(2) The way of nesting strengthens the mathematical model: The way of nesting is similar to analogy, that is, according to the similarities or similarities of two kinds or two objects, other similar or identical thinking methods are inferred, which is a special method in solving mathematical problems. Using analogy can find new problems, and the conclusion is accidental, but it can provide clues for the in-depth study of this problem and point out the direction of thinking, which is extremely beneficial to the final solution of the problem. Analogy is the most basic and important method in mathematical discovery. In primary school mathematics teaching, teachers should carry out analogy infiltration teaching in structural characteristics, quantitative relations, mathematical ideas and ideological content. For example, in additive commutative law's study, we can make full use of analogy. Equation1+2+3+4+5+6+7+8+9+10 =? There are many solutions to this problem. You can add addends in turn and finally get the structure. The addition exchange rate can also be used to adjust the addend of the formula. The original formula =1+2+3+4+5+6+7+8+9+10 = (1+9)+(2+8)+(3+7)+(4+6)+5+. The application of nested addition exchange rate in continuous addition formula can make the calculation more convenient. Constructing established mathematical laws or laws will not only help students consolidate their knowledge, but also help them develop the consciousness of solving practical problems with mathematical models. This is conducive to students' subsequent study and research on mathematical modeling ideas.
(3) the method of reverse thinking: reverse thinking is a divergent thinking, and its basic feature is to think from the opposite direction of existing thinking. This form of thinking embodies the discontinuity, mutation and anti-correlation of the thinking process, and overcomes the inertia of thinking. Its advantages are: firstly, it helps to overcome the conservatism of habitual thinking and open up a new field of mathematics; secondly, it helps to correct the wrong understanding caused by habitual thinking; finally, it helps to eliminate the habitual thinking process. The method of reverse thinking is often used to solve application problems. For example, Zhang Lan read the literary masterpiece Romance of the Three Kingdoms in the summer vacation. In the first week, he read half of the books with 40 pages less. The next week, he read the remaining half with 10 page. In the third week, he read 30 pages, and he has read them all so far. The question is, how many pages does The Romance of the Three Kingdoms have? Answering with reverse thinking, I read more than half of the remaining 10 pages in the second week, and 30 pages in the third week, that is, 30 pages plus 10 pages is exactly the remaining half, that is, 40 pages; The remaining 80 pages of the book; Half of the books read in the first week are missing 40 pages, that is, 40 pages are missing and 80 pages are missing, that is, 40 pages are read in the first week. So this book is 80 pages plus 40 pages, which is equal to 120 pages. The advantage of reverse thinking, a mathematical thinking, is that it can restore potential conditions according to some known conditions in questions and questions, and it can continue to accumulate by using the restored conditions. This interlocking, and finally solve the problem.
(4) Creating situations in connection with life: When people learn difficult knowledge, the biggest motivation is to be able to solve their own practical problems. In order to cultivate students' mathematical thinking, mathematics content can be linked with students' daily life. Only in this way can students realize that solving this problem will bring benefits to their lives, so they should study hard and eventually form a good habit of solving problems with mathematical thinking. On the contrary, in math class, connecting with life situations can help children better understand the methods of solving math problems by using life common sense and life experience. For example, in the teaching content about triangle stability, teachers can ask students to fix the wall chart on the blackboard with three magnetic buckles. In order to cooperate with teaching activities, the weight of the flip chart can be increased, which can make the flip chart unstable when the three magnetic buttons are placed in parallel. Students found through experiments that only when three magnetic buttons form a triangle can the wall chart be stable. After the teaching content is finished, students should be guided to contact with real life. For example, how to fix a picture frame with three nails is the most reasonable.