Dynamic geometry environments (DGE) have emerged in the last half-century with an ever-increasing impact in mathematics education. DGE enlarge the field of geometric objects subject to formal reasoning, for instance, simultaneous operations with many geometric objects. Today DGE open the possibility of investigating visually and formulating conjectures, comparing objects, discovery or proving rigorously properties over geometric constructions, and Euclidean elementary geometry is required to reason about them.

Along these decades various utilities have been added to these environments, such as the manipulation of algebraic equations of geometric objects or the automated proving and discovering, based on computer algebra algorithms, of elementary geometry statements. Moreover, some intelligent tutoring systems for Euclidean geometry based in DGE have been developed. 

The merging of these tools (DGE, automated proving and intelligent tutoring systems) is, thus, a very natural, challenging and promising issue, currently involving logic, symbolic computation, software development, algebraic geometry and mathematics education experts all from over the world.

The Special Session intends to be a forum for:

• presenting the current state of the art concerning the design and implementation of automatic reasoning features on dynamic geometry systems and intelligent tutoring systems;

• proposing applications in different contexts, such a generation of algebraic curves, linkages or augmented reality;
  

• fostering a debate concerning the role and use of such features in mathematics education, in general, and their potential impact in proof and proving conception in the classroom, in particular. 

• Pedro Quaresma (Coimbra University): Tracing the Evolution of Current Automatic Proving Technologies [Presentation]

• Daniel McDonald (Wolfram Research Institute), Peter Barendse (Wolfram Research Institute, Massachusetts Institute of Technology): Automated Plane Geometry in Wolfram Mathematica [Presentation]

• Thierry Dana-Picard (Jerusalem College of Technology), Zoltán Kovacs (The Private University College of Education of the Diocese of Linz):  Experiments on isoptics by dynamic coloring [Presentation]

• Alain Kuzniak (Université de Paris), Assia Nechache  (Université de Cergy):  Vers un travail géométrique conforme et correct en contexte d’usages d’outils géométriques classiques et numériques  [Presentation]

• Jirí Blažek, Pavel Pech (University of South Bohemia): Discovering in DGE — A case study  [Presentation]

• Roman Hašek (University of South Bohemia in Ceské Budejovice): One method of trisecting an angle and its interpretation for teaching purposes using a dynamic geometry and computer algebra system  [Presentation]

• Ludovic Font, Philippe R. Richard, Othmane Farid, Sébastien Cyr, Michel Gagnon, Fabienne Venant (École Polytechnique de Montréal and Université de Montréal): The realization of a proof support system in a process of adaptation to the human perspective  [Presentation]

• Viktor Freiman (Université de Moncton), Alexei Volkov  (National Tsing-Hua University): Rearrangement method for area of a circle: complex paths from historical roots to modern visual and dynamic models in discovery-based teaching approach  [Presentation]
  

• Ludovic Font, Michel Gagnon, Nicolas Leduc, Pascal-Alexandre Morel (École Polytechnique de Montréal),  Philippe R. Richard, Michèle Tessier-Baillargeon (Université de Montréal): The Modelisation of the Possible Proofs for High School Geometry Problems in the Tutoring Software QED-Tutrix  [Presentation]

• Jean-Jacques Dahan (IRES of Toulouse, Paul Sabatier University): Investigations with DGS and CAS dealing with problems of equal area and particularly a possible generalization to 3D of the known results of the Lhuillier problem  [Presentation]