The Web Geometry Laboratory (WGL) project's goal is, to build an adaptive and collaborative blended-learning Web-environment for geometry. In its current version (1.2) the WGL is already a collaborative blendedlearning Web-environment integrating a dynamic geometry system (DGS) and with some adaptive features. The building of the adaptive module is a two steps task, a rst task, already almost completed, is the collection of data, textual, navigation and also geometric data. A second task will be, using the collected data, the construction of student pro les and/or learning paths. In this article the process of collection of the data and its visualisation will be described. The actual testing of the WGL platform by high-school teachers is underway and eld-tests with high-school students are being prepared. The next steps in the development of this platform will be the construction of student pro les and/or learning paths. The integration of a geometric automated theorem prover, allowing the exploration of geometric reasoning in a learning environment is also planned.
The use of intelligent computational tools in a learning environment can greatly enhance its dynamic, adaptive and collaborative features. It could also extend the learning environment from the classroom to outside of the xed walls of the school.
To build an adaptive and collaborative blended-learning environment for
geometry, we claim that we should integrate DGSs, GATPs and repositories of
geometric problems (RGPs) in a Web system capable of individualised access
and asynchronous and synchronous interactions. A system with that level of
integration will allow building an environment where each student can have a
broad experimental, but with a strong formal support, learning platform. The
WGL, a collaborative [
Such an integration it is still to be done, there are already many excellent
DGSs [
The WGL is thought mostly for a blended-learning setting, that is, a classroom/laboratory where the computer-mediated activities are combined with a face-to-face classroom interaction. Nevertheless given the fact that the WGL is a Web application its use can extend itself to the outside of the classroom and be used to develop work at home, e.g. solving a given homework.
The WGL has two distinct session types. The collaborative sessions and the normal, individual work, sessions.
In a collaborative session the students are working in groups, the WGL
provides an environment with two DGS, one where the group construction is being
done and another where the students can work, following the group construction,
or pursuing other ways to build the construction [
The construction of group pro les/learning paths and/or using the collaborative work to build student pro les/learning paths is a task to be develop in the future. For the moment we concentrate in using the individual work of the students to collect the data of his/her interaction with the system in order to be able to build student's pro les and individualised learning paths.
In the normal mode the student has access to a workbench where, using a DGS, he/she can work on problems given by the teachers and also in his/her own studies. A permissions system, similar to the \traditional Unix permissions" system allows the sharing of construction between groups of students, students and teachers. Although a given student has access to the constructions made available by other students and/or the teachers, this is an individual working mode.
It is in this individual mode that the collection of the data is being done. The navigation information: the browsing of the group list constructions; the administrative tasks and all the steps done when working in the Workbench. The geometric information: all the steps made when using the DGS applet during the construction of a geometric gure. In this mode the WGL doesn't provide a chat window between its users, this is only provided group-wise in the collaborative sessions, so, for the moment, this textual information is not being collected.
The construction of an adaptive module for WGL with the construction of
student pro les and individualised learning paths, following Van Hiele levels of
geometric reasoning [
Collection of Navigation Data In a normal session the students has access to: \Forum/Help"; \List of Constructions"; \Workbench"; \Constructions Administration". In each of this sections we collect the following data: Forum / Help which pages where visited; which documents where downloaded; List of Constructions which constructions where selected; which actions (save, update, remove) where done for each selected construction; Workbench which constructions where selected and or new constructions saved; which actions, in the DGS, where done to each construction; Constructions Administration which pages where visited.
Using the WGL the student has access to the DGS applet in two stages: when browsing the list of constructions made available by other; when working in the workbench.
When using the DGS applet all the actions about the creation, the modi cation and the erasing of geometric elements are recorded in the database. Using listeners, JavaScript functions provided by the applet, all the actions are saved in the database.
Again no automatic processing of this information is currently being made. All this information is made available to the student's teachers, and only to then. This time the interface provided allow the teachers to see the \movie" (see
No automatic processing of this information is made at this moment.
All this information is made available to the student's teachers, and only to then (see Fig. 1). It is the teachers responsibility to process this information and, eventually, provide some individualised help, in a form of a list of geometric constructions, to each of
Using this information, adding to the navigation information and all inclass information, the teacher can infer the van Hiele levels of each of his/her students and, again, to provide some set of constructions/tasks that allow each student achieve the desired learning goals.
Learning environments supported
Fig. 2. Geometric Data by computer are seen as a
important mean for non classroom
education. The DGS are also important in classroom environments, as a much
enhanced substitutes for the ruler and compass physical instruments, allowing the
development of experiments, stimulating learning by experience. There are
several DGS available, such as: GeoGebra, Cinderella, Geometric Supposer,
GeometerSketchpad, CaR, Cabri, GCLC but none of then de nes a Web learning
environment with adaptive and collaborative features [
When we consider a computer system for an educational setting in geometry, we feel that a collaborative, adaptive blended-learning environment with DGS and GATP integration is the most interesting solution. That leads to a Web system capable of being used in the classroom but also outside the classroom, with collaborative and adaptive features and with a DGS and GATPs integrated.
The WGL system (version 1.2) is a work-on-progress system. It is a
client/server modular system incorporating a DGS, some adaptive features, i.e., the
individualised scrapbook where all the users can keep their own constructions
and with a collaborative module. Given the fact that it is a client/server system
the incorporation of a GATP (on the server) it will not be di cult. One of the
authors has already experience on that type of integration [
A workshop with high-school teachers on the use of the WGL collaborative platform is being done, November 2013 { February 2014. In this workshop teachers played the roles of student and teacher at di erent times, performing collaborative tasks. With this workshop it was intended to help teachers to include in their teaching practice the WGL platform providing a collaborative environment for geometry in their classrooms. The preliminary results of this workshop are very positive and this, and past, experiences are also being used to improve the WGL platform with more features suggested during these experiences.
The next task will be to nish the adaptive module providing some automatic, or semi-automatic, help to the teacher to the construction of student's pro les. A last task will be the integration of the GATP in the WGL. We hope that at the end the WGL can became a very challenging learning environment for geometry.
The WGL system is available at hilbert.mat.uc.pt/WebGeometryLab/. You can enter as \anonymous/anonymous", a student-level user. A use of the WGL platform in the role of a teacher is also possible but it is subject to approval by the WGL administrators.