In fact, the connotation of mathematics is very rich. Mathematics should enter the classroom as a kind of culture, penetrate into the actual mathematics teaching, and strive to make students experience mathematics culture in learning mathematics, be infected by culture, and produce a buzz of culture, so as to truly realize that everyone can learn valuable mathematics, and everyone can obtain the necessary mathematics, and actively explore the practical application value of this knowledge from the perspective of mathematics.
So, how to make "mathematical culture" penetrate into classroom teaching? Here are some of my experiences:
First, the necessity of infiltrating mathematical culture in classroom teaching
1. Mathematical culture permeates the teaching of mathematical concepts, theorems and formulas.
Learning concepts, theorems and formulas is always boring. If there is a wonderful story about the history of mathematics, it will be enough to enliven the overall atmosphere in the teaching class of concepts, theorems and formulas, arouse students' infinite reverie, and inspire and guide them into the hall of mathematics.
For example, when introducing geometry to students, you can introduce the short story of Descartes, the founder of geometry.
Descartes woke up one day and observed flies crawling on the ceiling. Inspired by Descartes, he invented geometry, which is a milestone in the history of mathematics development and has epoch-making significance.
Through such a short story, including the mathematical background in the familiar situation will make students feel more intimate and natural, let students experience the interest in mathematical discovery, stimulate students' great interest in loving and learning mathematics, and achieve the role of "mathematical culture" in mathematics teaching.
2. Infiltrate mathematical culture in the creation of teaching situations.
A good teaching situation is conducive to stimulating students' desire for learning and interest in active participation, making students actively think about problems and actively participate in the atmosphere of independent exploration, cooperation and exchange, thus successfully highlighting the key points of this class and breaking through difficulties.
Using some interesting stories in "mathematical culture" can help us create teaching situations.
For example, when teaching "the understanding of circle", the teacher guides it like this: The teacher asks the students, "What objects with circles have you seen in your life?" The students gave many examples: the table top of the round table is round, the front of the one-dollar coin is round, the CD is round, and the tires of the car are round ... The teacher asked, "Why should the wheels be round instead of square and oval?" The student replied, "wheels made of squares and ellipses will not roll smoothly." "Why do round wheels roll smoothly?" Teachers' questions make it difficult for students to make scientific and accurate answers with what they have learned. This is the theoretical story of the ancient mathematician-Zu Zhongzhi.
The teacher introduced a new lesson: "After learning the characteristics of circle today, students will have a clear understanding of this problem." Students enter the new curriculum with a desire to seek answers to practical questions.
I believe there are no students who don't like stories, so going deep into the subject from the perspective of mathematical history and mathematical culture like this can make the introduction of the subject attractive to students, attract students' attention from the beginning, and easily make students feel good about mathematics.
3. Infiltrate mathematical culture in the analysis and explanation of examples.
Mathematical examples are indispensable teaching links in classroom teaching.
Therefore, we always hope that the role model setting in the classroom can not only achieve the purpose of knowledge function, but also not lose the educational function.
For example, in the application part of the ninth grade quadratic function, Malthusian population model is used to analyze the actual population situation in China, so that students can understand the basic national policy of China-the necessity of implementing family planning and the unbearable population pressure that the country is facing at present, so that students can get the necessary national education.
4. Infiltrate mathematical culture in homework.
Math homework is a math activity that students carry out independently after class in math teaching.
One of the highlights of the new curriculum reform is the increase of a certain amount of reading and thinking materials, and the opening of expanded columns such as "observation and guess", "reading and thinking", "exploration and discovery" and "information technology and application", which provides a space for students with interest, expertise and ability to explore.
Therefore, in the arrangement of homework after class, we should make selective use of this bright spot to guide students to carry out mathematical inquiry, so that in-class inquiry naturally extends to extracurricular activities, so as to achieve the purpose of organic combination of in-class inquiry and extracurricular inquiry.
For example, after students learn the chapter of Projection and View in the ninth grade, we can arrange for students to consult materials, understand the historical process of the development of Three Views, and feel the persistent pursuit and unremitting efforts of mathematicians.
Second, the importance of infiltrating mathematical culture in classroom teaching
Mathematics education is not only an education of scientific quality, but also an education of cultural quality, which is an essential basic quality for a modern person.
Mathematics education is education first, educating people is fundamental, and mathematics knowledge is just a carrier.
Therefore, people learn mathematics not only to acquire knowledge, but also to accept the application of mathematical spirit, mathematical ideas and methods, improve their thinking ability and exercise their will quality, and transfer them to various fields of study, work and life.
Therefore, the new curriculum standard requires the infiltration of mathematics culture in various forms, aiming at enabling students to understand the interaction between mathematics science and the development of human society through the study of mathematics culture in junior high school, to reflect the scientific value, application value and humanistic value of mathematics, to broaden their horizons, to seek the historical track of mathematics progress, to stimulate their understanding of the driving force of mathematics innovation, to be influenced by excellent culture, to understand the learning value of mathematics, and to improve their own cultural literacy and innovation consciousness.
Thirdly, we should pay attention to three aspects in infiltrating mathematical culture into classroom teaching.
1, let students feel the scientific spirit of mathematicians studying hard.
Infiltrating mathematical culture can also provide a favorable opportunity for moral education.
For example, when learning quadratic function, introducing the "God of Mathematics" to students-Archimedes' circle measurement, parabola quadrature and other famous mathematical problems were discovered by mathematicians through reasonable reasoning. These short stories tell students how indispensable it is to cultivate the excellent qualities of diligent observation, good thinking, good at asking questions and solving problems from an early age.
In order to prove the correctness of these conjectures, how many mathematicians in history have devoted their lives to it, such as Mr. Chen Jingrun, a mathematician in China, whose persistent research spirit made a breakthrough in Goldbach's conjecture.
For another example, in order to refute the wrong diagnosis made by Aristotle, an ancient Greek philosopher, that "the speed at which objects with different weights fall from the air is directly proportional to their weight", young Galileo made an experiment in the leaning tower of Pisa to explain it in public, and he also skillfully used the reduction to absurdity to prove it. Such a short story is helpful to the formation of students' dialectical thinking, and to cultivate their rational thinking habit of seeking truth and their scientific attitude of daring to pursue truth.
In fact, in our usual mathematics teaching, there are many examples of infiltrating moral education through the study of mathematical culture. The key is to be good at digging.
2. Let students understand the ideological content of mathematics.
Mathematical thought is the crystallization of the research results of mathematicians in past dynasties. They are contained in mathematical materials and are rich in content.
We should be good at digging them in our usual teaching.
For example, projection and view can introduce the "intercept method" in China's ancient vision.
For another example, Euler abstracted the famous problem of the Seven Bridges in Konigsberg into a one-line problem, and applied mathematical transformation ideas, and so on.
By showing the mathematicians' creative thinking process, we can cultivate students' correct thinking mode and understand mathematical thinking methods.
3. Let students know the track of mathematics development.
For example, the emergence and perfection of geometry theory, the evolution of function concept several times, the establishment of plane geometry, the establishment and development of probability theory, the rise and application of statistics and so on. By letting students know the background of each part of our knowledge, the formation and development of mathematical concepts and the process of putting forward mathematical theorems after class, we can guide students to understand the interaction between mathematical science and the development of human society, broaden their horizons and appreciate the scientific, applied and humanistic values of mathematics, thus effectively improving students' scientific literacy.
In short, although the new curriculum standard does not set up a special course of "mathematical culture", it does not mean that this part can be omitted.
On the contrary, we should pay more attention to the organic infiltration of "mathematical culture" in different teaching contents, so that students can be subtly influenced through various channels in the process of learning, exploration and communication, and guide students to use the knowledge and methods they have learned to solve simple practical problems in life, thus increasing the opportunities for practical activities, so as to achieve the purpose of cultivating innovative consciousness and solving practical problems in mathematics teaching.