? In addition, in teaching, it is often found that many students make mistakes in solving problems because of misunderstanding of the meaning of the questions. As long as students reread under the guidance of teachers, they will find mistakes and correct them. Why is this happening? The reason is related to students' bad reading habits. It is inevitable to make mistakes or solve problems only by browsing the questions line by line without analyzing the quantitative relationship word by word! Teaching practice also shows that students with low level of mathematical language development have poor sensitivity to mathematical language in class, slow thinking transformation, and often encounter obstacles and mistakes when understanding problems. Stolyar, a mathematics educator in the former Soviet Union, pointed out: "Mathematics teaching is also the teaching of mathematics language". To teach students to learn mathematics, we must attach importance to the cultivation of mathematics reading ability.
? Based on this, the author tries to develop the course of "Mathematics Reading" in teaching. The so-called "math reading class" is a new math class developed to pursue "interesting math" and promote the improvement of math reading ability. The value orientation of "mathematics reading class" is interest, process and experience, that is, based on cultivating students' interest in learning and studying mathematics; Based on allowing students to accumulate experience in mathematics activities in the process of mathematics reading, improve mathematics reading ability and mathematics thinking quality; Based on promoting students to form good mathematical concepts and consciousness, so that they have a positive mathematical emotional experience; Based on broadening students' vision of mathematics, feel the charm of mathematics.
First, the design principles of "Mathematics Reading Course"
1. Pursuing "Mathematics Fun" in Mathematics Reading Class
? "Mathematics is fun" is an inscription given to children by Mr. Chen Shengshen, a master of mathematics. Mathematics reading class pays attention to excavating the interest and wonder of mathematics, and carefully selects learning materials that students are interested in, which can inspire thinking and broaden their horizons, so that students can think in reading, experience "mathematics fun" in thinking, broaden their horizons and increase their knowledge in reading. For example, when studying "Comparative Understanding", the author designed a math reading class with "Why does Auntie like to wear high heels" as the core issue, so that students can understand "Auntie wears high heels to stretch her long legs and make her ratio to height tend to 0.6 18: 1" in reading, thinking and discussion. Mathematics reading connects boring mathematics knowledge with real life, which enables students to have a more thorough understanding of knowledge and a deeper understanding of the value of mathematics. For another example, while studying "factors and multiples", the author developed a math reading class of "guessing game", which not only cultivated students' reasoning ability in the game, but also fascinated students because of "learning in the game", and "guessing game" became an interesting program that children liked to play during recess. With this interesting experience, the emotional seeds like mathematics take root in students' hearts.
2. Grasp the characteristics of math reading in math reading class.
? The content selection, material design and teaching implementation of "Mathematics Reading Course" should grasp the characteristics of mathematics reading itself and follow its inherent laws. Mathematics reading, like general reading, is a complete psychological activity process of perception, understanding and memory of written language, mathematical symbols, formulas, charts and other reading materials. Because of the abstraction and rigor of mathematical language, mathematical reading has its own characteristics:
? First, math reading is very accurate reading. When reading mathematics, you must know the exact meaning of every mathematical term and symbol that appears in mathematical data. If you ignore or omit a word, it is probably a thousand miles away, such as "increase by 8 meters", "increase to 8 meters", "cut off 1/4 meters", "cut off 1/4 meters" and so on. Therefore, math reading should be read word for word, not at a glance.
? Secondly, mathematics reading is a kind of thinking reading. The process of mathematical reading is the process of understanding and comprehending mathematical language, including colorful symbolic language, rigorous and standardized written language and profound graphic language. Therefore, we should not just browse with our eyes, but draw keywords, symbols or pictures to help us understand when reading, and form the habit of reading while thinking and thinking.
? Thirdly, mathematics reading needs "internal speech conversion". When reading mathematics, the brain must establish a flexible language conversion mechanism, that is, to convert abstract and difficult reading content into acceptable language forms, such as converting mathematical terms into everyday language; Convert written language into concise symbolic language or intuitive graphic language; "Put it another way" for rigorous and abstract mathematical problems, and so on.
3. Mathematics reading class should be "learning-centered"
? The teaching benefit of mathematics reading class lies in enhancing the understanding of mathematics language, accumulating the experience of mathematics activities, and discovering and sharing it by yourself. All this should not and cannot be achieved only through explanation, questioning and discussion, but must be based on independent reading, experience, thinking and communication. Therefore, the teaching implementation of mathematics reading class must be "learning-centered". First of all, teachers should treat students as mathematics researchers from the heart, leave enough time and space for students to read, explore and communicate, encourage students to read independently and repeatedly, and don't easily interfere with students' reading and learning process. Secondly, we should design a "question string" to guide reading. "Learning begins with thinking, and thinking begins with asking". Under the guidance of enlightening questions, students gradually grope for answers in reading, practice, exploration, thinking and communication. Third, pay attention to the mathematical communication between peers. Especially when students are "at a loss" in the research process, through the guidance of teachers and the communication between students, solving problems can make students taste the fun of autonomous reading and the sense of accomplishment after solving doubts, and promote students to develop good habits of autonomous reading.
Second, the content setting of "Mathematics Reading Course"
? In the course content selection of Mathematics Reading Course, we should establish the concept of big mathematics and big education, aim at planting "seeds", and don't excessively pursue immediate interests. In practice, the author regards the following aspects as an important source of course content selection of "Mathematics Reading Course".
1. Choose teaching materials suitable for students to study by themselves.
? In actual teaching, front-line teachers are used to digging the essence of teaching materials and expressing them to students through their own understanding, thus ignoring the cultivation of students' ability and habit of reading mathematics teaching materials. Reading math textbooks seems to be just a teacher's business. Unconsciously, the reading ability and thinking ability that should have been formed in the reading process are gradually drifting away from the teacher. Therefore, we should attach importance to students' reading and understanding of mathematics textbooks and make full use of their reading value.
? For example, in the teaching of "positive proportion", the Beijing version of the textbook used by the author is rich in content, illustrated and clear in level, which is beneficial for students to understand the meaning of positive proportion in comparative analysis and is more suitable for students to learn by themselves.
? The author adopts the way of "self-study before communication" to teach, consciously and pertinently permeates the guidance of reading methods, and designs the self-study guide as follows:
(1) Is there anything you can't understand or understand in the self-study textbook? Please mark the book and write your own questions.
(2) Think about it: What are the similarities and differences between the relationship between "distance and time" in Example 2 and the relationship between "age and height" and "month and temperature" in Example 1?
(3) Circle the meaning of "proportional relationship" in the book. Can you sum up what conditions are needed for the proportional relationship?
? On the basis of students' full self-study of teaching materials, organize students to communicate. Teachers can solve students' puzzles, ask questions at key points of knowledge, guide students to learn to find answers from textbooks and explain abstract mathematical language in their own words. In this learning process, students not only have a thorough understanding of the concept of "positive proportion", but also improve their mathematics reading ability and self-study ability.
2. Properly transform and extend the content of "Do you know" arranged in the textbook.
? With the deepening of curriculum reform, the cultural value of mathematics has been paid more and more attention. Looking at all versions of primary school mathematics textbooks, we not only consciously infiltrated mathematics culture in the compilation of knowledge, but also specially set up a column "Do you know" for explicit expression. The specific contents include mathematical historical materials, mathematical background knowledge, mathematical life applications, mathematicians' stories, etc. In order to stimulate students' interest in learning mathematics, broaden their horizons and guide them to feel the charm of mathematics culture. However, due to the limitation of space, most of them are "peer-to-peer". The author takes the content of "Do You Know" as a curriculum resource for moderate transformation and extension, in order to play its greater educational value.
? For example, when I was teaching the unit "Factor and Multiply", I developed the math reading class "Goldbach Conjecture and Chen Theorem". At the beginning of the class, let the students fill in the appropriate prime numbers in brackets: 8= (? )+(? ), 10=(? )+(? ), and then ask this question: "Can you write more such formulas? Guess what? " Then introduce Goldbach conjecture and Chen Theorem (N= 1+2 for short), which is the research result of China mathematician Chen Jingrun on Goldbach conjecture, and then let students try to verify Chen Jingrun's research result with examples. Driven by challenging questions, students have gone through the process of "rediscovery" and "re-creation". They not only developed their thinking and gained experience in mathematics activities, but also deeply realized the mathematicians' tireless research spirit through reading and practical experience, which invisibly shaped their outlook on life and values.
3. Add some valuable and exploratory extracurricular reading materials.
? Mr. Chen Shengshen said, "Not all mathematics is good mathematics." Therefore, in order to truly realize the "fun of mathematics", on the one hand, we should do a good job of students' research and find out what students are interested in, and the selection of reading content and the arrangement of time should be based on the results of students' research; On the other hand, we should do a good job in learning mathematics content and grasp the essence of the content. The combination of these two aspects is the so-called "to the point".
? Since the implementation of "Mathematics Reading" course, the author has excavated and developed many course contents that make students "happy". For example, interesting 222; Exploration of "digital black hole": the magical "number of galloping horses"-142857; Hail conjecture; Wonderful digital pyramid-Yang Hui Triangle; Archimedes skillfully broke the "Crown" case; Palindrome number conjecture; Strange solution to the problem of "chickens and rabbits in the same cage": The magical "perfect number"; Wait a minute.
Third, the teaching operation of "Mathematics Reading Class"
? The teaching operation of mathematics reading class is to study and organize the content before class, and carefully design the "reading and learning list"; Hidden in the classroom, highlighting students' reading and exploration, highlighting the autonomy and experience of learning, and not easily interfering; After learning, students should be guided, explained and promoted in communication, and the learning content should be extended to extracurricular, expanding the time and space of mathematics learning.
1. Carefully design the "Reading and Learning List"
? The design of "reading learning plan" is the basis of "mathematics reading class" and the key to determine the efficiency of reading teaching. The design of "reading learning plan" should contain rich practical inquiry and driving force, and take content as the carrier, which is conducive to students' operation, attempt and epiphany. The problem is the core of mathematics. The author carefully designs the reading materials as "question series", so that students can read, think, calculate and explore purposefully and find the answers to the questions driven by enlightening questions. The process of students' reading is a process of "guessing-verifying-guessing-verifying again", that is, a process of getting deep pleasure after experiencing "mountains and heavy waters are doubtful and there is no way to go, and a village is bright and bright".
2. The basic process of mathematics reading class
? Generally speaking, the teaching process of mathematics reading class is: creating situations, stimulating interest-independent reading, trying to explore-interactive dialogue and improving communication.
(1) Create a situation to stimulate interest. Once students are interested in learning, all kinds of senses are easily activated, thus providing excellent psychological preparation for participating in learning. Therefore, in mathematics reading, teachers must create novel, interesting and enlightening situations according to students' age characteristics and personality characteristics, so as to induce and maintain students' reading interest. For example, when teaching "Hail Conjecture", the author introduced it with a story:1One day in 976, the famous American Washington post reported a math news: At present, college students and teachers in American universities are playing a math game crazily. What game is so attractive? The rules of this game are simple: first write a natural number at will, if it is singular, multiply it by 3 and add1; If it is an even number, divide it by 2.
? Why is this game so attractive? Because people find that if any natural number is calculated continuously in this way, it will eventually fall into a "digital black hole". Do you want to try it yourself?
? This problem situation brings students a strong desire to explore and a rich space for practical exploration. They began to read the text carefully and seek the mystery.
(2) Read independently and try to explore. After students' interest is stimulated, we should provide them with a broad and independent space for inquiry. Teachers should really become organizers and instructors, and let students read the "learning list" independently. The progressive "question string" on the "study list" helps students really enter the state of thinking. Students seek answers through reading, thinking, calculating, guessing and reasoning. Take "Mathematical Reading: the Product Parity of Numbers" as an example. Students read under the guidance of the following "study list".
? After observation and thinking, some people put forward the following conjecture about the parity of natural numbers:
Guess one: odd number+odd number = even number.
Guess 2: even number+even number = even number.
Guess 3: odd number+even number = odd number.
Is his statement correct? You can give an example to verify it.
Test conjecture 1:
Test conjecture 2:
Test conjecture 3:
The next question arouses students' deeper thinking-students, what we have just studied is the "parity of sum", so what about the "parity of product"? Do you have any guesses? Please write it down. Did you guess right? Please give an example to verify. If you have no "guess" for the time being, it doesn't matter! Someone put forward the following conjecture. Is he right? Please check it.
Guess one: odd number × odd number = odd number?
Example verification:
Conjecture 2: even number × even number = even number
Example verification:
Guess 3: odd × even = odd.
Example verification:
Then, doubt again-
If any number of nonzero integers are multiplied, and one of the factors is even, then the product must be (). (Guess 4)
For example:1× 3×11× 5× 4, product = (), which is the number of ().
Can you give another example to verify your guess? ? Think about it: do you understand the reason of guess 4 above? Please write it down. ? In the above-mentioned reading and research process, the differences among students are considered, which reflects the learning style based on practical activities and process experience.
(3) Interactive dialogue and communication. Facing the objective differences among students, the goal design of "Mathematics Reading Course" is highly flexible, rather than a unified teaching requirement, to meet students' individualized learning needs. Some students should be allowed to complete reading tasks in class, some students can leave their seats to help other children after class, and some students can extend reading research to extracurricular activities. In teaching, we should make full use of the differences between students and pay attention to organizing learning exchanges at two levels. In the first round, let the students who learn faster and take the lead in completing the reading task act as "little teachers" to help teachers guide and help individual students with difficulties. The process of interactive learning is a process of "teaching soldiers". The second round is the whole class exchange study. The multilateral interactive dialogue and communication between teachers and students is the collision, absorption and promotion of each other's ideas. Teachers should shoulder the heavy responsibility of "making the finishing point" and strive to extend students' research to extracurricular activities.
? Taking "Long Live Conway" as an example, the author once again inspires students in the next class: john conway, a professor at Cambridge University in England, discovered a natural number of 27. If we operate according to the above method, the whole process of falling into a "digital black hole" needs11step. Interested students can try it after class. Besides, I'll tell you a secret. So far, no one has been able to prove the "hail conjecture". 1 Is this number a black hole that attracts all natural numbers? This world-class problem is just waiting for someone to solve it. Dear students, are you interested in studying?
? After class, many students continued to carry out research with great interest. It took them nearly two hours to write a whole number of11mathematical formulas on A4 paper, and they gained the fun experience brought by the learning activities themselves in the research practice.
Fourthly, the practical gains of "Mathematics Reading Course"
? The course of "Mathematics Reading" aims to make students learn, understand and feel mathematics better. After nearly a year's teaching practice, the effect of "mathematics reading" has initially appeared. Children broaden their horizons in mathematics reading, feel the profoundness and charm of mathematics knowledge, become more and more interested in learning mathematics, and are full of love and expectation for mathematics reading class: "Teacher, I like this kind of mathematics class very much!" "Teacher, when will the math reading class begin again?" "Teacher, is there a math reading class next semester?" ……
? Practice also fully shows that when students are fascinated by mathematics learning, everything is possible!