What are the main problems in students' problem-solving ability?

In actual teaching, we find that quite a few students lack the ability to solve problems in mathematics, which seriously affects students' interest in further learning mathematics and the improvement of their ability to solve problems. Only by identifying the basic problems of students' problem-solving ability can we accurately formulate its countermeasures. So what are the main problems in students' problem-solving ability? 1. Observe your students. 1. What problems are obvious when solving problems?

1. The basic knowledge is not solid and cannot be integrated.

"the State Council's Decision on the Reform and Development of Basic Education" points out: "Pay attention to the teaching of basic knowledge and skills, and pay attention to the cultivation of emotions and attitudes." Among the three-dimensional goals, knowledge and skill goals are the primary goals and play a fundamental role. Students' mathematical problem-solving ability and mathematical literacy are formed in the process of mastering, constructing, internalizing and applying knowledge. Pupils are psychologically unstable, impatient and active, which leads to the failure to implement basic knowledge in the learning process. For example, they can't correctly understand and master various mathematical concepts, laws, formulas and skills, and are often in a state of incomprehension. When solving problems, there is no solid basic knowledge to pave the way, and no effective method to solve mathematical problems can be found, which seriously affects the effect of solving problems.

2. The examination questions are not careful, resulting in a fixed mindset.

Psychological research shows that people use certain cognitive ways to think in the process of learning. The more times they repeat, the better the effect, and then they will give priority to this method in new similar situations. Students often do a lot of exercises or repeated exercises without careful examination of the questions, and only see the appearance of the questions and begin to use the existing experience to solve them. This is a phenomenon of thinking inertia. Although fixed thinking helps people to think analogically, so as to solve some problems more smoothly and quickly, it is easy for students to blindly treat some seemingly magical problems with specific experiences and habits, leading to wrong problem solving.

3. Lack of learning initiative and serious dependence.

Mathematics learning should be a process in which students actively construct knowledge. In real life, parents are too careful about their students' study, and it is easy for children to become dependent. For example, every time parents do homework, they carefully check their children and circle the wrong places for them to correct, instead of teaching them how to check, so that they can learn to check and correct mistakes. Sometimes the teacher's single teaching method will also make students feel dependent. For example, teachers pay too much attention to the teaching of problem-solving methods, but don't let students take the initiative to try to learn and solve problems, ignoring the "helping and teaching" of students, which makes a large number of students afraid to try boldly in the face of new problems and rely on listening to the teacher's correct answers. Because students have not experienced the process of gradual internalization of concepts such as observation and operation, comparative analysis, exchange and reflection, their problem-solving ability and thinking ability have not been improved, which makes them feel dependent, lose their initiative and independence in mathematics learning, and lose their problem-solving and reasoning ability.

4. Fear of difficulties is serious.

In order for students to solve mathematical problems successfully, they need to have good ability to solve mathematical problems. In the teacher's teaching, we can easily find that many students are afraid of difficulties in front of math problems. Fear of difficulties means that students dare not face the difficulties in learning activities correctly and have no rational understanding and thinking, which is harmful.

Fear of difficulties, even avoiding difficulties, seems helpless in the face of more difficult mathematical problems. Fear of difficulties is mainly caused by improper family education and school education. In family education, some parents overindulge their children, and everything is arranged instead. The child has never suffered setbacks, so he doesn't know how to face difficulties. In school education, teachers lack good teaching ability, fail to grasp the scale of "acceptance", and fail to give students enough space and time to think and solve math problems independently, which also leads to students' inability to face difficulties independently. Therefore, fear of difficulties affects, restricts and hinders students' learning enthusiasm and initiative, which seriously affects the efficiency of students in solving mathematical problems.

5. Lack of flexibility in thinking and thinking of seeking differences.

Differential thinking is a kind of creative thinking and the core of cultivating creative thinking. It requires students to think about a problem from different angles and directions, and solve the problem creatively with their own knowledge and ability. The thinking of primary school students is mainly concrete thinking, which is easy to produce negative thinking patterns, causing some mechanical thinking patterns and interfering with the accuracy and flexibility of solving problems. In the face of a mathematical problem, we can express and think from different angles, and we can fully and profoundly understand this problem. To eliminate the interference of students' negative thinking mode, we should strive to create conditions in solving problems, guide students to analyze and think from all angles, develop students' thinking of seeking differences, and make them solve problems creatively. The commonly used methods are "multiple solutions to one problem", "multiple solutions to one problem" and "multiple solutions to one problem". When solving problems, we should always pay attention to guiding students to explore ways to solve problems from different aspects in order to find the best solution. For example, the author explores and explains the new category of "engineering problems" in different ways. "Build a village road. Team a completed it alone 10 week, and team b completed it alone 15 week. How many weeks can two teams repair from both ends of the road at the same time? " When students put forward hypothetical methods to solve problems, I encourage students to boldly assume the length of this road and calculate with their own different assumptions, so as to verify that the result is the same regardless of the length of this road, whether it is 600, 300, 60, 1 or X, thus breaking the mindset, inspiring students to think new ways, and obtaining the optimization of the algorithm, which fully shows the flexibility of students' thinking.

6. Poor math study habits lead to low problem-solving ability.

The cultivation of good study habits is one of the important tasks put forward by curriculum standards for current teaching. Good study habits will benefit students for life and avoid unnecessary mistakes in solving math problems. In daily teaching, students are often prone to make mistakes of one kind or another. If students are asked to examine the questions carefully, most of them can solve the problems independently. This shows that many students have bad study habits in mathematics, which leads to mistakes in solving problems, such as lack of reflective inspection habits, careless examination of questions, good hands-on habits and poor independent inquiry ability.

7. Teachers' improper teaching methods

In daily teaching, teachers sometimes blindly instill knowledge because of their lack of understanding of textbooks, which makes students passively accept learning. This will cause students to remember the knowledge, but they don't really understand and master it, and they don't know how to solve practical problems comprehensively. If teachers do not accurately grasp the actual situation of students in teaching, the design of teaching activities will deviate from students' knowledge grasp, and will also affect students' ability to solve problems. In the process of teaching, many teachers are always worried that they can't finish the teaching task or the teaching content is incomplete. They often replace the examination process. Students just read the topic and go through the motions. Students lost this opportunity to exercise, which also caused this.

Insufficient ability. In this way, students lose the opportunity to examine and think about problems, and over time, the formation and development of problem-solving ability are seriously affected.

The course expounds the research and teaching regulation suggestions of junior high school mathematics problem-solving methods and skills teaching from three aspects: problem-solving significance, problem-solving methods and skills, and problem-solving methods and skills teaching suggestions. In the course content, it is fully analyzed and explained with practical teaching cases, in order to share with teachers the effective help for junior high school students' mathematics learning after effective teaching regulation, so as to promote students' effective learning, better understand and master junior high school mathematics knowledge, and cultivate students' interest in mathematics learning and innovation ability.

2. What solutions and skills do students have in solving problems?

Methods and skills to solve new problems in middle school mathematics

1. Mathematical inquiry questions

The so-called exploration of the problem is to explore the corresponding conclusions from the given conditions of the problem and prove them.

Ming, or from the given topic requirements, explore the corresponding necessary conditions and ways to solve the problem. Conditional inquiry questions: One of the problem-solving strategies is to regard the questions and conclusions as known, and at the same time make reasoning, so as to find out the corresponding required conditions in the process of derivation.

Conclusion exploration question: usually refers to the conclusion is uncertain and not unique, or the conclusion needs analogy, promotion, promotion, or special circumstances need to be summarized. You can guess first and then prove it; You can also seek to prove the conclusion under specific circumstances; Or direct deduction.

Law inquiry: actually, it is to explore a variety of methods to solve problems and formulate a variety of strategies to solve problems. Activity-based problem exploration: let students participate in certain social practice and solve problems through in-class and out-of-class exploration.

Popular inquiry questions, which summarize a simple question and can produce new conclusions, are more common in junior high school teaching.

For example, the judgment of parallelogram can produce many new generalizations, on the one hand, it is its own generalization, on the other hand, it can be extended to rhombus and square.

Exploration is the lifeline of mathematics, and solving exploration problems is a creative thinking activity. The exploration of a mathematical form is by no means the result of a single way of thinking, but the connection and infiltration of multiple ways of thinking, which can make students dare to question, ask questions, reflect and popularize in the process of learning mathematics. Through exploration, experience the process of mathematical discovery, mathematical inquiry and mathematical creation, and experience the happiness brought by creation.

2. Mathematical situation problem

Situation problem is to put forward mathematical ideas and methods in the situation according to the life reality, stories, history, games and mathematical problems in a period of time. This kind of questions are often lively and interesting, which stimulates students' strong research motivation, but at the same time, mathematical situational questions have the characteristics of large amount of information and strong openness, which requires students to extract mathematical problems from the scene and experience the mathematical process of studying practical problems with the help of mathematical knowledge.

For example, when the teacher is talking about the mixed operation of rational numbers,

3. Open mathematical problems

The open problem of mathematics is a new kind of problem compared with the traditional closed problem, which is characterized by insufficient conditions or no definite conclusion. Because of this, the strategies for solving open-ended problems are often varied.

(1) Open math problems generally have the following characteristics:

Uncertainty: The questions raised are often uncertain and general, and the background is also described in general terms, so we need to collect other necessary information to solve the problem.

② Inquiry: There is no ready-made problem-solving model, and some answers may be easily found by intuition, but in the process of solving problems, we often need to think and explore from multiple angles.

③ Incompleteness: The answers to some questions are uncertain and there are various answers, but what matters is not the diversity of the answers themselves, but the reconstruction of students' cognitive structure in the process of seeking answers.

Divergence: In the process of solving, new problems can often be brought out, or the problems can be generalized to find more general and general conclusions.

⑤ Hierarchy: It is often put forward through practical problems, and students must use mathematical language to mathematize it, that is, establish a mathematical model.

⑥ Development: It can arouse the curiosity of most students, and all students can participate in the solution process. ⑦ Innovation: It is difficult for teachers to teach by injection, and students can naturally take the initiative to participate. Teachers' position in the process of solving problems is demonstrator, enlightener, encourager and collaborator.

(2) According to the four elements (conditions, basis, methods and conclusions) that constitute the system of mathematical problems, the classification of open-ended mathematical problems can be classified into four categories; If the answer sought is the condition of a mathematical problem, it is called conditional open problem; If the answer sought is a basis or method, it is called a policy open question; If the answer sought is a conclusion, it is called a conclusive open question; If the conditions, solving strategies or conclusions of a mathematical problem need to be set and searched by the solver in a given situation, it is called a comprehensive open problem.

Collect materials from students' study life and familiar things, and design various forms of mathematics open questions, aiming at opening students' thinking and potential learning ability. The opening of mathematics is entitled that students of different levels have created opportunities to learn mathematics well. The application of various problem-solving strategies effectively develops students' innovative thinking, cultivates students' innovative skills and improves students' innovative ability.

(3) Opening up the teaching characteristics of "carrier" with mathematics.

① Open teacher-student relationship: Teachers and students become problem-solving collaborators and researchers.

② Open teaching content: Open questions often have incomplete conditions or conclusions, which need to be analyzed and studied by collecting data, leaving room for innovation in mathematics.

③ Openness of teaching process: Because the openness of research content can arouse students' curiosity, and because of the openness of questions, there is no ready-made problem-solving model, so there will be room for imagination for all students to participate in imagination and answer.