First, grasp the essence and cultivate the profundity of thinking by means of communicating the internal connection between knowledge.
The profundity of thinking lies in being good at discovering the essence of problems through complex phenomena, which is the basis of all thinking qualities. It focuses on thinking deeply about problems, discovering and grasping the laws and essence of things from complex superficial phenomena, so as to solve problems satisfactorily. Therefore, the internal connection between communication knowledge has become the main means to cultivate students' profound thinking.
For example, when teaching "Basic Properties of Constant Quotient", first show a set of oral arithmetic problems:
12÷4= 1200÷400= 120000÷40000=
120÷40= 12000÷4000= 1200000÷400000=
See who calculates quickly and accurately. As a result, while most of the students were still nervously calculating, several students had already calculated it and were all right. The reason is that they said: when I calculated three problems, I found that the dividend and divisor were expanded at the same time 10 times and 100 times, and the quotient was still 3, so I decided that the quotient of the last three problems must also be 3, because their dividend and divisor were expanded at the same time 1000 times and 10000 times. Then I showed a set of questions:
12÷4= 24÷8= 36÷ 12= 6÷2= 3÷ 1=
After careful observation and comparison, the students found that the quotient was still 3. Therefore, by communicating the internal relations of several groups of problems, it is concluded that divisor and divisor expand or shrink the same multiple at the same time, and the quotient remains unchanged, which naturally produces the quotient invariance. Therefore, in classroom teaching, teachers should consciously ask students to sum up some problems in teaching, so that every student can actively participate in the process of exploring the internal relationship between knowledge, discovering the essence of problems and getting answers.
Second, based on multi-angle thinking, be flexible and cultivate the flexibility of thinking.
The flexibility of thinking is to be good at adjusting ideas in time according to the specific situation of things' development and change, and find out the best solution to the problem that is in line with reality. In mathematics teaching, teachers pay attention to inspiring students to think from multiple angles, encouraging association and advocating multiple solutions to a problem, which is helpful to cultivate students' thinking flexibility.
For example, when teaching "an application problem", I came up with a problem: a car travels 240 kilometers in 4 hours. At this speed, the car traveled 65,438+00 hours from A to B. What is the distance from A to B? As soon as the topic is put forward, the students with quick thinking immediately raise their hands, and the formula is 240÷4× 10. I asked students with this idea to raise their hands, and most of them raised their hands. I didn't stop there, and continued to guide: 4 hours and 240 kilometers, so how many kilometers in 2 hours? How many kilometers did you walk in 8 hours? Before I finished, one of my classmates couldn't wait to stand up and say, 10÷4×240, because 10 divided by 4 means that 10 has 2.5 4 hours, while 1 4 hours walks 240 meters 2.5 hours (/kloc
Third, take strengthening skill training as the carrier, strive to be fast and accurate, and cultivate the agility of thinking.
The agility of thinking means that when thinking about mathematical problems, we should be sensitive, get in touch with the essence quickly, learn from the old to the new, from the easy to the difficult, with few steps, a big span and high thinking efficiency. In primary school mathematics teaching, strengthening skills training is an important way to cultivate students' agility.
For example: (8+3)+(7+2), according to additive commutative law, it is easier for students to calculate with the method of ten:
Another example: (30+9)+(40+4), let the students add ten integers and one digit, which makes the calculation easier:
With the improvement of students' operation skills, the intermediate links in the calculation process are gradually compressed, and students are trained and trained to gradually transition from detailed thinking to compressed ellipsis thinking, so that students can quickly calculate numbers through perception as soon as they see the topic. Of course, strengthening skills training must be based on students' practical understanding of the operation rules, laws and nature, memorizing some commonly used data and adhering to appropriate oral calculation and application exercises at ordinary times, so as to achieve the purpose of cultivating agile thinking through training methods such as visual calculation, listening calculation, oral calculation and quick calculation competition.
Fourth, on the premise of improving the ability of fault diagnosis, we should boldly question and cultivate critical thinking.
Critical thinking means that you are good at independent thinking, dare to question, have strong discrimination and can consciously correct your mistakes. When solving problems, teachers are good at finding problems by themselves and improving their self-correcting ability by guiding students to think more; Guide students to test the rationality of reasoning process from different angles, put forward correction schemes and explore new ways to solve problems; Encourage students to ask "can you do it" and "why", improve their questioning ability and cultivate critical thinking.
For example, when teaching "Characteristics of Numbers Divisible by 3", I first show a set of data: (63, 36, 69, 123, 96, 39) so that students can judge which numbers are divisible by 3, and then I ask them what are the characteristics of numbers divisible by 3. According to the characteristics of some numbers above, students are influenced by the characteristics of numbers divisible by 2 and 5. I then showed a set of data: (13, 26, 19, 23, 46, 59) to let them judge which numbers can be divisible by 3 according to the conclusion just reached. As soon as the students calculated, they immediately overturned the conclusion just reached. When students found that numbers with 3, 6 and 9 were not necessarily divisible by 3, I didn't immediately summarize the characteristics, but asked the students to discuss in groups under my guidance to find a solution to the problem. Finally, on the basis of self-discussion, discrimination and self-denial, the students summed up the characteristics of numbers divisible by 3. Therefore, in primary school mathematics teaching, teachers should be good at making use of students' mistakes and making analysis and diagnosis, which can not only make students understand the essence of concepts, but also help to cultivate students' critical thinking.
Five, to break through the conventional thinking as the core, dare to explore and cultivate the creativity of thinking.
Creativity of thinking means that on the basis of existing knowledge and experience, you can creatively discover new problems, put forward your own unique opinions and find the best way to solve problems. The creativity of thinking is unique, unconventional and flexible, which is the core of thinking quality. For example, there is a child whose teacher asked for 3, 5 and 9 digital cards to form numbers. According to conventional thinking, people can only form numbers like 3, 5, 9, 35, 39, 59, 53, 93 and 359. Moreover, he can turn the card 9 upside down and use it as a 6, more than others. This somewhat "stubborn" child moves from static to dynamic, which reflects the creativity of thinking.
In solving math application problems in primary schools, we usually analyze problems from conditions and deduce results from conditions, which is a conventional way of thinking. If there is such a problem: the water surface of the pond is gradually covered with lotus leaves, and the coverage area doubles every day. After 30 days, the whole pond will be covered, so how many days will it take to cover half the pond? This problem can't be solved by conventional methods, but it is easier to be solved by reverse thinking. Because it doubles every day, it just covered half of the pond water 30 days ago. This kind of thinking further develops students' creative ability, arouses their enthusiasm and initiative in learning, makes them have a deeper understanding of what they have learned, and cultivates and develops the quality of creative thinking.
In a word, the cultivation of mathematical thinking quality is a long-term task in mathematics teaching. Primary school mathematics teachers should organically combine the cultivation of various thinking qualities, and constantly explore effective methods and ways to train their thinking according to the actual acceptance ability of primary school students and the principle of gradual progress.