**5. Usability of the system**

In order to increase the usability and effectiveness of the platform [45], two different modes have been created for user experience: one uses VR only, the other uses AR. In both cases the graphic engine used is the same: Unity3D.

In the Virtual Reality case, a room has been created, and inside the room the three-dimensional figures have been positioned, as shown in **Figure 5**. This software allows the composition of virtual environments starting from basic elements

**Figure 5.** *Students during training session to learn how to use the platform.*

## *Learning Mathematics in an Immersive Way DOI: http://dx.doi.org/10.5772/intechopen.96533*

called Assets which make up the scene. The VR environment is generated and compiled by WebGL technology: this means that the application is compatible with all devices (computers or smartphones) on the market since the virtual world can be viewed with a web browser, regardless of the operating system used (Windows, Linux, Android, iOS, etc). In particular, in the experience we made for collecting the student's usability evaluations, we focused on smartphones with Android operating system. The graphic quality of the scene adapts according to the computational power of the device, while remaining undemanding in terms of hardware requirements. The scene can be observed through a virtual reality viewer, such as HTC Vive, or through a normal computer monitor. The user has the possibility to move around the virtual environment using the touchscreen on the smartphone, or the mouse and the keyboard on a computer. Inside the environment are visible three-dimensional geometric shapes that support the learning of mathematical functions that are otherwise difficult to be drawn (see **Figures 6** and **7**).

As far as the use with Augmented Reality is concerned, Vuforia software has been used. It is a framework integrated in Unity3D and allows to create projects that

**Figure 6.** *Evaluation of the experience by the students.*

**Figure 7.** *Environment for the VR experience.*

#### **Figure 8.**

*Example of Vumark to draw the function ln x*<sup>2</sup> <sup>þ</sup> *<sup>y</sup>*<sup>2</sup> ð Þ *(on the left) three-dimensional image generated by Vuforia for the object described by the previous Vumarks (on the right).*

use Augmented Reality by providing all functions essential for operating on mobile phones. The system is very dynamic, since every time one of the markers in the database is framed by the user's device camera, Vuforia warns Unity to show the object on the scene (and therefore on the user's screen) associated with the framed Vumark. Furthermore, this SDK manages the spatial orientation of the object based on the user's position relative to the Vumark. If we frame a Vumark and move around it, the object associated with it will also rotate, allowing us to appreciate it in a realistic way (see **Figure 8**).

### **6. Discussion of results**

We collected students' feedback to evaluate the usability of the proposed system and to enhance the user's experience, making the AR and VR environments more interactive and attractive. This is the reason why we asked high school students to express their opinion about the quality of the experience, by filling out a questionnaire. Our sample set was composed by 90 high school students, homogeneous by age, gender, social and cultural levels. In **Figure 9** is shown the distribution of the sample per age, while in **Figure 10** is shown the distribution per gender.

The aim of the experiment conducted during a morning class was to obtain a set of coherent and indicative answers on the following main topic: *how much virtual reality and augmented reality can impact the perception of mathematics*. To do that, each class of the school composing the sample, was taken to the computer room, equipped with Vmarks, and left it *playing* with the application on both computers and smartphones for 50 minutes. Finally, the students filled in the questionnaire.

One of the most remarkable aspects of this experience was to observe so clearly and explicitly how the introduction of a play environment stimulated girls and boys in an incredible way. It seemed that the game scenario by itself made them feel comfortable and willing to experience approaching mathematics in a new way.

The results have been being very promising, as most students found the experience of VR and AR applied to some mathematical functions very useful and *Learning Mathematics in an Immersive Way DOI: http://dx.doi.org/10.5772/intechopen.96533*

#### **Figure 9.**

*Distribution by age of the sample of students.*

**Figure 10.** *Distribution by gender of the sample of students.*

instructive. Some even asked for an enhancement of the experience, with the addition of new entities and animations.

In **Figure 11** the degree of appreciation of Virtual Reality, i.e. the exploration of the virtual world on a PC, is shown. It appears that the *usability* has been really appreciated, a bit worse were the results in terms of *easy of use*, *user experience* and *graphic quality*.

In **Figure 12** the degree of appreciation of Augmented Reality, i.e. the exploration of the virtual world on a smartphone, is shown. Also in this case the *usability*

**Figure 11.** *Degree of appreciation of virtual reality.*

**Figure 12.**

*Degree of appreciation of augmented reality.*

has been really appreciated, while a bit worse were the results in terms of *easy of use*, *user experience* and *graphic quality*.

The result about comparison between Virtual Reality and Augmented Reality evaluations are very similar, as it can be seen in the **Figures 11** and **12**.

We think that, if this approach would be largely adopted by teachers, the interest of students on the discipline may significantly raise up and the score of the students may significantly increase, especially in the case of students with problems approaching mathematics.
