Infiltrating Mathematical Spirit and Thought in Mathematics Teaching +0 65438
What are the old sayings? Diligent and thoughtful? Over the years, who have we been? Diligence? More than enough? Think? Insufficient.
Now, two kinds? A little difference, thousands of miles away? In front of us, which is lighter or heavier is worth weighing.
Combining teaching practice and teaching experience, it is emphasized that paying attention to the cultivation of students' mathematical thoughts and spirit in basic mathematics education will help students learn and master mathematics better, develop their sound personality and cultivate their scientific and humanistic qualities.
Mathematics teaching, mathematics knowledge, mathematics method, mathematics thought and mathematics spirit.
M Klein, a famous historian of mathematics, said: "Mathematics is a kind of spirit, a kind of rational spirit. It is this spirit that inspires, pushes, inspires and urges human thinking to be applied to the most perfect degree. " This mathematical spirit is actually the foundation of mathematics.
The educational examination circle divides and systematically classifies the important thinking methods of middle schools, and divides the mathematical thinking methods into three categories:
The first category, mathematical thinking method, mainly includes the idea of function and equation, the idea of combining numbers and shapes, the idea of classification and synthesis, the idea of transformation and transformation, the idea of special and general, the idea of finite and infinite, the idea of possibility and inevitability, and the idea of algorithm.
These are all important mathematical thinking methods that must be tested in the college entrance examination.
The second category, mathematical thinking method, mainly includes analysis, synthesis, induction, deduction, observation, verification, specialization and so on.
The third category, mathematical methods, mainly refers to specific methods with narrow application scope, such as collocation method, method of substitution method and undetermined coefficient method.
The relationship between these three categories can be summarized in one sentence, that is, people use the second kind of mathematical thinking method in the process of solving problems, and under the guidance of the first kind of mathematical thinking method, they use the third kind of concrete mathematical methods to solve problems.
In our college entrance examination questions, this is the way to take the exam.
I put emphasis on reminding students to be careful in teaching practice.
However, more and more practice makes me find that this is not only caused by students' carelessness, but because students fail to really understand the deep meaning of an equation.
For example, when I was correcting this mistake of a student with good math scores, he was puzzled and said: Teacher, why did a number move from one side of the equal sign to the other side of the equal sign, and then changed the previous addition and subtraction sign to be completely opposite to that before moving? He even gave an example: If I walk from the west end of a bridge to the east end, will I become a girl from a boy? At that time, I didn't care too much about the students' problems. I just told him that this was the requirement of the algorithm, and it would be wrong not to do so.
Then I forgot.
I had the opportunity to see the western mathematics classroom, only to suddenly find that I didn't really understand the subject of mathematics at all.
In some western classes, I see that children's computing ability is poor, but teachers don't mind, because teachers are committed to cultivating children's mathematical thinking ability, teaching children why numbers are a number, and what's the use of numbers, trying to make children design math problems in combination with their own lives, so that mathematics can form a life ability.
Speaking of which, some people will definitely ask: what if the computing ability is poor? People are not so single-minded when considering problems. Try to invent a calculator and make it serve people.
Do you think, no matter how accurate your calculation is, can it be as accurate as a calculator? It is sad to turn the human brain into a computer, and it is wisdom to let the computer serve the human brain.
Put forward? Try to penetrate the basic mathematical thinking method? ,? Cultivate the habit of dialectical and comprehensive thinking? Let readers pass these basic knowledge? Do the branches and leaves understand what's inside? Mathematical thinking method? .
Seeing this view, I suddenly remembered the student's words.
Obviously, he didn't understand why he did it, and he tried to understand. He wants to correct his frequent mistakes on the basis of understanding.
But I didn't give him the correct guidance in time, just let him be careful from the perspective of operating rules and don't make similar mistakes again.
I am more deeply aware of a problem in our mathematics teaching, that is, almost all our teaching focuses on imparting mathematics knowledge and methods to students, while ignoring the excavation of mathematics thoughts and spirits, which is the key to helping students deepen their understanding and improve their mathematics learning ability.
Mathematics learning and daily training are still closely related, which is a pair of contradictions. How to resolve the contradiction can only be achieved through good study habits at ordinary times, that is, to improve the efficiency of math classroom lectures, improve the quality of math homework, and make up missed lessons.
The tactics of asking the sea are not the way to improve efficiency. We should get rid of the tactics of repeatedly doing the same type of questions in the past, pay attention to the practice and correction of mistakes in training, and make up the missed lessons in learning? Mathematical thinking refers to the spatial form and quantitative relationship of the real world reflected in people's consciousness, which is the result of thinking activities.
Mathematical thought is the essential understanding after summarizing mathematical facts and theories.
Through the cultivation of mathematical thinking, mathematical ability will be greatly improved.
Mastering mathematical thought means mastering the essence of mathematics. ?
Paying attention to cultivating students' mathematical thoughts and spirit in teaching practice will help our mathematics education to change from focusing on developing intelligence to coordinating the development of intelligence and non-intelligence, to guide mathematics education to change from short-term utilitarianism to lifelong quality education, and to promote the organic integration of mathematics quality education and humanistic quality education from simply improving the level of mathematics knowledge.
In the practice of mathematics teaching, paying attention to the cultivation of students' mathematical thought and spirit can make students really understand and master mathematics; Students learn mathematics on the basis of understanding, and their math scores and learning effects will really improve.
Therefore, it is necessary for us to integrate the spirit of mathematics into mathematics curriculum and classroom teaching, including mathematical thinking methods, mathematical consciousness and mathematical concepts.
Mathematics education is an important part of education, which plays an important role in developing and perfecting people's educational activities, forming people's attitude and way of thinking towards the world and promoting social progress and development.
In modern society, mathematics education is an important aspect of lifelong education and the need of lifelong development!
References:
[1] edited by D.A. Drenan. Modern Introduction to Metaphysics, new york: Glencoe Free Press, 1962.
[2] Zhang Hua. On Experience Curriculum [M]. Shanghai: Shanghai Education Press, 2000.126-131.
[3] Zhong Qiquan's "For the rejuvenation of the Chinese nation and the development of every student: Interpretation of the Outline of Basic Education Curriculum Reform (Trial)" (East China Normal University Press 200 1)
[4] Mi Shan National Anthology "The Spirit and Method of Mathematics" (Sichuan Education Press 1986)
[5] Li Xingmin; On the spiritual function of science [J]; Journal of Xiamen University (Philosophy and Social Sciences Edition); Issue 5, 2005
The Value and Significance of Mathematics Education II
This paper analyzes the function of mathematics education to people from the practical value of mathematics, and then analyzes the function of mathematics culture in mathematics education and its significance to people's development.
Keywords: mathematics education; Educational value; Mathematical culture; Mathematical significance
Mathematics, from primary school to junior high school, is an important course that must be studied.
Even in universities, many majors still have to offer advanced mathematics.
Why do we have to learn so much math? What role does mathematics play in one's educational experience? What is the significance of mathematics to a person's development? Generally speaking, we can easily see the benefits of advanced technology to social life, but behind this, the role of basic science is often ignored, especially the role of mathematics.
It is difficult for us to find a correct and simple explanation about the meaning of mathematics.
In mathematics education, the understanding of the meaning of mathematics is deepening and improving.
In mathematics teaching, some teachers and students often think? Whether mathematics is useful or not.
For mathematics, we should not only consider its significance to human development, but also consider its practical significance.
Below we will analyze the practical value of mathematics, the cultural value of mathematics and the mathematical significance of mathematics education.
First, the practical value of mathematics
Mathematics always occupies a very large proportion and plays a very important role in everyone's knowledge-seeking process from small to large.
So, why on earth should people learn mathematics? This question has such an answer. Mathematics tells us how to understand the world around us, how to deal with problems in daily life and how to prepare for future career. .
[1] A very important feature of mathematics is that its research object is abstract.
The abstraction of mathematical research objects makes mathematics widely used.
In mathematics, we must rely on strict logical reasoning to determine a theorem or law. It is far from enough to rely only on some experimental data or ordinary experience summary, let alone rely on intuition or imagination. This is a rigorous mathematical spirit.
Historically, mathematics is very important. Looking back at the history of scientific development, we will find that the progress of mathematics has influenced many major developments in astronomy, physics and biology.
For example, Riemann geometry is the basis of Einstein's theory of relativity, and the creation of calculus has promoted the development of physics, especially the discovery of the law of universal gravitation in Newtonian mechanics. The words of many celebrities also make us feel the important position of mathematics in the history of scientific development.
Engels said: Mathematics is a science that studies the quantitative relations and spatial forms in the real world.
This sentence tells us that in exploring the unknown science, mathematics provides us with tools to analyze and deal with problems.
In today's modernization, mathematics seems less important.
In fact, mathematics is still an important foundation for the rapid development of high technology, and the development of high technology also makes the application field of mathematics more and more extensive.
The invention and application of electronic computers have brought mankind into the information age, and the invention of electronic computers should be attributed to mathematicians Turing and von Neumann.
Turing machines existed in mathematical logic before computers appeared. Turing machine is a simple mathematical model of computer, which induces the appearance of electronic computer.
Mathematics has played a fundamental role in the rapid development of computer technology and its more and more extensive application in other fields.
There are many examples, such as medical CT technology, network system security technology, fingerprint identification, network system security and so on. Behind these technologies, mathematics plays a very important role.
In these fields, mathematics is often the key basic tool to solve practical problems.
The practical value of mathematics is also reflected in all aspects of our modern social life. Mathematics has become a basic tool in our life, such as the percentage of air pollution, the rainfall probability used in weather forecast, the specific schemes and strategies adopted in investment activities such as buying a house, selling a car and buying stocks, the conversion of various discount methods in the shopping process, the estimation of house decoration design and decoration cost, and the statistical analysis of various information in the media.
Without mathematics, modern people can hardly live, at least not better.
Once people have mastered the formula, they can make practical and empirical predictions about the events in the concrete, practical and intuitive life world.
Therefore, mathematicization and its formula are of decisive significance to our lives [2].
Second, mathematical culture and its significance to human development
? Why teach? Mathematical culture is the main problem that needs to be expounded in mathematics education in primary and secondary schools.
As far as its function is concerned, mathematical culture can cultivate students' ability, cultivate students' interest in learning, promote the development of moral education, and play a very important role in cultivating students' comprehensive quality.
Mathematical culture teaching can change students' mathematical concepts and improve their mathematical literacy; Students' good mathematical literacy can improve their comprehensive quality and help them better adapt to the development of the future society.
Mathematics education can cultivate people's thinking, which will affect people's life.
Mr. Zhu Zheng mentioned that all the academic research I did in those years depended on mathematics? Gymnastics? Trained thinking ability.
My book 1957 Summer: From a hundred schools of thought to a hundred schools of thought, I actually benefited from mathematics. ? [3] Mr. Wang Meng has a passage in the book My Philosophy of Life. Looking back on my childhood, I spent a lot of time doing math problems. These mathematical knowledge are rarely used directly afterwards, but learning mathematics is extremely beneficial to my thinking training. ? [4] Are the two writers right? Why do you study math? This question gives a perfect answer.
It makes us understand a truth: even if a person's career after work has little to do with mathematics, he has almost forgotten all the definitions and theorems of mathematics he has learned. But the study of mathematics at that time was still useful for his thinking training, and it will always play a subtle role in his later work.
Mathematics can make people form a good habit of speaking and doing things rigorously, and mathematics can make people more profound and wise.
All schools require students to study and practice mathematics from primary school to middle school, and cultivate the logic and rigor of students' thinking by learning a lot of mathematical knowledge and practicing mathematical problems.
The logic and rigor of mathematics itself can train people's scientific thinking mode, which is necessary for modern people's survival and development.
Someone summed up the role of mathematical culture in mathematics classroom teaching: using mathematical culture to cultivate students' rational spirit, scientific spirit, innovative spirit and application consciousness [6].
With the development of society and the progress of science and technology, when selecting talents, more and more employers realize that a person's ability, that is, the ability to analyze and solve problems and the ability to innovate, is very important to employers.
When learning mathematics in primary and secondary schools, we need strict reasoning of mathematical proof and well-founded mathematical problem solving. It is necessary and meaningful to prove the correctness of this concept theorem and rigorous reasoning training, which is the embodiment of mathematical culture and significance in mathematics education and the only process to cultivate good mathematical literacy.
These mathematical trainings can promote and develop teenagers' minds and potentials, and have a far-reaching impact on teenagers' lives, which is irreplaceable by any other discipline.
References:
[1]ICMI Research 14: Application and Modeling in Mathematics Education-Discussion Paper. ZDM 2002，34(5)，229-239。
[2][ Germany] edmund husserl. European scientific crisis and transcendental phenomenology [M]. Zhang Qingxiong, translated. Shanghai Translation Publishing House, 2005: 57.
[3] Zhu Zheng. Waste paper basket [M]. Guangzhou: Guangdong People's Publishing House, 2000.
[4] Wang Meng. My philosophy of life [M]. Beijing: People's Literature Publishing House, 2003.
[5] Zhang Chuting. Mathematical culture [M]. Beijing: Higher Education Press, 2006.
Zhang. Mathematics Culture and Mathematics Curriculum Reform [J]. Journal of Chongqing Normal University (Natural Science Edition), 2002, (3): 59-62.