Based on related research, the application of augmented reality technology in mathematics education is briefly analyzed

Augmented Reality (hereinafter referred to as AR), the term was first put forward by researchers of Boeing Company in the early 1960s. After decades of development, the technology has become increasingly mature and is now widely used in many fields, such as military defense, medicine, entertainment, education and so on. As early as 2008, Gartner Inc predicted that AR technology would become one of the disruptive technologies in 2008-2012, affecting various fields and even the whole society.

Among them, AR education integrates augmented reality technology into the traditional education environment, so that students can obtain a visual and immersive learning experience. It can break the barriers of traditional education, provide new opportunities and ways for learning, and has a very promising prospect. The following is a brief analysis of the applications of AR in math education, including "Numbers and Algebra", "Graphics and Geometry", and "Statistics and Probability".

Figure 1 shows the research status of the application of augmented reality technology in mathematics education. From the perspective of teachers' teaching, AR technology can be involved in teaching mode, content development, teaching design, teaching integration, resource construction, etc. From the perspective of students' learning, AR technology involves learning process, learning results, learning experience, learners' characteristics, cognitive process, cognitive structure and other aspects. There are two kinds of AR interaction, one is based on image interaction, the other is based on position interaction. When it is applied to mathematics learning, from the perspective of learning content, it involves several main subjects of mathematics learning, including "number and algebra", "graphics and geometry", and "statistics and probability". In addition, AR technology can also be combined with specific activity mode to highlight students' dominant position and emphasize the process of students' learning.

Figure 1 Application of Augmented Reality Technology in Mathematics Education

1. AR and "Number and Algebra"

"Numbers and Algebra" contains many concise and abstract concepts, and there is a strong logical relationship between these concepts, for beginners, there are great difficulties to understand. For example, variables, quadratic equations, exponential and trigonometric (sine and cosine) functions, logarithms, etc., in middle school, if they cannot understand their "why", then they can only learn by rote the rough way of calculating formulas to cope with the exam. AR mathematics teaching, text, graphics, video and audio integration into the real-time learning environment, compared with the traditional learning methods, the former provides a wealth of enhanced functions, a high degree of participation to increase the motivation of students to learn. As a strategy tool, AR can also show students the processes involved in problem solving through its visual nature.

Mobile games based on math education can provide better learning opportunities and be more engaging. For this, the researchers used AR Foundation of Unity 3 d software package, designed the mathematics learning method based on AR of mobile games, with the aid of mobile devices in the AR and position sensor, can let students in their own home environment and virtual pet and objects interact, beneficial supplement for the traditional mathematics classroom teaching, and provide more opportunities to explore the world of mathematics learning. In order to comprehensively evaluate the impact of this AR mobile game on math learning, the researchers conducted experimental research on middle school algebra as the theme, and found that this AR mobile game can improve students' motivation for math test preparation, their math test scores, and their overall confidence in math subjects.

At present, many researches are based on a certain knowledge point in "Mathematics and Algebra", which enables students to master the knowledge and ability of this topic well. When solve the subtraction of negative, for example, to remedy paradigm of AR as a negative subtraction operation, through the different role to play in the AR, let the students compare different situation will produce subtraction problem, notice different digital simulation by the different roles of irreplaceability, subtly understand the subtraction is an exchange of facts. Based on this work, some researchers developed an augmented reality remedial worksheet system aimed at helping learners to recover the correct thinking process visualized by the subtraction of negative numbers.

As a tool of mathematics education, AR games can provide students with rich learning materials and facilitate learning, especially in the areas of problem-based learning and logical reasoning. Some researchers developed an AR game called FootMath to simulate football for serious games of middle school students. Users can adjust different parameter values by themselves to manipulate and explore different functions to obtain the objective function. In addition to primary and secondary school mathematics, there are also related applied research in preschool education. The Malaysian education team designed the AR Magic Book for preschool students, which visually presents the relevant mathematical content of "counting" in situational AR stories, fully mobilizing the learning enthusiasm of kindergarten students.

2. AR and "Graphics and Geometry"

The study of "graphics and geometry" is the direct carrier of developing students' abstract thinking and spatial concept. With the support of AR technology, the phenomenon that is difficult to observe by naked eyes can be visually presented through its visual features. The study found that by presenting rich visual images and giving students hands-on control over them, they could develop their visual thinking.

Compared with the information technology means commonly used in the past, AR can realize more friendly user interaction through its interactive interface, ignite students' motivation and interest in learning, and let students immerse themselves in the learning situation of the target subject. In recent years, the focus of core concepts and literacy, such as "spatial concept" and "intuitive imagination", has made the knowledge in the field of geometry more and more important. Some scholars have conducted research on the feasibility of AR application in geometry teaching design, showing that the intuitive spatial visual simulation presented by AR can assist students' mathematical learning. There are abundant empirical studies on the subject of "graphics and geometry". Numerous studies have shown that AR technology has obvious positive effects on the learning of "graphics and geometry" in terms of knowledge, content and emotional attitude. For example, Punama et al. created an OpenCV-based AR geometry learning tool to help primary school students learn to use protractor, so as to enhance students' learning interest in math subjects.

The concept of space is the intuitive feeling of the surrounding environment and objects. A number of studies have shown that the application of AR in geometry learning can improve students' concept of space. For example, Kaufmann and Schmalstieg designed an AR system named Construct 3D, which is easy to use. This system can improve students' spatial concept and cooperative learning ability. Lin Haojiang et al. designed an AR assisted learning system to help junior high school students learn solid geometry, to improve math performance and spatial perception performance, and promote students' effective learning.

3. AR and "Statistics and Probability"

The subject of "statistics and probability" in the curriculum of primary and secondary schools is closely related to daily life, and more and more attention is paid to it. AR provides a rich contextual learning experience for understanding concepts related to statistics. The existing design and research of AR applied to "statistics and probability" learning are mostly from living situations, and the application forms of AR in education are also rich and interesting. In primary school, Lee et al. developed an AR version of "Monopoly Educational Game", allowing pupils to "incidentally" learn mathematics knowledge under typical situations that often appear in the "Statistics and Probability" module in the context of AR games. In middle school, when learning the concepts of "frequency" and "probability", Li et al. asked students to use AR application to conduct classic experimental exploration of "coin flipping". AR was used as a tool to record the result of "coin flipping" and automatically generated frequency curve. The research results show that by using AR to carry on the inquiry learning, can in the limited class time quick record large sample experiment results, the efficiency of inquiry activity, in the real "throwing" on-the-spot experiences and real-time observation of the frequency curve change process, students can understand the difference between two concepts and connections, the enthusiasm of the students have improved significantly. In the stage of higher education, Conley et al. studied and compared the learning outcomes before and after high AR experience, low AR experience and no AR experience with the theme of "Statistics and Probability". The results show that students with high and low AR experience are more engaged in learning statistical knowledge than students with no AR experience. The researchers also conducted a predictive test and post-test on the students' statistical knowledge, and found that the students with good academic performance had no significant change under the AR experience, while the students with poor academic performance benefited more and improved their academic performance more significantly.

Overall, AR in basic education and higher education stage students "statistics and probability" emotional attitude has a positive impact, not only can provide processing statistics intuitive experience, helping students to accumulate experience in basic activities, in practice is helpful to the understanding of statistical concepts perceptual to the rational understanding of the transition.

4, summary

Based on the above studies, the research on AR in various fields of mathematics mainly has three conclusions :(1) AR has different degrees of improvement in students' mathematics academic performance in different fields, and has a significant effect on auxiliary geometry learning; (2) AR can only significantly improve the math academic performance of students with greater room for improvement; (3) AR has a significant promoting effect on students' learning enthusiasm. In these studies, most researchers of students before and after AR application performance before and after the test, to the student the knowledge of measurement, in the interview, has carried on the investigation to the students' learning motivation and participation, in addition to pay attention to academic performance and the influence of emotional attitude of aspects such as learning motivation, learning ability, learning literacy, learning paradigm also deserves further dig.

In addition, from the above analysis, we can see that augmented reality technology has many applications and advantages, and still faces many problems in the actual teaching practice. For example, (1) the influence scope is limited. Not all studies show that augmented reality significantly improves learning outcomes. Several applications of augmented reality empirical research data show that although augmented reality of students played a significant role in learning motivation, emotion attitude, but for some students mathematics study results and no significant effect, especially for achievement has been at a higher level of students, did not show excellent effects. There may be the following reasons: First, the test period was short, and no significant difference was found in a short period of time; Second, AR itself is an emerging technology, and traditional pen-and-paper standardized tests may not be a good way to assess the impact of this technology and its ability to solve real-world problems. (2) Lack of interdisciplinary research teams and technical experts. Despite the number of educational apps that have flooded the market in recent years, few have been specifically designed for math. Even fewer are using emerging AR technologies. (3) Difficulties in classroom integration. In Lithuania, the education system is quite static, lacking different learning methods and styles. AR technology bring opportunities to their education reform, has drawn much attention in Lithuania, but in the country's AR has not been widely used in the process of education, the reason is that many teachers how do not find AR technology into the learning process, when used in mathematics the specialized subject is lack of effective and targeted teaching design. For AR to be used in an educational environment, each application is unique and must be designed for a specific discipline and specific knowledge content. AR is only the carrier of mathematics teaching content, and only with appropriate content selection and teaching design can it exert its effect on learning. Its design and use must be guided by subject experts or thematic experts. However, the current quality of relevant digital resources is not high and there is no real connection with the demands of learners, which often leads to problems in the integration of AR and classroom. In many cases, these new technologies only "show off" in the demonstration class, which is separated from and simply superimposed with the teaching content, and cannot be widely used in normal classes.

From the perspective of application technology, image-based (mark-based) augmented reality technology is the most common method to support the development of AR learning experience, followed by location-based augmented reality technology. Compared with unlabeled tracking technology, the tracking process of current markers is better and more stable, and the connection with the real world in space and time is more natural, which is conducive to realizing more immersive AR learning experience rather than intrusive. The above two methods mainly push text and pictures to learners based on the recognition of geographical location and markers. In recent years, they have gradually formed a trend of pushing 3D objects to users. They tend to be more perfect in terms of the sense of reality and magic, but there is still a lot of room for optimization in the aspects of rendering and tracking algorithm in the real environment. For example, there are technical issues such as insufficient light that can cause shading, motion blur from handheld devices, and tracking delay. The robustness, real-time performance and flexibility of the program still have great room for improvement.

At present, the most popular tools that can access and create AR applications are Atomic, Unity 3D, AMIRE and Compos AR, etc., which all require users to have certain computer knowledge and programming language, which is also the biggest barrier to the further promotion and application of this technology. With the maturity of mobile technology, AR technology has been widely integrated into mobile devices such as smart phones and tablet computers. The ease of application affects the popularity of this technology. For example, making the operation interface more intuitive and allowing users to create a learning environment without using programming language is the direction of future technical efforts. It is an important direction for future research to enable teachers of all disciplines without programming experience to create AR programs according to their teaching objectives and make AR truly become a "creative tool" to reflect the deep integration of disciplines and technologies and realize deep interaction.

In general, AR mathematics education has broad application prospects, but it is still in its infancy. According to the current research, most of them focus on the research of teaching mode and teaching design. A small number of researches focus on students' learning results, learning process, learning experience and learners' characteristics. Some researches focus on content development for different activity modes. However, the research on students' cognitive process, cognitive structure, teaching integration and resource construction is almost blank, which needs further attention.