Paper Keywords: education? New mathematics curriculum? The scientific value of mathematics? way of life
1. Introduction to Mathematics Education.
(1) What is education? [①]
1. In a broad sense, all activities that enhance people's knowledge and skills and affect people's ideology and morality are education. In a narrow sense, it mainly refers to school education, which refers to the activities that educators exert influence on the body and mind of the educated in a purposeful, planned and organized way according to the requirements of a certain society or class, and cultivate them into people needed by a certain society or class. In a narrow sense, it sometimes refers to ideological education activities.
2. Confucius said: "The way to a university is to be well-known, to be close to the people, and to stop at perfection." Lu Xun: "Education is to cultivate people." Children's education is mainly about understanding, guidance and liberation. Cai Yuanpei: "Education is to help the educated develop their abilities, improve their personality and do their part in human culture, rather than making the educated a special tool."
(2) What is mathematics education?
1. Combine mathematical thoughts with theoretical knowledge, exert purposeful and organized influence on the body and mind of the educated, and cultivate their mathematical abstract logical thinking and practical ability.
2. The role of mathematics education
Of course, the value of mathematics is multifaceted, and mathematics education should strive to fully reflect the value of mathematics.
Second, the value of mathematics education
Valuable mathematics teaching should be "life-oriented" mathematics teaching. Based on students' life experience and existing knowledge background, we should provide them with sufficient opportunities to engage in mathematics activities and exchanges, help them truly understand and master the basic teaching content in the process of independent exploration, and solve practical problems in life by gaining rich experience in mathematics activities. "
1. The scientific value of mathematics education
There should be no doubt about the "scientific value of mathematics" in mathematics education, but now it has become a complex subject. With the continuous development of people's understanding of the essence and value of mathematics, people are rethinking how to understand the relationship between science and humanity in mathematics education, how to treat the natural orientation and value orientation of mathematics content in primary and secondary schools, and what kind of mathematics should be taught in primary and secondary schools.
Under the traditional examination system in China, "elite education" and "genius education" have a long history, which seems to have formed "the tradition of China" and become more and more intense since 1990s (obviously, basic education should not be "elite education" or "genius education"). This educational thought and social trend of thought have had a profound and significant impact on mathematics curriculum and mathematics teaching, and caused many people to criticize the past mathematics education. Some people think that this kind of mathematics education is "the education of cultivating mathematicians" and "the education of mathematical geniuses". Some people think that it only pays attention to the scientific value orientation of mathematics and ignores the humanistic value orientation; Wait a minute. These criticisms are reasonable to some extent. Obviously, mathematics education should not be "the education of cultivating mathematicians" or "the education of mathematical geniuses". However, we should also carefully analyze and think about the following questions: In what sense did the past mathematics education mean "education to cultivate mathematicians" or "education to mathematical geniuses"? Are the ideas and reforms such as "popularizing mathematics" and "solving problems" advocated by the United States necessarily fair and reasonable value orientation of mathematics curriculum (or must conform to China's national conditions)? How to grasp the "scientificity" and humanity of mathematics in mathematics curriculum —— The relationship between "mathematics" and "education" in mathematics education? These problems need further analysis and thinking.
2. Mathematics education is not a simple addition of "mathematics" and "education", it includes at least two aspects, that is, "mathematics" is both the "purpose" and the "means" of education. As a means, students learn mathematics (mainly knowledge, theory and corresponding mathematical activities, such as mathematical problem solving and mathematical proof). ) improve their thinking ability and ability to analyze and solve problems, form a good personality quality and psychological structure, and enhance national self-esteem and pride; As an aim, students should learn, understand and master mathematics, that is, through mathematics education, students can acquire basic mathematical knowledge, basic mathematical skills and important mathematical thinking methods, and form a correct mathematical view and a certain mathematical consciousness.
3. How to carry out meaningful mathematics teaching?
In our daily teaching work, we often pay attention to "top students" and "underachievers", but these "middle students" who occupy the majority have become "vulnerable groups" that are easily ignored in classroom teaching and study life. These students are in the middle position for a long time, unable to get up or down, unable to attract too much attention from teachers, and have a sense of inferiority in their hearts. They envy good students for their sharp thinking, but they are afraid that they can't express their ideas, thus losing many opportunities for exercise. The lively classroom makes them even more neglected and aggravates their inferiority complex. Consciously enhance the successful experience of "ordinary students" in classroom activities, and design more topics that "ordinary students" can complete and produce a sense of success after completion. Cultivate students' cooperation and communication skills. In classroom teaching, we should guide students to unite and cooperate, help each other, learn from each other, establish self-confidence in cooperation, learn to compete, and finally make progress together. Go deep into students' group activities and correctly guide middle school students to "how to listen to others' opinions", "how to express their views accurately" and "how to help underachievers". Let "ordinary students" enhance their self-confidence and feel the fun of cooperative learning in activities.
In order to pursue the life of mathematics education, the new round of mathematics curriculum reform in China also reflects this trend. Interpretation of Mathematics Curriculum Standard of Full-time Compulsory Education "The content of mathematics curriculum must fully consider the trajectory of human activities in the process of mathematics development, be close to students' familiar real life, and constantly communicate mathematics in life with mathematics exercises in textbooks, so that life and mathematics can be integrated". Life is the source of mathematics, and the process of mathematics learning is also the process of returning to life, which leads to mathematical problems and discovers mathematical laws from real life. "
Four. Problems faced
It should be said that our middle school mathematics teaching is a kind of "target teaching". On the one hand, we always want to teach students useful mathematics, but if students don't learn mathematics after graduating from high school, they think mathematics is useless except the college entrance examination. On the other hand, our "ten-style method" teaching method has indeed improved students' "ability to take exams", but once students encounter unfamiliar problems or problems related to practice, they will not use mathematical methods to solve them. Most students have studied mathematics for twelve years, but they have no basic mathematical thinking, let alone find and solve problems by themselves with creative thinking. From this point of view, the contradiction between mathematics teaching and learning in middle schools is particularly acute. Pay attention to the relationship with other related disciplines. Because mathematics is a tool for students to learn other natural sciences and even social sciences, and other disciplines are closely related to mathematics. Therefore, we should pay attention to the echo with other disciplines in teaching. In many thinking activities, innovative thinking is the highest level of thinking activities, and it is the necessary ability to develop innovative talents. The Innovation Center of Massachusetts Institute of Technology puts forward that cultivating creative thinking ability should mainly cultivate students' ability to flexibly use basic theories to solve practical problems. Therefore, in the process of mathematics learning and teaching, teachers must pay attention to cultivating students' creativity and ability to solve practical problems, so as to make mathematics education more concrete.
In addition, mathematical activity is not only a "mathematical cognitive activity" but also a perceptual activity with emotional and psychological participation. Successful math activities are often accompanied by the best mentality. Therefore, how to make students have the best state in the learning process is another key factor for our teachers to teach mathematics well. Teenagers are a sensitive period. Teachers can introduce some ways to build self-confidence: use imagination to imply that they are popular and sociable, and create an environment conducive to the development of teenagers, so that students' learning environment will not affect their positive thinking level. Fully respect students, communicate with students in study and emotion, and create a good learning environment for students.
"Psychological research shows that when people are in a relaxed state, neurons in the cerebral cortex can form an excitation center, so that the channels for nerve cells to transmit information are unimpeded and their thinking becomes rapid and agile. This can speed up the process of receiving, storing, processing, combining and extracting knowledge, and quickly consolidate knowledge and transform it into ability. In order to make students feel that mathematical cognitive activities are a kind of relaxed pleasure, not a burden, the following must be done: 1. Teaching activities are emotional communication and thinking communication between teachers and students. The relationship between teachers and students directly restricts students' emotions and will and affects students' learning activities. Teaching practice also proves that love is the guarantee of teaching success. Therefore, teachers should attach importance to emotional input, and take the close relationship between teachers and students and stimulate students' interest in learning as a breakthrough to correct students' fear of mathematics. " [②]
[1] Yuan Zhenguo's Contemporary Pedagogy [1] revised edition in 2004.
[②] High School Mathematics Teaching Paper: "The Composition of the Best Mentality in Mathematics Learning"
Precautions:
Yuan Zhenguo. Contemporary pedagogy [M] Education Science Press, 2004
3 edited by Kailov, translated by Chen Xia, etc. Pedagogy [M]. People's Education Press, 1990.
4 Yuan Zhenguo: "On Education Reform" [M]. Jiangsu Education Press, 1992.
5 Wang, editor-in-chief: Curriculum and Teaching Theory [M]. Higher Education Press, 2009