During a kayaking expedition in 1983, the author was sucked into an underwater tunnel in Mexico's Rio Urique. He miraculously emerged unharmed, but this near-death experience awakened in him a primal awareness that had been coddled to sleep by his so-called civilized perceptions. He gained intuitive insights from this awakening that enabled him to…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

Using current mind/brain research, this paper explores the "hidden curriculum" in the contexts of teaching, learning and supervision. It explains ways in which current research on the nature of learning can fit into today's typical, "clinical" teaching techniques. The importance of respecting individual modes of learning is stressed; further to…