Give a simple example: find the sum of the numbers 1, 2, 4, 5, 7, 8, 9, 10.

If a pupil who has never studied arithmetic progression is asked to do this problem, he will naturally add one number at a time to get the result.

If senior students are asked to do this problem, it is obvious that this is actually a arithmetic progression, except for three and six items. Then just use the arithmetic sequence summation formula to calculate the sum of 1 to 10, and then subtract three plus six to get the result.

You can get the answer you want from the above example:

(1) Why construct it? The purpose of construction is to use known more effective methods to solve current problems.

(2) How to construct it? The premise of the construction is to have a corresponding known and feasible model, which should be learned by students before, and the purpose of the teacher's explanation is only to point out this problem-solving idea.

Let's go back to the simple example above. For primary school students who have never studied arithmetic progression, if you tell them to construct arithmetic progression first and then calculate it, they will definitely not understand it, because they don't know what arithmetic progression is. At this time, even if you spend a long class explaining to them what arithmetic progression is, they still can't use it freely, because their understanding ability at this stage, no matter how well you speak it. For senior students, if you tell them to construct arithmetic progression first and then calculate it, they can easily accept this idea. The difference here is nothing more than the difference in "cognitive" level between primary school students and senior students.

Therefore, you should explain the structural problems to students, provided that the structural problems you want to talk about are problems that they can understand at this stage.

Personally, I think the most practical method is to establish it through some common, typical and easily accepted examples.