Cabri-géomètre, un logiciel d’aide à l’enseignement de la géométrie, logiciel et manuel d’utilisation. Columbus, OH.īaulac, Y., Bellemain, F., & Laborde, J. Paper presented at the Nineteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. A computer microworld for promoting dynamic imagery in support of geometric reasoning. London: Hodder and Stoughton.īattista, M. Pimm (Ed.), Mathematics, teachers and children (pp. Aspects of proof in pupils’ practice of school mathematics. International Journal of Computers for Mathematical Learning, 7(3), 245–274. Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Most sounds in the universe are unpleasant sounds, at least when randomly produced by 20 different classroom computers simultaneously! By choosing a formulation requiring some pre-requisite understanding of the mathematical structure of sound to engage, Sketchpad 5 limits the production of unwelcome noise to, at least, intentionally-created unwelcome noise.Īrtigue, M.
Finally, early classroom feedback suggested that with this feature, accessibility was a double-edged sword. However, this simpler representation eliminates various sonic possibilities (for example, the difference between a violin and a piano playing the same note) that can be captured in a richer notation, so concerns of expressivity also contribute to sound’s present identity in the software.
#Gsp5 sketchpad software#
Sound could be made much more accessible in the software if its fundamental expression was by a simple (“volume, pitch”) value pair rather than the more ornate amp × sin( freq × t) expression.
But there are other design rationales favoring an airpressure/time notation over other possible mathematical models of sound. The connection to harmonic motion and waveform analysis is intentional from a curriculum perspective- Sketchpad 5’s formulation is the same found in commonly-appearing textbook chapter on “the mathematics of sound,” or in the occasional undergraduate seminar on the same topic. 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.įrom a design perspective, this is only half true. 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). Custom tools icon: Use this icon to define, use, and manage custom tools.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.Information tool: Use this tool to explore how a sketch is constructed and how the objects relate to each other.Marker tool: Use this tool to create angle markers and tick marks, and to make freehand drawings and notations.Text tool: Use this tool to create and edit text and labels.The three variations of the tool allow you to construct a polygon, a polygon and the segments that form its edges, or the edge segments only.
Selection Arrow tools: Use these tools to select and drag objects in your sketch.
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