Several transformations have been suggested for proportions x. Most of these require that 0 < x < 1 and therefore fail when x = 0 or x = 1, which is quite common in practice. The paper proposes a ...

Vol. 26, No. 2/3, Learning Mathematics: Constructivist and Interactionist Theories of Mathematical Development (Mar., 1994), pp. 135-164 (30 pages) Conventional treatments of functions start by ...