There is nothing wrong with eating fruit, because it is just eating some kind of fruit. In mathematical terms, it is to eat an element, or some elements, in a fruit collection. But daily speaking can't be as strict as math, as long as everyone understands it.
I learned a lot about large sets and subsets from this story. Please read this book if you are free. I hope you will gain a lot after reading it, stimulate your enthusiasm and interest in learning mathematics, feel the beauty of learning mathematics from it, and further improve your knowledge and interest in reading.
How to help you learn math? "Helping you with your math" is a gift from Academician Zhang Jingzhong to the children. After reading this book, I learned a lot of new knowledge and left a deep impression on me. He not only cultivated children's mathematical thinking habits, but also stimulated children's interest in mathematics and was able to apply life experience knowledge to reality. The scientific way of thinking benefits people for life, and skillfully uses logical thinking to create, mobilize and stimulate children's interest in mathematics learning. After reading this book, I have the following experience:
1. Mathematics education should adapt to children's learning, carefully study children's psychology, stimulate children's inherent interest in learning, and cultivate children's enthusiasm for creating mathematics learning.
2. Encourage children to use their imagination to describe mathematical phenomena in their own language and turn mathematical knowledge into their own experience.
It is a good book to help you learn math. It teaches us a teaching idea and a teaching method. Reading is a good learning method, which will lead us to constantly update and keep pace with the times.
After reading this book, I felt deeply, which made me understand a lot of mathematics and helped me learn more. The history of mathematics is a very effective and indispensable tool in college mathematics teaching. Recognizing the role of mathematics history in college mathematics teaching and combining it closely can not only effectively stimulate students' interest in learning mathematics, but also play a very important role in improving students' mathematical literacy and logical thinking ability, inspiring liberal arts students' personality growth and developing their cognitive ability.
1. The history of mathematics is an important part of college mathematics teaching.
As the saying goes, "Rome was not built in a day". The occurrence and development of mathematical knowledge is actually the history of struggle between mathematicians and difficulties and problems. Mathematics itself is not only a science, but also a spirit, a spirit of exploration. Calculus, for example, was established and developed by many great mathematicians, such as Newton, Leibniz, Euler, Wilstrass, etc., and it took thousands of years to establish and improve it. Understanding the history of the establishment of mathematical theoretical knowledge can not only make students have a comprehensive and complete understanding of what they have learned, but also enable students to learn to overcome obstacles step by step and learn through exploration from easy to difficult, from known to unknown.
2. The history of mathematics can build a bridge between mathematics and humanities and stimulate students' interest in learning college mathematics well.
The abstraction and strict logic of mathematics make many students feel afraid of difficulties, and the study of college mathematics correspondingly degenerates into boring formula memory and problem-solving drills. Rydenthal, a Dutch mathematician and educator, criticized this kind of education that pays attention to strict logic without any sense of history as "turning fiery inventions into cold beauty" [2]. Therefore, how to build a bridge between mathematics and humanities to stimulate students' interest in learning has become the primary task of teachers. Mathematics is one of the symbols of human civilization throughout the ages. Whether it is material civilization or spiritual civilization, mathematics has had an unquestionable influence on the whole human civilization. The most prominent influence of mathematics on human material civilization is that it directly or indirectly participated in three major industrial revolutions that fundamentally changed human material life style. For example, the main technologies of the first industrial revolution were steam engines and textile machines. Their design includes the calculation of movement and change, which was only possible after the invention of calculus. For another example, the release of atomic energy is first due to Einstein's famous formula deduced with mathematical tools, which reveals the possibility of mass-energy conversion. Moreover, the development of the aerospace industry is inseparable from the participation of mathematics. Shenzhou spaceship's successful flight is inseparable from the participation of mathematicians. The influence of mathematics on human spiritual civilization is also profound. For example, Heliocentrism's decisive victory was after Newton used the latest mathematical tools at that time-calculus and strict mathematical reasoning to deduce the motion of the solar system from the laws of dynamics and gravity. Astronomer Galle discovered a new planet, Neptune, according to the mathematical calculations and predictions of several mathematicians, which confirmed Copernicus' theory. In the teaching of college mathematics, when we study related mathematics knowledge, we should timely connect mathematics knowledge with its promotion to social development at that time, so that students can realize that mathematics is closely related to people's lives, and mathematics comes from and serves life. This will help to establish students' correct understanding of math class and improve their interest in learning.
3. The history of mathematics has an important moral education function in college mathematics teaching.
Mathematics contains abundant dialectical materialism. In the history of mathematics, the formation and evolution of mathematical concepts, the establishment and development of important thinking methods and the establishment and reform of major theories all embody the core ideas of materialist dialectics-development, movement and change. For example, since the introduction of variables in mathematics, movement has entered mathematics. The idea of dynamic variables runs through higher mathematics, and function is the concrete embodiment of this idea. Through the introduction of function history, students can be taught to look at things and the world from the perspective of change and movement. Integrating the history of mathematics into college mathematics teaching can not only make students realize the value of mathematics, but also help to cultivate students' dialectical materialism. Dialectical materialism is very important for cultivating students' scientific thinking methods and innovative consciousness.
4. Integrating the teaching of mathematics history into college mathematics teaching is helpful for students to develop non-intellectual factors.
First of all, it helps to cultivate students' good qualities of being practical, meticulous, earnest and striving for perfection. Newton once said, "In mathematics, the smallest error cannot be ignored." A remarkable feature of mathematics is accuracy. As the saying goes, "A tiny difference is a thousand miles away." In the process of realizing the dream of "flying", human beings staged a tragedy because of "carelessness"
Historical drama. 1 On August 23rd, 967, Feradimir Komalov, a famous astronaut of the former Soviet Union, piloted the Soyuz1spacecraft alone. After a day and night flight, he successfully completed his mission and returned to China. However, when the spacecraft returned to the atmosphere, ready to open the parachute to slow down the spacecraft, komarov found that the parachute could not be opened anyway. Two hours later, under the gaze of hundreds of millions of TV viewers, there was an explosion, the spaceship crashed and the national hero was martyred. The reason why Soyuz 1 crashed was that a decimal point was ignored during the ground inspection. This tragedy can also be called the neglect of a decimal point. This true story related to mathematics not only shows how rigorous, cautious, practical and meticulous work style is needed in mathematics activities, but also vividly shows how the laws of nature play an objective, fair and iron role. In the teaching activities of college mathematics, giving some similar examples in time will make the class lively and interesting, and more importantly, it will be of great help to the formation of students' practical and subtle excellent character. And this excellent quality is a must for all major students. Secondly, it helps to cultivate students' rational thinking ability. For liberal arts students studying college mathematics, they have strong thinking ability in images and rich and colorful thinking in images. Throughout the history of mathematics development, it can be said that it is an evolutionary history of creation. In the creative process, more is the power of rational thinking. For example, the emergence of ε, δ language describing limit is the embodiment of the beauty of human rational thinking, which overcomes the randomness and abstraction of intuitive description of limit in the past. Mathematics is the most rigorous rationality that human thinking can achieve. Combined with the teaching of mathematical history, students' rational thinking ability can be better improved, thus promoting the improvement of students' comprehensive quality.
Finally, it helps to form a good habit of being eclectic and good at learning. Newton once said, "If I see farther, it is because I stand on the shoulders of giants". From the study of the history of mathematics, students can also realize that science needs the joint efforts of all mankind and critically inherits a lot of predecessors' knowledge. Behind closed doors, behind closed doors can only lead to arrogance and backwardness. After Newton initiated calculus, the lag in the development of local mathematics in Britain is a typical result of self-enclosure. As a college student in the new era, I should have a broad vision and dare to learn advanced scientific knowledge at home and abroad for my use.
In a word, because the object of college mathematics teaching has certain particularity-mainly liberal arts students, it will not only help to impart mathematics knowledge, but also help to improve students' comprehensive quality, and ultimately get twice the result with half the effort.
During the summer vacation, I was lucky enough to read this book written by Academician Zhang Jingzhong, which made me feel the charm of mathematics.
Ever since I opened its first page, I have been constantly discovering surprises. Some laws in mathematics can also be reflected in life. What the author said is very reasonable after careful consideration, but I just lack the perseverance to persist. If you take a step forward, you will be surprised to find that it is exactly as he said. I always nod my head when reading his books, but I can't figure out why. The author is like a magician. The math problems in his book are all set one by one. This problem tells you one solution and leads you to think about another, just like peeling an onion. You can't stop until you see it.
I admire Mr Zhang Jingzhong very much. What he said in the book is not only mathematical knowledge, but also many language skills and stories, which make me feel how rigorous mathematical thinking is. Take the first chapter as an example. Exchange and condition, additive commutative law in mathematics, can exchange and add these numbers. But in a language, many things or word orders are reversed, and the meaning is completely different. If you say that Xiao Ming is reading while eating fruit, it will make people feel that he loves learning, even reading while eating fruit; But if the word order is reversed, it is completely different. Xiao Ming eats fruit while reading, which shows that he is not serious in reading and is half-hearted. He's absolutely right. This is so interesting.
From this book, I read the charm of language; From the mathematician's pen, I saw the world of mathematics; I am in the world of mathematics, experiencing its magic.
This book helped me learn math, no, not just math, it brought me to another world.