How to better penetrate the mathematical culture in teaching

Mathematical culture can not be separated from the history of mathematics, each nation has its own culture, there must be mathematics belonging to this culture, Chinese traditional mathematics have brilliant achievements, excellent tradition. In my daily teaching, I let students know the national and global nature of mathematical culture through the introduction of mathematical culture celebrities. Such as the first year of learning fraction multiplication, I told students about the Warring States period of the Hundred Schools of Thought "a foot of whip, the day to take its half, the world is not exhausted," the Mohist disagreed with the proposition "a foot of whip", put forward a "non-half "The proposition to refute: a line segment by half and half of the infinite division down, there will be a can not be divided "non-half", this "non-half" is the point. Another example is to speak of the four operations of fractions to introduce students to the "nine chapters of arithmetic" is the Warring States, Qin, Han feudal society was founded in the Sui and Tang dynasties had been transmitted to North Korea, Japan, and become these countries at the time of the mathematical textbooks, in terms of its mathematical achievements, can be regarded as the world's mathematical masterpieces. Then, in the second year of junior study of irrational numbers through the introduction of Zu Chongzhi on the basis of Liu Hui's note "Nine Chapters of Arithmetic", the traditional mathematics greatly advanced a step forward. He calculated pi between 3.1415926 ~ 3.1415927, Zu Chongzhi this work, so that China in the calculation of pi, than the West about a thousand years ahead of the long time; through this to cultivate students' national pride.

Ancient Chinese mathematics, mostly in the form of "management mathematics," was designed to measure acres of land, build water conservancies, distribute labor, calculate taxes, transport grain, and other practical goals of state management. Therefore, from a cultural point of view, Chinese mathematics can be said to be "management mathematics" and "carpenter's mathematics", which existed in the form of official documents. We fully value the practical and algorithmic traditions of traditional Chinese mathematics, and at the same time we must absorb all the useful mathematical cultural creations of mankind, including the cultural traditions of ancient Greece. We as 21st century math teachers must dissolve traditional Chinese culture into the world's mathematical culture, and organically combine national and global, which is what we should do in our daily math teaching.

Second, in the math teaching to reveal the connotation of mathematical culture

Chinese mathematical education, there is often "math = logic" concept. Math teaching has sometimes become a kind of empty problem-solving training. Mathematical research has seen a tendency to over-specialization and over-emphasis on abstraction, while neglecting the application of mathematics and its connection with other fields, and striving to show the culture of mathematics in many aspects.

1. Mathematics and language. The ways of thinking about math and language are often similar. For example: Su Shi's poem wrote "cross look into the mountain side into a peak, near and far, different heights" is the secondary school textbook from different directions to see the object, the main view, left view, top view and other three views are not the same. Another example: the idiom of "seven up, eight down" in language corresponds to the fraction 7/8 in math. There are also junior high school math in the "axisymmetric figures" and the language of the "battle" is inevitably linked.

Mathematics and idiomatic stories: such as the rabbit race can be in the same plane right-angle coordinate system, draw a proportional function and segmented primary function of the image, through the image to tell the story, the students very much like to improve the enthusiasm of students to learn the function.

2, math and language. Language is the carrier and shell of culture. A cultural expression of mathematics is to dissolve mathematics into language. "No matter what" involves multiplication mnemonics, "three, two, five, solve it" is the abacus mnemonic. Another example is "a hundred shots a hundred hits" to explain it as 100% "life trajectory" and other familiar words are the expression of mathematical culture.

3, math and physics. Various disciplines, physics and mathematics, the relationship between the most pro-physics and mathematics is to promote the relationship between each other, the ultimate goal of mankind on the study of nature, a lot of mathematical new tools are human beings in the study of nature in the process of encountering difficulties, can not be solved, they want to think of a different mathematical tools with the previous mathematical tools of a brand new mathematical tools to study and analyze the new problems. For example, trigonometry and many plane geometries were invented when measuring and dividing land, and logarithms and calculus were invented when studying motion in astrophysics. The invention of these tools greatly simplified and even solved previously impossible problems. It gave mankind a better understanding of nature. So as a math teacher we let students know from childhood that mathematics and physics in science are inevitably linked, so that students learn math, to grow up to study the natural sciences to lay a solid foundation.

Three, penetration of mathematical culture of teaching strategies

1, change the book math for life math. The Mathematics Curriculum Standard proposes that "mathematics teaching should be closely related to the actual life of the students, from the students' life experience and their own knowledge", and "everyone learns valuable mathematics", only in this way can we stimulate the students' interest and motivation to learn, and deepen the students' experience of mathematics everywhere around them. The experience of math everywhere around. For example: the first year in the teaching of absolute value, let the students calculate |3 | and |-3 |, I do not let the students rote memorization of "the absolute value of a positive number is itself, the absolute value of a negative number is its opposite," but through the students to pay for the ride is only related to the distance, but not related to the direction of the students understand that the absolute value has nothing to do with the direction of the representative is the distance from the origin of the absolute value. of the distance.

2, change "teaching materials" for "teaching with materials". Mathematics textbook is an important basis for teachers to carry out classroom teaching, but definitely not the only basis. No matter which place the choice of teaching materials is very small, and the actual situation of students around the world is very different, which requires us to teach, teachers should dare to use materials creatively, based on the actual students, from the development of students and the need to consider, not for the sake of the materials to teach students, but for the sake of the students and the use of teaching materials, so that the materials really become conducive to the students to think independently, independent exploration, cooperation and communication. "Learning materials". For example, when teaching the meaning of percentages, I let the students collect their own materials of percentages, some students bring milk, some bring tissues, some bring drinks, some bring labels on clothes, so that the students can use their own language to understand the meaning of percentages.

3. Change passive training into independent inquiry. The way of learning mathematics should not be a single, boring, passive way of listening to lectures and exercises, but should be a journey full of vitality. For example, when teaching the nature of similar triangles, I let a group of four students cooperate to make their own device for imaging small holes, then measure the object height, image height, and the related distance, and through calculation, observation, and comparison, I concluded that the ratio of the corresponding heights of similar triangles is equal to the similarity ratio. The exploration of this property cultivates the spirit of mutual cooperation and the ability of students to interact with each other, and also lays the foundation for the development of the habit of independent investigation and learning. Throughout the teaching process, the students' activities are a lively, active and personalized process, fully embodies the teaching concept of "hands-on practice, independent exploration and cooperative exchange is an important way for students to learn mathematics" proposed by the Mathematics Curriculum Standards, and the teacher really plays a role in organizing, guiding and cooperating.

Of course, there are many teaching strategies for infiltrating mathematical culture, and every math teacher on the front line of teaching should not only explore, but also find their own methods and strategies.

In short, when the charm of mathematical culture really penetrates into the teaching materials, reaches the classroom, and dissolves into the teaching, the mathematical teaching of mathematical culture will make students further understand mathematics, like mathematics, and love mathematics through the cultural dimension.