How to educate mathematical culture in primary and secondary mathematics education

1Creating a Mathematical Culture

(1) Introducing Mathematicians' Stories, Feeling Mathematicians' Scientific Spirit

Mathematicians' attitude of sleeplessness and tirelessness, their will to never give up after repeated failures, and their spirit of perseverance in the face of adversity are all great inspirations for students. We should utilize this spiritual food in classroom teaching, and introduce the stories of mathematicians to students in combination with teaching materials, so that students can feel the scientific spirit of mathematicians and be inspired to learn. For example, when introducing the perfect square formula, we can introduce the deeds and achievements of Yang Hui; when starting to learn the plane coordinate system, we can introduce to students the contribution of French mathematician Descartes to analytical geometry; by using the rich resources of the book "Read it" ......, we can also ask students to make use of their spare time to study from outside the classroom. Students can also be asked to use their spare time to search for the childhood stories of ancient and modern mathematicians and their deeds of rigorous study and climbing the peak of science from extracurricular books and the Internet, and then the collected stories will be compiled and printed and distributed to the students to communicate with each other.

(2) Find the source of mathematical symbols, experience the process of scientific invention

Learning mathematics, from learning mathematical symbols. Every mathematical symbol has a little-known experience. Let the students through the access to information, on their traces to explore the source, can let the students in the understanding of the history of mathematics at the same time, appreciate the mathematical symbols is not boring, but full of wisdom, sparkling life vitality. Such as students learning arithmetic square root, check the square root "" 1220 Italian mathematician Fibonacci used R as a square root number. Seventeenth-century French mathematician Descartes in his book "Geometry" for the first time with " " to indicate the root sign. " " is derived from the first letter "r" of the Latin root (square root), and the short line above it is a bracket line, which is equivalent to parentheses. Mathematical symbols story will also trigger students' strong curiosity about mathematics and enhance their interest in learning mathematics.

(3) Visiting famous historical mathematical problems to appreciate the charm of mathematical thinking

In the math activity class, according to the degree of students' mastery of mathematics, appropriate arrangements are made to introduce some famous problems in the history of mathematics in the past and present, both in China and abroad. Such as to introduce students to Chinese and foreign mathematicians to solve the "phantom cube" of different strategies: Yang Hui method, Robb method; the introduction of the Euler K?nigsberg's "seven bridges problem", Newton's "oxen eating grass problem" and so on. etc. These famous historical mathematical problems, because of its subtle solution ideas and strategies, to show students the infinite charm of mathematics, will be y attracted to them, enlightened their minds, stirring their hearts.

Case 1: the hook and strand theorem famous evidence to appreciate the fragment

As shown in Figure 1, △ABC is a right triangle, in which ∠CAB is a right angle, in the side AB, BC and AC on the outwardly square ABFG, BCED and ACKH, respectively, over the point A as a straight line AL perpendicular to DE to DE at the point L, cross BC at the point M, connecting the CF, AD. Figure 1 Euclid's proof

This proof skillfully uses congruent triangles and the relationship between the area of a triangle and the area of a rectangle to do so. Not only that, but it explains in concrete terms the geometric significance of "the sum of the squares of two right-angled sides", which is the division of the square into two parts, BMLD and MCEL, by ML! This is the most famous Euclidean proof of all!

This case introduces the proof of the Pythagorean Theorem, which is divided into four typical ways of thinking, namely, the area method, the collocation method, the dissecting method, and the direct method. Through the introduction of some famous proof methods in history, such as: Euclid's proof method and its dynamic demonstration, Zhao Shuang's string diagram proof method, Gamfield's proof method, etc., to guide the students in the appreciation of the history of the famous proof of the hook and strand to appreciate the subtlety of the mathematician's thinking, mathematical proof of the flexibility, grace and sophistication, and marvel at the beauty of mathematics!

In the traditional teaching of the collinear theorem, the teacher tends to prove the method of a passing glance, and focus on the theorem's conclusions and application of the training to explore the cultural connotations of the theorem is only the use of its "who is older than how many years ago" to the students to carry on the education of patriotism.

Designing such a "hook and strand theorem famous evidence appreciation class", multiculturalism into the mathematics classroom, we will find that "who is older than how many years" is not the most important, the important thing is that: mathematics is the whole of mankind **** the same heritage, the different cultural backgrounds of mathematical ideas and applications. The mathematical ideas and creations of different cultures are inseparable branches of the world's mathematical tree, thus eliminating the prejudice of ethnocentrism and recognizing the mathematical achievements of ancient civilizations from a broader perspective. At the same time, through the comparison of different mathematical ideas and methods, such as the introduction of a variety of methods involved in the advance and retreat, division and combination, movement and static, change and invariance, number and shape, one and many, etc., we can improve the mathematical thinking of all cultures, and enhance the ability of all cultures to understand mathematics. The discursive thinking can improve students' ability to think creatively in mathematics, and learn to appreciate the rich and colorful mathematical culture.

In the process of teaching, enough time can be arranged to let students in the appreciation of the basis of their own hands in the spelling, fill in, put together the practical activities, personally experience the process of discovery, feel the fun of hands.

2. Reproduce the process of knowledge production and development

Soviet mathematics educator Stolyar believes that the history of the development of mathematics provides us with important information on the historical path of the development of mathematical concepts, methods, language, which often instructs us to form and develop these concepts, methods, language in the school teaching path. It can be seen that the teaching of mathematics should make full use of the knowledge of the history of mathematics to show students the process of the emergence and development of mathematical knowledge.

(1) Revealing the Background of Knowledge Generation

The generation of mathematical knowledge is inseparable from natural and objective needs, and it indicates the course of human progress and development. Explaining the background of knowledge to students can help them realize and understand knowledge more y. For example, when learning about square roots, students realize that when people calculate square roots, they often can't get exactly the same result as integers, and then they need to create a new kind of number - irrational numbers. Students clearly see the reason for the introduction of knowledge, you can unveil the mystery of mathematics, eliminate the fear of students of mathematics, so that they are close to mathematics in the heart.

(2) Demonstrate the process of knowledge formation

Friedenthal believes that every student may be under certain guidance, through their own practice to obtain mathematical knowledge. Teaching, teachers should prevent the occurrence of the phenomenon of the conclusion of the light process, to provide students with certain learning materials, encourage students through their own exploratory activities, the process of the formation of knowledge to establish a clear representation, and take the initiative to complete the construction of knowledge. For example, in the teaching of area calculation of parallelograms, teachers can prepare transparent squares of paper and scissors, rulers and other learning aids for students, requiring students to either think independently, or work in small groups to explore the method of area calculation. Some students find the area by counting the squares, while others find the area by cutting, shifting, assembling, and transforming a parallelogram into a rectangle. In the end, students realized that these two methods are in essence the same, can be reduced to the base × height.

(3) Foretelling the prospect of knowledge development

The connection between the previous and the next knowledge in mathematics is very close, and what is learned first often prepares the knowledge and methodology for what is learned later. In teaching, teachers should be good at looking ahead and giving room for the development of knowledge. For example, in the study of real numbers, we find that whether it is rational numbers or formula or real numbers, addition, subtraction, multiplication and division are very important parts of the operation, and their learning methods in a sense there is a certain pattern, but also to deepen the understanding of the students.

Mathematics is both creative and discovery, mathematics teaching should strive to restore and reproduce the discovery process, so that students experience the process of knowledge generation, formation and development of their mathematical culture has a very practical significance.

3. Appreciate the aesthetic value of mathematics

The value of aesthetics is not only to cultivate emotions and improve the quality of life, but also to help develop intelligence and promote the overall development of students. The straight line of the rigid and smooth, the curve of the symmetry of the soft, undulating image, the golden section ...... As the mathematical philosopher Russell said: "Mathematics, if you look at it correctly, not only has the truth, but also has the highest beauty". This beauty is precisely the mathematicians will be the fruits of their labor according to their aesthetic view of their own most satisfactory form summarized and dedicated to the beauty of mankind, has a special aesthetic value.

4. Penetration of philosophical concepts in mathematics

Bordas Demollin said: "Without mathematics, we can not see through the depth of philosophy; without philosophy, people can not see through the depth of mathematics; without both, people can not see through anything." Comparatively speaking, the discursive elements in mathematics teaching materials are relatively hidden, which requires teachers to first have the consciousness of "digging deep", consciously digging into the discursive elements in the teaching materials, which also reveals the essential connection between knowledge.

Case 3: exploring the collinear theorem

In the explanation of the collinear theorem, the teacher pointed out to the students: in the right triangle, right-angled sides a, b, hypotenuse c, then a2 + b2 = c2; in the acute triangle, a2 + b2 c2. Understanding, so that students stand in the dialectical height to understand the relationship between quality and quantity changes in mathematics.

5. Enriching the form of extracurricular homework

(1) Writing mathematics diary, self-managed mathematics newspaper

Students, due to their cultural environment, family background and their own way of thinking, their way of thinking and problem solving has a strong individual color. Teachers can guide students to record their own thinking process in an organized way, which can not only grasp the students' thinking trends, but also can prompt students to reflect on the problem and help students to improve their problem-solving skills. Under the guidance of teachers, students are urged to write math diaries and publish math newspapers after school, which is a good way to penetrate the mathematical culture, broaden the horizons of mathematics and create a mathematical atmosphere.

(2) Making Handmade Models

Sukhomlinsky said: "There is a thousand links between the hand and the brain, and these links work in two ways: the hand develops the brain and makes it wiser; the brain develops the hand and makes it a clever instrument of creation". In conjunction with the progress of the textbook, some hands-on assignments are assigned, such as making clock faces, designing architectural models, drawing school plans, etc. These assignments require students to synthesize their ideas. These assignments require students to synthesize and apply what they have learned in a creative way. These extracurricular assignments can leave students with more room for exploration and space for reflection, and play a positive role in promoting the cultivation of students' innovative spirit and practical ability.