When it comes to elementary school algebra basic learning, we have to mention the important enlightenment of algebraic thinking-using letters to represent numbers, which is not something that students can learn thoroughly in one or two sentences. Taking our teaching case as an example, we usually teach the knowledge of using letters to represent numbers thoroughly from the following places.

Example 1. Find the law first, and then think about what numbers m and n represent respectively.

This question is not difficult. Maybe some students who have done a lot of exercises in advance will vomit and say "it's too simple". However, when the teacher asks the students to do this problem, it is obviously not as simple as getting the answer, but after the students finish this problem, they will ask the following questions: Are M and N in the picture replaced by other lines, such as M is 10 and N is 33? (Of course not) Then the teacher will sum up for the students: In some cases, letters can only represent specific numbers. This is the foreshadowing of the meaning of the equation.

Example 2. If additive commutative law is represented by "a+b=b+a", will you represent the additive associative law by letter formula?

This question is not difficult either. The key point is to make students think: if the letters in the equation are replaced by any numbers, is the equation still valid? (Of course) How many groups of answers do A and B meet the requirements? (countless groups)

This kind of thinking aims to make students understand that letters can represent any number in some specific cases, which lays a foundation for students to learn algebraic identities in the future.

Example 3. If s represents the area of a rectangle, and A and B represent the length and width respectively, how to write the area formula of a rectangle?

Similarly, at this time, students need to think: in the formula S=ab, can three numbers be found to replace the letters in it, so that the equation can be established? How many sets of qualified numbers can you find? (Countless groups) If a=3, b=2 and S=9, does the equation hold?

Usually, when the teacher is in class, this series of guiding questions for students is very meaningful. First of all, there are countless groups of numbers A, B and S that can hold the formula S=ab. This situation is very similar to the previous example 2, but A, B and S are not random three numbers, and there is a restrictive relationship between them, and S=ab must be satisfied. This guidance aims at infiltrating the idea of function into students, that is, "there is a restrictive relationship between independent variables and function values, and the change of independent variables affects the change of function values." Let students think about "how many groups of qualified numbers can you find", which is equivalent to establishing the initial concepts of definition domain and value domain.

Xiaohong is one year old, and her mother is 26 years older than her. How old is mom this year?

Usually, after finishing this kind of questions, the teacher will give the students a summary: the letter "a+26" has two meanings, which means both the mother's age this year and the relationship between her age and Xiaohong's age (the mother is 26 years older than Xiaohong).

The former means the basis for writing "sentences" after solving equations. For example, Xiaohong is one year old this year, so the mother's age doesn't need to be set with another letter, just "a+26". The latter means the basis for writing equations according to quantitative relations in the future. Mom is 26 years older than Xiaohong, and the equation can be translated as "a+26".

Through the analysis and thinking of the above four examples, I believe parents will understand that successful and effective mathematics teaching is not only to solve complex problems to understand the hierarchy of their thinking. On the contrary, in most cases, mathematics teaching embodies the "great truth" through "small problems". However, many educational institutions and schools that blindly pursue "scores" and "difficulties" often fail to notice these budding thinking points. But even if your child is not a master, he (she) can understand the above truth, and in the process of learning, he (she) will subtly understand a lot of mathematics knowledge to be learned and used in the future. These are the most dazzling "pearls" in primary school mathematics learning, which will benefit children all their lives.