First, the definition of induction?
Induction is the reasoning that derives general knowledge from individual knowledge, that is, some objects of a certain kind of things have certain characteristics, and all objects of this kind of things have these characteristics. Mathematical induction is a reasoning process that summarizes mathematical concepts, laws and conclusions from some special mathematical facts in life. The application of induction in primary school mathematics teaching can not only teach students knowledge, but also teach students mathematical thinking mode, mathematical thinking method and ability, thus improving the effectiveness and effectiveness of mathematics classroom teaching. ?
Second, design teaching by induction to improve students' reasoning ability?
Mathematics curriculum standard points out: "Students' mathematics learning content should be conducive to students' active observation, experiment, guess, verification, reasoning and communication." Observation, experiment, guessing and verification are all effective means for students to acquire knowledge, while reasoning is an important means for students to turn fragmentary knowledge into systematic knowledge in the learning process. Reasoning itself is a rather rigorous thinking process, which must be based on correct knowledge or theory. Therefore, it is unrealistic to only carry out isolated reasoning teaching in teaching, and it must be organically combined with other teaching methods. Observation, experiment, guessing and verification provide students with knowledge preparation for correct reasoning. Therefore, observation, experiment, guessing, verification and reasoning must be organically combined in order to better use induction in teaching. Below, the author takes part of the teaching content of the first volume of the third grade of the People's Education Edition as an example to explain in detail:
1. "Addition and subtraction within 10,000." This part of the content is the basic knowledge and skills that primary school students should master and form, and it is also the basis for further learning the multiplication and division method of multi-digit written calculation. For example, in the multiplication of two digits, adding up the products of two parts is actually calculating the addition of three or four digits. In two-digit division, three-digit subtraction is usually done after each quotient test. In teaching, students are most likely to forget "1" or "1" with the same digit alignment and decimal places. To this end, the author summarizes it as "one pair of two notes". "A pair" means that the same numbers should be aligned, and "two notes" means "1" to be added or "1" to be dropped. Remind students to mention "one to two notes" when doing problems, so as to improve the accuracy of calculation. ?
2. The teaching content of "Division with Remainder" is not only an extension and expansion of the knowledge of division in tables, but also an important basis for learning the division of one digit divided by multiple digits in the future. So this part of knowledge plays a connecting role. Before teaching examples, students are completely unfamiliar with division with remainder, but in real life, division cannot be completely divisible. If students are taught arithmetic directly in teaching, this teaching method is boring for students, especially underachievers, and it is difficult for students to understand, and the calculation results are often more wrong, so the teaching effect is not ideal. Therefore, according to students' learning characteristics, the author summarizes the easily confused knowledge points as "one pair and two small ones". "One pair" means that the quotient should face the dividend, and "two small" means that the product of quotient and dividend is less than dividend; The remainder should be less than the divisor. Then ask students to use "one is smaller than two" to check the division with remainder, which greatly reduces the students' calculation errors. ?
3. "Get a preliminary understanding of the score." This part requires students to master the comparison of scores with the same denominator, different numerators and the same numerator and different denominator. In teaching, the comparison of scores with the same denominator and different numerators appears first. Through simple guidance, students can get a big score with the same denominator and large numerator. Because according to "the size of molecules, whoever is big is big", this is positive thinking, which is easy for students to master; In the comparison of numbers with the same numerator but different denominators, most students draw the conclusion that "the score with a large denominator is small" through the steps of knowledge transfer, thinking and guessing according to their existing knowledge and experience. But there are still a few students who can't master it well. To this end, the author summarizes the comparison of scores as "big and small". That is, "big" means that the denominator is the same as the numerator (because the numerator is above the fractional line), and whoever is big will be big; "Low" means that the numerator is the same as the denominator (because the denominator is below the fractional line), and whoever has a higher denominator is smaller. Once the students remember the meaning of "go to the big room and go to the small room", there will never be any mistakes in comparing scores in this book. ?
Third, teachers should guide students correctly?
In mathematics teaching, it is not enough for teachers to generalize. The main task of teachers is to enable students to form their own generalization and induction ability. The author believes that teachers should guide students from the following aspects: First, mobilize students to observe, establish the connection between old and new knowledge, and lead to problems. Guide students to observe, let students discover new knowledge independently, understand what they want to learn, and clarify the purpose of learning. The second is to guide students to guess and stimulate their interest in learning. Students' guesses are not made out of nothing, but based on their own observation and understanding. At the same time, students' intelligence has also been developed to varying degrees. Therefore, efforts should be made to create conditions in teaching and guide students to make bold guesses. The third is hands-on practice to guide students to observe again and find problems. The fourth is to exercise reasoning ability in the process of speaking and reasoning, integrate what you know and complete reasoning. This can not only train students' thinking, but also deepen their understanding of new knowledge. Fifth, organize students to verify conclusions and form new knowledge. To cultivate students' inductive reasoning ability in teaching, we must pay attention to the organic combination of observation, experiment, guess, verification and reasoning, so as to better realize the teaching objectives and cultivate students' thinking ability. ?
To sum up, the cultivation of students' inductive ability and its teaching application are of great significance. It can make students form some scientific concepts in their minds and discover some laws, which will lay a solid foundation for learning more advanced scientific knowledge in the future. The application of induction in primary school mathematics teaching can cultivate students' independent thinking ability, observation ability, comparative discrimination ability and abstract generalization ability, and enhance the effectiveness of mathematics classroom teaching, so as to achieve the effect of drawing inferences from one instance and getting twice the result with half the effort.