AVRAM: Ambientes Virtuales Remotos para el Aprendizaje de las Matemáticas

(Remote Virtual Environments for Learning Mathematics)


Este proyecto fue realizado gracias al apoyo de                                       

NOVUS 2013- AVRAM 2.0 NOVUS 2017

This is a NOVUS 2013. 2017  funded project.

Participantes del proyecto:

Project Participants:

There is very little research on visualization in three-dimensional space and even fewer where the influence of technology on 3D visualization is inquired.  AVRAM  is a technological tool that allows authoring, manipulation and visualization of geometric surface models in a remote 3D environment. AVRAM arises from the need to improve the ability of spatial abstraction in the students. AVRAM is very useful in order to understand mathematical concepts related to n-dimensional spaces. It is designed to improve the teaching-learning process of multivariate calculus by using mobile technologies, a remote display and a series of activities designed for that purpose.

AVRAM has two versions, one where the professor works from a mobile device (tablet or phone) and sends the information to the student´s mobile device. Another one where the professor works on a PC and sends the information to the student´s mobile device. Fig. 2 shows the three screens of AVRAM mobile version. The first screen shows how to connect to the server. The second screen shows where the surfaces are drawn in 3D space. The third screen shows where the equations are written, the way the variables are defined and how the color of the graphics are selected.

Four surfaces on the same screen, with two tabs for each surface, can be drawn form the PC version. Fig. 3 shows on the left, the tab where the ranking of the variables can be set, how the union/intersection/difference between the surfaces can be done and where the pallet of colors can be chosen. A list of surfaces´ equations to be graphed can also be found. The application not only draws the graph but also calculates the volume as well as the area of ​​the chosen surface. On the right hand side an equation tab allows the user to change the coefficients of a surface equation. At any time the camera position can be adjusted so that the figure can be observed from different angles. The projections on the coordinate planes, the view of the axes, the color and the mesh can be changed at will.


Dra. Linda Medina

Dr. Benjamín Hernández

Dr. Sergio Ruiz (AVRAM 2.0)

Programación y diseño de interfaz

Computing Programmers and Interface


Dr. Sergio Ruiz

Alvaro Herrasti (ITC)

Daniel Dovalí (ITC)

AVRAM 2.0 : Héctor Carlos Flores Reynoso (ITC)

Profesores usuarios/ pruebas


Dr. Gerardo Aguilar

Dra. Linda Medina

Mtra. Marlene Aguilar

Lic. Alejandro Flores Benitez

Revisión de la Traducción/Translation Reviewer: Dra. Rosa María Guadalupe García Castelán