Montessori, math, and materials: a case of extended cognition

Abstract In this article, we bring Maria Montessori’s pedagogy into conversation with contemporary developments in cognitive science and the philosophy of mind. In particular, we seek to show that Montessori’s “prepared environment” provides a context within which cognitive tasks are performed in the interfaces and interactions among brains, bodies, and concrete mathematical materials. For ease of illustration, we will focus on one particular Montessori material—the “Stamp Game,” used by children of approximately ages 4–7 for ordinary arithmetic. In both cases, our goal is, first, to show the way in which this particular material can be enmeshed with a particular child’s brain and body in order to become capable of complex mathematical operations. In that sense, we argue that the child + stamp-game or child + square-root-board constitutes a case of what contemporary philosophers call “extended cognition,” that is, a “cognitive process … constituted or realized by resources distributed across the brain, the body, and the environment” Kirchhoff & Kiverstein ( Extended consciousness and predictive processing: A third wave view , 2019, 8). Here we highlight that extended cognitive systems can not merely enact mathematical operations but can actualize mathematical understanding .