Mathematics comes from and serves life. Real-life materials can stimulate students' interest in studying problems, produce a sense of intimacy, help students pay more attention to real life, find mathematical problems in life, put forward mathematical problems, enhance students' application awareness and cultivate students' ability to solve problems. Teachers should try to consciously and skillfully integrate questions into practical basic knowledge in teaching to stimulate students' thirst for knowledge. Mathematics learning is closely related to the reality of life. Only by bringing students into contact with society and life and giving them practical exercises can we better understand the application of mathematical knowledge in real life and industrial and agricultural production. Understand the profound meaning of the sentence "Mathematics comes from life and serves life", form the idea of applying what you have learned and applying what you have learned, truly realize that learning must be combined with productive labor, and gradually improve the ability to look at life from a mathematical point of view and solve problems with mathematical knowledge. For example, when exploring the application of solving right triangle to solve practical problems, students' enthusiasm and thirst for knowledge can be fully mobilized by calculating the height of flagpole, the width of river and other issues closely related to reality.
Second, carefully design the problem to make the design problem more valuable.
A good math problem should have strong inquiry. There should be some room for inspiration and development, and there should be some openness. Asking questions must have certain obstacles and acceptability, that is, asking questions must be difficult, not a matter of knowing the result at a glance, but also of exploitable value, and at the same time, it must conform to students' cognitive rules and existing knowledge base, so that students can accept such questions and stimulate their interest in learning. For example:
Third, cultivate students' practical ability and help them understand the elements of problem solving through the process of teaching and learning.
Mathematics teaching activities are the process of constantly asking questions and constantly solving problems. Cultivating students' problem-solving ability is to cultivate students' ability to find, ask, dare to solve and evaluate problems in teaching. In teaching, we should strengthen students' hands-on operation and exercise, fully display the formation process of mathematical knowledge, and let students experience the emergence, development and solution of mathematical problems. For example, when exploring the trilateral relationship of a triangle, try to let students measure the length with some small sticks to see which ones can form a triangle; When exploring the shortest line segment between two points, ask students to measure the shortest line segment between two points with lines and rulers. Understand the properties of functions by drawing lists, and so on.
Fourth, problem induction, guiding students' ability and skills to solve problems with mathematical activities.
When students try to solve problems, they often can't find the way and direction of solving problems, and it is difficult to establish a connection between old and new knowledge, and they can't figure out whether the application of knowledge is accurate, whether the methods are reasonable and effective, and whether the problems are accurate. Therefore, teachers need to do inspiration and guidance here, cultivate students' methods and skills to solve problems, and form mathematical ideas to solve problems, so as to achieve the purpose of drawing inferences from others. For example, when students do geometry proof problems, they must carefully examine the problems, first know what the known conditions are in solving the problems, and what conclusions each known condition tells us, and then combine all the conclusions to find out what this problem requires. If you want to know the result, you must know something, and then students can combine the known conditions and problems, and this problem can be basically solved. You can also ask more questions in teaching, which can arouse students' enthusiasm for solving problems and stimulate their thirst for knowledge, thus solving problems. Among them, the guidance of teachers plays a vital role.
5. Self-determination, taking cultivating students' problem-solving ability as a long-term interest in teaching.
In order for students to learn and form the thinking method of problem-solving ability, it is necessary to repeatedly implement the process of independent problem-solving in teaching. Teachers should take the cultivation of mathematical reasoning and problem-solving ability as a long-term goal and task, and constantly strengthen the cultivation consciousness of this ability in the classroom, not to teach students to solve a certain problem, but to teach students to solve a class of problems, especially to teach students to learn mathematical thinking in solving problems.
In the teaching process, relatively simple problems can be completed by students independently, so that students can experience the happiness of solving problems by using mathematical reasoning methods; For some difficult problems, students should be given enough time to think independently before trying to solve them; For difficult problems, students should cooperate with each other on the basis of discussion and exchange to get solutions to the problems.
In short, in order to cultivate students' problem-solving ability, teachers should carefully design mathematical problems in combination with students' life experience, guide and encourage students to actively explore, cooperate and communicate, let students experience the process of problem-solving and cultivate students' mathematical literacy.