First of all, start with simple questions and cultivate students' learning methods.
In classroom teaching, the author takes students' common mathematical problems as examples to guide students to experience the application of hypothetical methods in solving problems. For example, 2/3 of the number A equals 3/4 of the number B. Compare the size of the number A and the number B ... Method 1: According to the equivalence relation in the question, assuming that they are all equal to "1", then A ×2/3= B ×3/4= 1, and then use reciprocal knowledge to find out A =3/2, B =4/3, A >；; Number B. Method 2: Assuming that number A = 1, then/kloc-0 /× 2/3 = number B× 3/4, and taking number B as unknown in the equation, we can get number B =8/9, because1>; 8/9, so a number >; Of course, this question can also be answered graphically, so I won't explain it in detail.
Second, we should start with the seemingly unqualified application questions to enhance students' confidence.
Primary school students' thinking ability has certain limitations, and the analysis of topics is often not in place, especially for special topics, teachers should analyze them reasonably. Example: A car travels from A to B at a speed of 100 km/h, and then travels from B to A at a speed of 60 km/h.. What is the average speed of this car? Students often mistake it for (100+60)÷2, and teachers need total distance ÷ total time to find the average speed. These two conditions are not available in this problem, but if the total distance is known, the problem is very simple. Suppose the distance between Party A and Party B is 300 kilometers (taking the least common multiple of 100 and 60, so the calculation is relatively simple), the time for going is 300÷ 100, the time for returning is 300÷60, the total distance is 300×2, and the comprehensive formula is 300× 2 ÷. Teachers can guide students to assume that the whole process is "1", that is,1× 2 ÷ (1100+1/60), thus raising this issue to a certain theoretical level.
Third, take the topics in the textbook as an example and use them reasonably.
The chapter "Problem-solving Strategies" in the eleventh volume of the mathematics textbook published by Jiangsu Education Press talked about the hypothesis method. For example, 42 people in the class went boating in the park, one * * rented a boat of 10, 5 people in the big boat and 3 people in the small boat. How many big boats and small boats have you rented? Method 1: let's assume that the big boat and the small boat are half.
Method 2: Assume that 10 is a ship.
Suppose that a ship with 10 can take 3× 10=30 people.
Difference from the total population: 42-30= 12.
A big boat can be replaced by a small boat: 5-3=2 people.
How many big ships can be found: 12÷2=6.
How many ships can be found: 10-6=4.
Mathematics is characterized by abstract form and strict logic. The knowledge of mathematical exercises is from the unknown to the known, and the unknown is sought by the known, which is very conducive to cultivating the logic, accuracy and creativity of students' thinking. Therefore, in teaching, teachers should fully guide students to make bold assumptions. In addition, it needs to be clear that the application of hypothesis method must be close to students' real life and easy to calculate. The purpose of hypothesis is not only to solve problems, but more importantly, to make students' thinking not limited to the methods mentioned in teachers and textbooks, and to create divergent thinking and divergent thinking, so as to cultivate their spirit of daring to explore and innovate and better develop students' creative ability. ;