Mathematics is not only "brushing questions"!Where are you from the master?

Literature ｜ Zhang Jianyue (Editor -in -Chief of the Active High School Textbook · Mathematics and Chairman of the Mathematics Teaching Professional Committee of the Chinese Education Society)

The parents of Francis Su, the author of "Mathematics: The Power of Mathematics: Let us Be a Better", are all Chinese. In 2015, he became the first non -white chairman of the American Mathematics Association (MAA). Successful mathematicians.

He delivered a moving and sensational farewell speech when he was about to step down as President MAA.

In his speech, he described mathematics as avenue to human prosperity, and believed that the search for mathematics could meet the five basic needs of human beings: games, beauty, truth, justice and love.

This book is expanded on the basis of this speech.

对于这样一本出自一位有深厚数学造诣、对数学及数学教育的本质有深刻领悟的真正专家之手的书，一本被评价为“阐明数学之于个体作为一个人的意义，以及如何让"The book that is more abundant in life" is known as a book that can change the public's views on mathematics.

Here I can only read myself in more than a month to read the fragmented time, take nearly 20,000 words of notes, and write it repeated thinking, chewing experience, and look forward to causing readers to think more deeply and discuss mathematics in mathematics. What does mathematical education mean?

1

What is the significance of mathematics to a person? A matter of equal price is what kind of educating function of mathematics.

Unlike abstract emphasis, "mathematics has an irreplaceable role in the process of forming adult rational thinking, scientific spirit, and promoting personal intelligence development." Francis believes that "how mathematics should be closely linked to the desire of the human heart" from the minds of maths " Start to discuss what mathematics is and why mathematics.

Francis's answer is "mathematics to promote human prosperity", and "human prosperity" refers to the unification of existence and behavior. , Even in a challenging environment, maintain an upright personality.

How to achieve human prosperity? Francis respects Aristotle's views -the practice of prosperity comes from virtue, and believes that "the correct mathematical practice can cultivate virtues that help humans prosperity."

So, what are the virtues that help human beings to prosper? Francis gave a comprehensive and profound explanation in this book. He believes that the core significance of mathematics research lies in exploration and understanding.

Exploration is the desire deep in the heart of human beings and a sign of human prosperity. Exploring the virtue of imagination, inspiring the virtue of creativity, and breeding the expectations of charming charm.

Understanding is the pursuit of the meaning of things, it has created an important virtue: First, the virtue of building a story (the "story" here can be understood as a background, scene, relationship, connection, etc. The idea of ​​concepts is linked to realize the significance of mathematics, and the "story" into new knowledge to make it vitality); second, the virtue of abstract thinking (abstract, establish a connection between two things with similar structures or similar expression The meaning of rich things); Third, the pursuit of meaning has an additional virtue of persistence and contemplation.

He pointed out that the meaning of identifying an idea requires a long time. This is the hard work of solving the problem. You must sit down and focus on a mathematical issue and think about it. The laws you see.

Francis emphasized that the core of appropriate mathematics practice is the pursuit of meaning. If you do not find meaning in your efforts, you cannot flourish in mathematics or life.

The significance of mathematics is far more than its effectiveness, but the beauty of mathematics is found in the process of reflecting on the multiple meaning of one thought from one perspective to another.

Therefore, Francis believes that "mathematics is a regular science and the art that gives these regular significance."

Exploration and understanding are the core of the correct mathematical practice. In contrast, our mathematics class can find that exploring and understanding has become a chorus, and memory plus imitation has become the main theme.

How to change this situation? Francis believes that the only requirement for becoming a mathematical explorer is to have the ability to propose "why? How? If ... then ...".

As long as there is a chance, we must refute the views of math, that is, and replace it with the perspective of mathematics.

A mathematical memory person does not know how to deal with unfamiliar situations, but a mathematical explorer can flexibly adapt to changing conditions, because he has learned to ask questions, which will allow him to be able to respond calmly when facing strange situations.

Therefore, changing the classroom starting from cultivating students' questions.

At the same time, in order to create virtues that build stories and abstract thinking, and cultivate the virtues of persistence and contemplation, we must take "the pursuit of meaning" as the core task of the classroom.

在新课程实施过程中，我们曾经提出如下观点：以研究一个数学对象的“基本套路”为指导，设计出体现数学的整体性、逻辑的连贯性、思想的一致性、方法的普适性、 The systemic series of mathematics activities of thinking, guide students to obtain mathematical objects through mathematical abstraction of real problems, build the basic path of studying mathematical objects, discover the mathematical problems worth studying, explore the mathematical methods to solve problems, obtain valuable mathematics mathematics Conclusion The establishment of a mathematical model to solve the problem. To enable students to master the methods of abstract mathematical objects, discover and raise mathematical problems, take this as a key task of teaching to achieve the leap from "knowing it" to "knowing it" to Essence

In contrast to Francis's point of view, we can find that what we emphasize is also "exploration and meaning pursuit", which coincides with the "correct mathematical practice" he pays attention to.

2

So, from the perspective of mathematical cognitive activities, how should the math teaching be carried out "correct mathematical practice" in the way? Francis believes that the correct mathematical practice should be based on the desire of the human mind.

In this book, he discussed the desire deepened from the heart of human beings, and the deep -seated needs of people who marked the prosperity of human beings and mathematics, including exploration, meaning, game, beauty, eternal, truth, struggle, power, fairness, fairness, justice, fairness, justice, fairness, justice, fairness, fairness, justice, fairness, justice, fairness, and fairness, justice, fairness, and fairness, justice, justice, fairness, and fairness, justice, justice, justice, fairness, justice, fairness, and justice Freedom, group, love, etc.

He believes that if these needs are met, more and more people from various backgrounds will be attracted to the kingdom of mathematics.

It can be seen that many of these needs and mathematics are familiar with us. For example, the demand for truth, beauty, eternal, strength, freedom, etc. through mathematics, but some are strange Game, etc.

Let ’s take the connection between establishing games and mathematics as an example to see how we should implement the correct mathematical practice.

The author believes that games are a deep desire for human beings and a sign of human prosperity.

The game is usually voluntary; the game is meaningful, otherwise people will not immerse themselves; the game is structured and follows certain rules; the game will be freely implanted in the rules, and the free exploration under the rules will bring surprises to surprise Essence

The characteristics of human games have expanded the role of creative thinking and imagination.

How are these characteristics of the game reflected in the exploration of mathematics?

Francis believes that mathematics makes the brain the paradise of the game.

Mathematical exploration is a fascinating game: in the process of exploring the laws and cultivating curiosity of things about things, fun will be stimulated with the emergence of various ideas.

Mathematic Chen's Said said "Mathematics is fun", which is also Francis's point of view. It seems that this is a common experience of mathematics researchers.

Mathematic research on a project usually stems from "fun": thinking about laws, playful ideas, exploring what is true, and enjoying various surprises from the process.

Francis believes that the appropriate practice of mathematics games has cultivated virtues, so that we have the ability to continue to grow in every field of life.

For example, mathematical games have established hope -when you explore a problem for a long time, your heart must be with the hope of "I will solve it". This hopeful experience can continue to the solution of other problems.

In the process of exploration, mathematical games have cultivated curiosity and developing concentration. This is a strong and pleasant spiritual activity that can avoid the disturbances of daily life.

Mathematical games cultivate self -confidence in hard work -you know what efforts are, because you are accustomed to this and are happy to accept it. You realize that if your brain is painful due to hard work, then it is a pleasant thinking activity.

Mathematical games cultivate the patience in the waiting process. The resolution of a mathematical problem may take a few years until you find its result.

Mathematical games have cultivated perseverance, and weekly mathematics inquiry makes us more urgent to welcome the next problem, no matter what it is.

Mathematical games have cultivated the ability to change views, so that we can see problems from multiple perspectives, forming an open spirit to contribute to society.

Game is a kind of essential demand for human beings. The desire for mathematical games will attract people to study and enjoy mathematics. In the process of studying and enjoying mathematics, hope, curiosity, concentration, confidence, patience, perseverance and opening up Virtues such as attitude are cultivated.

These views of Francis are very inspiring, making us clearly see how the current popular "tutoring" stifle students 'nature, hurt students' desire for mathematics research, how to depart from mathematics and educate people's original people. Goal.

Such teaching treats mathematics as a bunch of cold laws of cold ice. There is no process of ups and downs in mathematical games that appear in the ups and downs, which makes Francis depict, curiosity, concentration, self -confidence, patience, perseverance, The cultivation of virtues such as open attitudes and other virtues will definitely destroy students' desire for mathematics.

If our teaching can make full use of the mathematical nature of "fun", and to form a real intellectual challenge to students through the problem of mathematical gold content, and inspire students' deep desire for the human beings, then fun mathematics can encourage them to encourage them to encourage them To try, the boring "brushing" can also be converted into exciting exploration, regular and meaningful pursuit. In this way, the cultivation of human virtues is naturally natural. From the above perspective of the core significance of mathematics research and the basic way of mathematical cognitive activities, I talked about the inspiration I have obtained from this book. This is a place where I impressed me deeply and caused me strong resonance.

In fact, we can get more from the reading of this book.

In the current popular statement, there are a lot of "golden sentences" in this book, which is thought -provoking, and can change our views on mathematics.

"China Science News" (2022-07-08 The 3rd edition of the original title "This is a book that changes your views on mathematics"))

Edit | Zhao Lu

Capture | Guo Gang

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