There are many views on grasping primary school mathematics as a whole. In order to sort out the mess and grasp the key points, the most important thing is to "focus on the long-term, pay attention to the long-term."

Focusing on the long-term is the core

In the long run, it is in terms of goals. No matter whether a person studies or works in the field of mathematics when he grows up, the problem-solving strategies, thinking modes, thinking methods and tool application abilities obtained through mathematics learning will play an important role. Although the primary school mathematics curriculum is far from the goal of college entrance examination and employment, it is the most important part of the whole basic education mathematics curriculum. Therefore, primary school mathematics education should have long-term and long-term functions.

However, the reality is not optimistic. The negative effects of exam-oriented education are lingering, and the evaluation system marked by the lack of constraints on "correctness, quickness and accuracy" is still suppressing students' vitality. Mathematics is mostly exposed in exams, which is not seen in life and not used in work. Once you don't have to take the exam, you will meet again. What is the long-term prospect of such mathematics?

There is no doubt that mathematics is of great use. But whether mathematics education has a long-term vision will depend on whether we provide an environment for children to cultivate interest, application, adaptation, self-confidence, reality, responsibility, imagination and creation. Have we got rid of the shackles of question-based education and exam-oriented education, and have we given children enough space to think and try independently, instead of copying it completely according to the teacher's understanding or a certain model in the book? These are all related to students' "desire and ability of lifelong learning".

Mathematics education is mathematics education, and mathematics education cannot be separated from mathematics. Many predecessors have repeatedly stressed that learning mathematics must be able to sit on the bench and stand the test of boredom and abstraction. There is no doubt about this for professional mathematicians, but it is basically fallacious to apply this idea to primary schools. With a straight face, boring and lonely mathematics is difficult to enter the child's heart.

Paying attention to long-term effects is the key.

Whether the long-term goal of primary school mathematics can be achieved depends on whether long-term effective support can be provided.

Effective teaching is a particularly hot topic in primary school mathematics education research. Effective teaching refers to the high matching between teaching results and expected teaching objectives. It should be noted that "effective" can be divided into long-term and short-term Simply put, the long-term and lifelong impact is long-term; Managing immediate and special skills is a short-term effect. In terms of time, long-term effect should be accumulated for a long time, and it is difficult to achieve it overnight; Short-term effects can be immediate, and a class is easy to form. At the same time, the immediate and long-term are interdependent and indispensable.

What is the relationship between short-term effect and long-term effect? On the one hand, without the tempering and accumulation of short-term effects, long-term effects are difficult to form; On the other hand, some definitions, theorems, formulas and algorithms that need to be memorized and mastered through high-intensity and high-density training are destined to stay in people's minds for a long time. Without books at night, you may not remember what you learned during the day. However, the accumulation formed in the process of exploring and discovering these definitions, theorems, formulas and algorithms, as well as the experience and understanding of using these definitions, theorems, formulas and algorithms to solve practical problems, may remain for a long time. The more such experiences, the more accumulated. Inadvertently, some relatively stable views or ideas related to mathematics will often be formed. These can stay in students' minds for a long time, and can be used in their life-long study, life and career, and become an important support point for personal development. Therefore, ignoring the process of "exploring and discovering those definitions, theorems, formulas and algorithms" in mathematics teaching is mostly short-lived, and teaching that comes quickly and forgets quickly is generally ineffective.

Therefore, although short-term effects are easy to obtain, long-term effects are the key. The short-term effect should be long-term service, and the long-term effect should be the goal. On the one hand, "process and method" and "emotion, attitude and values" are brought into the vision of effective teaching. At the same time, we should have a clear understanding of the teaching strategies characterized by reinforcement, machinery, speed and hard indicators.

Practice paying attention to long-term "unique kungfu"

Take "measurement" as an example. When students begin to understand the angle, when they are faced with various angles, the problem of size comes to the surface, and measurement becomes the theme of quantitative understanding of angle, including two meanings: unit and actual measurement. The first is the "unit", which is recognized as the unit of measurement. The focus of "unit" in primary school is to understand and feel the practical significance of the unit, such as weighing a bag of 500 grams of salt, feeling the size of a 0.4 square meter desktop, measuring how tall you are, and so on. These seemingly "mathematical" movements are all indispensable attempts to feel and understand the unit. More importantly, the unit itself is the result of the regulations. The necessity and stipulation of commensurability come from the * * * knowledge formed by human beings through different channels and long-term exploration, and it is the common language of human beings. For students, there is a lot of room for discussion, activities and exploration. Working hard in teaching can help students understand the standard function and platform function of the unit, understand the relationship between the individual and the general, know how to choose between estimation and accuracy, and gradually realize why mathematics needs abstraction, etc., which will help students approach and discover the essence of mathematics, which is linked with long-term effect. The second is "quantity", that is, how to measure it. The focus of teaching should start from students' own experience and the problem of "real knife and real gun". By encouraging students to use their own tools and units, we will gradually guide standardized tools and units, guide students to explore measurement methods from multiple angles, and gradually approach less formal measurement units and methods until scientific measurement can be realized. Measurement class should be a "discovery" class with a series of "why", and each conclusion should be discovered, summarized and sorted out by students themselves. Students should not only know how to measure, but also know where the measurement method comes from, the relationship between the measured object in books and the measured object in life, and the significance of measurement.