This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

The need for development of a curriculum that provides vertical links between earlier and later work and horizontal links with other topics in mathematics and other subjects is promoted. Much of the material describes explorations of circles and cones suitable for many levels. (MP)