Live(d) Topographies: The Emergent and Dynamical Nature of Ideas in Secondary Mathematics Classes

In this chapter, we consider the images, meanings, and metaphors provoked by the phrase in the title of the opening section of the book: The Changing Landscape. Inspired by our Indigenous and ecological sensibilities, we develop new images, meanings, and metaphors that illuminate the collective nature of secondary mathematics classes. We explore the Pirie-Kieren (1989) model in terms of how it relates to the collective level of the class. Using a video based excerpt from a secondary mathematics class, we map the observed ideas onto the Pirie-Kieren model as they emerge and evolve, moment to moment. The results reveal a dynamic ideational topography of the classroom. Through illustrative exemplars and the analyses that accompany these, we reflect on how paying attention to the ideas of the class as live(d) topographies occasion new questions for further investigation into mathematics classroom collectives.