TEACHING MATHEMATICS WITH AUGMENTED REALITY

Mauro Figueiredo

Algarve University; mfiguei@ualg.pt

Low achievement in mathematics education has been an increasing problem in the recent years in Portugal. According to a 2010 study from the U.S. Department of Education, blended learning classes produce statistically better results than their face-to-face. There is also an increasing number of students using smartphones and tablets in schools. Mobile devices gained popularity as an educational tool and there are many schools that used them frequently in educational activities to improve learning. In this paper, we introduce the use of Augmented Reality for providing activities that students can do at home and increase the time they spend learning and practicing mathematics. We present teaching activities that use different augmented reality technologies for presenting solutions to practical problems by multiple types of media, including videos, to be shown on top of interactive documents.

Keywords: e-learning, b-learning, augmented reality.

INTRODUCTION

Low achievement in mathematics education has been an increasing problem in the recent years in Portugal.

In 2014, the average classification in the 12th grade exam, from 0-20, was of 7.8. Mathematics exams in the 1st cycle, 2nd cycle and 3rd cycle had an excessive percentage of negatives (levels 1 or 2), 36%, 54% and 47%, respectively.

According to a 2010 study from the U.S. Department of Education, blended learning classes produce statistically better results than their face-to-face. B-learning combines face-to-face instruction with online learning and has yielded strong results since officially being researched as an education model. An advantage of this approach is that it increases the flexibility and individualization of student learning experiences, and it also allows teachers to expand the time they spend as facilitators of learning.

The recent availability of smartphones and tablets with increased processing power and usability, accessible on a large scale, allow an exponential expansion of social and participative web technologies.

It is also important to note that these students are the generation of digital games and social networks. We cannot ignore that they are no longer the same for which the education system was designed a few decades ago. See, for example, the prospect of Heide and Stilborne (2000), for whom "the technological revolution has produced a generation of students who grew up with multidimensional and interactive media sources. A generation whose expectations and world views are different from those that preceded it" (p. 27).

In this context it is wise to consider the integration of digital media and mobile devices (iPad, iPod, tablets, smartphones), allowing students to set personal goals, to manage educational content and to communicate with others in the right context.

The increased availability of smartphones and tablets with Internet connectivity and increasing power computing makes possible the use of augmented reality (AR) applications in these mobile devices.

In the near future, eventually everyone has a smartphone or a tablet that is capable of displaying augmented information. This makes it possible for a teacher to develop educational activities that can take advantage of the augmented reality technologies for improving learning activities.

According to Fernandes and Ferreira (2012), the use of information technology made many changes in the way of teaching and learning. We believe that the use of augmented reality will change significantly the teaching activities by enabling the addition of supplementary information that is seen on a mobile device. Several examples are already showing that this is happening. For example, the recent work of Restivo et al. (2014) with Augmented Reality involving STEM students, using markers for teaching DC circuit fundamentals, revealed very good student perceptions and satisfaction.

In this paper, we want to expand the use of Augmented Reality for STEM teaching and learning by describing several educational activities created for teaching mathematics using augmented reality tools that do not require programming knowledge to be used by any teacher. With the produced material students can do their home works and see the complete solutions for problems making learning more interactive.

We describe educational activities using several types of augmented reality technologies. Examples presented cover the marker and marker less based augmented reality technologies to show how to create learning activities to visualize augmented information like text and video that help students understand the educational content.

AUGMENTED REALITY

Augmented Reality applications combine 3-D virtual objects with a 3-D real environment in real time. Virtual and real objects appear together in a real time system in a way that the user sees the real world and the virtual objects superimposed with the real objects. The user’s perception of the real world is enhanced and the user interacts in a more natural way. The virtual objects can be used to display additional information about the real world that are not directly perceived.

Milgram and Kishino (1994) introduced the concept of a Virtuality Continuum classifying the different ways that virtual and real objects can be realized. In this taxonomy scheme Augmented Reality is closer to the real world.

Azuma (1997) defines augmented reality systems as those that have three characteristics: 1) combines real and virtual; 2) interactive in real time; 3) registered in 3-D. In general, augmented reality applications fall in two categories: geo-base and computer vision based.

Geo-based applications use the mobile’s GPS, accelerometer, gyroscope, and other technology to determine the location, heading, and direction of the mobile device. The user can see 3D objects that are superimposed to the world in the direction he is looking at. However, this technology has some problems. The major problem is imprecise location which makes difficult for example the creation of photo overlays.

Computer vision based applications use image recognition capabilities to recognize images and overlay information on top of this image. These can be based on markers, such as QR (Quick Response), Microsoft tags or LLA (latitude/longitude/altitude), or marker less that recognize an image that triggers the overlay data.

There are currently many augmented reality applications and development systems for Android and iOS (iPhone Operating System) smartphones and tablets.

CREATING LEARNING ACTIVITIES USING MARKER BASED AR TECHNOLOGIES

In this section, we use marker based augmented reality technologies to provide the solutions of problems so that students at home solve math problems and know if it is correct.

We would prefer to use the Microsoft tags because we want to use smaller codes that become less intrusive. Reading smaller Microsoft tags are more reliable then the equivalent QR codes. Unfortunately Microsoft selected Scanbuy to support Microsoft Tag Technology and it will be not free.

In this way, figure 1 shows the use of marker based augmented reality to present problems solutions for students.

Figure 1: Math test with QR codes to provide solutions to the problems.

Using marker based codes for presenting additional information in a mobile device is very simple to use and straightforward. The teacher can use simple QR (Quick Response) two dimensional codes for associating information such as text, URL or any other data. Quick response codes are much more popular than the other code formats and there are several sites where the teacher can easily create such codes.

The example of figure 2 uses a QR code to show the correct answer to problem 1. Figure 3 shows the use of a QR code to show a pdf file that is stored in dropbox and the QR code encodes the URL

of the pdf file that is shown with the resolution of the problem. Figure 4 presents a video with the resolution of problem 3 that is activated with the QR code that links to the dropbox where the video is stored.

Figure 2: The first QR code was activated using the i-nigma app to show the letter of the correct option.

Figure 3: The QR code of problem 2 shows the resolution.

CREATING LEARNING ACTIVITIES USING MARKER LESS AR TECHNOLOGIES

This section presents interactive mathematics activities that students can do at home based on marker less augmented reality technologies.

The teacher gives students the printed augmented reality maths activities or a PDF file. Students using augmented reality technologies and point a tablet or smartphone on top of the paper or the PDF file in the computer to see the videos about the theoretical materials and the problems resolution step by step (Figures 5 and 6).

In this way, teachers can extend the class into a virtual class in a form of blended learning in which students can view video lectures and home works at home. This can be especially interesting for learning mathematics. If students can learn at home from watching video lectures and solving

problems, time in-class can be dedicated to explore more motivating problem solving. Math teachers have a difficult situation. Studying math is many times a cumbersome task. But this can be changed if the teacher takes advantage of the technology that is currently available in the classroom. Students are surrounded by multiple devices, such as smartphones and tablets, that give them access to multiple media that is easily available. This is an opportunity for the teacher. The technology related to teaching/learning will have a vital role in the coming years in the education field.

Figure 4: The QR code of problem 3 shows a video explaining the problem resolution.

One of the problems identified by in the re-design of mathematical programs was that students had difficulties due to the fact that they were not familiar to the new room setting (Yi and Mogilski, 2014). To overcome this problem we decided to have always the same layout for the activities based in augmented reality. In this way, all the activities follow always the same layout (Figure 5).

There is an A part that is outlined with an orange box and the student knows that there is a corresponding video about an introduction to theoretical concepts. In this example, there are two B parts that are outlined with blue boxes that let the student know that there are videos about an introduction to more practical problems that help understand the new concepts.

There are many applications that can be used to capture the teacher actions on computer screen, accompanied by audio narration, to produce the videos for the virtual classroom. Video recording is well suited for demonstrating basic concepts. It allows students to learn at their own pace and in their own learning style. Video lectures are well adapted for classes with students who have different levels of knowledge of the subject. There are students that can view the materials once and have a good understanding of the subject. Other students can view the videos several times to better understand the subject. This is an advantage over the traditional classroom where many times the students do not understand and do not ask to repeat the subject until they are able to understand. The use of videos for teaching and learning is effective for both visual and auditory learners as there is video and narration that is less complicated than written explanations (Spilka and Manenova, 2013).

With the number of students increasing in the class this is an important tool to enable students to work at home and leave classroom time to implement problem based learning methodologies together with virtual learning classrooms.

For this project we are developing an augmented reality application that can integrate also gaming technologies (Figure 7). We want to bring together augmented reality technologies and gaming to study how motivation can be improved through these methods. The application has a tracker

manager that recognizes trigger images seen by the smartphone or tablet and fetches the corresponding videos from the database. The game manager integrates augmented reality and game-based activities to enhance the learning process. The student specific achievements are stored in the user database.

Figure 5. Page layout for the activities to study at home that is used to trigger Augmented Reality

contents. A - Theoretical video lectures. B - Practical video lectures.

Figure 6. The student can study the lectures at home using Augmented Reality.

Figure 7. The application architecture includes a tracker and a game manager.

Producing course contents requires too much time and cost. An alternate way to produce course contents is to use the textbook companies provided materials, such as PowerPoint files, lecture videos and exercises that are readily available for teachers to create augmented reality activities for students.

In this way, teachers can use their own produced materials or textbook companies contents to create their own activities targeted to the particular needs of each class and individual student. We believe that this can be very motivating for students and it also helps in delivering lectures, hands-on activities and customized study modules. This is a main advantage of using augmented reality for education because teachers can tailor activities to each student.

CONCLUSIONS

The increasing processing power of mobile devices, the increasing number of augmented reality applications and the increasing number of mobile devices, makes possible the use of augmented reality in the classroom.

Math teachers have a difficult situation. Studying math is many times a cumbersome task. Low achievement in mathematics education has been an increasing problem in the recent years in Portugal.

In this paper, we show that using Augmented Reality to produce interactive materials can be motivating for students and contribute to extend the class into a virtual space where students can have more time practicing problem solving.

We show that technology is accessible and easy to use by math teachers and students. In this paper it is explored the creation of educational activities supported on marker based and marker less augmented reality technologies for teaching and learning mathematics.

REFERENCES

Azuma, R.T. (1997). A survey of augmented reality. Presence: Teleoperators and Virtual Environments, 6, 55–385.

Fernandes, G., & Ferreira, C. (2012). Desenho de conteúdos e-learning: Quais teorias de aprendizagem podemos encontrar?. RIED: revista iberoamericana de educação à distancia, 15(1), 79–102.

Heide, A., & Stilborne, L. 2000. Guia do Professor para a Internet - Completo e fácil. Porto Alegre – Brasil, Artmed Editora.

Milgram, P., & Kishino, F. (1994). A taxonomy of mixed reality visual displays. IEICE Trans. Information Systems, E77-D, 1321–1329.

Nielsen, (2012). Smartphones account for half of all mobile phones, dominate new phone purchases in the us. [Online]. Available: http://www.nielsen.com/

Restivo, T., Chouzal, F., Rodrigues, J., Menezes, P., & Lopes, J.B. (2014). Augmented reality to improve stem motivation. Proceedings of Global Engineering Education Conference (EDUCON), 2014 IEEE, 803–806.

Spilka, R. and Manenova , M. (2013). Screencasts as web-based learning method for math students on upper primary school, WSEAS Conference Proceedings, 4th Eu- ropean Conference of Computer Science, World Scientific and Engineering Academy and Society (WSEAS), 246–250.

Yi, T. and Mogilski, J. (2014). A lesson learned from course re-design for flipped classroom, WSEAS Conference Pro- ceedings, 13th International Conference on Education and Educational Technology, World Scientific and Engineering Academy and Society (WSEAS), 21–26.