Sounds and pictures: dynamism and dualism in Dynamic Geometry

Abstract

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. 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). 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). 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 socalled 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. Thus we focus on this second aspect-sensory interaction with mathematical representations-in evaluating how novel dynamic representations in GSP5 affect mathematical modeling opportunities, student activity and engagement.

Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing

“…As such, one can go beyond the perceptual level to identify components comprising a figure and to understand the notion of angles and angular rotation (Papert & Harel, 1991). A key contribution to digital technologies such as Logo, and DGEs in general, was in offering a powerful, temporalized representation of mathematical ideas through the lens of continuity and continuous change (Jackiw & Sinclair, 2009). In terms of 3D geometry learning, the representations generated by a 3D DGE are complicated by the media of flat screen through which they are presented on.…”

“…This approach also demands that students are actively "making" 3D models with their own hands besides coordinating their vision with the artefacts. Given our interests in embodied mathematics learning, 3D Pens afford increased immediacy and sensory interactions with mathematical representations that are lacking in screen-based tools (Jackiw & Sinclair, 2009). In this light, this study explores differences in geometry learning in two technology-enhanced environments to further our understanding of the effect of embodied interactions on school mathematics learning.…”

Recent research on geometry education: an ICME-13 survey team report

“…Schimpf and Spannagel (2011) compared full and reduced icon sets in DGEs with eye-tracking technology and found no significant effects of graphical user inter-face (GUI) reduction on the findability of already-known icons. Jackiw and Sinclair (2009) discuss how the concept of 'dynamic mathematics' -involving new mathematical structures and their auditory and visual representations -can carry the concept of dynamism from DGEs in both its mathematical aspect of continuity and its pedagogic aspect of immediacy. They focus on the second aspect "in evaluating how novel dynamic representations in GSP5 affect mathematical modelling opportunities, student activity and engagement" (p. 413).…”

Geometry Education, Including the Use of New Technologies: A Survey of Recent Research

“…Trends for digital geometry tools include (1) how geometry on the web is encountering various technological difficulties associated with the need to replace Java; (2) the issue of interface design and how users interact with onscreen geometry (Jackiw & Sinclair, 2009;Kortenkamp & Dohrmann, 2010;Laborde & Laborde, 2014;Mackrell 2011;Schimpf & Spannagel, 2011; (3) the rise of mobile devices and touch technology; and (4) new modes of interaction such as multi-touch and multi-collaboration.…”