This time we have asked P. K. Chaurasia (Ph.D.) from the National Council of Educational Research and Training (NCERT), New Delhi to share his thoughts about GeoGebra and its use in math curriculum.

The mathematics education community is constantly engaged in finding out how children best learn mathematics. The current National Curriculum Framework (NCF-2005) in India, developed by NCERT describes two goals, a “narrow aim” and a “higher aim” of mathematics education. The higher aim is about developing the children’s inner resources to think and reason mathematically, so that they become capable of making logical conclusions and handling abstractions. While following the „narrow aims” means equipping children with very good algorithmic skills by just having them remember the formulas. At NCERT our ambition is to chieve this „higher aim” rather than only the „narrow aim”.

As NCF recommends, the teacher’s role is to create opportunities for children to build their own understanding of concepts. However, if only we could discover precisely how children best learn mathematics then we could work out exactly how to teach them the subject in the most effective way.

It is easy to realize that GeoGebra promotes experimental learning and can be used to represent mathematical content in multiple ways. So, the question – is can an innovative integration of GeoGebra in Mathematics curriculum support the learning of mathematics adapted to the children’s own learning styles?

Even though GeoGebra can influence what is taught, teachers need to design the suitable instructions and environment that best support this approach. Well-applied GeoGebra can support requirements of learning outcomes as it helps the children process mathematical concepts through investigation and problem solving.

GeoGebra can also be seen as a catalyst for a paradigm shift. Since educational materials and books became accessible for everyone jn an electronic form, education has experienced a gradual shift away from the idea that its success relies on the student’s capacity to memorize and accurately recall large amounts of information.

Instead, greater emphasis has been placed on developing research and problem-solving skills; on equipping students with effective inquiry skills, including the ability to find and process new information using digital technologies. Many educators now see GeoGebra, with its interconnectedness, as an environment rather than just a tool for learning and teaching. The difference between these two perspectives is significant, the former requiring a fundamental change in methodology and teaching practice for many teachers. We should draw a road map for achieving the ultimate target of the highly progressive GeoGebra enabled Mathematics curriculum.

P.K. Chaurasia will be one of our key-note speakers at the pre-ATCM GeoGebra conference in Mumbai, December 2013. Follow his work at http://pkchaurasia.iitiancollege.info.

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.

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.