The Application of Bantong in Mathematics Teaching

Abstract: Class pass is an important part of the construction of "Internet + education", but also one of the grips of reform in the field of education. It embodies the scientific consideration of the state in the investment of educational resources to measure the strength of software and hardware investment, not only contains the "Internet + education" concept of universal, fair and efficient, but also embodies the essence of education involves the law of evolution of thinking and subject literacy enhancement of the demand. Based on the above understanding, this paper discusses the philosophical basis for the efficient use of the latter in the mathematics classroom, in relation to the function of Bantong, and in the light of the characteristics of high school mathematics and the educational demands of the subject.

Keywords: Bantong, high school mathematics, intuition, philosophical basis

With the popularization of information technology and the state's strong investment in and support of education, Bantong has gradually been introduced into the mathematics classroom. In a sense, this can be said to have brought about a change in the mode of mathematics teaching, because not only on the surface, the wide application of Bantong replaces the traditional mode of "a blackboard + a piece of chalk", which makes the mathematics classroom full of vitality and interest, and thus improves the effectiveness of classroom teaching; more importantly, it also brings about a change in both teaching and learning. The new system is a new way of thinking about teaching and learning. For both teachers and students, the emergence of Bantong in the classroom means that the output and input modes of teaching and learning have changed, and even evolved.

So, for teachers, the application of Bantong is not only a challenge but also an opportunity. It is a great opportunity for teachers to update their educational concepts and reform their teaching mode. In terms of specific teaching skills, they should actively learn about information technology and explore new educational methods to improve their quality and business skills to adapt to the new form of development. Specifically for high school mathematics teaching, linking the functions and background advantages of Bantong, based on the analysis of pure mathematics, combining the characteristics of the discipline of high school mathematics and educational demands, and ultimately further analyzing the basis of the use of Bantong in the mathematics classroom from the philosophical height, it will be more conducive to the enhancement of the understanding of the two ends of the "teaching-learning" and a change in the mindset. The first is to make sure that you have a good idea of what you're doing, and what you're doing.

I. Functions and Background Advantages of Bantong

Under the current background of "Internet+Education", accompanied by the development of information technology, and combined with the characteristics of the students' learning styles, Bantong possesses great advantages. Simply put, Bantong is a set of teaching devices that introduce the network into the classroom hardware devices (multimedia, projectors, electronic whiteboards, etc.) to be used.

But our understanding of Bantong should not stay in this simple, mechanical level, it is not only a device, device, rather it is the software and hardware, virtual and real, abstract and intuitive, the human brain and the computer's integrated links. It bears not only the teacher's information launching function to students, but also the mapping of the two sides, as well as the interactive communication function to the whole powerful Internet resources, and it can even be said that Bantong is one of the nodes in the whole Internet world, but this node is connected to the living classroom. Therefore, in such a combination point, Bantong has great advantages and wide application scenarios in the current and future teaching.

Second, analyzing the subject characteristics and teaching demands of high school mathematics from pure mathematics

What is pure mathematics? We have to go back to Kant and his "Copernican Revolution" in the field of philosophy. According to Kant, true mathematical propositions are always innate judgments rather than empirical judgments, because they have a necessity that cannot be obtained from experience. So when Kant confines mathematics to pure mathematics, this restriction contains the proper implication that mathematics does not contain empirical knowledge, but only pure innate knowledge. If we combine this with the Pythagorean idea that number is the origin of all things, we may gain a deeper and more accurate understanding of the word "pure" here. Whether in terms of what is internal to our thinking or external to the origin of all things, number here has the highest prescriptive character, and thus implies the most abstract and overwhelming generalization. In this respect, pure mathematics seems to be a purely analytic proposition. What is remarkable about Kant, however, is that here he reverses the traditional understanding - the Copernican revolution is manifested here. In the case of 7+5=12, for example, from the purely analytic analysis of 7 and 5, we cannot get the concept of 12, but at most we can get another concept of number - the concept of sum - from 7+5. However, this concept of sum is not necessarily 12, that is, neither the analysis of 7, nor of 5, nor of 7+5 can go beyond them to another concept, 12. The notion of 12 can only be reached by going beyond the analysis of the numbers themselves, by means of intuition, in which each of the units that make up 5 is added to 7, one by one. This philosophical description of the process embodies the very assertion of the Copernican revolution of the innate synthesis of judgment.

We know that disciplinary literacy cannot be improved without the transformation and evolution of disciplinary thinking, and the study of mathematics in high school should and must go deeper into mathematical thinking. If we can't think mathematically from the abstract and figurative, that is, abstract and intuitive levels, it is difficult to get involved in the level of disciplinary thinking, not to mention the enhancement of disciplinary literacy. As the saying goes, the only way we can form a thought about a line is to draw a line from the thought. In the most abstract cover and the most figurative intuition to find the most appropriate point of combination between the formation of mathematical thinking is the key point, but also the characteristics of the subject of high school mathematics and teaching requirements.

Third, the philosophical basis for the use of classroom communication in the math classroom

Socrates said that education is a skill to unearth what is already ours. And that which is already hidden in the depths of our souls is the innate knowledge of our reason. Uncovering them has become not only a skill, but an art. In this respect, what Socrates called the midwifery of knowledge, and the role of the teacher as midwife, is a very modest statement. For the formation of our knowledge requires not only two innate forms of intuition, time and space, but also another innate category. How to add something to these innate foundations, that is to say, how to add to those given concepts something that is not contained in them, and how to extend our innate knowledge through innate synthesizing judgments that go far beyond the existing concepts themselves, so as to turn the embryo that has already been formed into a real fetus, is the skill of the midwife, the art of the teacher's education.

But in the past, education was limited by the technological and instrumental conditions of the time, and the need to raise the demands on teachers to the level of art was a requirement in the context of elite education. However, modern education fosters not a few elite groups, but the elitism of the masses, and thus the nature of education has also taken on a universal character. In this context, if we then ask every teacher to become an educational artist, it will create a practical conflict with the concept of inclusive education. Therefore, we have to realize a breakthrough in technology and tools, and so such teaching resources as Bantong came into being. Specifically for the teaching of high school mathematics, combined with the analysis we made earlier, the functions and background advantages of Bantong can realize the organic combination of abstraction to concrete, cover to vivid. Teachers can present complex and abstract mathematical theorems and definitions through Bantong to make them vivid and graphic, visualize the thinking process and visualize mathematical ideas. This is the practical and philosophical basis for the use of Bantong in high school math classroom teaching (and other subjects as well).

Reference: Zhang Lei; Ruicheng Site Conference on the Application of "Class Pass" and "Everyone Pass" Teaching and Learning in Shanxi Province.