How to Infiltrate Multi-ethnic Traditional Education in Primary Mathematics Teaching

Teacher Zhang Qihua, a famous teacher who has in-depth research on mathematical culture, gave two demonstration classes during the Eighth Primary School Mathematics Teaching Reform Conference in Fujian Province, and gave a special lecture on "Research on Primary School Mathematics Culture Education", giving personal thoughts and expressions on the new curriculum of primary school mathematics culture education: "The so-called mathematical culture is the material and spiritual wealth created by mathematicians-led mathematics * * * engaged in mathematical research activities. Explicit such as concrete mathematical knowledge and its materialized presentation form, while invisible is mathematical method, mathematical thought, mathematical concept, mathematical spirit and so on. " Therefore, can we think that the new mathematics curriculum reform, which emphasizes human development and comprehensively cultivates and promotes students' mathematical scientific and cultural literacy, should carry out primary school mathematics teaching from the perspective of mathematical culture, infiltrate mathematical culture in the classroom teaching process, make culture become the true color of mathematics classroom, and let students understand the spirit, ideas, concepts and consciousness contained in mathematics, know the truth, goodness and beauty of mathematics, apply mathematical ideas and methods, and inherit the scientific humanistic spirit of mathematicians in the process of learning mathematical knowledge and skills.

How to organically integrate mathematics culture into mathematics teaching, realize the effective infiltration of mathematics culture, and let mathematics culture flow in the hearts of primary school students simply and peacefully? Readers may get some useful enlightenment from several related articles published in this issue. Infiltrating humanistic education with mathematics teaching materials

Looking at the educational research materials at home and abroad in recent years, it is found that the research on the spiritual level of "humanities" is more than the practical research on integrating it with disciplines. In the mid-1990s, there was a heated discussion about "humanistic spirit" in China academic circles. Because the discussion involves the establishment of the value scale of cultural choice in modern China, it has realistic and far-reaching historical significance, which has aroused widespread concern in the theoretical circle, but it is relatively cold in the education circle. For a long time, there has been a misunderstanding in educational understanding and practice that humanistic education is only humanistic education. On the surface, mathematics is undoubtedly closely related to science, but it seems strange to human beings. Traditional mathematics teaching often simplifies the colorful and dynamically generated mathematics classroom into a special cognitive activity of "emphasizing practice, reasoning and forming ability", which leads to the mechanical, boring and stylized mathematics classroom teaching and the lack of emotion, attitude and values.

Since the beginning of 2 1 century, our country has implemented a new round of basic education curriculum reform, which not only strengthens science education, but also pays more attention to humanities education and promotes the all-round development of every student. Mathematics is the core course of basic education. With the new round of basic education curriculum reform, mathematics education has also entered a period of drastic and profound change. The new curriculum reform puts forward new requirements for mathematics education. Mathematics curriculum standard (experimental draft) points out: "Mathematics is a kind of human culture, and its content, thought, method and language are important components of modern civilization." At the same time, it is emphasized that the basic starting point of mathematics curriculum in compulsory education stage is to promote students' all-round, sustained and harmonious development. Therefore, mathematics education should not only strengthen science education, but also attach importance to humanities education to realize the integration of science and humanities. At present, all kinds of primary school mathematics experimental textbooks attach great importance to the humanistic education of the curriculum, which has rich humanistic connotation. In teaching, teachers should dig deep into the humanistic education factors in teaching materials, guide the situation according to the situation, pay attention to the cultivation of students' humanistic spirit while imparting knowledge, and make mathematics classroom full of humanistic colors!

First, infiltrate mathematical thinking methods and develop mathematical thinking.

Mathematical thinking method is the essence of mathematics humanistic education in primary schools. In the mathematics classroom under the new curriculum concept, teachers should help students to understand and master basic mathematics knowledge and skills, mathematics ideas and methods in the process of mathematics learning, and gain rich experience in mathematics activities. Mathematical knowledge and skills are the basis of students' further study, and mathematical thinking method is an important basis for students' thinking development and lifelong learning.

Different people have different understandings of mathematical thinking methods. Generally speaking, the mathematical thinking method refers to the thinking mode or principle that is separated from the specific mathematical content and has more universal significance. Mathematical thinking is the essential understanding of mathematical knowledge, and mathematical methods are the strategies to solve mathematical problems. Mathematical thinking includes mathematical methods, and mathematical methods include mathematical thoughts. There are many important thinking methods in mathematics, such as set, combination of numbers and shapes, equivalent substitution, operation optimization, transformation and transformation, symbolization and preliminary algebraic ideas. According to the age characteristics, life experience and mathematical knowledge of primary school students, the textbooks are mainly arranged by infiltration, which is reflected in two aspects.

(A) combined with the specific content of infiltration. Many mathematical knowledge contains rich mathematical thinking methods in the development process, and the arrangement of teaching materials pays great attention to the infiltration with specific content, so that students can experience these thinking methods initially in the process of learning specific mathematical knowledge. For example, reduction is an important mathematical thinking method. Through transformation, the relationship between unknown knowledge and learned knowledge is established, and the way to understand and master new knowledge is found. The study of decimal multiplication and division in grade five is based on integer multiplication and division, and the decimal multiplication is transformed into integer multiplication by using the changing law of factor and product, so that students can understand the calculation theory of decimal multiplication and summarize the general calculation method of decimal multiplication. Similarly, fractional division is also solved by transforming quotient invariance and decimal point movement law into division of divisor into integer. For another example, the area formulas of parallelogram, triangle, trapezoid and circle are all converted into previously learned and derived from graphs, and the addition and subtraction of fractions with different denominators are also converted into fractions with the same denominator to calculate. For another example, in the first grade, the knowledge infiltration set of counting and comparison is combined with the corresponding ideas, and the understanding and classification of objects and graphics are combined to let students experience the idea of classification. The fifth grade simple equation combines symbolic thought and preliminary algebraic thought; The sixth grade combines the ideas of the area penetration limit of the circle. Through this arrangement, the teaching materials not only enable students to master mathematics knowledge and establish the connection between old and new knowledge, but more importantly, let them naturally experience these mathematical thinking methods and initially obtain the methods of mathematics learning.

(2) Separate "mathematical wide angle" for infiltration.

Since the second grade, the experimental textbook has arranged a unit-"Mathematics Wide Angle", which systematically and gradually permeates some important mathematical thinking methods to students through simple examples and interesting mathematical problems. For example, in the lower grades, the content of "finding the law" is arranged, so that students can discover the simple arrangement law of figures and numbers through observation, experiment, guessing and reasoning in a specific situation, from the arrangement law of figures, the arrangement law of the combination of figures and numbers to the arrangement law of numbers, and cultivate their preliminary observation and reasoning ability; In the fourth grade, the content of "optimization" is arranged, and students can experience the application of logistics thinking in solving practical problems through simple daily life examples, such as pancakes, tea making and unloading. In the sixth grade, the content of "chickens and rabbits in the same cage" was arranged to stimulate students' interest in learning mathematics by using the interest of ancient famous questions. At the same time, through exploration and analysis, the method to solve the problem is found, and the students' logical reasoning ability is cultivated in the "hypothesis" method, so that students can create many ingenious problem-solving ideas through "hypothesis". This method can train people's logical reasoning ability.

Second, excavate the ancient mathematical culture and stimulate the national spirit.

China is one of the ancient civilizations in the world, with 5,000 years of civilization and rich historical and cultural resources. Mathematics itself is not only some numbers, formulas and figures, but also contains a strong cultural atmosphere, and there is a vibrant spirit behind every content. In practical teaching, teachers can tell students some relevant mathematical history, interesting stories about mathematics or stories about mathematicians based on the knowledge points in textbooks, so that students can understand the rich historical origin of mathematical knowledge, thus stimulating students' national pride and national pride. For example, in the teaching of "Calculation of Rectangular and Square Area", under the guidance of the teacher, after the students have deduced the calculation formulas of rectangular area and square area through learning activities such as "guess-experiment-verification", the teacher provides such materials for the students to read: About two thousand years ago, China's famous mathematical experts discussed the algorithm of rectangular area, and the book said: "Square field" refers to a rectangular field with "width". After reading this material, students will be proud of the cleverness of our ancestors!

The above-mentioned teaching examples: the teacher skillfully combined the relevant research results of the ancients with the teaching content, broadened the knowledge background of the learning content, and added some classic historical details in the rigorous teaching inquiry process, which made the mathematics classroom full of rich humanistic charm. There are many examples like this in textbooks, such as teaching "East, West, North and South" and introducing the great invention of our country-compass; When teaching "circumference", introduce Zu Chongzhi and Pi; When teaching "the meaning of decimals and reading and writing methods", this paper introduces Liu Hui's proposal and use of "decimals (later decimals)" ... This ingenious combination of learning mathematical knowledge with the traditional civilization of the motherland not only stimulates students' enthusiasm for exploration, develops students' thinking ability, but also cultivates students' sentiment, so that students can further feel the value of mathematical culture, and the humanistic connotation of mathematics itself has been deeply expanded.

Third, close to social life and create a humanistic atmosphere.

There are many factors related to social life in the examples and exercises of primary school mathematics textbooks. In teaching, teachers should be good at combining these life facts to let students experience life and know the society in their study, and skillfully combine mathematics teaching with social life. This can not only stimulate interest in learning, but also create a good humanistic atmosphere, so that students can feel the richness of social life and the application value of mathematics, and their ideas are affected! "Mathematics Curriculum Standard (Experimental Draft)" points out: "Students' mathematics learning content should be realistic, meaningful and challenging ... the content should be presented in different ways to meet different needs. "Mathematics comes from life, and the content of humanities mathematics is based on the reality of students' lives. Teachers should be able to use teaching materials creatively, break the formal narrative and present learning materials with life background to students in time.

Please take a look at a wonderful teaching case in the first volume of Mathematics Wide Angle 2 (Reasonable Arrangement), the fourth grade of People's Education Press:

(1) First, the teacher creates a life situation for students to entertain guests: there are guests at home. As a small host, what preparations do you need to make tea to entertain guests? (Wash the teacup for 2 minutes, wash the kettle 1 minute, take water 1 minute, boil water for 8 minutes, find tea 1 minute, make tea 1 minute).

(2) Study the reasonable arrangement of group work, that is, how to arrange it scientifically and do these jobs well.

Reporting and communication:

Scheme 1: Wash the pot (1 min) → Receive water (1 min) → Wash the teacup (2 min) → Find tea (1 min) → Boil water (8 min) → Make tea (1 min) [* *]

Scheme 2: Wash the pot (1 min) → Receive water (1 min) → Boil water (looking for tea while washing the cup) (8 minutes) → Make tea (1 min) [* * * Need 1 1 min].

(3): In-depth discussion, discussion and communication, which group of programs is the best?

Health: Although the first scheme is feasible, it is not as good as the second scheme.

Teacher: What is the main performance of this "good"?

Health: Save time. The first scheme * * * takes 14 minutes, and the second scheme can wash the teacups and find tea while boiling water, saving 3 minutes, and * * * takes 1 1 minute.

Teacher: You are good at thinking and doing things. It's amazing that you can reflect the optimization idea on the basis of reasonable arrangement.

(4) Consolidate the application and show the value.

In consolidating the application of this teaching link, the teacher also provided living materials such as making breakfast, before going to school, doing housework and taking medicine when sick, so that students can choose their favorite living materials and design the best scheme. Through simple life cases, let students realize the diversity of problem-solving strategies, initially experience the application of optimization thought in solving practical problems, form the consciousness of finding the best solution to the problem, and gradually develop the good habit of arranging time reasonably.

(5) Summarize the feedback and talk about the gains.

In this teaching session, the teacher asked the students to talk about what other things in life can be improved through reasonable arrangements, and what they got from the study of this lesson.

Health: I used to look around when I got up in the morning. I was in such a hurry that I didn't even have time to have breakfast. Now I know how to arrange my time reasonably and do things in a certain order. Through today's study, I also understand that I have to learn everything, and mathematics is everywhere in my life.

"Do everything with learning!" What a wonderful summary. Finally, the teacher defined the theme of this lesson as "learning by doing". The generation of humanities teaching content makes students not only gain real cognitive gains, but also have a more or less understanding of life, which is the ideal realm of classroom generation.

Fourth, cultivate the spirit of the times with the help of current affairs materials.

The textbook of experimental mathematics is deliberately interspersed with some current events about "Olympic bid", "tax payment", "environmental protection" and "resources". These topics have a sense of the times, which is conducive to guiding students to pay attention to society, people and things around them, and thus receive humanities education. For example, in the teaching of "tax payment", before class, the teacher arranges students to conduct a national tax survey and collect some tax payment data for classroom communication; In class, the teacher showed some materials: ① In 2007, the national fiscal revenue was 5 13 trillion yuan, of which taxes accounted for 4.94 trillion yuan; (2) The development and launch of Shenzhou 5 manned spacecraft cost 654.38 billion yuan; The state invested 900 million yuan in the development and launch of the Shenzhou VI manned spacecraft. ③ In 2007, the central financial expenditure on education reached 858? 5.4 billion yuan; (4) In 2007, the funds used by the state finance to support returning farmland to forests reached 277? 8.6 billion yuan. Teachers guide students to discuss and exchange the above information: "What is the main source of national fiscal revenue? How does the state deal with the taxes collected? Why pay taxes? " Through the above discussion and exchange, let students realize that tax is the main source of national financial revenue, and the state uses the tax collected for the development of economy, science and technology, education, culture and national defense, and it is the obligation of every citizen to pay taxes according to law. This will help to cultivate students' awareness of "active tax payment" from an early age.

Fifth, show the beauty of mathematics and cultivate noble sentiments.

The mathematics textbook itself has many beautiful features. In the process of learning and applying mathematics, we feel the beauty of mathematics everywhere. Therefore, teachers should be good at using these beautiful materials to cultivate students' aesthetic taste in teaching.

Please enjoy the wonderful teaching clips of "Axisymmetric Graphics" for Grade 6 in the textbook "Nine Meanings":

When class is over, teachers and students enjoy the beautiful landscape of Guilin with wonderful music. The teacher said: Students, in this class today, we walked into the world of "axisymmetric graphics" together. In fact, nature's creation of symmetry is far more than that. Looking up at the sky and overlooking the earth, the charm of symmetry is everywhere! Butterflies and bees dancing among the flowers, geese and pigeons soaring in the sky, rainbows across the sky and falling leaves make each of us, every smiling face, present a symmetrical charm. It can be said that because of beauty, nature chose symmetry, because with symmetry, nature added infinite beauty!

This conclusion, like a beautiful prose poem, not only makes students feel the beauty of symmetry and mathematics again, but also is philosophical and enlightening.