The content of primary school mathematics teaching is all-encompassing, and each class has its own teaching emphasis and teaching difficulty. Teaching difficulties are the most confusing knowledge points for students in the classroom and the focus of students' cognitive contradictions. It is like a stumbling block in students' study, which prevents students from further acquiring new knowledge and solving problems and doubts, which is an important guarantee for the smooth and effective teaching process. Therefore, in a sense, the teaching difficulty itself belongs to the teaching focus. Teaching emphasis refers to the basic knowledge and skills that students must master in the teaching process, such as concepts, properties, rules, calculations, etc. In order to help students solve key points, understand difficulties, rationalize perceptual knowledge and realize long-term memory and flexible application of knowledge, teachers should pay attention to the intuition, visualization and concreteness of teaching methods, the relationship between old and new knowledge, and supplement relevant perceptual materials when breaking through key points. Teachers' teaching can only be combined with students' reality.

Let's talk about the author's methods to break through difficulties in teaching practice:

The first is to strengthen perceptual participation, highlight key points and break through difficulties with intuitive methods.

Intuitive teaching plays an important role in primary school mathematics teaching. In view of the fact that primary school students' thinking is still in the stage of concrete thinking in images, and in primary school mathematics teaching, the mathematical knowledge they want to contact and master is abstract, so it is necessary to build a bridge between concreteness and abstraction. Intuition is an effective means to solve the contradiction from concrete to abstract. In teaching, teachers should give students more opportunities to use learning tools to swing, spell and operate. Enable students to perceive new knowledge, gain representation, understand and master the essential characteristics of related concepts in hands-on operation. For example, in teaching, students can make some cube models by drawing, measuring, folding and cutting geometric figures, so that students can perceive the formation process, characteristics and quantitative relationship of geometric figures. For example, students can draw a circle with compasses by fixing a point, determining a constant distance and rotating it once to adjust the center and radius.

Second, grasp that mathematics comes from life, and use the method of connecting with life to highlight key points and break through difficulties.

Modern educational concept points out: "Mathematics teaching should start from students' existing knowledge and experience, let students experience and participate in specific teaching activities, let students feel the close connection between mathematics and daily life, gain some experience from it, abstract practical problems into mathematical models through independent exploration and cooperative exchange, and understand and apply them. Therefore, we should start from the existing experience of primary school students' mathematics life, and look for "mathematics materials" from life, so that students can "discover" and "think" mathematics in life and truly feel that "there is mathematics everywhere in life". For example, we all know that "interest" knowledge comes from life and is widely used in daily life. When I teach "interest", students are required to deposit 5000 yuan in the bank, which is calculated once every three years. Let students be "masters" in class, and guide them to understand the meaning of interest, interest rate and principal from real life, and understand the truth of mathematics. Only by bringing mathematics into life will students be willing to learn and enjoy learning, thus stimulating their enthusiasm for learning and using mathematics.

Third, grasp the characteristics of primary school students, highlight key points and break through difficulties with games.

Pupils are curious, active and interested in games. In general, their attention can only be maintained for about 15 minutes. In teaching, if students are organized to learn mathematics knowledge through flexible game activities, they will have a strong interest in mathematics learning and keep their attention on the learning object for a long time, so that the teaching will receive good results and the classroom atmosphere will become interesting. Teachers and students are emotionally integrated. For example, when learning the concept of "time", they play clapping games with students. The teacher clapped twice first, then four times, and asked the students to answer that the second clap was several times that of the first clap. Then, teachers and students high-five each other as required, and classmates at the same table high-five each other. In this teaching process, students are always focused and in high spirits. This simple game is deeply loved by students, thus achieving the goal.

Fourth, using comparative method, grasp the similarities and differences of knowledge, highlight key points and break through difficulties.

Ushinski, a famous educator, said: "Comparison is the basis of all understanding and thinking. It is through comparison that we know everything in the world." There are many connections and differences in primary school mathematics. Making full use of comparative method in teaching will help to highlight the teaching focus, break through the teaching difficulties, make students easily accept new knowledge, prevent knowledge confusion, and improve their discrimination ability, so as to firmly grasp mathematical knowledge. Develop logical thinking ability. For example, in classroom teaching, some teachers always try their best to make no mistakes in answering questions or performing. Even for some problems that are slightly difficult and prone to typical mistakes, teachers have "ingenious methods" to let students solve them according to the correct methods designed by teachers, resulting in the bad consequences of understanding them as soon as they listen in class and making mistakes as soon as they do it after class. This is actually a reflection that teachers have not fully understood the teaching difficulties and made no breakthrough in teaching. Through one or two typical examples, let students expose their wrong solutions, teachers and students analyze the causes of errors together, compare the correct and wrong solutions, and learn from both positive and negative aspects, so that students can truly understand the difficulties and flexibly use new knowledge.

Fifth, grasp the connection between knowledge, adopt the strategy of transformation, and break through the key and difficult points.

The transformation method is to use the existing knowledge and experience to transform the complex into the simple, the unknown into the known, and the seemingly unsolvable into the solvable. Simply put, it is to turn the unknown into the known, simplify the complex, and turn the song into the straight. In teaching, if teachers can "change the new into the old", grasp the "vertical and horizontal connection" between knowledge, help students form a knowledge network, and gradually teach students some ways to transform their thinking.