The goal of this qualitative case study was to reveal how students make sense of mathematics in the setting where their learning occurs; that is, through interactions with their teacher and peers, through the enactment of curriculum, and in their development of disciplinary tools. Prior to entering the research setting, a small, innovative, urban high school, care was taken to uncover my epistemological and pedagogical beliefs. This was necessary in view of the research design: (1) I collected data in my classroom, and (2) I authored the standards-based curriculum unit in use (sanctioned by Education Development Center and the school site). Given my views on the humanistic nature of the development of mathematical thinking, I used a socio-cultural lens comprised of a bricolage of theories, including Activity Theory, Structure Theory, and socio-semiotics.

An exploration of classroom structures revealed that: (1) I called upon my expert authority in ways that, at times, interfered with students' thought processes; (2) the structuring capacity of the curriculum unit both enabled and constrained subjects' agency; and (3) students' identity formation would be more consistent with structures shaped around shared authority relations. Shifts in classroom structures, and in particular the ability for subjects to negotiate authority relationships, catalyzed transformations in our classroom learning activity. Increased agency for students and myself resulted in a revised activity system that could reveal ways in which students learned mathematics. Through discourse analysis, a detailed exploration of the use of mediating tools shed light on the relationship between interpersonal and intrapersonal levels of learning. Such understanding has powerful implications for structuring learning environments, for informing the work of teachers and curriculum developers, and for mathematics educational research.