Theoretical perspective: As a theoretical notion, participation recognises the different degrees and types of relationship that can exist between individuals and their environment. In education, participation often involves cognitive, linguistic and social action as students respond to assigned tasks, yet students can employ different actions in response to the same task. This paper investigates the actions and interactions of students as they respond to an open-ended mathematics task in order to answer the questions "In what ways do contrasting ‘repertoires of participation’ suggest different understandings of an assigned task?" and, "How do different ‘repertoires of participation’ mediate engagement within a task?" Data: The data for this study was generated in a laboratory classroom equipped to capture spoken, written and embodied classroom interactions in rich detail. The Year 7 students (12 to 13 years old), monitored by their usual teacher, participated in a 60-minute session involving three separate problem-solving tasks - task one individually, task two in pairs, and task three in groups of four to six. As an 'activity setting' the laboratory classroom incorporates action that corresponds with and goes beyond the usual tasks of school. As such, the design of the study constitutes a forward-looking form of assessment, which for many participants arguably went beyond their current level of development (Vygotsky, 1978). This paper draws on the written solutions, transcripts, and video record from four pairs of students. Analysis: The analysis involved three steps to map 1) the actions and interactions of the participants - what was said and done by whom at what point during the task, 2) the intonation and responsivity of participants’ words and actions in order to understand the meaning, and 3) the actions and interactions of each individual in order to identify individual repertoires of participation. Results and implications: Participation repertoires are indicative of the way in which participants make sense of and strategically choose to respond to a task. This paper illustrates the significant differences that can exist within and between the participation repertoires of the students from a single class and the need for greater sensitivity when negotiating pathways from current levels of development to expected levels of achievement.

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