The reason why students find mathematics difficult to learn is, in the final analysis, the lack of mathematical abstraction ability. In traditional teaching, the teacher directly tells the students what the abstract conclusion is, but does not let the students participate in the abstract process, which leads to rote memorization. Therefore, teachers should play a leading role in guiding students to observe the essence through phenomena, understand "abstraction" and learn to summarize. Let students form their own mathematical propositions and ideas, and teachers should correct and improve them. After a long time, students will have the ability to learn knowledge independently.
2. Cultivate students' logical reasoning ability
Thinking about every innovation and discovery in human history is inseparable from induction and analogy. In classroom teaching, analogy is widely used to introduce the relationship between major human inventions and logical reasoning in mathematics, and situational teaching is fully used to cultivate students' interest in learning mathematics, which requires students to boldly discover and put forward propositions, and some of their ideas will be new inventions in the near future, that is, axioms of theorems; Meanwhile, the essence of mathematical reasoning lies in deductive reasoning. The famous syllogism constitutes the knowledge system of mathematics. The proof methods of reasoning are mostly syllogism, and deductive reasoning is the cornerstone of modern civilization. When telling students about syllogism reasoning methods, let them reason, master the basic forms and rules of reasoning, correctly write the steps of reasoning, write in a logical order, and explore and express the process of argumentation. Construct a proposition system, apply what you have learned at the same time, and use logical reasoning to solve problems in mathematics and life.
Third, cultivate students' mathematical modeling ability.
Ask students to find problems, ask questions and build models by using known knowledge; Solve the model; Test the results and improve the model. Mathematical modeling can cultivate students' practical ability and understanding of knowledge, so as to apply what they have learned and integrate theory with practice. It shows that mathematics comes from life and will be applied to life. Mathematical modeling is an inevitable requirement of the new curriculum standard and an important embodiment of the combination of theory and practice, which enables students to apply what they have learned. In general teaching, students are required to pay attention to collecting models and materials, paying attention to classification, and preparing materials for mathematical modeling for a long time, so as to be prepared for danger in times of peace.
Fourth, cultivate students' intuitive imagination.
The cultivation of students' intuitive imagination ability depends on hands-on. For example, in the teaching of solid geometry and plane geometry, students are encouraged to make their own models first, so that when we show geometric figures again, students will no longer be unfamiliar, and they can also find the positional relationship of points, lines and surfaces, successfully avoiding blunt explanations and achieving twice the result with half the effort. At the same time, students are required to pay attention to observation in life, seeing is believing, form some mathematical intuitive models in their minds, and feel the beauty of symmetry and curves in mathematics. Cultivate students' imagination and combine numbers and shapes organically. Therefore, in the teaching process, we should guide students to look at problems from the perspective of imagination, be imaginative and bold, and let students open up in the classroom, instead of tying students to the traditional model and cultivating imaginative talents in the new era.
5. Cultivate students' mathematical operation ability.
The algebra part of mathematics, in general, is to define addition, subtraction, multiplication, division and related operations on a set, form an algebraic system and related conclusions, and require students to understand operations, master operation rules, explore operation ideas, and design operation programs for operations. Operation is an important part of deductive reasoning, a tool for the inheritance of human civilization and a means to cultivate a rigorous and realistic scientific spirit. Let students fully perceive the creativity of operation. Nowadays, many programs are realized through the processing of big data, all of which are calculating and taking values. Only with high computing power can these programs be identified. This is the call of the times and meets the requirements of historical development.
Intransitive verbs cultivate students' data analysis ability
In today's world, the ever-changing achievements such as cloud computing and big data processing are inseparable from data. Today's competition has become a competition of time, ability and survival of the fittest, which requires students to have the ability of data collection, data analysis and knowledge construction. At present, we live in a diversified information age, which requires human beings to have the ability to process information and data in order to make computer technology serve human beings better. Let students pay attention to the collection, sorting and classification of data at ordinary times, which can cultivate students' ability in this respect. Starting from scratch, they will eventually achieve great achievements.