We examined the function of mathematical tasks in eighth-grade mathematics classrooms in five countries. A three-camera method of video data generation (see Clarke, 2006) was supplemented by post-lesson video-stimulated reconstructive interviews with teacher and students. Our analysis characterized the tasks employed in each classroom with respect to intention, action and interpretation and related the instructional purpose that guided the teacher’s task selection and use to student interpretation and action, and, ultimately, to the learning that post-lesson interviews encouraged us to associate with each task. The classrooms were drawn from the data set generated by the Learner’s Perspective Study (LPS) (Clarke, Keitel, & Shimizu, 2006). The tasks were selected for their disparity across the key attributes: mathematics invoked (both content category and level of sophistication); figurative context (real-world or decontextualised); resources utilised in task completion (diagrams and other representations); and the nature of the role of the task participants. Students were given a significant “voice” in the completion of each task, and this distribution of responsibility (or enhanced agency) was a consequence of each teacher’s strategic decision, moment by moment, of how best to orchestrate student work on the task. The “entry point” for our analysis was a tabulation of the details related to the social performance of the task. Using these tables, our analysis drew on the video-stimulated, post-lesson interview data to identify intention and interpretation and relate both to social performance of the task. The particular tension that is the focus of this report occurs through the recurrent commitment by the teachers to delegate significant agency to students, thereby placing their curricular intentions at risk. The extent to which the teachers succeeded in this delegation, while successfully maintaining their curricular agenda is, we would argue, one of the most powerful examples of sophisticated teaching competence.

Clarke, D.J. (2006). The LPS Research Design. Chapter 2 in D.J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics Classrooms in Twelve Countries: The Insider’s Perspective. Rotterdam: Sense Publishers, 15-37. Clarke, D., Keitel, C., & Shimizu, Y. (2006). The learner’s perspective study. In D. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspective (pp. 1-14). Rotterdam: Sense Publishers.