Geometry and spatial reasoning

Spatial understandings are necessary for interpreting, understanding, and appreciating our inherently geometric world. (National Council of Teachers of Mathematics, 1989, p. 48) Geometry is grasping space ... that space in which the child lives, breathes and moves. The space that the child must learn to knOw, explore, conquer; in order to live, breathe, and move better in it. (Freudenthal, in National Council of Teachers of Mathematics, 1989, p. 48) Arising out of practical activity and man's need to describe his surroundings, geometric forms were slowly conceptualized until they took on an abstract meaning of their own. Thus from a practical theory of earth measure, there developed a growing set of relations or theorems that culminated in Euclid's Elements, the collection, synthesis, and elaboration of all this knowledge. (Fehr; 1973, p. 370) EquatiOns are just the boring part of mathematics. I attempt to see things in terms of geometry. (Hawking, National Research Council, 1989, p. 35) School