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How to use the knowledge learned in mathematics flexibly?
Research-based learning in primary school mathematics is to guide students to find unknown problems, solve problems by mathematical means, and transfer mathematical problem-solving strategies to other problems. For example, the teaching content of Unit 3 "Common Multiples and Common Factors" in fifth grade mathematics seems quite simple, but in essence it requires students to learn common multiples and common factors on the basis of knowing them in fourth grade. Students are required to find the common multiple and common factor, the minimum common multiple and the maximum common factor of two numbers. Most students will find it, but it is very difficult to put this knowledge into problem solving, although I know it in teaching. Once such a problem appears in the exam, most students don't know the meaning of the problem, can't analyze the problem, and don't know how to find strategies and methods to solve the problem, so the students in our class scored lower in this unit exam. From this lesson, I realized the necessity of cultivating students' research-based learning, because when we teach students knowledge, it is more important to teach them learning methods. Mathematics is particularly flexible, and now mathematics especially loves to test students' ability to understand, analyze and solve problems. Therefore, teaching students research-based learning is the basis of improving students' mathematical ability.

Then, how to carry out research-based learning in primary school mathematics teaching? According to my own research on teaching theory and my own teaching practice, I think that to carry out research-based learning in primary school mathematics teaching, we should do the following. 1. Stimulate students' interest in active participation. Suhomlinski said: "In people's hearts, there is a deep-rooted need to feel like a discoverer, researcher and explorer, and this need is particularly strong in children's spiritual world." Teachers should guide students into research-based learning, stimulate students' deep desire to explore, and thus generate strong internal motivation. For example, when I teach the knowledge of "parallelogram and trapezoid", it is only a learning tool for students, teaching them the characteristics of parallelogram and trapezoid, guiding them to discover the characteristics of graphics themselves, and finally exchanging and summarizing. This kind of teaching can not only enable students to learn new knowledge, but also cultivate students' research-based learning methods. 2. Pay attention to contact with students' real life. Modern educational theory holds that mathematics originates from life, and life is full of mathematics, so mathematics teaching should be embodied and applied to life practice. Therefore, in mathematics teaching, I consciously guide students to communicate the connection between specific problems in life and related mathematical problems, stimulate students' thirst for knowledge in learning mathematics, discover mathematical problems in life, use what they have learned to solve practical problems, and guide them to conduct research-based learning. For example, the teaching of "liters and milliliters" is to closely connect with students' real life, so that students can know liters and milliliters by investigating the capacity of household containers, make containers of 1 liter by hand, feel the capacity of 1 liter, and then pour the liquid of 1 liter into a 500-ml measuring cup by hand and find 1 liter. 3. Try to let students learn by themselves and discover by themselves. In teaching, teachers should always provide students with an environment that can arouse observation and research, be good at asking questions that students are familiar with but can't solve immediately, guide them to find and find answers to questions themselves, give students the initiative in learning, and give them more research opportunities, more successful experiences and more creative confidence. For example, in the teaching of "determining the position", "What are the characteristics when the position of the same column or row is represented by a number pair?" I just want students to find out the answer through actual observation and experience. 4. Pay attention to cultivating students' creative thinking. For primary school students, being able to solve problems independently and having unique opinions is the epitome of scientific research and their initial attempt to explore and innovate on the road of life. In teaching, I often encourage students to break away from convention, be brave in innovation and find unique solutions to problems, inspire them to make bold attempts from multiple angles, sides and channels, and put forward novel and unique solutions to problems, which is conducive to developing students' creative thinking. Based on the above understanding, I think that carrying out research-based learning in primary school mathematics teaching can stimulate students' desire to learn, help students truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in hands-on practice, independent exploration and cooperative exchange, improve students' mathematical ability, make students develop in an all-round way and truly become the masters of mathematics learning.