On forests, trees, elephants, and classrooms: a brief for the study of learning ecologies

The classroom intervention studies in this volume, ranging from the study of gestures to that of systemic implementation, are at very different grain sizes. A challenge is to see the forest for the trees – to see how these studies, focusing on different aspects of mathematical activity at different grain sizes, can be seen as aspects of a coherent whole. I propose an ecological metaphor for the study of mathematical activity. In ecological terms, the biosphere is comprised of interconnected and interrelated ecosystems. I argue that, analogously, there are nested and interrelated mathematical activity systems and structures in which “mathematical sense-making” plays the role of “health” in ecosystems. Moreover, what happens in the classroom environment shapes and is shaped by what happens in sub-ecologies of the classroom (e.g., sociomathematical norms, participation structures, communicational forms such as gesture, and representational tools and their use) and the larger social and organizational ecologies of which it is a part (building culture, support structures for teachers and teaching, external pressures such as testing and accountability systems etc).