Deep learning is a meaningful way of learning. On the basis of understanding, learners can critically learn new ideas and analyze facts, and integrate them into the original cognitive structure, so as to improve their learning level, strengthen their learning ability, adapt to new situations, explore new problems and generate new abilities. At present, there are still problems and phenomena such as formalization, stylization and fragmentation in teaching. In fact, in order for students to achieve the best results in mathematics learning, only through in-depth study in the classroom can they constantly construct their own mathematics system and experience the fun of thinking.

First, "seeking truth"-a preservative for deep learning

The real display of learning situation and the real development of learning process are the necessary conditions for students to construct their own knowledge structure. Only when they really experience the process of constantly solving new problems with existing experience in mathematics activities can students' deep learning happen.

1. Carry out real research.

It is a good way to make use of students' known experience for autonomous learning, but it is often limited by time and space in class, and sometimes it is difficult to finish it effectively, either ignoring the water, or turning it into individual students' learning, and finally turning it into fake learning. For example, when studying Understanding Cylinders, the sixth edition of the Soviet Education Edition, students are often required to observe and communicate with the cylindrical objects they bring, and summarize their characteristics. Judging from the classroom teaching, some students did not participate in the research. If every student is allowed to move, in the process of hands-on, the thinking will be aroused and enlightened, and the characteristics of the column will be truly felt, and the classroom communication and discussion will be more quality and the understanding of the column will be deeper.

2. Implement the real experience.

The real experience in learning must follow the cognitive law. Only when students have experienced the process of the formation and development of mathematical knowledge and "repeated the key steps of the development of human thinking" can they have in-depth study.

For example, when studying the meaning of decimals in the fifth volume of the Soviet Education Edition, a student explained that "the width of a table is 0.5 meters" and said: "0.5 meters is decimeter." Why is there such a problem? Looking back at the teacher's blackboard, it is not difficult to find the root of the problem.

Blackboard writing:

One decimal place, two decimal places and three decimal places.

0. 1= 0.0 1= 0.00 1=

0.3= 0.04= 0.005=

Although teachers rely on situations in teaching, they block the units when writing on the blackboard, which leads to the disconnection of students' cognition. According to the students' answers, if we extract formulas with unit names on the blackboard, such as 0. 1 m = m, 0.04 cm = cm, organize students to read, fully understand the relationship between decimals and fractions, find that the units are the same, and then erase the units on the blackboard, we will get twice the result with half the effort.

Second, "innovation"-the catalyst of deep learning

Mathematics class should be the class that students expect. Every day there are new things, new discoveries and new gains. Teachers need to turn boring mathematics knowledge into vitality, bring different mathematics classes to students and catalyze the in-depth development of learning.

1. task-driven thinking.

In actual teaching, teachers can properly process the teaching materials according to the actual situation of students and design some problems that students can "jump" to solve, so that they will feel fresh and naturally want to start learning.

For example, when teaching "Two Numbers Plus One Number (Carry Plus)" published by Jiangsu Education Publishing House, considering that in this semester, the arrangement of teaching materials is to ask questions from real life situations and learn the calculation mode in solving problems, so when teaching the content of this lesson, the author tries to change the learning situation and directly adopt open-ended questions for teaching.

The teacher asked, "It seems, make up an addition formula of 26+□. When you have finished editing yourself, talk about what counts first, and then talk about what counts. " The students made up carry-free addition and carry-free addition. In view of the students' differences, the author started the layered teaching, such as reviewing the oral arithmetic method without carry addition through "26+2", and completing the teaching tasks of examples in the textbook through "26+4" and "26+7" respectively. Using the materials generated by students themselves can not only arouse students' learning enthusiasm, but also satisfy their sense of achievement in learning.

2. Accumulate new knowledge through practice.

The rigor of mathematics is a double-edged sword, which can cut off those illogical mistakes and maintain the purity of mathematics. If it is not handled well in teaching, it will also cut off the fresh ideas in mathematics. In the process of constructing new knowledge, we should practice more and experience more to find back the vitality of mathematics.

For example, in the course of "Understanding Centimeter" in Jiangsu Education Edition, in order to let students clearly establish the concept of centimeter, the author and classmates cooperated to connect their respective 1 cm sticks to understand 2 cm. When you know 5 cm, you estimate it first, then measure it with a stick of 1 cm, and mark it with a short vertical line while measuring, thus creating a simple ruler unconsciously. In various activities, students not only experienced the evolution and making process of rulers, but also felt the magic and interest of mathematics culture and mathematics learning.

Third, "seeking association"-an active promoter of deep learning

Mathematics teaching should not only have a horizontal perspective, but also have a vertical penetration to seek the source and flow of mathematics. In teaching, we should strive to present a dynamic, unified, interrelated and vivid mathematical image, rather than fragmented and local knowledge blocks and memory banks.

1. Integrate and establish contact.

Textbooks provide rich materials for classroom teaching. Around the teaching objectives, find their internal relations, organically integrate and establish a reasonable and orderly knowledge structure. In such deep learning, students' thinking can be developed.

For example, when "12×3" is taught by multiplying two digits by one digit in the third edition of the Soviet Education Edition, there are three methods in the textbook: throwing the stick, mouth algorithm and vertical column method. Faced with these materials, teachers should establish their internal relations according to their own characteristics.

(1) stick calculation and oral calculation should be done by hand. Combined with the swinging wooden stick, let the students observe that there are three 2,2× 3 = 6 in a single root and three 10 and 10×3=30 in the whole bundle, making a total of 36. With the help of sticks, prepare for the mathematical understanding of written calculation.

(2) Compare the two algorithms. Students have learned to write a number multiplied by a number before, and students can freely try the vertical form here. In teaching, students can talk about arithmetic according to the listed vertical forms, combined with the methods of throwing sticks and oral calculation, and combine the process of arithmetic to show the complete process of vertical calculation and clearly calculate the significance of each step.

(3) Combing the relationship among stick, oral calculation and written calculation. Calculate 12×3, we can kill them with a stick, orally or in writing, so what are their similarities in calculation? The combing of knowledge can reduce students' thinking burden, and at the same time, it can penetrate students' thinking mode of learning mathematics.

2. Communication builds a whole.

The continuity between units and the connection of knowledge points in each unit require us to think more in lesson preparation and teaching, teach children the method of "packaging" knowledge points, and let them master learning methods in the process of learning knowledge. For example, when learning the area and volume of plane graphics and three-dimensional graphics, we should constantly convert them into the area or volume of the graphics we have already learned to learn new knowledge. Teachers should have forward-looking consciousness and backward-looking consciousness in teaching. Although these knowledge points are scattered in different units and grades, they should have a sense of plate and integrity in teaching, so that students can effectively build a mathematical knowledge system and master thinking methods in the learning process.

Deep learning is a higher requirement for students to learn. As a teacher, only by in-depth study and in-depth reflection can students study hard, learn to learn and enjoy learning, and finally reach the best state of in-depth learning, so that students can really enjoy mathematics learning.