## Welcome to Touching Math!

We live in a world made of spaces and volumes. Our three-dimensional reality is inhabited and explored by each human being, at first intuitively through our 5 senses. The language of mathematics allows us to describe and model the world around us. With it we can represent all objects as well as the surrounding space.

Most of the times, the way mathematics is taught in the classroom, does not involve, in a proper way, the senses of sight and touch. Spatial reasoning is a fundamental component of Mathematical Thinking. Nevertheless, there are times when spatial visualization skills are not developed.

###### The Goal

The goal of this project is to improve the way mathematics is taught in the classroom. The main objective can be achieved by increasing spatial visualization skills through the use of augmented reality, virtual environments and 3D impressions. A natural reality description is taught using important mathematical concepts by adding the senses of touch and sight. At last, long lasting mathematical ideas make sense in the lives of the students.

Since 2010, the development of math visualization skills in our students have been studied. The conclusion is that new technologies as well as new methodologies must be used.

Two tools have been developed, one of augmented reality (ARC) and one of remote virtual environment (AVRAM) that, together with 3D prints, have a notorious impact on the student´s visualization skills. The former tools can be used either individually or in teams.

The traditional teaching of mathematics changes with the use of ARC and AVRAM. The students are motivated to learn mathematics by watching and playing. In this way, they really achieve meaningful learning. With the use of these tools, pedagogical activities have been designed for different courses in physics and mathematics at a higher level. Research is done to measure learning gain and to track the development of visualization skills.