What is GeoGebra？

Since the late 1990s, investigation of geometric relations can be done by experiment in dynamic geometry environment (DGE). DGE is a computer micro-world and embedded with two-dimensional and three-dimensional geometry as its infrastructure. Nowadays, many educators create DGE materials and share through the internet which enable other teachers and students to use them in teaching and learning various topics in geometry and algebra.

GeoGebra is one of the DGE tool which is free of charge and used frequently in mathematics classrooms nowadays. In addition, GeoGebra Institutes are establishing in worldwide which aims to improve the uses and design of GeoGebra materials through researches and workshops. It supports the sustainable development of DGE, and keep DGE as an important pedagogical tool in mathematics classrooms.

For more information, please visit the following websites:

GeoGebra official website: https://www.geogebra.org/

GeoGebra Institute of Hong Kong: http://www.geogebra.org.hk/

What is Euclid Geometry？

Euclidean geometry is one of the cornerstone in mathematics. It is rooted with comprehensive deductive and logical system, and it demonstrates how to establish various geometric relations (proposition) about geometric objects (points, lines, angles, etc.) by proceeding from basic properties (axioms) logically and systematically. Therefore, studying of Euclidean geometry is regarded as an essential path to develop logical thinking and reasoning in worldwide for over 2000 years. Nowadays, Euclidean geometry is still a compulsory component of mathematics curriculum in high schools worldwide.

For more information, please visit the following websites:

Euclid's Elements from Wiki: https://en.wikipedia.org/wiki/Euclid%27s_Elements

Euclid's Elements online version: https://mathcs.clarku.edu/~djoyce/java/elements/toc.html

What are the purposes of "Euclidean Geometry in Action"？

Although DGE (especially GeoGebra) is well-developed nowadays, its explorative and inductive nature is different from the deductive and formal nature of Euclidean geometry. Such contrast leads to an experimental-theoretical gap between the acquisition and justification of geometrical knowledge. How DGE can bridge the gap between exploratory and deductive geometry? "Euclidean Geometry in Action" may be one of the possible answers.

What is the difference between using GeoGebra and paper-and-pencil in learning Euclidean Geometry？

By using GeoGebra, Euclidean proof could starts with perception and action, then the perception could be clarified and refined to verbal discussion. It could lead to description of existing objects, especially definitions, eventually lead to a process of deduction. It is believed that such perception and action could be reinforced by the uses of the annotation tools in DGE. Furthermore, the annotation tools will act as an artifact to facilitate the discernment of invariants in DGE, hence facilitate geometric reasoning of users in both empirical and deductive ways.

Will GeoGebra be a better tool in learning Euclid Geometry？

The study is continuing and the answer will be sought out soon.