This paper suggests that mathematics teacher educators should listen carefully to what their students are saying. More specifically, it demonstrates how from one pre-teacher's non-traditional geometric representation of a unit fraction, a variety of learning environments that lead to the enrichment of mathematics for teaching can be developed. The paper shows how new knowledge may be generated through an attempt to validate an intuitive idea; in other words, how the quest for rigour may serve as a catalyst for the growth of mathematical concepts in the context of K-16 mathematics. (Contains 9 figures.)