E.A.  (2009). Selecting video clips for teacher learning about student thinking. Journal of Teacher Education, 60(3), 213-230.

Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E.  (2000). Implementing Standards-Based Mathematics Instruction:  A casebook for professional development.  New York:  Teachers College.