Ability is a necessary psychological feature for people to successfully complete certain activities. In western psychology, the word ability has two meanings: it can be interpreted as both practical ability and potential ability. Practical ability refers to what an individual can actually do now, expressed by knowledge and skills, which are mainly the result of study or training. When students solve problems, the axioms, definitions and formulas applied in the process of solving problems belong to knowledge, while the rigor and flexibility of thinking activities in the process of solving problems belong to ability. It can be seen that ability and knowledge are closely linked and inseparable. To improve students' problem-solving ability, we should pay attention to both knowledge and ability. I talk about my own views on my own teaching experience:

First, give an example. Examples are an important part of teaching materials. Examples teaching is the main channel for students to acquire mathematical knowledge, master problem-solving skills and skills, understand the mathematical thinking methods involved and improve their thinking ability by guiding students to explore the potential educational and teaching value of topics.

In the new curriculum teaching, after a new mathematical concept or formula, rule and theorem is finished, some imitative examples are usually selected to let students understand and master the basic knowledge of mathematics and cultivate basic skills. But this is only the role of appearances. Examples often contain many mathematical ideas: function and equation, combination of numbers and shapes, classified discussion, reduction and transformation, and mathematical methods: collocation method, elimination method, method of substitution, undetermined coefficient method, mathematical induction method, coordinate method, parameter method, construction method, mathematical model method, etc. . Therefore, in the teaching of examples, students should not only understand the basic knowledge of mathematics and master basic skills, but also pay attention to the infiltration teaching of mathematical thinking methods contained in examples.

Paulia said, "What does it mean to be proficient in mathematics? This means being good at solving problems. " Of course, the explanation of examples can not completely improve students' problem-solving ability, but also needs practice.

Second, the second is student practice. If you don't go swimming by yourself, you'll never learn to swim. Therefore, if you want to get the ability to solve problems, you must do more problems.

Through intensive training of some questions, students can improve the utilization rate of various exercises, not only avoid a lot of repeated exercises, but also do more exercises, so that students can form skills and skills in the process of solving problems and improve their ability to solve problems. I have the following suggestions for the specific implementation methods to solve the problem:

1. When studying the conditions of the problem, if necessary and possible, you can draw corresponding graphs or ideas to help you think. Because it means a clear and concrete understanding of the overall situation of the topic.

2. Clearly understand every element in the situation; Be sure to find out which elements are known and which are unknown.

3. Deeply analyze and think about the meaning of each symbol and term in the exercise narrative, find out the important elements of the exercise, mark the known elements and unknown elements, and try to change the position of each element in the topic to see if there are any important discoveries.

4. Try to solve the problem as a whole and find out the characteristics. Have Lenovo encountered similar problems before?

5. Carefully consider whether there are other different understandings of the meaning of the question. Whether the conditions of the topic are redundant, contradictory and lacking.

6. Seriously study the objectives proposed by the topic. Find out which rules are related to topics or other elements through goals.

7. If you find a familiar mathematical method in solving a problem, try to express the elements of the problem in the language of this method, which will help solve the problem.

Third, to improve their ability to solve problems, it is not enough to rely solely on model practice, but also to require students to use their brains. For example, it is not enough to understand the solution and proof of theorems in textbooks. Students must understand how people come up with this method and why they solve problems like that. Is there any other way to solve the problem? I think this is the most important thing. If students really understand other people's problem-solving ideas, then they can innovate on this basis and improve their problem-solving ability.

Fourth, knowing how to calculate problems does not mean high scores. Therefore, we must also strengthen the standardization of solving problems in mathematics teaching. Judging from the examination questions of college entrance examination and senior high school entrance examination, the grading standard is very meticulous and strict, and the answers are clear, logical reasoning, and words or formulas are reasonable.

1, the specification of the problem-solving process includes: starting from what is known, writing corresponding conclusions according to axioms, theorems, definitions and other theoretical foundations, and finally solving the problem. In order to make the process of solving problems logical, it is necessary to correctly understand the key meaning of the problem, discover and analyze the implicit conditions, and draw inferences from one another.

2. Strengthening measures: In the usual teaching practice, students must write on the blackboard or use multimedia to solve problems, and tell students what to write or what not to write according to the normative requirements of writing. Homework correction and examination paper correction are strictly standardized. In this way, students will develop standardized problem-solving habits over time; Always show students the reference answers and grading standards of calculation questions to promote the standardization of students' problem solving.

3. Strive to improve the calculation accuracy in solving problems. Many students lose points because of carelessness and careless calculation, so students should be strictly required to have correct calculation habits in peacetime in order to calmly deduce the calculation.

4. When solving problems, each question type and different content have different requirements, procedures and steps. The exam is based only on the test paper. This requires candidates not only to know, but also to be correct, correct, complete, complete and standardized in the exam. Unfortunately, it will be wrong; Yeah, it's incomplete, the score is not high, and it's sad. For example, many candidates do solid geometry problems, and the process of doing, proving and seeking is not standardized; The application problem lacks the necessary modeling process; There is a lack of necessary analysis and expression when solving probability problems. The problem of image translation of narrative function only talks about image, and we don't know the changes of abscissa and ordinate of points that should be described. These are all manifestations of irregular answers, thus losing the opportunity to score. Therefore, we must pay attention to the accurate use of mathematical language when answering questions, and strive to make the symbols, characters and graphics used accurate and logical.