Keeping the Roots of Mathematics —— Thoughts on Reading Beware of Demathematization Recently, Professor Zhang Dianzhou published an article entitled Beware of Demathematization in Mathematics Teaching. The article is not long, only 700 words, but I feel a lot after reading it! Professor Zhang Dianzhou said in the article: "Mathematics education naturally takes' mathematics' as the core. The quality of mathematics classroom teaching naturally depends on whether students can learn' mathematics' well. In other words, educational means must serve the teaching content. Unfortunately, this common sense seems to be no longer correct recently. Haven't you noticed that commenting on the merits of a class only asks whether the teacher has created a realistic situation, whether the students explore independently and whether the atmosphere is active? Do you work in groups? Whether multimedia is used or not, as for the mathematical content, it is dispensable. " Professor Zhang Dianzhou called this phenomenon "de-mathematization" and thought that the tendency of de-mathematization would endanger the life of mathematics education. Therefore, the author thinks that the criticism of "the taste of mathematics is weak and there are more formal things" in the current mathematics classroom teaching is deeply targeted and timely reminded. In these classes, teachers often pursue "form" more than pay attention to the content of mathematics teaching itself; The pursuit of "stimulation" is often more than the consideration of the actual teaching effect in the classroom. Then, what are the manifestations of the tendency of "de-theming" in primary school mathematics classroom? How to make mathematics teaching come back from the road of "de-mathematization" The author tries to analyze some hot issues in current mathematics classroom teaching from the perspective of reflection, so as to arouse people's continuous attention to this phenomenon. First, the situation creation-Mo's "Buy the Core and Return the Pearl" is no exaggeration to say that creating a situation has become a painstaking thing for mathematics teachers at present. Many teachers lamented: "Now, in the last math open class, or taking part in class activities, if the situation was not created, I don't know how the teachers and the jury evaluated this class?" There is no denying that many math classes create vivid and interesting situations, which improve students' interest in learning and make the originally boring classroom attractive. But at the same time, we have to admit that the quiet environment in the classroom is mixed with good and bad. Too many, too many, too mediocre or too strange situations fill the math classroom. If some teachers create situations for the sake of creating situations and ignore the purpose of creating situations, there will be many invalid situations in the classroom that are divorced from the teaching content and far from the teaching objectives. In order to win by surprise, some teachers unilaterally pursue the "novelty" of the situation and ignore the authenticity of the situation. There are many artificially fabricated lying situations in the classroom. Some teachers create situations related to state affairs and far away from students' real life; Long-term tracking of international countries can not be calm, affecting the learning of new knowledge. Of course, the situation creation should be interesting and attractive, but not all interesting and attractive events and life scenes can be used as the situation of mathematics teaching, without selection or restriction. The author believes that in order to effectively create mathematical situations, we must grasp two basic requirements, otherwise it is just a formality. First, moderation, lack of "degree" restrictions, situation creation is often overused. Without situational teaching, it seems that the concept of "absolute" situational creation is not new, and the concept that classroom is not a good classroom is even more unacceptable. Second, effectiveness, lack of "efficiency" requirements, situation creation is often a mere formality. For example, the contents of many mathematical situations are adults, such as moving, buying a house, buying a car, shopping, decorating, telecom consumption and other adult life events. Entering the mathematics classroom seems to be closely related to life, but because it is far away from students' real life, the situation often lacks practical attraction and often gets twice the result with half the effort. Second, the breath of life-don't "steal the limelight" and "make mathematics teaching live" is a popular formulation and practice at present. But in practice, teachers often can't handle the relationship between mathematics and life. Some contact for the sake of contact, or far-fetched, or hard to pull; Some indiscriminately copy life scenes and pursue the original flavor of life; Some confuse the two and regard math as a life lesson. In these classes, teachers are keen on connecting with life, creating life situations at the beginning of the class, connecting with life reality in the class and solving life problems at the end of the class. The breath of life has a tendency to "usurp the role of master", as if the protagonist in mathematics class is no longer mathematics itself. In this regard, some experts commented: "In these classes, only the' forest' of life was seen, but the' trees' of mathematics were not seen. Life is full of flavor, but the cultivation of mathematical thinking is also absent. " For example, a teaching case of "multiplication table" published in a magazine, which is how the author connects with life. 1. Songs lead the way. (Playing the recording) "Hello, my name is Xiao Fang. There are three people in my family, father, mother and me. Every morning, it is my mother who wakes me up, and it is also my mother who buys me breakfast and makes milk. It was my father who sent me to school, and it was also my father who guided me and urged me to do my homework. I love my father, I love my mother, and I love my parents. " In order to impress, the teacher asked the students to read the last sentence together. Show: 6xls+6x7o6x (15+7) 20x15+20x90zox (15+9) Teacher: Calculate the left and right formulas first, and then compare the sizes. What did you find in the ether class? Student: The left and right sides have equal scores. Teacher: What did you find from the above story? I found that these two equations are the song that Xiao Fang sang: I love my father, I love my mother, and I love my father and mother. Teacher: Really? Can you explain it to everyone? Question 1, 6 is me, 18 is my father, 7 is my mother, and love is multiplication. 6 times 18 means I love my father, 6 times 7 means I love my mother, and the sum of 6 times 18 plus 7 means I love my father and mother. Teacher: What a wonderful speech! Teaching example 6: (15+7) x60zsx6+7x6zox (15+9) 020x15+20xg Teacher: Can these two equations also be expressed by songs sung by Xiao Fang? Student 2: You can only use the second question, but it becomes "I love mom and dad, I love dad, I love mom". S3: The question 1 is also acceptable, that is, "Mom and Dad love me, Dad loves me, and Mom loves me". Teacher: Great! 3. Consolidate the law. Teacher: Let's do an exercise of "Find your father, find your mother and find yourself". (Think independently first, then communicate in groups) (43+25) XZ = SX (7+6) = 8X47+8X53 "3x6+6x7 = Teacher: Find out" Mom and Dad and yourself ". Can you write what follows the equal sign? 4. Class summary. Teacher: What is the law of multiplication and distribution? The law of multiplication and division is "I love my parents, that is, I love my father and I love my mother". Health 2: You can also say, "My parents love me, that is, my father loves me and my mother loves me". From the above description, we can easily see: If the life examples of "Mom, Dad and Me" are removed from this "life-rich" math class, what will be left for students to understand the multiplication and division method? In this class, mathematical knowledge has become a vassal of life examples. Without the annotation of ballads, students can't express the meaning of multiplication and division, and the cultivation of mathematical ability becomes empty talk! What is more worth reflecting on is the comment written by the author: "The knowledge of mathematics' multiplication and division' is closely linked with' Mom, Dad and Me' in life, and students feel the mathematics around them personally and enjoy the happiness of learning mathematics happily." The author thinks that although mathematics and life are closely related, they are two different concepts and two different categories after all. Appropriate and appropriate contact with life is of great benefit to mathematics teaching. However, just as life is difficult to be mathematicized, if mathematics teaching blindly pursues life and loses itself, it will not be worth the candle! The "protagonist" of mathematics class can only be mathematics itself forever. Mathematics teaching can absorb interesting and beneficial examples from life to serve mathematics teaching, and also cultivate students' application consciousness and mathematics ability in life, but we can't "lose ourselves"! Thirdly, the "anti-customer-oriented" learning method has broken through the traditional single teaching method and realized the diversification of learning methods, which is another focus of this curriculum reform. "Mathematics Curriculum Standards" clearly points out in the preface: "Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics." However, in actual teaching, there are countless cases in which "important" is interpreted as "necessary" and "unique". When designing a class, many teachers often "tailor-made" what kind of learning style this class is suitable for, not from the knowledge content itself, but from the form and demand, "tailor-made" the teaching content to meet the learning style and unilaterally pursue the new curriculum of teaching methods. Therefore, for a period of time, cooperative learning and inquiry learning flooded the classroom: if there is no need for cooperation, there will be no cooperation; Students can explore whether it is suitable for inquiry, but the form cannot be absent. For example, a teacher made an exploration of this 5-s6-47-ss-7 when teaching True Score and False Score. Teachers first show a set of scores: Wei, Si, Li and Zhu. Ask students to observe this group of scores independently first, and then classify them with12151065438. The teacher will arrange group activities to exchange classification information and classification standards, and finally the whole class will communicate. Results Five classification methods appeared in the whole class: 1. Divide odd and even numbers by numerator and odd and even numbers by denominator; 3. In terms of molecules, it is a prime number and a composite number; 4. Denominators are prime numbers and composite numbers; 5. Divide according to the size of numerator and denominator. After the whole class exchanged five classification methods, the classroom teaching time was more than half. At this time, the teacher will focus on the fifth classification and ask the students to name each score. There were different opinions in the classroom at that time. Finally, under the pressure of time, the teacher decided to reveal the concept of true and false scores. In the above cases, the teacher did create a relaxed and free teaching environment for students, and really let students cooperate, communicate and explore, but it is not difficult to find that due to the lack of effective guidance from teachers, the teaching efficiency is also low. There are many such examples in teaching! Tracing back to the source, it is because the relationship between teaching form and teaching content is reversed-not to determine the appropriate learning method according to the teaching content, but to make the teaching content meet the needs of form. This form-oriented classroom deduction will only make the classroom lively. Fourth, math activities-don't "hang your head upside down" and equate math activities with general activities. One-sided pursuit of classroom activities is a noteworthy problem in mathematics teaching at present, and it is also the fundamental reason why many mathematics classes can't be quiet. In these classes, the students are busy, or doing things, or cooperating and communicating, or painting or dancing, which is very lively, and even doing a group of problems and doing some activities (this situation is especially common in lower-grade classes), but they just lack the time and opportunity for independent thinking and meditation. For example, when teaching "Understanding of Time and Minutes", a teacher arranged various activities for students to experience the length of one minute, including one minute of dictation, one minute of writing, one minute of reciting Tang poems, one minute of skipping rope and one minute of racket ball. With the teacher's command, the class suddenly boiled up, and the students were immersed in excitement, or writing hard, or talking eloquently, or dancing, and then stopped suddenly with the teacher's command. However, during the activity, students did not experience the length of time as the teacher hoped, but only cared about their own or others' performance. "There are activities without experience, there are experiences without feelings, there are activities with limbs, and there is rest for the brain", which is not uncommon in the current mathematics classroom teaching. The main reason is that some teachers equate mathematics activities with general activities in their understanding. Indeed, in the mathematics curriculum standards, it is mentioned in many places that "mathematics teaching is the teaching of mathematics activities" and "teachers should provide students with opportunities to fully engage in mathematics activities". However, the "activity" referred to in the mathematics curriculum standard does not refer to the movement of limbs, but refers to a series of mathematical cognitive activities such as observation, experiment, operation, induction, analogy, conjecture, reasoning, verification, communication and reflection. In addition, another reason is that some teachers conceptually equate "lively classroom" with "new curriculum" and think that the classroom of new curriculum must be lively classroom. Therefore, it is better to pursue more activities, and I believe that more activities can drive the classroom atmosphere. As the saying goes, "Mathematics is the gymnastics of thinking." Therefore, the activities pursued in mathematics classroom must be the activities of mathematical thinking, not the simple movements of limbs. Mathematical thinking should be the "soul" of mathematical activities. Fifth, pay attention to generation-Mo's "opposite direction" and "dynamic generation" are a hot topic at present. All kinds of teaching cases that make the classroom wonderful because of focusing on generation can be seen everywhere in major teaching publications. It seems that as long as there is generation in the classroom, as long as we pay full attention to generation, classroom teaching is bound to be wonderful. But this is not entirely the case. There are many math classes, and teachers attach great importance to generation, but classroom teaching has never been icing on the cake. On the contrary, it is often due to improper generation, which leads to complicated teaching or even the opposite. Why do the same generation have different influences in different classes? The reason is that many teachers lack a profound and rational understanding of how to generate classroom needs. At present, there are three tendencies worth noting. The first is to make generations absolute. The opposition between generation and presupposition exaggerates the function of generation unilaterally, and thinks that the classroom is wonderful because of generation, and regards dynamic generation as the main reason for the wonderful classroom. For example, in the discussion of "Do you want to write lesson plans now" planned by a magazine, it is advocated not to write lesson plans or that the party who writes simple cases should take "classroom dynamic generation" as the theoretical basis. The second is the randomization scheme. Separate lesson preparation from class, unilaterally deny the role of presupposition, regard teaching presupposition as a temporary scheme that can be changed at will, change teaching links at will in the teaching process, and even raise and lower teaching requirements at will. For example, when a young teacher was teaching "the area of a circle", after revealing the concept of "the area of a circle", he asked, "How to calculate the area of a circle? Do you know that?/You know what? I'm afraid many students answered, "I know the old district S 22R2O." At this time, the teacher said decisively, "Now that everyone knows, the teacher will stop talking. Let's practice. "The third is the excessive pursuit of a generation. Compared with traditional teaching, which overemphasizes presupposition and ignores generation, current classroom teaching attaches importance to generation and treats "accidents" well, but some classrooms have become too eager to generate. Some teachers are too prominent in teaching, and often waste precious time on irrelevant or even irrelevant issues. Other teachers are not good at leading when encountering problems, but are led by students. As a result, the watermelon skin slipped to where. The author thinks that over-emphasizing presupposition and over-pursuing generation are two undesirable extremes. The former imprisons the classroom on rigid teaching plans, and the classroom lacks vitality; The latter is easy to wander around Xinjiang, and the achievement of teaching goals is often greatly reduced. An efficient and agile classroom must be the perfect unity of presupposition and generation, which is pregnant with generation and rich in presupposition. To sum up, we can easily find the fact that many new ideas and methods advocated by mathematics curriculum standards are often one-sided, enlarged or even absolute in practice. As Mr. Cui Luan said: "We have magnified the problems that we didn't pay attention to in the past, and our thoughts have become absolute and our actions have gone to extremes." Therefore, while the curriculum reform has made many achievements, it has also appeared the phenomenon of overcorrection. Perhaps this is the intention of Professor Zhang Dianzhou in writing Beware of "De-theming". Further tracing back to the reasons, it is not difficult to find such a root: that is, many mathematics teachers lack a deep understanding of the characteristics and essence of mathematics and mathematics teaching, are easily influenced by ideological trends, and are easy to deny themselves and traditions in the process of accepting new things. Therefore, if mathematics teaching wants to return from the road of "de-mathematization", the key is that every mathematics teacher should learn to think rationally and be good at making choices. Hold the "root" of mathematics, and mathematics teaching will have its own wonderful! To keep the "root" of mathematics is to teach mathematics like a math class, pay more attention to the characteristics of mathematics, fully display the charm of mathematics and lead students to understand the unique connotation of mathematics culture.