However, in primary school mathematics classroom teaching, many teachers and students think that learning mathematics depends on either the teacher's lecture, hands-on operation and cooperative inquiry, or discussion, report and communication. In class, students have no chance to read examples, formulas, concepts and conclusions in textbooks. After class, students don't know what they have learned in the textbook, which is very common, because the teacher didn't look at the textbook in the teaching design. The most common way to display the content of teaching materials is to use courseware, and teaching materials are increasingly regarded as students' workbooks. Over time, students lose the habit of reading math textbooks, and even don't think of building new knowledge by reading textbooks. When you encounter problems, you often go directly to teachers or classmates or parents, and you don't want to look for ideas and methods to solve problems by reading textbooks.
In fact, compared with other learning methods, reading has the characteristics of "helping to standardize students' language, deepening students' understanding of mathematical thinking methods, developing students' habit of independent thinking and cultivating students' self-learning ability". It should be said that reading is an important link in mathematics teaching and learning, and it is also a problem that should be seriously studied in mathematics teaching reform. At the same time, improving students' reading ability is also in line with the modern educational thought of "lifelong education, lifelong learning".
However, in primary school, teachers always feel that students are young, have weak understanding and poor autonomous learning ability, and dare not let students acquire new knowledge through reading. In class, students often listen more, engage in more activities, discuss more, and have more courseware, but rarely go back to textbooks to read. In fact, the mathematics textbooks used by primary school students are compiled by many experts according to the new curriculum standards and combined with the knowledge structure and age characteristics of primary school students. In the process of writing, students' acceptance ability has been fully considered, and primary school students should be able to understand it.
Therefore, in the usual classroom teaching, the author takes cultivating students' reading ability as an important teaching goal and permeates reading into every teaching link.
First, enrich students' mathematical activities through reading.
The new curriculum standard points out that teachers should stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematical activities. Students are the masters of mathematics learning. It is mentioned here that "providing students with opportunities to fully engage in mathematics activities". What does this opportunity mean? It is independent exploration and cooperation and exchange. Of course. However, the author believes that reading should also be a mathematical activity. In the classroom, students should be provided with the opportunity of "independent exploration and cooperative communication" and the opportunity of reading. Does this not fully show that students are "masters of mathematics learning"?
Indeed, in the teaching of mathematics textbooks, teachers find some contents difficult to deal with, so they usually have to adopt teaching methods in order to successfully complete the teaching tasks. This teaching method is widely used in practice. Think about it, what are the benefits of doing so? At most, I can finish the teaching task as scheduled. For classroom teaching, completing the teaching task is only a relatively simple and primary teaching goal. If we can consider the realization of other teaching goals, students' dominant position and the cultivation of students' ability, we may adopt more reasonable methods to achieve teaching goals.
For example, in the teaching of understanding the median, considering the particularity of the concept of the median, in the new teaching, the author abandoned the teaching mode, but designed a reading outline, so that students can initially perceive the statistical significance of the median and the general method of finding the median by reading the contents of the textbook, and achieved good teaching results.
Courseware shows reading outline:
1. What figures are introduced in the textbook?
2. What are the advantages of using this number?
3. What is the appropriate number to indicate?
Can you try to sum up the median in one sentence?
After reading, teachers organize students to communicate, discuss and report, coordinate students' speeches, participate in students' discussions, and guide students to find out more important contents and paragraphs in the textbook for analysis and understanding.
Teacher: Students, just now, according to the reading outline, you have carefully read Example 4 in the textbook, and you should have a preliminary understanding of the problems we are going to study. So, which student would like to talk about what you have learned from reading just now? You can answer any questions.
Student: Teacher, I want to answer the first question: I see. Today we are going to study the median.
(The teacher writes on the blackboard: median)
Student: The advantage of the median is that it is not affected by large numbers or decimals.
Teacher: Under what circumstances is it appropriate to choose the median to describe a set of data? (Combined with the results of Class 502)
Teacher: Can you try to sum up the median in one sentence?
Answer the teacher's blackboard: In a set of () numbers, the middle number is the median of this set of numbers. This is an incomplete conclusion. After learning Example 5, students will be able to understand the meaning of relatively complete median. It is enough for this year's students to understand this level. )
This kind of teaching fully highlights the main position of students' learning. The process of students' reading is the process of learning, and the process of students' exchange and discussion is the process of further deepening their understanding of knowledge. During reading, students know that if there is a big number or a small number in a group of numbers, it is not appropriate to use the average value to represent the general level of a group of data. Therefore, it is necessary to introduce the concept of "median" and gradually realize the statistical significance of the median while feeling a strong demand for knowledge, so as to lay the foundation for the next teaching.
For another example, the knowledge point of "abbreviation and ellipsis of multiplication" in the teaching of "expressing numbers with unknowns" is usually the method and matters needing attention for teachers to teach abbreviation and ellipsis of multiplication. But in my teaching, I didn't do this. I also ask students to complete this part of their study by reading textbooks. By reading the relevant contents in the textbook, students know that when letters are multiplied by letters, the multiplication sign can be written as ""or not; If letters and numbers are multiplied, you don't have to write the multiplication sign, but the letters must come before mathematics. This knowledge is learned by the students themselves in reading, and the precautions for omitting the multiplication sign are also found by the students in the teaching materials, and the students remind them to pay attention. It is not instilled in students by teachers, but plays a guiding and emphasizing role. This learning process is the "active and personalized" learning process advocated by the new curriculum standard. Students' initiative, enthusiasm and understanding ability will be more profound. While learning knowledge, they also feel the fun of learning. More importantly, students have mastered a good learning method in the process of such activities: reading with questions.
Second, deepen students' understanding of what they have learned through reading.
I think there is a big difference between math reading and Chinese reading. Chinese reading materials are generally abundant, and the stories are vivid, which is relatively easy for students to understand. However, the materials available for reading in mathematics textbooks are limited. Some knowledge is presented in words, and the contents expressed in these words mainly include concepts, conclusions, or laws. In the new textbooks, the content presented in words is less and less, especially in the lower grade textbooks. A large number of pictures have replaced words, and everyone feels that there is nothing to see. Actually, this is a misunderstanding. It is precisely because of the lack of words that the relevant conclusive words in the materials are even more precious. Without careful study, it is difficult to understand the true meaning of the concept.
For example, when I teach vertical parallelism, students will encounter a familiar but unfamiliar concept: distance. This term is often heard in life, so students feel familiar with it. However, do students know the "distance" mentioned here? Do you understand? The answer is no, in order to make students grasp this concept more clearly and accurately, I spare no effort in this teaching link and organize the teaching by means of "reading-drawing-discussing-rereading".
The first is reading. Let the students read Example 2 on page 66 of the textbook and think while reading. Did you find anything? The students quickly said that the vertical line segment is the shortest. At this time, let the students look at the conclusion in the textbook: "The vertical line drawn from a point outside the straight line is the shortest, and its length is called the distance from that point to the straight line" to get a preliminary understanding of the meaning of "distance".
The second is drawing. The painting here has two meanings, one is to draw pictures, and the other is to mark keywords. After reading it, some students feel that they have mastered it, and they seem to be absent-minded. At this time, my feelings are just the opposite. According to previous teaching experience, students may only know the meaning of "the shortest vertical line segment" and the following sentence: "Its length is called the distance from this point to a straight line." Students don't think so, and this sentence is just more important and crucial. Because this is the distance from this point to a straight line, rather than studying other distances (such as point to point). At this time, the teacher organizes students to study this sentence carefully while drawing pictures, and marks the words they think are important with emphasis symbols. In the process of "drawing" keywords, students have a further understanding of the meaning of distance.
The third is to discuss communication. After drawing the key words you think, students at the same table check with each other whether the drawn key words are the same. If they are different, they can persuade each other to accept their own views or keep their own. If you find that your point of view is wrong during the discussion, you can accept other people's points of view. Whether it is acceptance or reservation, this discussion process is a process of thinking collision and a vivid learning process for students.
The fourth is to read again. This kind of reading is different from the first reading. It is based on communication and understanding. Ask the students to read aloud the meaning of distance. The teacher can judge the students' understanding of this sentence from the speed of reading aloud. If the reading is fluent, it means that he (she) can basically understand; If the reading is not smooth or the sentence is not accurate, it is enough to show that the student still has problems in understanding, and the teacher should give him some guidance and help.
After the above four steps, most students can deeply understand the meaning of "distance" and describe the meaning of "distance" in accurate language. In this teaching process, reading plays a role in deepening the understanding of concepts. In the whole process of reading discussion, students not only understand the knowledge points, but also further understand the reading methods, and their ability to discuss and communicate is also enhanced, which is better than simple teaching.
Third, strengthen reading, clarify the requirements of the topic, and improve the correct rate of solving problems.
Suhomlinski said that learning to learn must first learn to read. Students with poor reading ability are potential "poor students". I often hear parents and teachers say that my children always make many mistakes in their homework. Three is copied into five, and the addition is reduced. The topic requires students to draw a vertical line, but they draw a parallel line ... In this regard, teachers and parents have no good way but to sigh "too hasty". And if you think about this "sloppy" phenomenon carefully, it feels that it should be related to the students' ability in a certain aspect. In my opinion, that is reading ability. The difference of students' reading ability directly affects the accuracy and speed of students' problem solving.
Question 7: What conclusion can be drawn by observing the diagonal of the square on the right? , the following answer will appear:
1: There are four triangles of the same size in this square.
Health 2: This square has eight triangles.
The author asked two students to reread the topic word for word twice, and asked them to find out the words they thought were important in the topic and circle them with pens. Find out the words you don't understand, and you'd better ask your classmates for help. The student quickly found the word "diagonal" that he had just missed or didn't quite understand. After some discussion, the two students quickly came to a new conclusion.
Health 1: These two diagonals intersect.
Health 2: I measured it with a triangular ruler. The two lines intersect at 90 degrees, which means they are perpendicular to each other.
Other students also added their speeches:
Health 3: I use a protractor to measure that an angle is a right angle, that is, the diagonal lines of a square are perpendicular to each other. (Teacher writes on the blackboard: Diagonal lines of squares are perpendicular to each other)
By the way, through observation and measurement, the students found an important conclusion: the diagonals of squares are perpendicular to each other. Who can tell us what to pay attention to when doing the problem?
Health 4: Read the stem carefully and make clear the meaning of the question.
Teacher: Yes, you must understand the meaning of the topic before solving the problem, and the best way to understand the meaning of the topic is to read it carefully. "If you read a book a hundred times, you will understand its meaning." You don't need to read it a hundred times before you do the problem, but you should read it at least three times.
As can be seen from the above examples, the reason why students make mistakes is not the problem of methods, but the problem of examining the questions, that is, they didn't read the requirements of the questions carefully, or didn't read them, but just scanned them with their eyes, didn't grasp the key words of the questions, and didn't understand the meaning of the questions. Reading out of context, or losing or dropping is quite common, and the appearance of these phenomena will lead students to fail to understand the requirements of the topic correctly, let alone solve the problem correctly, and will also affect the speed of solving the problem. Why do you say it affects speed? Because some students began to do it after reading it without understanding the meaning of the topic. If they can't do it, they will read it again and do it again, which is a waste of time. It's best to read the topic carefully and understand the meaning of the topic before you start to do it, especially the meaning of keywords and words in the topic. As the saying goes: sharpening a knife does not miss the woodcutter. In normal teaching, teachers must pay attention to the cultivation of students' reading ability, which is also a habit. Good habits are beneficial to a person's life, and bad habits will also affect students' life.
To sum up, students can construct new knowledge independently through reading, deepen their understanding of knowledge through reading, master knowledge on the basis of understanding, and solve problems correctly and quickly. However, the formation of reading ability and reading habits can not be completed by teaching, forcing and teaching one lesson a day, but by infiltrating into the teaching of each lesson every day. As long as teachers consciously give students the opportunity to read textbooks in each class and give appropriate guidance, students' mathematics reading ability will be enhanced. If students have the ability to read independently and develop the habit of active reading, they will benefit for life.