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In this paper, I will discuss the viability of a mathematical classroom practice that employs both mathematical and philosophical inquiry. I will argue that the two inquiry approaches taken in the context of classroom mathematical practice can complement each other, and that each type of inquiry can add an extra depth to the other, and help students increase their awareness of what each approach can and cannot accomplish.
This integrated reasoning approach promises to provide bridges for establishing richer and more meaningful connections and interactions with students’ personal experience, with other disciplines, and with the broader culture.