![gsp5 kaliedescope gsp5 kaliedescope](https://geraintsmith.com/wp-content/uploads/2020/06/santa_crz_ojo_caliente_0802-4517047.jpg)
But at the same time, this expansion has come at the cost of a decrease in the immediacy of sensory interactions with mathematical representations, as in so-called dynamic graphing, wherein users modify a graph “at a distance” (through slider-based manipulation of the coefficients of its symbolic equation), or in solid geometry tools, in which users’ interactions with represented solids are mediated and distanced by the inevitably-2D communication interfaces of the computer mouse and screen. Seen from this perspective, the growth of “Dynamic Mathematics software,” beyond the initial conception of first-generation planar geometry systems, represents a tremendous diversification and expansion of the mathematical domain of the dynamic principle’s applicability (for example, to dynamic statistics, graphing and 3D geometry). We claim the primary contributions of Dynamic Geometry’s principle of dynamism to the emerging concept of “Dynamic Mathematics” to be twofold: first, the powerful, temporalized representation of continuity and continuous change (dynamism’s mathematical aspect), and second, the sensory immediacy of direct interaction with mathematical representations (dynamism’s pedagogic aspect). In this paper, we examine and evaluate several new mathematical representations developed for The Geometer’s Sketchpad v5 (GSP5) from the perspective of their dynamic mathematical and pedagogic utility or expressibility.