A Primer on the Tradition and Development of Chinese Mathematics Education in China: A Textbook Perspective

It is well known that mathematics textbooks, as the main carrier of mathematics curriculum, are the main channel through which mathematics education can be implemented, and mathematics textbooks in different periods often truly reflect the theoretical level and practical situation of mathematics education at that time to a large extent: mathematics textbooks are not only a true reflection of the ideological concepts of mathematics education, but also the quality and level of mathematics textbooks truly reflect the development of the society The quality and level of mathematics textbooks can not only truly reflect the actual level of mathematics education research, but also more comprehensively reflect the reality of mathematics classroom teaching. In particular, the reform of mathematics textbooks is the core work of mathematics curriculum reform and one of the focal points of successive reform and development of mathematics education.

This paper attempts to gain an insight into the basic pulse and trajectory of the development of Chinese primary and secondary mathematics education from the basic pulse of the development of Chinese primary and secondary mathematics textbooks.

I. Salient Features of Ancient Chinese Mathematics Textbooks

(I) The Basic Vein of the Development of Mathematics Education in Ancient China

Ancient China was one of the earliest countries in the world to carry out mathematics education: our country, from the end of the primitive communal system to the early stage of the slavery society, had already built up, year by year, the specialized educational institutions - -schools. According to ancient records and the Yin ruins oracle bone inscriptions, the Shang Dynasty has a more complete school education. Western Zhou has focused on mathematics education, mathematics has become a "national son" of one of the required courses. Legend has it that the Zhou Gong system ritual (equivalent to the current Constitution) "Zhou official, Paul's (officials responsible for education)" said: "save the state son of six arts, one said that the ritual, two said that music, three said that shooting, four said that the Royal, five said that the book, six said that the number of". To the Sui and Tang dynasties, math education has made new progress. Tang early State Prison was not set up in the "arithmetic", 656 years (the first year of Hanqing) began to add the arithmetic hall, Li Chunfeng as Tang Emperor Gaozong dynasty officials, by imperial decree, and the State Prison arithmetic Dr. Liang Shu, the University of Wang Zhenru and other school notes and compilation of the "thighs", "nine chapters" and other ten arithmetic scriptures as a national general textbook of mathematics. Of course, the official rank of Dr. Arithmetic was under the ninth rank (the lowest rank in the official hierarchy). Students of arithmetic study "ten arithmetic scriptures" too many years, the teaching efficiency is not high.

Ju Shijie in the Song and Yuan Dynasties was the greatest mathematician in the medieval world. He traveled around the world for more than 20 years, teaching mathematics for a long time. His Arithmetic Enlightenment (1299) and Siyuan Yujian (1303) are important milestones in the history of China's ancient mathematical development.Starting from 1487, the Ming and Qing dynasties introduced the eight-legged imperial examination system, which played a very bad role in mathematical education, and was one of the major reasons for bringing China's native mathematics high calling to a low ebb.

(2) Outstanding Features of Ancient Chinese Mathematics Textbooks

Ancient China had a very early start in mathematics education, and it was unique: the first feature was that mathematics education was always under the control of the government, and as far back as in the Zhou Dynasty, mathematics was included in the education of aristocrats' sons and daughters as one of the six arts. After the middle of the Tang Dynasty, the "Ten Calculating Scriptures" were promulgated by the state for use in the State Sonship, and were used as the classics on which the imperial examinations were based. The compilation, updating and annotation of mathematical texts were generally carried out under the auspices of government officials. This kind of implementation of mathematics education is rare in the history of the world, which undoubtedly had a positive impact on both social progress and scientific and technological development. The second feature is with the nature of technical education, the purpose of government-run mathematics education is to train professional calculators for the government.

Based on the above analysis, we believe that in ancient Chinese mathematical education, the materials that appeared as mathematical textbooks embodied the following characteristics:

1. Practicality - the use of the world: the majority of mathematical writings in ancient China were intended to guide practice, and inevitably took into account how to facilitate the teaching of the mastery of the people, focusing more on the shallow to the deep, and more focused on the use of the world. Although there are many ancient Chinese mathematical works, such as the commercial mathematics of the Ming Dynasty, Wu Jing, "nine chapters of the algorithm than the class book" (1450) and so on. However, ancient Chinese mathematics textbooks in general have the characteristics of the Nine Chapters of Algorithms. As can be seen from the content of the Nine Chapters of Algorithms, it was a book compiled in the form of integrated solutions to applied problems, including almost all areas of social production and life at that time. Its purpose was to solve all kinds of calculation problems raised by social production and life at that time, and to serve the applications in all fields of the society at that time.

2. Applied Problem Sets: Emphasizing the solution of relatively systematic practical mathematical problems. Take the Nine Chapters on Mathematics as an example. The whole theory of the Nine Chapters of the Art of Arithmetic is centered on the search for universal solutions to various applied problems, an open inductive system with a strong color of "applied mathematics", which is established in accordance with the derivation of the system from individual to general: usually one or several individual problems in a certain field of social life are cited, from which a certain class of problems can be summarized. Usually, one or several individual problems in a certain field of social life are cited first, from which the general solution to a certain type of problem, i.e., the algorithm (art), is summarized; then various types of algorithms are synthesized to get the methods for solving various problems in the field, which constitutes a chapter; finally, the mathematical methods for solving the problems in the various fields of social production and life are synthesized to get the whole Nine Chapters of the Art of Arithmetic. There is another layer of meaning in this characteristic of induction, namely, induction according to the different mathematical methods of solving problems. Many practical problems in different fields may require the same calculation methods, from which mathematical models are extracted and finally written into the Nine Chapters of the Art of Arithmetic in the form of mathematical model chapters, surplus and deficit, equations, and hook and strand chapters [①] is so ([①] by Liu Hui, annotated by Li Chunfeng. Nine Chapters of Arithmetic [M], Shanghai: Shanghai Ancient Books Publishing House, 1990). This is in sharp contrast to the pursuit of logical perfection in the Geometric Principles.

3. Open system of induction - lack of systematic logical and symbolic system.

The predominantly inductive narrative of the Nine Chapters of Arithmetic is markedly different from the predominantly deductive narrative of Euclid's Principia Geometria, a representative work of ancient Greek mathematics. Later, most of the ancient Chinese mathematical works adopted this inductive narrative. This is also a major feature of ancient Chinese mathematics and reflects the way of thinking of the ancient Chinese.

As Mr. Wu Wenjun pointed out, "The Nine Chapters of the Mathematical Art and the Original Geometry reflect the east and west, and are the two major sources of modern mathematical thought (Wu Wenjun. Preface to "Notes on the Nine Chapters of Arithmetic", in: Bai Shangshu. Commentary on the Nine Chapters of Arithmetic [M], Beijing: Science Press, 1988: p. 1). Mr. Wu's achievement in the field of machine proofs of geometric theorems is precisely the development of traditional Chinese mathematical features represented by the Nine Chapters of Arithmetic under modern conditions.

It is worth mentioning, and it is worth suggesting, that logic was also emphasized in ancient China. However, the "logic" here is different from the ancient Greek deductive logic represented by the "trinitarian theory", but a kind of natural logic, and its system is not relatively complete.

In short, the most essential method of traditional Chinese mathematics is induction, and the process of understanding is from the particular to the general, emphasizing heuristics in the method of mathematics education, and stressing the importance of thinking about some typical problems over and over again, and learning the general laws from them. The characteristics of traditional Chinese mathematics and the purpose of mathematical education determine that the content of mathematical education is designed for teaching application skills, and a whole set of patterns focusing on application, problem-centered, algorithm-based, relying mainly on induction to build mathematical models, and emphasizing the basic laws and their generalization are adopted in terms of ideas and methods.

The influence of "Western learning" on Chinese mathematics textbooks

"Western learning" refers to the historical process of the spread of Western academic thought to China in modern times, although it can also refer to a variety of Western things that have been introduced into China since ancient times and up to the present day.

The "Eastward Progression of Western Learning" refers to the historical process of the spread of Western academic thought to China in modern times, although it can also refer to a wide range of Western things that have been introduced to China since ancient times up to the present day.

The arrival of Jesuit missionaries during the Wanli period of the Ming dynasty touched Chinese academic thought, and in 1605 Matteo Ricci wrote a book called Qiankun yi, which the compilers of the Siku quanquan called "the beginning of the spread of Western learning to China. The Qing government in the 1860s, the implementation of the foreign affairs movement, the then foreign affairs people, mainly to take "secondary school for the body, Western learning for use" attitude to face Western learning. After the Sino-Japanese War, a great deal of Western knowledge was introduced into China, and its influence was very extensive. Many people accepted Western learning by translating the Western books written by the Japanese. After 1850, modern mathematics textbooks from Western capitalist countries were introduced, and Chinese mathematics education gradually embarked on the path of globalization.

The greatest influence on Chinese primary and secondary school mathematics education has been the influence of Western learning on the "Original Geometry". Ricci and Xu Guangqi's translation of Euclid's Geometria Originale introduced Euclidean geometry and its rigorous logical system and reasoning methods to China for the first time, and identified many of the geometric terms that are now familiar to us, such as point, straight line, plane, similarity, and external similarity. They only translated the first 6 volumes, and the last 9 volumes were translated by the mathematician Li Shanlan and the Englishman Alexander Wylie in 1857. At the same time, works such as Algebraic Techniques and Picking Up the Grades of Substitution and Microcalculus were translated, which were the first time for symbolic algebra and calculus to be introduced into China. In addition, mathematician Hua Hengfang translated a number of works in collaboration with Fu Lanya after the 1860s, introducing new mathematical concepts such as logarithmic tables and probability. In the late Qing Dynasty, most of the math textbooks in the new-style academies were adopted from the works of the two men. At the beginning of the 20th century, with the increase of foreign students, a large number of Western mathematics was introduced into China, and in 1913, Peking University established the Department of Mathematics, which was the first academic education unit specialized in mathematics.

Three, the early 20th century, the basic characteristics of Chinese primary and secondary mathematics textbooks

China's modern school education, began in 1862 (the first year of the Tongzhi) set up the Tongwenkuan in Beijing. At the end of the Qing dynasty, there is no systematic school system, math textbooks compiled by foreign missionaries, such as "algebra", "form of preparation", "eight lines of preparation", "generation of form and reference", etc. 1902 to 1910, the period, secondary school mathematics textbooks to the translation of the majority of the textbooks, but also appeared in our country to compile some of the textbooks, but the quality is poorer. 1911 the Republic of China was founded, and soon after the promulgation of the new school system, secondary school for four years. In 1911, the Republic of China was founded and soon promulgated a new school system, with a four-year secondary school system and a unified curriculum standard. China's own mathematics textbooks began to be published in a planned and systematic manner. The main ones were the **** and State Textbook and the New Textbook of the Republic of China. The main compilers were Qin Yuan, Qin Fen, Shou Xiaotian, Luo Shizeng, Huang Yuan, Wu Zaiyuan, etc. In November 1922, China carried out a reform of the school system and implemented the six-three-three school system. The drafting committee of the curriculum standard of the new school system drew up the outline of the curriculum of junior high school arithmetic, senior high school algebra, geometry, trigonometry and analytic geometry. Among other things, the middle school math curriculum is taught using a mixed method. Algebraic geometry was the main focus, supplemented by arithmetic and trigonometry, which were taught in a single course. To this end, the New School System Mixed Arithmetic Textbook (edited by Duan Yuhua, six volumes, 1926) was published, as well as the Elementary Mixed Mathematics written by Mr. Fu Zongsun. However, many schools objected to the mixed teaching and insisted on separate subjects. For this reason, the Commercial Press published another set of modern junior high school textbooks, including arithmetic, algebra, geometry and trigonometry. Among them, Algebra (two volumes) was written by Wu Zaiyuan (1884-1935).

In 1928 China began to formulate curriculum standards for secondary schools. Provisional standards were published first, and after revision for comments, the official curriculum standards for primary and secondary schools were published around 1933, so that secondary education in China gradually embarked on a more formal path of development. According to the curriculum standards, Wu Zaiyuan prepared the Textbook of Geometry for Higher Secondary Schools (Upper and Lower Books). With the revision of the curriculum standard, this textbook was revised and continued to be published after Wu Zaiyuan's death. For example, Revised Curriculum Standards Applied - High School Plane Geometry (Upper and Lower) signed by Wu Zaiyuan and Zhang Pengfei, and Revised Curriculum Standards Applied - High School Stereo Geometry signed by Wu Zaiyuan and Tao Hongxiang, were still in vogue at the end of the 1940s. It is worth noting that Wu Zaiyuan also wrote a set of "Chinese Junior High School Textbooks" based on the new curriculum standards from 1932 onwards, including Arithmetic for Junior High School (one volume), Algebra for Junior High School (above and below), Geometry for Junior High School (above, below and in the middle), and Trigonometry for Junior High School (one volume), which was published by the China Science Book and Instrument Company in Shanghai. This set of textbooks was published until the end of the 1940s, and in December 1947, 11 editions were published. Among them, Geometry for Junior High Schools changed the past pattern and divided the book into two main parts: experimental geometry and theoretical geometry. The purpose of teaching experimental geometry first was "to serve as a precursor to theory, especially to make students automatically realize that there are all kinds of graphical properties that are hidden in their minds and hearts, and that they are ready to come out". This is a prominent feature of the reform of secondary school geometry textbooks in the 1930s and 1940s.

It is worth mentioning that, in the early years of the Republic of China, most of our mathematics teaching using injective, "instructors speak, students listen; instructors write, students copy; instructors do, students see". The disadvantages of the injection of teaching methods are not yet emphasized by the majority of educators. And the reason is more than one aspect.

Four, the development of Chinese primary and secondary mathematics textbooks in the 1950s and 1960s

It is well known that in 1949, the new Chinese government centered on the Chinese ****anufacturing party began to operate. Eight large-scale reforms of primary and secondary mathematics education have been carried out so far.

The 1950s and 1960s were the first stage in the development of mathematics textbooks in China since the 1950s, which was characterized by a focus on the two fundamentals and on the characteristics of "teaching" materials.

During this period, three major reforms were carried out:

(I) The First Curriculum and Textbook Reform in 1949-1952

After the founding of New China, the Ministry of Education convened the first National Education Work Conference in December 1949, which began the first curriculum reform in China. This reform was carried out from top to bottom by the education department, implementing the transformation of the old curriculum, initially establishing a new curriculum system for primary and secondary schools in China, and forming a unified national teaching plan, a unified syllabus and a unified textbook, the "Great Unification" curriculum model. In August 1950, the Ministry of Education issued the Provisional Teaching Plan for Secondary Schools (Draft), which was the first teaching plan after the founding of New China; in September of the same year, it put forward the guideline that teaching materials for primary and secondary schools must be supplied uniformly throughout the country at the National Publishing Conference and set up the People's Education Publishing House, which undertook the task of compiling uniform teaching materials for the whole country. In October 1951, the State Council issued the Decision on the Reform of the School System, which re-established the school system for primary and secondary schools, stipulating that the five-year system should be implemented in elementary school, abolishing the segmented system of two grades for junior and senior high schools, and that secondary schools should have six years of study, with three years for each of the junior and senior high school grades. According to the requirements of the school system, in March 1952, the Ministry of Education issued the Provisional Regulations for Primary and Secondary Schools, which was the first government document issued after the founding of New China to comprehensively regulate the curricula of primary and secondary schools. The salient features of the primary and secondary school curricula and teaching materials of this period were: emphasis on centralization and national unification, with only compulsory courses and no electives; in terms of curriculum content, attention was paid to the organic combination of scientific and ideological aspects; traces of imitation of the former Soviet Union were obvious, and certain curricula were to a certain extent divorced from the actual situation in China.

(2) The Second Reform of Curriculum and Teaching Materials from 1953 to 1957

The meeting of the directors of the Regional Cultural and Educational Committees held in January 1953 and the Second National Educational Work Conference held in June sounded the trumpet for a new round of reform. The two conferences established that the focus of future educational work would be to reorganize, consolidate and develop primary and secondary schools. in April 1954, the State Council issued the Instructions on Improving and Developing Secondary Education, and in 1956, the Ministry of Education issued the first complete set of national syllabi since the founding of the country, the Revised Draft Syllabus for Primary and Secondary Schools. This round of reforms was completed ahead of schedule with the completion of the First Five-Year Plan, and ended in early 1957. The problems of this period of reform and development centered on the following: the initial formation of a relatively comprehensive primary and secondary school curriculum system, but the traces of imitation of the former Soviet Union are still very deep; too frequent changes in the curriculum, the textbooks can not keep up with the needs of the teaching work can not be carried out in full accordance with the teaching plan.

(C) The third and fourth reforms of the curriculum and teaching materials from 1957 to 1965

The basic establishment of the socialist system, the healthy development of the national economy, and the prosperity of the country and the people were all in good health; in February 1957, Mao Zedong made a report on the "correct handling of internal contradictions among the people", which suggested that "our educational policy should be based on the principle of the correct handling of internal contradictions among the people": "Our education policy should enable the educated to develop their moral, intellectual, and physical education, and to become socialist-conscious and educated workers. "In order to better implement this educational policy, under the careful planning of the Ministry of Education, a new wave of curriculum reform was launched, which went through three stages: the first stage was the adjustment from 1957 to 1958, which strengthened the combination of knowledge teaching and labor teaching and completed the "double-basic" task of secondary schools. The second stage was the Great Leap Forward in curriculum reform, in which the themes of curriculum reform were: shortening the school system and streamlining the curriculum. Specifically, in 1960, in accordance with the requirement of shortening the duration of primary and secondary schools, the People's Education Society compiled the third set of national teaching materials, compressing the contents of the original 12-year school system into 10 years for schools experimenting with the 10-year system. The third stage was the adjustment and reflection from 1961 to 1963, when the primary and secondary school curricula were reformed under the policy of "adjustment, consolidation, enrichment and improvement", new teaching plans and syllabi were formulated, and necessary adjustments were made to the primary and secondary school curricula; a fourth set of national teaching materials was compiled for the selection of schools with a 12-year school system, but the revised teaching materials were not accepted for a variety of reasons. For various reasons, the revised textbooks have not been officially used in schools. Although this reform has basically reversed the chaotic situation in the preparation and implementation of the curriculum, there are still some problems, such as the depth of the content of the textbooks, the weight of the textbooks, and the difficulty of the textbooks, as reflected in certain areas.

Around the 1960s, China's primary and secondary mathematics textbooks focused on the acquisition of basic knowledge and skills, marked by the 1963 syllabus and teaching materials (which came out in 1965), which demonstrated that China's mathematics education was gradually maturing. Its salient features lie in the fact that it emphasizes the consolidation of knowledge and the proficiency of skills. Although the 1963 Syllabus for Full-time Secondary School Mathematics (Draft) explicitly mentions the ability to compute, logical reasoning and spatial imagination, the concrete embodiment of this in the mathematics textbooks is still not too much focused on mathematical ability, and the process of mathematics is neglected. In the final analysis, the prominent feature of textbooks in this period is still "teaching" material, but, emphasize how to better facilitate students to receive.

V. The Development of Chinese Primary and Secondary Mathematics Textbooks in the 1970s and 1980s

This was the fifth reform of curriculum and teaching materials since the founding of New China. Its outstanding feature is that it pays attention to the cultivation of ability while focusing on the double fundamentals, and the characteristics of "teaching" materials are obvious.

In January 1978, the Ministry of Education issued the "Trial Teaching Plan for Full-time Ten-Year Primary and Secondary Schools (Draft)," promulgated a unified national curriculum, and concentrated on the preparation of the fifth set of ten-year primary and secondary school textbooks, which began to be used nationwide in the fall of 1978. This set of textbooks pays attention to the selection of basic knowledge, the enlightenment of the intellect and the cultivation of abilities, and its main shortcoming is "deep, difficult and heavy".

In the 1980s, attention was paid to the cultivation of ability while focusing on the acquisition of double basics. The symbol is the promulgation of the nine-year compulsory mathematics syllabus and the corresponding "eight and a half" nine-year compulsory education textbooks (eight sets of nine-year compulsory education textbooks, a set of elementary school teaching materials) of the gradual experiment. The mathematics textbooks of this period proposed to break the old model of "one program, one textbook" and to implement the "separation of editing and reviewing" by setting up a national (as well as provinces, autonomous regions and municipalities directly under the central government) primary and secondary school textbook reviewing organization, which was responsible for reviewing and approving the general textbooks and the local textbooks, and only after passing the review could the textbooks be used within the corresponding scope. Only after they have been approved can they be used on a trial basis within their respective areas. As analyzed by Mr. Cai Shanghe, its main features are (Cai Shanghe. 51 Years of Construction of Mathematics Teaching Materials for New Chinese Secondary Schools [J], Mathematics Bulletin, 2002 (10): 12-15): highlighting the basic mathematical ideas and mathematical methods, paying attention to the cultivation of ability while emphasizing the double foundations, combining the characteristics of the mathematical discipline with the cognitive characteristics of the students, combining unity with flexibility, combining the contents with the enhancement of ideology and morality education, attaching importance to the internship assignments, and introducing the sciences in accordance with the teaching contents. The use of calculators.

The outstanding features of primary and secondary school mathematics textbooks in the 1970s and 1980s were: highlighting the three major abilities (correct and rapid arithmetic, logical thinking and spatial imaginative ability), emphasizing the cultivation of analytical and problem-solving skills (although not ideal in practice), and raising the issue of the cultivation of the dialectical materialist point of view. Textbooks in this period are still characterized by "teaching" materials, but more emphasis on stimulating students' interest and external motivation for learning.

Sixth, the development of Chinese primary and secondary mathematics textbooks in the 1990s

Since the 1990s, China has proposed and begun to implement quality education. In order to fully implement quality education, to better solve the curriculum problems left over from the previous seven curriculum reforms, and to follow the trend of the world's curriculum reforms, the Chinese government started another extensive, comprehensive, deep and lasting reform of the curriculum system.

In 1993, the Central Government and the State Council issued the Outline for the Reform and Development of Education in China. The preparation and use of teaching materials for primary and secondary schools began to show a situation of "one program with many books" and "many programs with many books". In high school, more than 200,000 students who entered the first year of high school in the fall of 1997 in two provinces and one city (Tianjin, Shanxi and Jiangxi) completed their studies in the summer of 2000 and took the college entrance examination. Elementary and junior high schools to implement the nine-year compulsory education program in 1992 and 1993 in primary and junior high schools began to implement, in the summer of 1996, the first round of experiments in junior high schools ended in December 1996, the Ministry of Education to organize the relevant experts to carry out a survey of the nine-year compulsory education curriculum implementation program in December 1997 published the "nine-year compulsory education curriculum implementation program of the investigation report".

The 1990s, the new China was founded 50 years since the third stage of the development of China's primary and secondary mathematics textbook reform, its salient feature is to focus on the acquisition of knowledge, but also focus on the process of acquiring knowledge, and strive to build conducive to the acceptance of students and ability to cultivate the "teaching" material system.

VII. The Development of Chinese Primary and Secondary Mathematics Textbooks since the Early 21st Century

In February 2001, the State Council approved the Outline of Basic Education Curriculum Reform (for Trial Implementation), marking the full launch of China's basic education curriculum reform. As for the subject of mathematics, the promulgation of the Mathematics Curriculum Standards (Draft for Public Opinion) in March 2000 put forward the "trinity" of educational objectives, "focusing on the results, focusing on the process, and focusing on the emotional attitude and values," and the subsequent development of the experimental textbooks of the Mathematics Curriculum Standards from September 2001 onwards, the development of mathematics textbooks is now underway. In September 2001, the official experiment of the experimental textbooks of the Mathematics Curriculum Standards began. A new type of textbook is taking shape and gradually reflects the new style under the concept of "comprehensive human development". From the perspective of historical development, we believe that the prominent features of mathematics textbooks in this period are that they pay attention to the results, to the process, to the emotional attitude and values, and to the characteristics of the "learning" materials (Kong Fanzhe, "The Experimental Textbooks of Compulsory Education Curriculum Standards"). The main features of the experimental textbooks of compulsory education curriculum standards for mathematics [J], (NPC Newspaper and Journal Copying Materials) Secondary School Mathematics Teaching and Learning, 2004 (07): 38-43). That is to say, on the one hand, around the knowledge and skills, process and method, emotion, attitude and value, pay attention to the comprehensive, healthy and sustainable development of human beings, reflecting the inevitable connection between mathematics and disciplines inside and outside, reflecting the progress of society, science and technology and economic development, and pay attention to the practical enhancement of students' level of mathematical thinking. On the other hand, the "learning" material of the textbook is particularly obvious. This is a natural reflection of the concept of "comprehensive development of human beings" in textbooks, and also a natural reflection of quality education in mathematics textbooks. With the deepening of the reform, new requirements such as "student books and teachers' books should have clear and different responsibilities, and there is an urgent need for three-dimensional textbooks" and so on are becoming more and more prominent (Kong Fanzhe, "The Mathematics Curriculum Standard Experimental Textbooks", in Chinese). Problems and Countermeasures in the Development of Experimental Textbooks for Mathematics Curriculum Standards [J], Educational Science Research, 2005(03):53-56.)

VIII. Prospects for the Future Development Trend of Chinese Primary and Secondary Mathematics Textbooks

Since 2007, with the completion of the Mathematics Curriculum Standards for Full-time Compulsory Education (Revised Draft), primary and secondary mathematics textbooks, while focusing on the basic mathematical knowledge and skills, are also focusing to a large extent on the basic mathematical activity experience as well as on the core mathematical ways and methods of thinking (Deduction, abstraction, induction, analogy, etc.). That is to say:

Paying attention to basic knowledge and basic skills, paying attention to mathematical activity experience, mathematical thinking (mathematical ability, mathematical way of thinking), paying attention to both inductive thinking and deductive thinking training and development, paying attention to both the ability to find problems and raise questions, as well as analyzing problems and solving problems.

Reviewing the development of primary and secondary mathematics education (especially mathematics textbooks) in China over the past several thousand years, we can see that the development of mathematics textbooks has roughly gone through the following typical stages of development (see the following chart and table):

Open inductive system System of deductive system with emphasis on the training of logical thinking

The textbook system characterized by Euclidean geometry,

Focus on the development of the two foundations and the three abilities (created in China)

Focus on the inductive system, but do not abandon the deductive system Era

Cues Ancient times

China's "Western Learning" period 20th Century

First half of the 20th Century

Lower half of the 20th Century 21st Century "Induction"

Clue Subject Subject of education Retreating, still present Some traces, but not much attention Beginning to pay attention to "Deduction"

Clue Scattered Minority attention, not yet popular One of the main subjects Subjects Decreasing, still one of the main subjects; some modern mathematics One of the main content Somewhat reduced, but still one of the main characters; some modern mathematical content Development of mathematical sciences in China Pragmatic mathematics is the main focus The emergence and development of modern mathematics Foundation and development of modern mathematics Mathematical subdisciplines have been derived Mathematical development has brought about new challenges Among them, there were two styles in the 1920s and 1930s, namely, "mixing and arranging" and "arranging and arranging", and "arranging and arranging". In the 1920s and 1930s, there were two styles: "mixed" and "separate", while experimental geometry and integrated mathematics are valuable even today (although they did not become the dominant trend at that time). This development can give us some insights, namely: from the viewpoint of textbooks, it is the tradition of mathematics education in ancient China to emphasize induction and practicality, and in particular, the textbook presentation mode of "Question (Problem-Model)→Answer→Technique (Principle, Rule, and Algorithm)" has been formed. After the 1950s, a certain period of time once ignored (or even discarded) this tradition, and turn to the importance of deduction, the importance of basic knowledge, basic skills of the new habits of recent times, the formation of "concepts → axioms, theorems, laws, formulas → application, reinforcement of the" textbook presentation model, although this model is necessary, but too single,

In the last decade, Chinese primary and secondary mathematics education is moving towards the trend of taking into account both inductive and deductive ways of thinking, and the presentation of textbooks to a variety of styles coexist, and the exploration and discovery and meaningful acceptance of complementary coexistence, i.e., the exploration of the "problematic scenarios → modeling → explaining the application → expanding the reflection" model. Expansion of reflection" mode of presentation of inquiry, "can stimulate meaningful learning problem scenarios → concepts → axioms, theorems, laws, formulas → application, reinforcement → the formation of the mathematical content system" mode of presentation of acceptance.

It can also be understood in this way: just like the history of human culture, the history of the development of education tends to swing like a pendulum between two poles, and the development of Chinese mathematics education seems to follow such a law. The tradition of Chinese mathematics education is also in the process of development and change, in which there are both the historical tradition of mathematics education formed in ancient China and the new habits of mathematics education formed in modern China (or called the new modern tradition).