(2007- 1 1-22 20:03:2 1)

Reprinted ▼

Label:

Miscellaneous talk on education

Classification: Papers and Education

Zankov, a famous educator, pointed out: "In the teaching of various subjects, we should always pay attention to developing students' logical thinking and cultivating students' flexibility and creativity." The cultivation of mathematical thinking is the soul of mathematics teaching, and the development of students' thinking is the core of mathematics teaching. It can be said that without mathematical thinking, there is no real mathematics learning. Therefore, the new curriculum standard of primary school mathematics puts forward the goal of "mathematical thinking", which refers to the development of students' general thinking level related to mathematics in primary school mathematics teaching activities, and clearly requires teachers to pay attention to enlightening and developing students' thinking and forming and developing students' mathematical thinking ability while guiding students to learn mathematics knowledge. How to cultivate primary school students' mathematical thinking ability can take the following five ways:

First, stimulate curiosity and cultivate the initiative of thinking.

Students have poor independence of thinking. They are not good at organizing their own thinking activities, and often think of what they see. Cultivating students' logical thinking ability is mainly through the demonstration, guidance and guidance of teachers in the teaching process, so that students can acquire some thinking methods in a subtle way. In the teaching process, teachers can carefully design questions, put forward some enlightening questions, stimulate thinking, and mobilize students' enthusiasm and initiative to the maximum extent, so that students can always devote themselves to learning and thinking with high emotions and devote themselves wholeheartedly to learning.

For example, in the first class, "Understanding the Circle" is taught. The teacher first asks the students to take out a round piece of paper, fold it in half, then fold it in half before opening it. Repeatedly, let the students observe what they see on the circular piece of paper. The students' energy was suddenly concentrated, and they all wanted to see what was left on the round paper. I found in my life that there are creases on the round paper. In another life, I found countless creases on the round paper. The teacher asked the students to continue to observe carefully. Other students spoke in succession: all the creases on the circular surface intersect at one point, and the figures on both sides of the creases are completely coincident. At this time, the teacher asked the students to open their textbooks and see what the intersection was called. What is the name of the crease? The students quickly found the answer and remembered it. When learning the relationship between the diameter and radius in the same circle, the teacher asked the students to take out a ruler and measure the diameter and radius of the round paper in their hands and the round paper in their classmates' hands respectively, which inspired the students to find out. The students quickly came to a conclusion. If you want to draw a circle, the teacher still doesn't talk about painting. Let the students draw first, satisfy their curiosity of operating compasses, and let the students discover the methods and steps of drawing circles by themselves. Throughout the class, all students have the opportunity to operate with their hands, observe with their eyes, reason with their mouths, think with their brains, observe and find problems by themselves, and actively explore and draw conclusions. The teaching effect is good. For another example, when teaching "knowing corners", students list the corners they have seen in their lives. When it comes to corners, there are different views. Some students think it is a corner, while others think it is not. How did you know? I let students learn the concept of "angle" with this riddle, and then discuss it from several directions, so that students' learning mood is always in an exciting state in acquiring new knowledge, which is conducive to the positive development and in-depth discussion of students' thinking activities.

Second, change the angle of thinking and cultivate the opposite sex.

Students' thinking ability can be effectively developed only when they are active in thinking. In the teaching process, teachers should put forward questions with moderate depth and strong thinking according to the key points of textbooks and students' reality, cultivate them to dare to seek differences, develop their thinking of seeking differences, and then develop the habit of thinking and solving problems independently.

For example, in the first lesson on the meaning of multiplication, an addition question was put forward: 9+9+9+5+9=? Let the students calculate in a simple way. One student put forward the method of 9×4+5, and another student put forward a "new scheme", suggesting the method of 9×5- 4. The student's thinking is original, and this scheme was discovered by himself. In his thinking activities, he "saw" a nonexistent 9. He assumes that the position of 5 is 9, so the topic can be assumed as 9×5 first. Then his thinking participated in the argument: 9- 4 is the actual 5 in the original question. This kind of finding and asking questions in problems that others can't see is a flash of creative thinking, and teachers should cherish and cherish it. In teaching, I often find that some students are only used to positive thinking, but not to reverse thinking. In practical problem teaching, when guiding students to analyze the meaning of the problem, on the one hand, we can start with the problem and deduce the idea of solving the problem. On the other hand, we can also start from the conditions and gradually summarize the methods to solve the problem. More importantly, teachers should pay great attention to the training of positive and negative variants in the setting of topics. For example, the variant training of language narration, that is, let students change the narrative form from one sentence to several sentences. Teaching practice tells us that it is of positive significance to pay attention to the comparative training of positive and negative thinking from the beginning of junior grade to break the students' thinking set.

Third, pay attention to multiple solutions to one problem and cultivate the broadness of thinking.

Broadness of thinking is another feature of divergent thinking. The narrowness of thinking is manifested in knowing only one and not the other. If you change a little, you won't know what you are talking about. Repeated training with multiple solutions to one problem and changeable problems is an effective way to help students overcome narrow thinking. Through discussion, we can inspire students' thinking and explore ways to solve problems. On this basis, students can be trained many times, which not only increases their knowledge, but also cultivates their thinking ability. In the teaching process, teachers should not only pay attention to the calculation results, but also carefully design exercises with levels, slopes, clear requirements and multiple solutions to one problem according to the key points and difficulties of teaching, so that students can constantly explore shortcuts to solve problems through training and make the breadth of thinking develop continuously.

For example, the title "Measuring well depth with rope" is displayed. Fold the rope for three times and measure it, and the remaining rope outside the well is 4 meters; Fold the rope four times for measurement, and the remaining rope outside the well is 1 m. How deep is the well and how long is the rope? "

Students can list various solutions:

1. Engineering method: rope length: (4-1) ÷ (1/3-1/4) = 36 (m), well depth: 36 ÷ 4-1.

2. Arithmetic method: well depth: 4×3- 1×4=8 (m), rope length: (8+4) ×=36 (m), which can also be solved by equation method.

The title of another example is: "A ship can carry diesel for up to 6 hours. When driving out, it was downwind, with a speed of 30 kilometers per hour. When driving back against the wind, the distance per hour is 4 /5 of that when driving with the wind. How far does this ship have to go to return? " The teacher asked the students to solve the problem in several ways, and told them how to solve the problem.

Because the ship is going back and forth, the journey out is equal to the journey back. If it takes x hours to drive the longest distance, it will take (6- x) hours to drive back. The column equation is: 30x=( 30×4 /5) ×( 6- x) Solve this equation and you get x=8 /3. Then, the longest driving distance is 30x 8/3 = 80 (km).

(2) First, find out the headwind speed: 30×4 /5=24 (km), and then assume that the ship will return when it sails out of X km at most. According to the time relationship used for the round trip, we can list the equation: x/30+x/24=6. If this equation is solved, the ship should return when it has sailed out of 80 km at most.

The teacher asked: Is there any other solution? At this time, another student raised his hand and said, "I want to find out the speed of this ship when it runs against the wind: 30×4 /5=24 (km), and then take the maximum distance traveled by this ship as the unit'1'. According to the time relation of round trip, the formula can be listed as 6 ÷ (1/30+60). This student uses analogical thinking mode. Starting from the problem to be solved, he thinks of a familiar problem similar to it, that is, the engineering problem. It is necessary to make students enter a good broad thinking state through repeated and gradual expansion training.

4. Infiltrate and transform ideas and cultivate associations of thinking.

Associative thinking is a kind of thinking that expresses imagination, and it is a remarkable sign of divergent thinking. The process of associative thinking is from this to that, from the outside to the inside. Through the training of broad thinking, students' thinking can reach a certain breadth, while through the training of associative thinking, students' thinking can reach a certain depth. For example, after learning the surface area and volume of a cylinder, it shows that the surface area of a cuboid is 66. 16 cm2, the bottom area is 19 cm2, and the perimeter of the bottom surface is 17.6 cm. Find the volume of this cuboid. "To find the volume of a cuboid, you need to use" bottom area × height ". The problem is to ask the height of the cuboid first. Under the guidance of the teacher, the students linked the surface area of the cylinder with the surface area of the cuboid, and thus reached the conclusion that "the height of the cuboid = (using the surface area of the cuboid-the area of two bottom surfaces) ÷ the perimeter of the bottom surface", and successfully completed the answer to this question. When students are asked to discuss a variety of problem-solving ideas, some solutions require students to use mathematics to change their thinking, which can simplify the problem-solving ideas, achieve the effect of multiple solutions to one problem, and train the thinking transformation. As an important mathematical thought, "conversion thought" is widely used in primary school mathematics. In solving practical problems, it is beneficial to cultivate students' associative thinking by using transformation method and deepening migration.

Fifth, guide the transfer of knowledge and cultivate the comprehensiveness of thinking.

Mathematical knowledge has a strict logical system. As far as students' learning process is concerned, some old knowledge is the basis of new knowledge, and new knowledge is the extension and development of old knowledge. Students' cognitive activities are always based on existing old knowledge and experience. Therefore, when teaching every new knowledge point, teachers should try to integrate the old knowledge, make use of the existing knowledge to pave the way, and guide students to use the law of knowledge transfer and develop their thinking in the process of acquiring new knowledge. For example, the topic is "Two ships set off from the north and south banks of the Yangtze River at the same time, meet at a distance of 260 meters from the south bank, then move on, return immediately after reaching the other bank, and meet again at a distance of 200 meters from the north bank. How wide is the river? " Based on the known conditions, after careful thinking and synthesis, most students can draw the conclusion that the width of the great river is actually three 260m ships sailing from the south bank, which is 200m more than the width of the great river. The formula is 260×3-200=580 (m). This is entirely due to the cultivation of comprehensive mathematical thinking.

In mathematics teaching, teachers should pay special attention to cultivating students to consciously and flexibly use mathematical methods according to the specific conditions in the questions, find new methods and formulate new strategies through thinking from different angles. The purpose of mathematics teaching is not only to impart knowledge, so that students can learn, understand and master mathematics knowledge, but also to pay attention to teaching students learning methods and cultivating students' thinking ability and good thinking quality, which is the need to improve students' quality in an all-round way. Let's give students a broad world, give them an independent space, let them enjoy learning, be good at learning, and let their mathematical thinking ability be fully developed in classroom learning.

Share: