1, focusing on thinking in images. First of all, teachers should try to use images in teaching. Thinking in images can enrich students' psychological activities and help them to understand the nature and laws of things more deeply. Research shows that creative students' thinking in images can generally reach a higher level. The problem of "crossing the bridge by train" is a kind of travel problem that is difficult for students to understand. I remember that when I was teaching, I naturally and appropriately demonstrated the operation with things in the classroom: I used the podium as a bridge, the meter ruler as a train, and demonstrated the train crossing the bridge. I'll let the students understand and demonstrate "crossing the bridge" first. Through the demonstration, I made it clear that "the front of the train gets on the bridge and the rear of the train gets off the bridge" is called "crossing the bridge by train", and then I made it clear what the train is for. Intuition can turn abstract language into visible images, reduce the difficulty of students' thinking, and help students to understand and construct knowledge well.
Secondly, we should guide students to develop the habit of using intuitive strategies to solve problems. For example, if Xiao Ming and Xiao Jun buy the same book, the book with Xiao Ming's money is short of 1.6 yuan, and the book with Xiao Jun's money is short of 1.8 yuan. If they put all their money together to buy a book, they will spend 2 yuan more. What is the unit price of this book? If students adopt drawing strategy, the problem can be easily solved.
2. Guide students to learn abstraction step by step. First of all, teachers should pay attention to cultivating students' abstract thinking ability in teaching. Only by getting rid of the concrete image can abstraction make thinking get new results in the form of algorithm. For example, students learn the addition of "9 plus several" in Senior One. When they have a circle of ten and make up ten, the teacher must guide them back to the formula and abstract the algorithm. To calculate the addition of 9 addends, we should first think that 9 addends are equal to 10, then decompose the second addend, and finally calculate 9+ 1+ ().
Secondly, abstraction can not only make thinking general, simple and profound, but also have the function of discovering truth. Therefore, teachers should also guide students to solve problems in an abstract way. In learning, it can be expressed as the promotion from prototype to abstraction. For example, in the sixth grade, there is such a problem: "One batch of cloth can make 20 coats and 30 pairs of trousers. How many sets of clothes can this cloth make? " A suit is a coat and a pair of trousers. The sports committee buys sporting goods for the team. He has just enough money to buy 15 badminton rackets or 24 table tennis rackets. If he has already bought 10 badminton rackets, how many table tennis rackets can he buy with the remaining money? "These problems can be abstracted into engineering problems and solved in an abstract way.
3. Pay attention to the role of appearance. Representation is the reflection of the image of things that the human brain has previously perceived that do not directly act on the sensory organs at present. It is not only concrete, but also general. It not only reflects the main features and outlines of individual things, but also reflects the common surface features of a class of things. The basis of representation is perception, and teachers should enrich students' perception as much as possible, and mobilize students' multiple senses to participate in perception by observing, operating and experimenting. In the above-mentioned teaching cases, with the help of image thinking, the addition calculation within 10 and the calculation of adding two digits to integer ten and one digit are carried out. The premise is that students must have rich perception and related graphic representations in their minds, otherwise it is difficult to carry out. Thinking in images is a bridge between perceptual knowledge and rational knowledge. In the process of rising from thinking in images to abstract thinking, teachers should attach importance to the role of thinking in images.
4. Formal operation-a good way to train abstract thinking. There is a problem: "A cube is cut into the largest cylinder. What is the volume of this cylinder? " The solution of student 1 is: suppose the side length of a cube is 6 cm, then the diameter and height of the bottom of the cylinder are 6 cm. π×(6÷2)2×6=54π (cubic centimeter), 6×6×6=2 16 (cubic centimeter), 54π÷2 16=π÷4=78.5%. Student 2' s solution is: regard the side lengths of all cubes as a. π×(a÷2)2×a=πa2/4×a=πa3/4 (cubic centimeter), A× a = a3 (cubic centimeter), π a3/4÷ a3 = π/4 = 78.5. Both methods get positive answers, but the first one is to refer to specific data for operation, and the second one is to use letters instead of numbers for operation, that is, parameter method. Obviously, the second method is more abstract and more general. But only six or seven students can think of the second method.
The operational thinking structure can be divided into two levels, one is the concrete operational level, and the other is the formal operational level. According to Piaget's division of thinking development stages, children are about 7 years old to 1 1 years old, and the operation at this stage is generally inseparable from the support of specific things. From 1 1 years old to 15 years old, formal operation is the thinking of propositional operation, which can be carried out according to assumptions without concrete things. Primary schools have learned to represent numbers with letters and simple linear equations. The sixth-grade students' operational thinking level can be separated from concrete things and concrete data to carry out formal algebraic operations, which shows that they already have the foundation and possibility of formal operations. In solving math problems in primary schools, algebra is sometimes more universal, general and persuasive, which also lays the foundation for algebra learning in junior high schools. Therefore, as a senior primary school teacher, it should be the teaching content to cultivate students' ability to form operations.