Reflections on mathematics Learning and teaching concepts of teachers and students in China Priory Professor Dan

Reflections on mathematics Learning and teaching concepts of teachers and students in China

Professor Priory Zhong Dan

1. The origin of the problem

for a long time, we have a heartfelt sense of pride in the mathematics of Chinese students. However, in the past more than 20 years in the teaching process of the mathematics department of Beijing Normal University, we have seen a series of contradictions. I always thought it was only because of the insufficient investment in teacher teaching. Therefore, since 2001, Together with Professor Wang Kunyang and Professor Defense, we devote most of our energies to the teaching of undergraduate courses, which are based on advanced and modern teaching concepts, content and methods, and put the teaching center in the students ' mathematics development. We have first-class students who love maths and study hard. It is a teacher's heart, The students struggled. So it must be able to cultivate a group of excellent students. Undoubtedly, there have been many gratifying successes in the development of students. However, there are a number of seemingly simple and insurmountable problems in the teaching process (see discussion below). This prompted the author to ponder the reason. Thanks to the organizers of the mathematics Education salon for the author to provide this opportunity, can be more than eight years of thinking and observation to do a preliminary summary. There must be a lot of bias, I hope to have a point of effect.

2. Puzzling Phenomena

Beijing Normal University mathematics major students are very strict selection, in the author's admission survey, more than 80% of the students said they love mathematics, determined to learn maths, in the future to engage in mathematics. However, in the teaching, the following problems of students are again. Teachers in teaching, The discussion class and the experiment class tried to correct, after the three or four semester, the effect is still very little. These phenomena include: (1) Compare, prove oneself understand as the pursuit of Learning, (2) to learn mathematics equivalent to be able to do test questions, (3) will only back, not even dare to explore their own, no comprehend by analogy ability, For the need to use their own knowledge of logical reasoning and other problems, feeling very difficult to bear, (4) encountered can not immediately clear the topic, immediately looking around for reference materials, to find out the ready-made solution, (5) hope that the teacher to provide a successful guarantee, especially to be able to easily fame things to do.

3. Is there a problem with our math concept?

The following is a description of the nature of the phenomena that arise in the above-mentioned students from the phenomena seen in the fields of mathematical propaganda, teaching attitudes, teaching methods and guidance of learning methods.

3.1 propaganda on the mathematical concept and students to learn the concept of mathematics as with any other social activities, the achievement of mathematical activities need to work hard for the math workers, many of the efforts of several generations, so many of the results of mathematics often give people a deep and concise impression, so that there is a sense of craftsmanship, This makes many people involuntarily admire the genius of the corresponding mathematician. In our mathematical propaganda often deliberately highlighting the protagonist's genius, thought this can guide people to worship mathematicians, naturally make students love math, worship scientists. In the course of actual teaching, Teachers often consciously and unconsciously teach students all kinds of mathematical genius myths, so that students think the achievements of mathematicians and even the entire mathematics is a genius of the achievements. This explains why students have the impression that learning a certain mathematical content is because they are a genius, Learning is not good because you are not smart. This can explain that students are very concerned about the evaluation of their own mathematical ability, the pursuit of some recognition, to prove that they understand as the only important thing, rather than focus on the specific mathematical content, on the objective criteria, the students in the class as whether the ranking is the standard of genius, And when the ranking is not so forward, it is not consciously to learn to lose confidence.

3.2 Teachers ' teaching attitude and students ' learning attitude our students have a keen expectation for teachers: teachers are the way to show their success. However, when it is required to do the actual time is lack of sustained force, every step to seek the teacher's advice, every thing to do is afraid of problems, Dare not imagine more dare not to bear the imperfect, very concerned about the teacher's recognition of their mathematical ability. Interestingly, there is a similar phenomenon in the contact with the math teacher. This prompted the author of the teacher's teaching attitude has generated interest, that is, how teachers attitude towards students, They want to figure out what kind of image they have in their minds. Preliminary observation and thinking results are: teachers in the teaching attitude, most of them strive to make students believe that, as long as the teacher given the steps to do, can learn mathematics, if not well, it is because students are not suitable for learning maths. When it comes to specific math problems, Most teachers consciously and unconsciously make students feel that teachers are omnipotent, know everything about the content taught, and master how to learn how to grasp the key of these contents: learning methods. It's not surprising why the aforementioned phenomena occur. It is a reflection that many teachers talk about their teacher, Often consciously and unconsciously give a similar narrative. This is no wonder in the students common phenomenon: if you find that teachers who do not know, it is believed that teachers should not be, and students themselves feel at a loss.

3.3 Teaching methods and students ' learning expectation in teaching methods, teachers strive to lay an extremely meticulous and repeated training path for students, and to rectify the inconsistency between the students and the textbooks. Meanwhile, the teacher's research on key examinations is in depth to all aspects, Strive to provide students with a set of details (knowledge points) of the meticulous training process, so that students can quickly and correctly answer the questions in the exam, so as to obtain a high score in the exam. This makes the college students develop a kind of new knowledge to expect a high school-like repeated training process, otherwise they think they can not grasp; At the same time, whether the standard is the test scores, so that students devote a lot of energy to collect a variety of topics. What's more, devote your energy to the teacher's exam questions.

3.4 Subtle and attentive learning methods the teacher not only in the teaching methods have in-depth and meticulous design of the test, but also to the student's learning methods to make thoughtful design. Specifically, to provide students with a complete approach to learning, and the crown of "good students are so learning." The name says: Gradually. Further, the "gradual" learning method is interpreted as, as long as the 1.1-point study, we will be able to learn, in the teaching of our college students to see this "step-by-step learning" understanding of the consequences is that whenever encountered a moment do not understand the content, the first to accuse teachers not gradual; Then find a variety of other books to see, and strive to be able to find the right path to progress, in order to successfully achieve the learning objectives. Not only that, the students in the study of the help is not limited to the student learning method design, and open various classes, extracurricular classes, for students to design a set of tangible "progressive" Step. It seems to be believed that as long as you see any deficiencies in the student, you can solve the problem by opening some kind of course. The phenomenon is that students can control their own time is less and more, and the need to remember things more and more, in the mind accustomed to others to provide perfect advice, And I cannot and dare not try.

4. Reflections on Mathematics Education

The above attempts to find out from the mathematical concept for the author in Mathematics major students see the reasons for the various phenomena, but these discussions still make people have a shoe scratch itch feeling, because, these discussions can only be a discussion. If these analyses are basically correct, then why do people do this? And it is so selectmen, righteous to do it?

4.1 from the "Learning and time learning, not happy" explanation see what

this may be from the opening sentence of Confucius "the Analects" to learn and time, not also happy? Have friends from afar, the joy of the people do not know and not get mad bland, not also a gentleman? Can see a clue in the explanation. This is Confucius Master life in the wisdom of scholarship, even now can not but to make people sigh the greatness of Confucius: "Learning and internship to learn, not also delightful?" Even if the bosom friend is far away, is not the heart pleasant? But what does posterity think of these words? The following is the English translation of the Analects of Confucius, published by the Foreign Language teaching and Research press in 1998: "To learn and at due times to repeat. R all a pleasure? That friend should come to one from a far, was this not after all delightful? To remain unsoured even though one ' s merits be unrecognized by Others,is that's after all what's expected of a Gentlem En? " This translation is undoubtedly related to the interpretation we have been familiar with since childhood, especially the first sentence, in fact, most of us are only familiar with the first sentence: "Learning and time learning, not also happy?" How happy is it to be interpreted as "learning to read and reviewing in time?". Originally saw this explanation, Lenovo Movement put forward "down the hole home shop", really feel movement put forward the right. However, to think carefully, Confucius Life of the era is such a can "oblivious, as long as concentrate on the book" Of the Times? Of course not! So is Confucius really going to mean that? Look at Confucius himself and the virtuous people of his students, can find a few such explanations of the people come? Really go (this is probably impossible for the vast majority of people) to read the Analects of Confucius will also find that "learning to read and review in a timely manner" explanation is unreliable. So the above kind of words too literally, What is the reason for the fragmentation of the explanation? A lot of people will naturally use it with our long-standing learning situation as the basis for this explanation. This, although some of the reasons for the fruit, but it seems to be justified!

4.2 The Enlightenment of the talent selection system in the more than 1000 years after the Sui Dynasty

in the creation of talent selection system in China, the Imperial examination system perfected in Sui Dynasty (582-617) is a great progress in the selection of human talents: In theory, the members of society are no longer bound by their families, and can achieve their responsible position in the society according to their ability (official position). After the Imperial examination system was perfected and changed in successive dynasties, the abolition of the imperial Examinations in 1905 lasted nearly 1300 years. However, "the law is long and bad". Plus the feudal rulers as the maintenance of their home world domination tools of the actual operation, and the imperial examination can only be based on the limitations of scaled and people's mentality of quick success, Nature has created the social situation reflected in the awkward interpretation of the words too literally of "learning and time learning, not just". Although the abolition of the imperial examinations, people introduced a variety of new talent selection attempt, especially to the movement as the symbol of the scientific democratic spirit of the promotion, Nothing can be done in the selection system. Because the modern selection method is still the examination, this in the way and the Imperial examination Way and no big difference, in addition, the people's pursuit in society and the Imperial Examination times also have many similarities, this makes the imperial examination age existence of all kinds of ills also exist in the contemporary. It's ridiculous to say, Just as the relationship between chickens and eggs, on the one hand, the situation of society has resulted in a series of social consequences of the selection system, on the other hand, these social consequences further contributed to the social situation of bad social practices deepened. In other words, after thousands of years of evolution and development, China has formed a set of popular test scores of the selection mechanism , and it has proved to be the fairest system so far. Sadly, it backfired, a mechanism designed to inspire people to develop their talents, gradually evolved from the pursuit of knowledge and talent to the pursuit of test scores, more serious, one-sided pursuit of test scores have been deep into people's minds, In a sense, even become the only pursuit of education! This may be to why "learning and time learning, not also happy to" become "to learn to read and review in a timely manner, is a good thing ah?" Note!

4.3 Mathematics Education Lacking mathematics

with the previous discussion, I can have a reasonable explanation for the various phenomena encountered in the university mathematics education. In today's selection, especially in the entrance examination, mathematics is one of the most important, in the education alienation as the score of the cultural impact, in the gradual loss of the original meaning of mathematics education, And just become a carrier of the score. Mathematics education is nothing more than a stepping stone to a higher social status. It is not difficult to understand why a group of excellent, love math students actually lack the basic literacy of high school mathematics, let alone the mathematics syllabus or curriculum standards of secondary education to promise or requirements of the ability and skills .

4.4 Forming the theoretical system of professional development of mathematics teachers with Chinese characteristics

the study of the professional development of mathematics teachers in our country, on the one hand, should fully learn from foreign ideas, theories, methods and achievements, on the other hand to create their own theoretical system, to push their own things abroad, and international research, in the exchange of generation, growth. The construction of professional development theory of mathematics teachers with Chinese characteristics Based on the Chinese cultural tradition and the reality of the Chinese society, we should innovate and develop on the basis of the Chinese students ' educational goals. Practical exploration and practice, so perhaps there can be a breakthrough. But in today's age, if in mathematics education, cannot be below, Chinese mathematics and mathematics education should do something tangible at the following two points: (1) How to make mathematics education really have mathematics, (2) How to improve and popularize mathematics education do not go to extremes. The author thinks that the most urgent thing is: how to make the corresponding mathematical content clear, and strive to conform to the reality of mathematics, Instead of turning its center into a way for students to understand and learn about what they teach.

5. What is the way out

eight years in the history of the river is just a short moment, but for the author's thinking, it is a long night, in retrospect, that can get a satisfaction to their own confusion of an explanation and relief, and for this interpretation brought about by the conclusion of sleepless. A person should not be afraid to face the reality, Dare to admit and face the reality, however, this is still far from enough. It is also important to consider the possible way out. In fact, since the human society has a selection system, the pros and cons of the various selection system controversy. For the current problems in mathematics education, people have put forward a variety of solutions, the result is often a historical revolution, Swing left and right, the problem is more than the problem solved. To think carefully, and "education alienation as a fraction of" the same, mostly out of the desire for once or for all. As the current education system and the assessment system experience the evolution of the millennium, It will never be done with some reference. This requires the contemporary intellectuals and educators professional nature of the side, reflected in professional knowledge, professional skills, professional affection, professional autonomy, professional values, professional development awareness and other aspects from low to high, gradually meet the professional standards of teachers process. On the other hand, The particularity of different disciplines will lead to the difference of professional development of teachers in different disciplines. In our opinion, the particularity of the development of mathematics teachers ' speciality is decided by the particularity of mathematics education concept, mathematical knowledge structure, mathematics curriculum resource development and multidimensional teaching thinking. For these peculiarities, The professional development of mathematics teachers should study the corresponding strategies. Seeking the breakthrough of integration theory the formation of Mathematics teachers ' knowledge structure is the result of receiving multi-disciplinary education, while in teacher education, the education of many disciplines is often independent, which causes the coupling between knowledge difficult to realize, and the teacher's knowledge is difficult to form a complete and A harmonious structure.

sometimes to Confucius does not produce a sincere respect, if he, like most of his contemporaries, he may not be able to get all kinds of wealth, and he unmoved, concentrated on the inheritance of Chinese civilization, really for human civilization to make a contribution.

Reflections on mathematics Learning and teaching concepts of teachers and students in China Priory Professor Dan