Analysis of Digital Competencies of 21st Century Teachers of Mathematics Education by Pentagonal Fuzzy Number and Some of Its Arithmetic Operations

: Digital competencies is a collection of digital skills, categorized into five main areas of focus. They are designed as a tool for students to use to reflect on the digital skills and critical perspectives they develop while in school or college, in curricular and co-curricular experiences. The factors in digital competencies are digital survival skills, digital communication, data management and preservation, data analysis and presentation, critical making, design and development. In this paper we use pentagonal fuzzy number to find out the failure of digital competencies of 21st century teacher in mathematics education on the basis of the above criteria.


Digital Competencies
Each new stage in the development of society changes first of all the forms of learning. The school of the eighteenth to nineteenth centuries, the school of humanism of the Enlightenment, changed the attitude toward the child in accordance with the nature of their growing up, aimed learning on the study of nature. It was an era of great scientific research and geographical discoveries, travel, and knowledge of the evolution of life on earth. The school of the twentieth century, the school of the era of industrial society, became widespread and introduced into formal education scientific achievements, educational equipment, mathematics, as the language of science, and rationalism in cognition and design. It was a period of searching for new pedagogical methods, and as a result, the twentieth century became the century of universal literacy. The school of the twenty-first century, a digital school, made it possible to use the individualization of education in a global knowledge network that transformed the concept of school as a building where children study in classes. Network class, virtual network school, has become a reality. Digital forms of formal education in the open knowledge network have become part of a new educational environment, a smart education environment in which each student can build their own individual educational route outside formal education in accordance with their educational developmental interests. This new form of education is part of the social benefits of the digital age for everyone throughout their lives. The school of the twenty-first century is an open information resource of education for everyone; it is a school of universal education.

Fuzzy Sets and Number
In 1965, Lotfi A. Zadeh (Alefeld,G.,and Herzberger,J, 1983), delivered new concept namely Fuzzy Sets theory. The theory of unsharp amounts has been applied with great success in many various fields. Chang and Zadeh introduced the concept of fuzzy numbers (Cheng.C.H. and Mon. D.L, 1993). Different mathematicians have been studying the theory (one-dimension or n-dimension fuzzy numbers, see for example Refs. ( Cai.K.Y., Wen.C.Y. and Zhang. M.L , 1991;Cai. K.Y., Wen. C.Y. and Zhang. M.L;. With the various improvement of theories and applications of fuzzy sets theory the topic become a topic of great interest.

Pentagonal Fuzzy Number
Many researchers take pentagonal fuzzy number with different types of membership function. In this subsection we study on some published work which is associated with pentagonal fuzzy number:

Motivation
Fuzzy sets theory plays an important role in uncertainty modelling. Now the question is if we wish to take a fuzzy number then how its geometrical representations are. So, if decision maker takes a fuzzy number which can be graphically looks like a pentagon then how its membership function can be defined. From this point of view, we try to define different type of pentagonal fuzzy number which can be a better choice of a decision maker in different situation.

Novelties
There is various articles where pentagonal fuzzy sets and number are introduced and apply to different fields. But there are so many scopes to work on that topic. Some new interest and new work have done by our self which is mentioned below: i. Try to utilise the properties of pentagonal fuzzy number to described the failure of digital competencies of 21 st century teacher in mathematics education. ii. Described the factors of digital competencies. iii. Describe a numerical expression by pentagonal fuzzy number. iv. We used all the allocation of number in the reliability system by pentagonal fuzzy number.

CONCLUSION
Different technological tools are need for the math students. Such as computer algebra system, dynamic geometry environments, interactive applets, handheld computation, data collection and idea to different devices. This system gives a student to explore, identify math concept perfectly and also relationships. But fuzzy system only gives the idea of uncertainty or where the data are insufficient. But we have to learn it to know the reality, because it is an obstruction in the modern e-learning world. We use fuzzy data so present the barrier of digital competencies of mathematics in reliability system. Our approaches and computational procedures may be efficient and simple to implement for calculation in a pentagonal fuzzy environment for all fields of engineering and science where impreciseness occur.