"Students who can't ask questions are not good students." Students can think independently and have the ability to ask questions. No matter what kind of questions students ask, no matter whether their questions are valuable or not, as long as they are students' real ideas, teachers should fully affirm them and then take effective methods to guide and solve them. For innovative questions and opinions, we should not only give encouragement, but also praise students for being good at finding and asking questions, and guide everyone to think deeply and communicate together. For example, teaching additive commutative law, this class is mainly about exploring and discovering laws. In the process of exploring new knowledge, it is taught in the form of competition. After explaining the contents and rules of the contest, the two groups took turns to answer the questions: 25+48, 48+25, 68+27, 27+68 ... After the fourth question was answered, the group of students who answered the questions first immediately asked the question: "Teacher, the questions that our group did were not fair!" Then the teacher asked, "Why is it unfair? Tell me. " Then the students naturally talked about the essence of the problem: "Although the addend are in the opposite position, the addend are the same, so the result is the same." Let students take the initiative to find problems, ask questions and grasp the essence, so as to further clarify the connotation of additive commutative law. Another example is "Proportion in Life". When importing, ask: What proportions have you encountered in your life? From the students' answers, we can put forward "the proportion of sugar and water in syrup" and "the proportion in basketball match", and ask "are these two proportions the same?" If not, what is the difference? "The students gave different ideas through exchanges and discussions: the competition is mainly about winning or losing the size, and the ratio of sugar and water in syrup may change, but more attention is paid to the relationship between sugar and water. So as to grasp the essence of the problem and break through the difficulties.
Second, we should have the spirit of innovation, make reasonable guesses and infiltrate the core literacy.
Dewey once said: "Every great achievement of science is based on bold fantasy." The conjecture about mathematical problems is actually a kind of mathematical imagination and the embodiment of innovative spirit. In mathematics teaching, students should be encouraged to make bold guesses and learn mathematics creatively. Let students experience observation, experiment, guess, proof and other mathematical activities, share ideas and exercise mathematical thinking. For example, "the circumference of a circle", in the process of exploring what the circumference of a circle is related to, first guide students to make a guess: the circumference of a square is related to its side length, and guess what the circumference of a circle is related to. Then, according to the students' answers, demonstrate three circles with different sizes and scroll for one week. Ask the students to point out which circle has the largest diameter. Which diameter is the shortest? Which circle has the longest circumference? Which circle has the shortest circumference? Finally, it is concluded that the diameter of a circle determines its circumference.
For another example, when teaching "the multiple characteristics of 3", most students will have a guess that the unit is a multiple of 3 because of the influence of the multiple characteristics of 2 and 5 learned earlier. At this time, the teacher shows some data to guide the students to observe and verify. In the column 1, there are 9 "73,86, 193, 199,163,419,763,176,599". Can they be rounded to three? Through verification, students find that the previous guess is wrong, so they will have doubts and desire to explore new knowledge. At this time, teachers use mistakes to guide students to observe the second column of numbers "9,21,105,237,27,78,42,591,843,534". Can the number in the second column be divisible by 3? Observe again. what do you think? Then it is pointed out that whether a number is divisible by 3 depends not only on one digit, but also on the order of numbers. So, what is it related to and what are its characteristics? Inspired by the teacher, students can make the following guesses again: 1, which may be related to the product of each digit; 2, which may be related to the difference of each number; 3, which may be related to the sum of each number; And so on. At this time, the teacher let the students explore and verify themselves, and turn a big mistake into a small one.
Third, carry out reasonable refining, establish mathematical models, and infiltrate core literacy.
Mathematical model is indispensable in mathematics learning. It can not only provide a bridge for mathematical language expression and communication, but also be an important tool to solve practical problems. It can help students understand the significance of mathematics learning and solve problems in mathematics learning. For example, when teaching "area of parallelogram", when constructing the mathematical model of area formula, the counting grid method is first applied to explore a simple square of graphic area, which is easy for students to understand. In this process, students analyze the corresponding quantities of rectangle and parallelogram, and get a preliminary conclusion: when the length of rectangle is equal to the base of parallelogram and the width of rectangle is equal to the height of parallelogram, the areas of two figures are equal. So I guess the area of parallelogram may be equal to the base times the height. So, if you want to measure a large parallelogram field in real life, do you think the method of calculating the grid is appropriate? So as to guide students to convert parallelogram into rectangle for calculation.
Another example: When teaching "additive commutative law", after the students have initially perceived the law, the teacher asked: Can you express additive commutative law in your favorite way? Students use their favorite symbols in turn and put forward the form of a+b=b+a to guide students to discuss which numbers A and B can be. This not only pays attention to the formal expression of operation rules, but also cultivates students' abstract ability and model thinking.
Fourth, apply mathematical knowledge to solve practical problems and penetrate core literacy.
Learning mathematics should be used in real life. Mathematics is used by people to solve practical problems, and mathematical problems arise in life. Therefore, the connection between mathematics knowledge and life practice should be strengthened in classroom teaching. For example, "estimation" is a common calculation method in daily life. Some problems only need approximate results, and some are difficult to calculate accurate data, which requires estimation methods to help us solve the problems. Therefore, strengthening students' estimation consciousness and mastering some simple estimation methods are of positive significance for students to solve practical problems in daily life and cultivate their sense of numbers and their ability to apply mathematics. For example, how much do I need to bring to the supermarket? What is the approximate area of a room? How many people can a playground hold? ..... The formation of students' estimation consciousness and ability needs teachers' persistent and subtle influence in classroom teaching, so that students can internalize estimation and their estimation ability can be really improved. Another example is "appreciation and design". Based on students' existing knowledge, students can feel the beauty of symmetrical patterns, and experience that complex and beautiful patterns can actually be obtained by translating, rotating or symmetrical simple graphics. On the basis of appreciating all kinds of beautiful patterns, let the students design them themselves. The graphics created by students are rich and colorful, which makes students feel that our real life can not be separated from mathematics, and mathematics brings us good feelings.