Just as the tree bridges the worlds of earth and air-light, transforming energies so that there is a flow of nutrients between these two worlds, so too teachers can be seen as bridges or mediators between the world of learners and the world of mathematics. In this speech, the author suggests that one of the principal roles for mathematics teachers, having attracted learners to engage in activity, is to promote learning from an experience by drawing learners out of their immersion in "doing" and prompting them to "digest" that experience, in the sense of a tree transforming energies. In order to remind people that mathematics education is founded on an intricate and complex web of psychological and social constructs, the author explains the three forms of representation distinguished by Jerome Bruner (1966): enactive-iconic-symbolic.