The growth of a new generation of primary school mathematics teachers

Zheng Yuxin, Philosophy Department of Nanjing University *

* The writer is a professor of philosophy at Nanjing University, a doctoral supervisor, and a member of the International Project Committee of the International Conference on Mathematics Education (ICME- 10).

The author recently participated in some national primary school mathematics education seminars, gained a lot and produced many ideas. One of them is to attach great importance to the growth and cultivation of a new generation of primary school mathematics teachers.

The above problems can be regarded as the direct requirements of some obvious changes, such as the general education of primary school teachers has risen from the original technical secondary school to junior college or even undergraduate course, and the application of modern educational technology has put forward new requirements for primary school mathematics teachers from a special aspect, and so on. In addition, from a deeper level, this should be regarded as the inevitable requirement of the progress of the times and the development of mathematics education itself. For example, the new round of mathematics curriculum reform actually puts forward higher requirements for mathematics teachers. In particular, different from the traditional formulation that "teachers should stick to textbooks", the newly published mathematics textbooks have a common feature, which is to leave more space for teachers' creative work. That is, teachers are required to creatively use teaching materials according to specific teaching objects, contents and environment, including appropriately breaking through teaching materials when necessary. Obviously, this requires teachers to have a higher theoretical level and be able to better combine teaching activities with teaching research, that is, to have certain mathematics education and teaching research capabilities.

In order to explain the problem clearly, we can also analyze the international development trend of mathematics education here. Specifically, this is an important feature of the modern development of mathematics education, that is, it has grown into a relatively independent professional knowledge. In particular, "we should not think that mathematics education is completely attached to mathematics, nor should we think that mathematics education is completely attached to education;" More precisely, mathematics education has its special problems, and around these problems, a systematic theory of mathematics education is taking shape. " But as far as the reality of our country is concerned, people seem to pay more attention to the distinction between primary school mathematics education and middle school mathematics education, and if middle school mathematics education is often regarded as attached to mathematics, primary school mathematics education shows the influence of general pedagogy and psychology more obviously. For example, this can actually be regarded as a manifestation of this differentiation phenomenon, that is, in all normal universities in China, teachers who specialize in primary school mathematics education research often work in the department of education or psychology, while teachers who are considered to specialize in mathematics education research usually belong to the department of mathematics and rarely care about primary school mathematics education. It is worth pointing out that, in contrast, the above-mentioned phenomenon of strict differentiation of mathematics education in primary and secondary schools does not exist in developed countries. For example, as an authoritative work on mathematics education, the National Council of Mathematics Teachers in the United States

The Handbook of Mathematics Teaching and Learning compiled by NCTM has been included in all the important topics of mathematics teaching in primary and secondary schools at the same time (the topics belonging to the latter scope include Research on Integer Addition and Subtraction, Multiplication and Division as Situational Model, Rational Number, Ratio and Proportion, Estimation and Significance of Numbers, etc. ); However, when this book was translated into Chinese (although it was only an elective book), all the contents of primary school mathematics education were omitted, thus showing obvious tendency.

Of course, the above differentiation does not mean that middle school mathematics education in China is superior to primary school mathematics education; On the contrary, it only shows clearly from one angle that mathematics teachers in primary and secondary schools in China have their specific limitations. In view of the topic of this paper, the following will mainly analyze the growth of a new generation of primary school math teachers, especially point out the growth direction and some key factors of the new generation of primary school math teachers.

one

(A) A new generation of primary school mathematics teachers should pay more attention to the theoretical research of mathematics education.

At present, we can seriously reflect on the following questions: Do I have a strong desire to learn? How much do you know about the professional theory and modern development of mathematics education?

For example, as a simple "test", readers may wish to seriously consider the following questions-this is specially designed by the International Commission on Mathematics Education (1CMl) for university mathematics teachers, aiming at promoting the reform of university mathematics education. However, with a little modification, they are obviously also applicable to primary school math teachers.

1. What is mathematics understanding and learning? How can we understand and learn mathematics? What is the basic theory in this respect? What is the relationship between these theories and mathematics teaching in university?

2. What is the research method of mathematics education? What are the main findings of mathematics education research? What are the main obstacles to the infiltration of research results into mathematics teaching practice?

3. Is it possible to draw different conclusions about the nature of different levels of learning process? Does the theory applicable to general education also apply to the university level? Is it necessary to establish a special theory at the university level?

4. What research has been done on traditional and other possible teaching methods? What are the main conclusions of these studies?

5. How to adapt to students' different backgrounds, abilities and interests in teaching? What is an effective teaching method for large classes?

6. What have we learned about the teaching and learning of various topics, such as calculus and linear algebra? Does each topic have its own particularity? Is there any universality applicable to several topics?

7. Are there any other evaluation methods? How to use assessment to promote learning and understanding?

8. What are the specific requirements of different majors for mathematical ability?

9. What are students' attitudes and beliefs about mathematics? How to make it change? How do they affect students' choice of mathematical subjects and their success?

10. How does the application of technology affect the teaching and learning of mathematics? How to use technology to promote understanding?

1 1. What important topics have not been fully reflected in the research literature? How to promote research in these areas?

In my opinion, if I find that I lack a good understanding of the above problems, it clearly shows the necessity and urgency of studying the professional knowledge of mathematics education seriously.

In order to explain the problem more clearly, the author wants to put forward some ideas from another angle: in reality, primary school math teachers in China have a better grasp of the teaching art than middle school math teachers, such as high level of Putonghua, stronger appeal of teaching activities, and so on; But as far as the new generation of primary school mathematics teachers are concerned, the author thinks that it is not enough to master the traditional teaching art, but also to become an expert in mathematics education. Obviously, we should pay more attention to the high level of professional accomplishment than being versatile in playing and singing.

What needs to be pointed out here is that a high level of professionalism does not exclude a wide range of knowledge backgrounds. On the contrary, it is an important feature of the modern development of mathematics education, that is, it shows mutual infiltration and intersection with many disciplines (besides the traditional connection with mathematics, pedagogy and psychology, philosophy, sociology, linguistics, anthropology and other disciplines should also be mentioned here). Generally speaking, what we want to advocate here is the necessary knowledge expansion and reasonable reconstruction of knowledge structure [1].

(2) A new generation of primary school mathematics teachers should have certain educational, teaching and scientific research abilities in addition to their strong teaching ability.

Similarly, we can ask ourselves first: Do I consider myself a researcher in some sense? Do I know what people are most concerned about in mathematics education at present? What are the different views or opposing views on these issues?

Because curriculum reform is the biggest reality at present, the author thinks that mathematics teachers in the front line of teaching should actively carry out education and teaching research around the following problems, that is, how to better handle the following relations in teaching: "cultivating students' emotions, attitudes and values" and "learning mathematics knowledge and skills"; Popular mathematics "and" the development of the top 20% students in mathematics "; Close contact with students' real life "and" formal characteristics of mathematics "; Students' active construction and teachers' necessary guidance, students' personality differences, the reality of large class teaching, the innovation spirit, the reform of teaching methods and the necessary inheritance of excellent teaching traditions; Wait a minute.

For example, the cultivation of students' emotions, attitudes and values in mathematics education should obviously not be separated from their learning of mathematics knowledge and skills; On the contrary, we should actively help students develop appropriate emotions, attitudes and values through the teaching of specific mathematical knowledge and skills. Similarly, to cultivate students' good feelings, attitudes and values, it is obvious that they should be encouraged to study mathematics knowledge and skills more actively. For another example, in mathematics teaching, we should not only make full use of the knowledge and experience formed by students in daily life as a good foundation for school study, but also mobilize students' enthusiasm for learning mathematics in connection with real life, including initially learning how to apply the learned mathematics knowledge. At the same time, we should pay attention to prevent the "taste of life" from completely replacing the "taste of mathematics" that mathematics teaching should have, and help students clearly understand and realize the transition from "daily mathematics" to "school mathematics". [2]

Finally, it should be emphasized that the requirement for a new generation of primary school mathematics teachers to have certain educational, teaching and scientific research capabilities certainly does not mean that they are completely divorced from teaching and engaged in specialized academic research. In fact, frontline teachers are generally unlikely to engage in specialized theoretical research due to the nature of their work; On the contrary, we should give full play to the advantages of front-line teachers who are very familiar with actual teaching activities. For example, as far as the writing of scientific research papers is concerned, it is obvious that it should not be positioned as a big and empty "academic paper" wearing boots and hats, but should strive to maintain the flesh-and-blood and originality of front-line teaching work, that is, it should be based on actual teaching activities; Of course, the latter does not mean that we can only write articles about teaching methods or class evaluation all the time. The key here is not the size of the topic, but should strive to make it "meaningful and reasonable;" Pay equal attention to emptiness and smallness, and see the big with smallness. " [3]

two

Here are three examples to analyze some key factors in the process of teachers' growth.

[Example 1]

R scamp, a British scholar who died a few years ago, is an internationally renowned mathematics educator. At the beginning of his work, Skip worked as a primary school teacher for five years, and it was the practical problems he faced in teaching that prompted him to embark on the road of academic research. In this regard, Skip himself once described it like this: "When I was a teacher, I encountered some professional problems when teaching mathematics and physics to children over eleven years old. After teaching for five years, I gradually realized that I had failed to achieve what I had hoped to achieve. Although some students do well, others are always unknown so when studying mathematics. Not because I or they are stupid or lazy. This is by no means an accidental phenomenon, nor is it just a problem of my teacher or a group of students. In fact, since

Since the late 1940s, more and more people have begun to pay attention to this issue. This question made me interested in psychology. "Specifically, in Skip's view at that time, only through psychological research can we find the correct answer to the above questions; However, the latter is actually the actual beginning of his long academic career. Skip wrote: "This mental journey has lasted for more than 30 years. It begins and ends in the mathematics classroom, but it runs through the fields of developmental psychology, motivation theory, emotion theory, cybernetics, evolution theory, artificial intelligence and so on. "That is to say, because of relying only on psychology, Skip has not been able to find an effective way to solve the above problems, so he has to set foot in more disciplines and fields, which is actually the process of Skip's continuous academic growth. [4]

From this, we can clearly see the importance of extensive knowledge background. As far as the growth of a new generation of mathematics teachers is concerned, the author thinks that we can get the following important enlightenment from this example: theoretical study should have a clear purpose, that is, not to study theory blindly and indiscriminately, but to study purposefully around problems-it is in this sense that young teachers should pay great attention to cultivating their own problem consciousness and see clearly the dialectical relationship between asking questions and theoretical study: asking questions. On the other hand, new learning will make people think more deeply, so it is possible to constantly ask new and more important questions.

[Example 2]

If Skip eventually becomes a specialized theoretical researcher, then Wu Ruixiang, who is introduced below, will always be a primary school math teacher in the front line of teaching. Specifically, although Wu Ruixiang is only an ordinary primary school teacher in Taiwan Province Province, she enjoys a high reputation in the education field in Taiwan Province Province. For example, Professor Zhan Zhiyu of Taiwan Province University of Political Science once commented: "She explored and experienced constructivism teaching with practical teaching actions. The results of her efforts have made many people in education think of Wu Ruixiang as soon as they hear' Constructive Teaching'. " [5] For Mr. Wu's growth process, Mr. Lin Wensheng of Taiwan Province Province once summarized the following five stages according to Mr. Wu's dictation:

(1) traditional course period (before 1983). Teach students and impart mathematics knowledge in full accordance with the syllabus (teaching guidance book). (2) metamorphosis period

(1984 ——1987). After joining the Taipei Mathematics Tutoring Group, I began to have the opportunity to participate in the relevant research of mathematics education and began to seek new mathematics teaching methods. (3) Germination stage (1988-

1989). Influenced by Skip's thought, it is believed that mathematics education should not stay in mechanical practice, but should pay more attention to the understanding of relations. At the same time, I began to accept the teaching thought of constructivism. (4) Growth period (1990-1994). Try the reform of teaching methods, and begin to introduce the idea of constructivism into the classroom for experiments. Facts have proved that the structure of teaching materials must be changed. Began to break the limitation of "teaching guide" and design math problems by myself. (5) Mature period (after 1994). Form your own teaching mode and achieve obvious teaching results. So as to "grow from a novice to an expert teacher." [6]

From this example, we can get the following enlightenment. First, front-line teachers' education and teaching research should be firmly based on their own teaching work, that is, to improve their own teaching as the main goal. Second, positive criticism and serious reflection can be regarded as the main driving force for teachers' growth. For example, from Mr. Wu's self-introduction, we can know that it was because he was dissatisfied with the current mathematics teaching that he actively sought new teaching methods: "I made this mistake, too, until 1988, when I met my junior high school English teacher, she told me face to face:

Teacher, I didn't understand the math I studied before. We all recited it! Oh, my God! This child who gets 100 in every math exam, studies math so hard!

What about China? "Stick to the end!" What about high school? Is it miserable? I can't recite it! The students' words are like a wake-up call, awakening the dreamer to repent with tears; The famous teacher of that year was just an illusion! "[7] In the later reform process, it was through constant practice, constant summary and constant reflection that she was able to continuously make new progress. Just as Teacher Lin Wensheng mentioned, "Mr. Wu is a person with strong self-reflection. Her self-reflection and criticism can be found in her own articles or teaching diaries. After each teaching, she will write what happened in this class into the teaching diary to reflect and criticize her teaching process. " Thirdly, Wu's example also clearly shows the importance of theoretical study. For example, it was by participating in the Taipei Mathematics Tutoring Group that she came into contact with new theories, broadened her horizons, and made it possible for her to deeply criticize and reflect on her past teaching work. More importantly, it is the new educational thoughts and theories (Skimbo's and Constructivism's teaching thoughts) that provide important theoretical guidance for her to actively engage in teaching reform, that is to say, at this time, Ms. Wu has gone beyond the level of pure practice and rose to conscious practice under the guidance of theory. Fourthly, this should be regarded as the reasonable orientation of professional mathematics teachers, that is, the main position relative to teaching materials and teaching. In other words, teachers should use teaching materials creatively, not just "close to teaching materials"; Similarly, we can't imitate any teaching mode mechanically: "Constructivism teaching mode doesn't exist, and the best teaching mode is the result of teachers' self-construction."

[Example 3]

We can also get some important enlightenment and lessons from the growth of some local famous teachers. For example, by reading two books by Wu Zhengxian (Examples and Teaching Methods of Mathematics in Wu Zhengxian, People's Daily Press, 1998 edition;

"I and Primary School Mathematics", Beijing Education Press 200 1 edition), the author feels that Mr. Wu and Mr. Wu actually have many similarities. For example, both teachers are not geniuses, but they both have a hard growth process. "In the long river of my teaching career, I have hesitated, hesitated and lost ... but I never gave up my efforts and never gave up my pursuit. On the road of education and teaching for 30 years, I have been concentrating on exploring and moving forward step by step. " From teacher Wu's report at the third educational research seminar in Chongwen District on 1988, we can clearly see that her eagerness for teaching and extensive theoretical study can also be regarded as the key to her growth: "In the early 1980s, the phenomenon of one-sided pursuit of enrollment rate in education was very serious ... Faced with this reality, I fell into meditation: Can this train qualified talents? Is there no other way? Regardless of students' physical condition, moral cultivation and ability development, it is not only a dereliction of duty in education, but also a crime to society and the future! A strong sense of responsibility is condensed in my heart, and I am determined to use my own efforts to explore a new teaching path that is suitable for students' reality and conducive to students' development. " "I don't know if it is out of a need or because I have tasted the sweetness of learning theory. I began to pick up books on educational science theory from the unconscious to the conscious. I seem to have found a shining lighthouse in the misty sea. It helped me find the direction of exploration. ...... In recent years, I have stumbled onto the road of teaching and scientific research, and started the teaching reform from unconscious to conscious. ..... All this proves that education reform cannot be separated from scientific research! Advanced educational science theory has brought great vitality to teaching reform with magical power, and opened up a broad and bright prospect for in-depth teaching reform! " Furthermore, the two can better reflect the dominant position of teachers in teaching, as Teacher Wu Zhengxian said:

"Textbooks are just teaching materials. If you want to teach well, it depends on application. ..... In short, teachers should flexibly control the teaching materials and design the teaching process scientifically and reasonably; We should proceed from students' reality and take students' cognitive rules as the basis; It is necessary to scientifically deal with the main and substantive teaching contents, so that static teaching materials can be turned into dynamic teaching activities conducive to students' development. "

Finally, the author believes that young teachers can certainly get important enlightenment from Mr. Wu's following experiences: First, "I have a profound experience in the practice of teaching reform for many years, and everyone will have a little experience in teaching, either deep or superficial. If you relax, it will be fleeting; If you pay a little attention to it and write it down, even superficial feelings or irrational intuitive thinking will bring calm thinking in the future. Little by little, every little makes a mickle. " Second, "in the face of numerous academic research results and complicated educational information, we should keep a clear head and absorb and filter." Learn from the strengths of a hundred schools of thought, learn from the strengths of many schools of thought, and create their own characteristics in light of their own reality. "

The author thinks that the new round of mathematics curriculum reform has actually provided a good external environment for the growth of a new generation of teachers, and hopes that the younger generation can seize this opportunity well!

three

Finally, the author hopes that the new generation of primary school teachers can set up such an ambition from the beginning, that is, through their own research work, to push China's primary school mathematics education to the world. In fact, we can often see middle school teachers in special mathematics education seminars held in China and some related international conferences. In addition, from the following topics of the 10th International Conference on Mathematics Education to be held in Denmark in 2004 (1 CME- 10), it can be seen that mathematics teaching in primary schools, like other contents, constitutes an important part of mathematics education research.

(A) "Special Research Group" topic

(1) New development and trend of preschool and elementary mathematics education; (2) The new development and trend of secondary mathematics education; (3) The new development and trend of college mathematics education,

(4) the education of gifted students; (5) Education of children with special needs; (6) Adult and lifelong mathematics education; (7) Vocational mathematics education; (8) Research and develop the teaching and learning of numbers and arithmetic; (9) Research and development of algebra teaching; (10) Research and development of geometry teaching and learning;

(1 1) Research and development of teaching and learning of probability statistics; (12) Research and development of calculus teaching and learning;

(13) Research and development of modern mathematics teaching and learning; (14) Innovation in mathematics teaching; (15) The function and application of technology in mathematics teaching: (16) Intuition in mathematics teaching;

(17) The role of mathematics history in mathematics teaching and learning; (18) Problem solving in mathematics education; (19) Reasoning, proving and proving activities in mathematics education; (20) Mathematical application and modeling in mathematics teaching and learning;

(2 1) the relationship and connection between mathematics and other sciences or humanities; (22) Learning and cognition in mathematics: the formation of students' mathematical concepts, strategies and beliefs; (23) Training, specialization and development of mathematics teachers;

(24) Students' motivation and attitude towards mathematics and its learning; (25) Language and communication in mathematics education; (26) Gender and mathematics education; (27) Research and development of mathematics education evaluation;

(28) The new trend of mathematics education research; (29) History of Mathematics Teaching.

(b) The topic of "discussion group"

(1) The development, process and policy of curriculum reform;

(2) The relationship between research and practice in mathematics education; (3) Who should mathematics education serve? Why? The balance between "popular mathematics" and "advanced mathematics activities";

(4) the philosophy of mathematics education; (5) International cooperation in mathematics education; (6) the cultivation of mathematics teachers; (7) the public's understanding of mathematics and mathematics education; (8) The quality and relevance of mathematics education research;

(9) The formation of mathematical education researchers; (10) Different perspectives, positions and methods of mathematics education research; (1 1) international comparison of mathematics education;

(12) Exam-oriented Mathematics Education: Better or Worse? (13) Evaluation of teachers, courses and systems; (14) math textbook; (15) Do you want to implement shunting? (16) The role of mathematics competition in mathematics education; (17) Problems and challenges faced by preschool mathematics education; (18) Problems and challenges faced by primary school mathematics education; (19) Problems and challenges faced by junior high school mathematics education;

(20) Problems and challenges faced by senior high school mathematics education; (2 1) The problems and challenges faced by mathematics education in non-undergraduate universities; (22) Problems and challenges faced by college mathematics education

War; (23) Problems and challenges faced by students with special needs in mathematics education; (24) Problems and challenges faced by distance education.

(3) the topic of "free communication"

(1) Mathematics teachers: convening and continuous attraction, professional development and definition;

(2) Mathematics education in social culture; (3) Mathematics and mathematics education; (4) Technology in mathematics education; (5) Looking at the research of mathematics education from other disciplines.

In short, it is no exaggeration to say that the younger generation of primary school mathematics teachers and the international mathematics education community are waiting for you!

________________________

note:

[1] This can be seen in another article: "The urgent task of training mathematics teachers in China", Mathematics Teaching Newsletter, No.5, 2002.

[2] This can be seen in another article: "Cold Thinking in the Reform Boom", "Reference for Middle School Mathematics Teaching", No.9, 2002.

[3] This can be seen in another article:

Critique of Strengthening Mathematics Teaching and Research, 200 1 third issue for young primary school teachers; Analysis of a New Round of Curriculum Reform in Mathematics Classroom Teaching in Primary and Secondary Schools, Curriculum, Textbooks and Teaching Methods, No.4, 2003.

[4] See "Primary Mathematics" for details.

Routledge， 1989； Psychology of Mathematics Learning, Lawrence Elbaum,1987;

[5] This can be seen in another article: Constructivism: From Theory to Practice, Primary School Teaching1999 No. 10, 1 1.

[6] See Lin Wensheng: Vivid Classroom, Meaningful Learning, edited by Zhan Zhiyu: Constructivism, Taipei, Zhong Zheng Bookstore.

2002 edition.

[7] "My Mathematics Teaching Mode", edited by Zhan Zhiyu:

Constructivism, Taipei, Zhongzheng Press, 2002.