https://blog.geogebra.org/2013/06/geogebra-enabled-mathematics-curriculum-a-future-perspective/ Dynamic Mathematics for Everyone Tue, 07 Oct 2014 19:34:17 +0000 hourly 1 https://wordpress.org/?v=static-html https://blog.geogebra.org/2013/06/geogebra-enabled-mathematics-curriculum-a-future-perspective/comment-page-1/#comment-118 Thu, 20 Jun 2013 21:13:51 +0000 http://www.geogebra.org/blog/?p=647#comment-118 But when you can consider GeoGebra to be a paradigm shift in having concurrent multiple representations it is still far from a shift for real. And let me try to elaborate a little on this. Geogebra makes classic constructions based on a rule of a compass more intuitve and at the same time likewise making geometrical representation of algebraic expression intuitive as well. This is then combined into the instant multi-representation that originally gave name to the program. So far so good.
(But) This is just two possible ways of considering geometrical constructions. The program really doesn't make foldings more easy although they are very important. They can be simulated at least to a certain extent but not very easy. There is another software doing much better within this area.
Now what is much more important to me is that Geogebra has be missing an important point in the connection between algebra and geometry. The algebraic language is designed (or developed) to write relations. So relations is objects in themselves. Like the relation to be tangent is an object and not only a construction. But in Geogebra it is really none of the things more something in between. There is a tool for construction of tangents, but although it returns an algebraic expression for this tangent, the tangent is not turned into a object itself. And you can't use the relation tangent to make two objects tangent to each other as you could have if tangent was an object in itself, much more than a construction.
This step has Geogebra not taken, but other softwares have. Most important most of the professional computer aided softwares (CAD) which means that most of the students probably learn a lot of historical mathematics but not the mathematics after the shift in the paradigm. And what is much more worse: It will never turn geometric constructions into the intuitive thing is can be – and intuition is where the children are.

]]> https://blog.geogebra.org/2013/06/geogebra-enabled-mathematics-curriculum-a-future-perspective/comment-page-1/#comment-98 Fri, 14 Jun 2013 22:10:26 +0000 http://www.geogebra.org/blog/?p=647#comment-98 […] GeoGebra Dynamic Mathematics in India (GeoGebra Enabled Mathematics Curriculum – A Future Perspective http://t.co/vjWt1NOuTG)  […]

]]> https://blog.geogebra.org/2013/06/geogebra-enabled-mathematics-curriculum-a-future-perspective/comment-page-1/#comment-87 Fri, 07 Jun 2013 11:30:34 +0000 http://www.geogebra.org/blog/?p=647#comment-87 Terrific! I am inspired by Hans Freudenthal, who said that students learn math best by reinventing it for themselves. GeoGebra lets me give students that opportunity – even at the upper levels of secondary school math. It is certainly becoming the environment in which I learn best, and I continue to explore how to make it the environment in which my students can learn best.

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