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Making a Circle: Tool Use and the Spaces Where We Live

A group of high school students created a drawing of a circle using a device called the Drawing Machine. To describe their experiences, we propose an alternative to the idea that to master a tool one must create a mental version of the tool. We suggest, instead, that as students change their relationships to a tool over time, their lived-in spaces change. Drawing on studies of practice, we explore the roles of past experience, planning, and communication in the development of students' lived-in spaces as they increase their competence with the tool and with the mathematics of drawing a circle.