Projects — ThEMaT


themat 1 logo



Thought Experiments in Mathematics Teaching I
Thought Experiments in Mathematics Teaching (ThEMaT) was funded by NSF in 2004 and closed in 2011 (NSF Grant ESI-0353285). This research project explored the teaching of secondary algebra and geometry by examining the discussions among groups of teachers experienced in teaching each subject who were gathered to watch and discuss various representations of practice. The basic premise was that practicing teachers have a shared sense of what practices are viable in instruction, and that confronting them with representations of conceivable practice might elicit the rationality that makes some of those practices viable.

In order to elicit discussions among groups of experienced teachers, ThEMaT developed and used animations of cartoon characters to represent classroom scenarios in U.S. high school algebra and geometry classrooms. These animations represented episodes that intentionally straddled the boundaries between what is more and less customary in classrooms. Using discourse analysis techniques, the project investigators examined focus group discussions to understand whether and how the instructional practices represented in the scenarios fall within what experienced mathematics teachers might consider reasonable to do in the classroom. For the production of those animations, the ThEMaT I Project created casts of cartoon characters (including ThExpians B and ThExpians M). The ThExpians B characters and the animations, have been reused in later projects as well as in the LessonSketch platform (developed in a subsequent project).

As a theoretical contribution, ThEMaT I helped develop the notion of an instructional situation as a resource to account for the subject-specificity of classroom instruction: These can be described as the system of norms that regulate how work in a type of problem provides students opportunities to learn and evidence of students’ learning of a particular kind of knowledge. Instructional situations investigated in the context of ThEMat I include installing theorems and doing proofs in geometry, and solving equations and doing word problems in algebra. The project helped characterize those situations in terms of norms—observer statements of implicit regulations that classroom participants act as-if they were expected to follow. To explore those norms, both whether they were applicable and what the rationality that undergirded them was, the project designed and produced animations of classroom scenarios in which such norms had been breached. Researchers examined the conversations among practitioners about those scenarios to find evidence that practitioners perceived a breach of business as usual. The notion that some departures from norms might be justifiable came as a result of the inspection of those conversations. In efforts to name the sources of justification, the project contributed the proposal that the work of teaching is accountable to stakeholders, or that teachers need to respond to professional obligations to the discipline of mathematics, the students as individuals, social expectations and values, and the policies and practices of organizations larger than the classroom (e.g., the department, school, system, etc.).

As a methodological contribution, the project contributed a variant of the ethnomethodological breaching experiment—demonstrating that such experiments could be done virtually by immersing practitioners in videos and animations of practice and analyzing their response to those representations as data informing on their practice. The project also demonstrated how some resources from Systemic Functional Linguistics (in particular, the modality system) can be used to analyze stances towards norms in the discourse of groups of teachers.

NSF logo
This material is based upon work supported by the National Science Foundation under Grant ESI-0353285. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.