First of all, make clear the importance of reading mathematics textbooks.
The research of innovative psychology shows that self-study ability is of great significance to people's future, and reading is an important channel for self-study, and the core of self-study ability is reading ability.
Reading comprehension is a common question in the senior high school entrance examination in recent years, which consists of two parts: one is the reading material, and the other is the examination content. This kind of test questions embodies some characteristics of mathematics reading comprehension questions in senior high school entrance examination: symbolic, logical, rigorous deduction and induction of mathematics language, and sometimes presents abstract characteristics. It requires candidates to read and understand a strange mathematical problem scene in a short time, and then use the knowledge they have learned and the problem-solving skills they have mastered to solve the problem flexibly, mainly examining students' reading comprehension ability, analytical reasoning ability, text generalization ability, written expression ability, adaptability and knowledge transfer ability, so mathematical reading is different from language and words.
Whether it is the requirement of senior high school entrance examination or the need of lifelong learning, we must attach importance to the cultivation of mathematics reading ability.
The new mathematics curriculum standard has clearly pointed out that teachers must attach importance to "guiding students to read textbooks carefully". Bell, a famous American mathematics educator, made a comprehensive discussion on the function of mathematics textbooks and how to use them effectively. One of the most important points is that textbooks should be used as the source of students' learning materials, not just the source of teachers' own lecture materials. On the basis of collecting past experience, the teaching materials are carefully compiled by mathematics experts, taking into full consideration the psychological and physiological characteristics of students, the quality of education and teaching, the characteristics of mathematics subjects and many other factors. They have high reading value and can't be replaced by any supplementary books. Therefore, the fundamental of cultivating students' reading ability lies in the reading of mathematics textbooks.
Second, to stimulate students' interest in reading mathematics textbooks
Bruno, a famous American psychologist, said: "Knowledge acquisition is an active process. Learners should not be passive recipients of information, but participants in knowledge acquisition." Therefore, in the early stage of reading, we should first stimulate students' interest in reading, review the knowledge related to the problem, create the best situation and form reading expectations. Problem situation is the condition for students to cause cognitive conflict, and it is also the means for teachers to cause cognitive conflict. Teachers can use a variety of problem situations (such as unexpected situations, non-corresponding situations, choice situations, conflict situations, refutation situations, etc.). ) to stimulate students' interest and curiosity, so that students' reason and emotion are in a starting state.
For example, in the teaching of "geometric progression's Sum", a question is created: "Students, I am willing to give you 100 yuan every day for a month, but within this month, you must give me 1 minute on the first day; Give me a rebate of 2 cents the next day; ..... that is, the money given to me the next day was twice that of the previous day. Who wants to? " This question aroused students' great interest. Many students say yes, but they don't know the meaning of power. The rebate written to me should be 1+2+4+...+229. What's the total? The students are eager to try, but they can't start. Then I asked them to read the section "Peace of Geometric Series".
Third, let students master the method of reading textbooks.
The content of mathematics textbooks is nothing more than concepts, theorems, formulas, examples, charts and so on. Below I will talk about the reading methods to understand the above contents respectively.
1, concept reading
To correctly understand the words, words and sentences in the concept, and to correctly translate written language, graphic language and symbolic language; Understand the connotation and extension of concepts, that is, we can distinguish similar concepts and know their scope of application.
For example, read the definition that a straight line is perpendicular to the plane: "If a straight line is perpendicular to any straight line in the plane, it is perpendicular to the plane." It is not enough for students to read this sentence. First, let students use their intuitive understanding of "building a wall" in their lives, and then let them rotate one corner on the desktop with a triangular ruler to observe whether the other corner is perpendicular to the desktop. Further understand the meaning of the word "arbitrary", and then discuss the judgment theorem limited to plane verticality. On this basis, think again:
(1) Find a straight line perpendicular to the known straight line in the plane?
(2) How much is appropriate?
(3) What position relationship should these straight lines have?
Then, let the students find out the judgment theorem that the straight line is perpendicular to the plane with the help of the cuboid model, and point out that finding two intersecting straight lines in the plane should be perpendicular to the known straight lines. Then let the students try, the teacher uses the definition of a straight line perpendicular to the plane to guide the students to explain, so that students can constantly improve their understanding of the concept in reflection.
2. Read theorems and formulas
First of all, the generation of theorems and formulas basically serves the research content of formulas, but the process of their occurrence and development may be different for different formulas and theorems. Teachers must clearly understand the process of their occurrence and development, and then guide students to explore this process in reading. Students' abilities and materials are limited. These contents must be introduced by teachers to arouse students' interest, stimulate students' desire for self-discovery and experience the occurrence and development of knowledge in exploration. Understanding the theorem itself can be achieved through the following aspects:
(1) Analyze the known elements in the theorem and solve what problems.
(2) Seriously study the proof process, draw ideas, methods and strategies from it, and experience the methods used in the derivation of different theorems and formulas in textbooks.
(3) Pay attention to the application conditions and scope of the formula.
Every theorem and formula is a study of a certain aspect. Therefore, there is a certain scope of use, so we should understand these application conditions and scope from reading and learn some experience from them.
(4) Pay attention to the deformation and expansion of theorems and formulas.
For example, when learning the fan-shaped area formula, the students deduced it. By comparing the fan-shaped area formula with the arc length formula, another calculation method of the fan-shaped area was obtained. Then the teacher asked the students to solve two problems:
Question 1: Find the sector area with arc length and central angle of 120.
Question 2: The shape of the flower bed designed in a residential area, the shaded part in the picture. The center of the known and located circle is point O, where the length is, the length is, AC=BD=, so find.
Please answer the question1;
⑵ In the class communication after solving problem 2, some students found that the formula of sector area is similar to that of triangle area; He guessed the area of the flower bed by analogy with the trapezoid area formula. Is his guess correct? If it is correct, write out the derivation process; If not, please explain why.
This problem needs to make use of the relationship between sector area and arc length formula in teaching materials and the idea of transformation to make a breakthrough. If you only recite the formula at ordinary times and don't look at the source process of the formula in the textbook, you don't know how to deduce it.
Step 3 read the example
Examples are examples of applying what you have learned. The examples in textbooks are generally typical, demonstrative and relevant. They either permeate some mathematical methods, or embody some mathematical ideas, or provide some important conclusions. It not only has the application consciousness of the content, but also consolidates students' understanding and mastery of the content. Looking at examples requires students to do it by themselves first, and then compare it, from which they can know the rigor of their thinking and logical reasoning ability, and also see the standardization of their writing, find out the gap, so as to improve their problem-solving ability.
For example: required by Beijing Normal University Edition 1 Chapter 2 "4.2 Properties of Quadratic Functions" Example 3:
Lvyuan Store buys a bottle of 3 yuan drinks at ex-factory price every month. According to previous statistics, if the retail price is set at one bottle of 4 yuan, 400 bottles can be sold every month; If the price of each bottle is reduced by 0.05 yuan, you can sell 40 more bottles. On the premise that the monthly purchase volume is sold out in the current month, please design a plan for the store: how much is the price and how many bottles are imported from the factory to get the maximum profit?
Solutions in textbooks:
Set the sales price as X Yuan/bottle (x>3). According to the meaning of the question (sales volume = purchase quantity), the purchase quantity sold out in the current month is 400(9-2x) bottles.
At this time, the profit is
According to the nature of the function, when, f(x) gets the maximum value of 450.
At this time, the purchase quantity is 400(9-2x)=400(9-2x )=600 bottles.
So the selling price is RMB, and 450 yuan can get the biggest profit by buying 600 bottles.
Students should think about the following questions when reading:
(1) If every 0.05 yuan is reduced, how many bottles will be sold at this time, and the average profit per bottle will be several yuan?
(2) If the price is reduced by 0. 10 yuan, how many bottles will be sold at this time and the average profit per plant will be several yuan?
(3) If every X yuan is reduced, how many bottles will be sold at this time, and the average profit per plant will be several yuan?
(4) Profit per pot = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
With these in-depth questions, students can "read and examine questions" seriously, so as to deeply understand the problem-solving process of textbooks and master the ins and outs of knowledge, with remarkable results.
4, chart reading
We should pay attention to text reading, but we should also pay attention to chart reading. When reading math textbooks, many students often attach great importance to the text narration in the textbooks and can read them carefully, but they don't pay much attention to the graphics and tables in the textbooks, and their eyes are swept away. The combination of numbers and shapes is the basic thinking method of mathematics. It is meaningful for these charts to appear in the book. If you look carefully, you will have a more intuitive feeling and a deeper understanding of this chapter.
For example, in mathematical activities, Xiao Ming designed a geometric figure as shown in figure 1 (the result is represented by n) for evaluation, that is, a square with a side length of 1 is divided into two rectangles first, then one of the rectangles is divided into equal parts, and so on. (1) Please use this geometry to evaluate; (2) Please use Figure 2 to design an evaluable geometry.
For this summation problem, if we adopt the method of pure algebra, we need to set the sum as S, and calculate the sum through the difference of S-S. Although the problem can be solved, in the process of summation, the requirements for jumping thinking technology are quite high. It will be very intuitive to use the method of combining numbers with shapes, that is, to explain the fact of quantitative relationship by using the properties of graphics.
Fourth, cultivate students to develop good reading habits.
1. Teachers' reading requirements for students should be gradually improved.
First, we should gradually improve the content of teaching materials from easy to difficult. From popular, simple and intuitive content to complex and abstract content. Second, according to students' reading ability, step by step from low to high. At first, students can be guided to read after the teacher explains, and gradually transition to the difficult part of the teacher's explanation and the easy part of the students' reading. Finally, let the students read through the textbook, write an outline or make a table by themselves, and the teacher will check the reading effect and give comments and guidance.
2. Ask students to use their brains, read and write, and be careful.
You can skip reading novels, and sometimes you don't have to pay attention to details. However, due to the logical rigor of compiling mathematics textbooks, it is required that every sentence, every mathematical term and every chart should be carefully read and analyzed to understand its content and meaning. In the process of mathematics reading, important mathematical concepts, theorems and formulas need to be memorized, but the description of problems in mathematics textbooks is usually very concise, and some mathematical reasoning processes are often omitted. Sometimes, some inferences and properties of theorems are deduced by themselves, and the operation and proof processes are relatively simple. If the span from the previous step to the next step is large, you often need a pen and paper to "get through the joints" in order to read smoothly. There are also some important data, problem-solving formats, mathematical ideas, knowledge structure and so on. In mathematics reading, students are required to write in the margin in the form of footnotes for future review and consolidation.
3. Guide students to ask questions in reading.
Students are required to learn to find, ask, analyze and solve problems in reading. Asking questions makes students observe more carefully, gradually improve their ability to find problems and make their natural thinking more thorough and profound. Over time, when reading, students will also grasp the key points and ask more why, and the profundity of thinking will be cultivated.
Paying attention to the use of mathematics textbooks (the main materials for students to learn mathematics) in teaching can cultivate students' reading ability, increase the excellent rate of students' homework and improve students' mathematics academic performance. It enriches students' mathematics literacy, cultivates students' ability to acquire and process information actively, develops students' thinking, and makes students become people who can learn.