First, combine life to cultivate students' questioning ability.
Einstein pointed out: "It is more important to ask a question than to solve it, because solving a question may be a mathematical or experimental skill, and asking new questions and new possibilities to look at old problems from a new perspective requires creative imagination, which marks the real progress of science." Mr. Tao Xingzhi, an educator in China, also said: "The starting point of inventing millions is to ask." It can be seen that the problem is the starting point of innovation, and it is very important to cultivate students' questioning ability. How should teachers cultivate students' questioning ability? I have several views:
1, let students dare to ask questions.
Under the influence of traditional teaching, students are used to solving problems raised by teachers or textbooks, but they are not used to and have no chance to find and raise problems themselves. Questioning is the fuse of thinking. In teaching, teachers should consciously set up "questioning" situations according to the psychological characteristics of primary school students' strong curiosity, so that students can form cognitive conflicts and actively find, ask and solve problems. For example, when learning subtraction, I first show the goods and prices in a corner of the shop, and then ask the students, what questions do you want to ask after seeing these? After thinking, the students asked the following questions: How much is a badminton and a pen? How much is a book more than an exercise book? How much is table tennis cheaper than basketball? How much are three badminton and three ping-pong balls? Wait a minute. These problems include the addition problems I learned, so I solved them in time, reviewed the old knowledge and gained new knowledge. Although these questions cannot be answered one by one in this class, they are all put forward by students through their own positive thinking. They are eager to know this knowledge, so they can actively learn and explore it.
In teaching, teachers can also use stories, riddles, games, competitions and other forms to link abstract mathematical knowledge with vivid physical content, stimulate students' psychological doubts and form suspense problems. You can also create problem situations with the help of modern information technology, fully display the formation process of knowledge through the characteristics of multimedia teaching, and add infinite charm to classroom teaching. For example, when teaching "Understanding Graphics", teachers first show beautiful patterns composed of various colors of graphics, and use the animation function of multimedia to make them move to form a picture, which attracts students at once. While students appreciate this picture, let them talk about what is in it, so as to arouse students' desire for in-depth understanding: "What is the figure made of?" Let's make one too. Then scramble to ask many math questions.
2. Let students be good at asking questions.
First of all, we should teach students how to find problems, such as finding problems at the "growth point" of knowledge, that is, finding problems and asking questions in the process of transferring old knowledge to new knowledge, and finding problems at the "combination point" of knowledge, that is, finding problems and asking questions in the internal connection between old and new knowledge, and finding problems from places that they don't understand, understand or know. Let the students realize that if you ask a few more questions, you can find math problems everywhere.
Secondly, encourage students to ask questions in comparison. Comparison is to carefully identify the object and its parts, individual aspects and individual characteristics, and determine their similarities and differences and their thinking methods. Teachers should accustom students to comparing the similarities and differences between the two things, thus asking questions: What do they have in common? What is the difference?
Third, give students the method of analysis and synthesis. Trace back from the conclusion to the conditions that must be known, or gradually deduce the conclusion from the conditions. For example, what conditions must I know to ask this question? According to these conditions, what problems can be solved.
In teaching, teachers should not ask questions for the sake of asking questions, but should gradually improve the quality of questions, express them as clearly as possible, and encourage students to ask original questions, so that questions can really help students' development.
3. Make students willing to ask questions.
Timely positive evaluation makes students feel the joy of success, and students will be willing to ask questions. In teaching, even if students ask some simple or meaningless questions, teachers must make positive comments according to the situation, and seize the opportunity to guide and teach students how to analyze the meaning of the questions, and how to ask questions is meaningful. Don't blame or laugh at students who don't ask well, and never allow other students in the class to make fun of them, especially those with learning difficulties. As long as they ask questions, teachers should give them full praise and encouragement, and pay attention to protecting the enthusiasm of these students. In order to pursue success again and again, they think positively and devote themselves wholeheartedly. As long as there is an opportunity and doubt, they will rush to ask questions without restraint, thus improving learning efficiency.
Second, solid teaching to cultivate students' ability to solve problems
Problem solving is the core of mathematics, and the cultivation of problem solving ability is an important goal of mathematics education. Traditional mathematics courses at home and abroad all aim at problem solving. Learning mathematics is inseparable from solving problems. Halmos, a famous American mathematician, famously said, "Problems are the heart of mathematics", which expressed the importance of problems in mathematics. How to Solve a Problem, written by American mathematics educator Paulia, has become a classic in mathematics education research, which also shows the important position of problem solving in mathematics education. So in mathematics teaching, I have been trying to cultivate students' problem-solving ability, and I have also made some attempts of my own:
1, the training of basic quantitative relations in the problem
Mastering the quantitative relationship is the basis for students to analyze and solve application problems. Students can't judge the problem and don't understand the meaning of the problem, which is a difficult problem in mathematics teaching. In the teaching process, if we strengthen the training of students' basic quantitative relations, students will master the basic quantitative relations more skillfully and solve problems correctly and reasonably. For example, when teaching two-step application problems, the structural feature is that only two known conditions are given, but in the process of solving, one known condition is used twice. This is the difficulty in solving the two-step application problem. If we don't have a good grasp of the quantitative relationship, it will often lead to calculation errors, such as: "There are 10 red flowers, and there are 6 more white flowers than red flowers. How many flowers are there in a * * *? " In the process of solving this problem, "10" was used twice, but some students mistyped the formula as 10+6= 16 (flower), and the result was a * * with 16 flower. How to teach students to correctly understand and master the quantitative relationship in the questions? We can disassemble the questions, organically combine the analysis of the relationship between questions and quantities, and give time to discuss in groups first, so that every student has the opportunity to participate in the training.
2. Use line charts to help analyze, discuss and report, and stimulate students' interest.
In class, students should be organized to discuss in cooperation, which is an effective way to let students learn actively. In teaching, teachers should seize the opportunity and take various forms to let students actively participate in the discussion. They are doing the application problem "The feeding group raises 10 black rabbits, and the white rabbits have 6 more than the black rabbits. How many rabbits does a * * * have? Guide the students to draw a line graph. First, let the students discuss in groups: How to express the number of white rabbits in the line graph? This problem is the difficulty to solve this problem, leaving room for students to think: "How to draw this line segment to make six more white rabbits than black rabbits?" "Students inspire each other in the discussion, broaden their thinking and draw conclusions. This abstract problem is transformed into an intuitive line diagram through discussion, which sublimates students' mathematical thinking, plays a complementary role of students' advantages, improves the effectiveness of participation, and stimulates students' interest in independent learning and exploration.
3. Through observation and comparison, identify similarities and differences to solve the problem.
In the lower grades, guiding students to observe and compare is the best way to learn to solve problems. In teaching, we should pay attention to cultivating students' observation and thinking ability, grasp the connection between old and new knowledge, design comparative exercises that can break through difficulties, let students observe and compare, form conflicts between old and new knowledge, stimulate their cognitive psychological tendency, and get to the bottom, such as teaching two-step application problems and designing review questions: the feeding group raised 10 black rabbits, 16 white rabbits, and one * *. Example: "The feeding group raises 10 black rabbits, and there are 6 more white rabbits than black rabbits. A * * *, how many rabbits? " Change the second condition to: "The feeding group feeds 10 black rabbits, and there are 6 more white rabbits than black rabbits. How many rabbits are there? " After understanding the new knowledge, the teacher will show these three questions on the blackboard in a planned way, guide the students to observe the known conditions and problems of the application problems, and compare the similarities and differences of the solutions of these three problems. Through group discussion, solve problems independently, break through difficulties and master key points of knowledge.
In a word, in the process of mathematics learning, only teachers always pay attention to cultivating students' problem consciousness, guide students to ask questions, find problems and let students actively explore and find solutions, can effectively develop students' mathematical thinking ability and let students consciously embark on the road of creative learning. Mathematics teaching will achieve good teaching results and students' mathematics literacy will be improved in an all-round way.