The ability to examine questions is a comprehensive ability to obtain and process information. It needs to be based on a certain knowledge reserve and cognitive level, and also needs good reading habits and effective thinking methods to ensure it. The process of examining questions is to examine the plot content and quantitative relationship of questions, so that the conditions of questions, questions and their relationships can be completely impressed in students' minds, creating good preconditions for correctly analyzing quantitative relationships and solving application questions.
Cultivating primary school students to form a good habit of carefully examining questions and form a higher ability to examine questions can not be completed overnight, but must go through a long period of intensive training, which almost runs through our mathematics teaching. Teachers can ask students to read topics and establish representations; Second reading the topic and clarifying the question; Look at the topic three times, find out the key points and mark them. Its difficulty is mainly reflected in the requirement of "labeling key words". Teachers often ask some "trap questions"
It is relatively easy to "stimulate" students and make them realize the importance of reviewing topics ideologically.
Second, help students build mathematical models and improve their pattern recognition ability.
Mathematics is full of patterns. The research results of modern cognitive learning theory clearly show that an expert can quickly find out a strategy to solve a problem in a certain situation through perception because he has the ability to quickly retrieve the original knowledge and experience from memory. In the process of solving mathematical problems, if students can correctly identify the problem pattern, they can quickly converge the scope of thinking about the problem, which is a key step to correctly choose the problem-solving ideas.
At present, the ability of primary school students to solve practical problems is still quite weak, which is mainly manifested in their lack of common sense understanding of the situational language of the problem and their inability to solve the problem by using the equal relationship, that is, they cannot find the relationship between the quantities in the problem, which belongs to the scope of pattern recognition research. Variant training is a good strategy. Students can understand the terms closely related to the application problems from the change of the topic, and achieve the purpose of strengthening the model through the change of the background. In the process of training teaching with variants, teachers should grasp a key link and guide students to realize pattern recognition-make a detailed analysis of a representative problem, and never teach ideas on the topic, so as to achieve the goal of changing with the constant.
Third, guide students to summarize and understand common mathematical ideas.
The abstract logical thinking of senior pupils has been developed to some extent, and they have certain classification ability.
Compared with the basic knowledge of mathematics, mathematical thought has a higher level and status. It is contained in the process of the occurrence, development and application of mathematical knowledge, and it is a kind of mathematical consciousness, which belongs to the category of thinking and is used to understand, deal with and solve mathematical problems. Mathematical method is the concrete embodiment of mathematical thought, which has the characteristics of model and operability and can be used as a concrete means to solve problems. Only when we have a clear understanding of mathematical ideas and methods can we be handy in analyzing and solving problems; Only by understanding the ideas and methods of mathematics can books and other people's knowledge and skills become their own skills. For example, if students master the thinking method of combining numbers and shapes, they will be handy when solving problems.
Fourth, pay attention to the review and reflection of problem-solving strategies
Senior pupils have certain abilities of induction, generalization and strategic reflection.
In the process of solving mathematical problems, it is very necessary to review, discuss, analyze and study your own problem-solving activities after solving problems ("not thinking after solving problems means not harvesting" and "reflection is the golden season of harvesting"). This is the last stage in the process of solving mathematical problems, and it is also the most meaningful stage to improve students' ability to analyze and solve problems.
The teaching purpose of solving practical problems is not simply to get the results of problems. The real purpose is to improve students' ability to analyze and solve problems (experience can only be upgraded through generalization, and the higher the level of generalization, the greater the radius of migration), and to cultivate students' creative spirit, and this teaching purpose is mainly achieved through the review of problem-solving teaching. Therefore, in mathematics teaching, we should attach great importance to the review of solving problems, analyze the results and solutions of solving problems in detail with students, and summarize the main ideas, key factors and solutions of the same type of problems, which can help students sum up the basic ideas and methods of mathematics from solving problems and apply them to new problems, thus becoming a powerful weapon for analyzing and solving problems in the future.
Fifth, properly train openness and new questions to broaden students' knowledge.
Appropriate training for students in mathematics teaching is a necessary supplement to improve students' ability to analyze and solve practical problems. We can use places that students are very familiar with, such as school libraries and classrooms, to create various realistic problem situations. Students can solve problems according to these materials, have a strong thirst for knowledge and experience the happiness of success. It can also cultivate students' awareness of applying mathematics, let them know that there is a lot of mathematical information in real life and feel that it has a wide range of applications in the real world. You can also adapt a question into several different types of questions by changing conditions or questions, so that students can understand and analyze the truth, thus forming a knowledge chain, improving the ability to draw inferences from others and further developing their thinking.
The characteristic of open problem is that there are many solutions. For example, the well-known problem of "not enough, chickens and rabbits in the same cage" can be solved by list, guess, hypothesis and equation strategy. In addition to the strategies mentioned above, there are many strategies to solve problems, such as drawing lines, associating related problems, reasoning strategies such as relationship, transmission and reverse transmission, induction, residue, drawing with models, exclusion strategies and so on.
For example, the teaching of the unit "Finding the Law" can be supplemented by: 1, 1, 2, 4, 3, 9, 4, 16, 25, 6, ... If you want to find out the strategy of this problem, you must find out its law from the arranged numbers, and also find out the strategy to solve the problem.
The order of three, four, five and six ... is arranged as odd terms, or even terms can be drawn to find the law, so that each even term is the sum of its first three terms, thus obtaining a new problem-solving strategy.
In short, we can pay attention to the above points in the teaching of solving practical problems, which can not only arouse students' interest and make them participate in the whole learning process with great interest, but also help students extract and understand the quantitative relationship from real life and master the general methods to solve similar problems. At the same time, it also cultivates students' ability to observe life from a mathematical perspective, find and put forward mathematical problems, screen and process information as needed, and actively seek problem-solving strategies. In particular, the application of this teaching strategy has promoted the cultivation of students' learning qualities such as observation, listening, communication and reflection, and made students realize that mathematics exists everywhere in life and cannot be separated from mathematics everywhere, thus achieving the goal of improving students' mathematical literacy.