I have learned a lot from studying mathematics: just like Gai Lou. While laying the foundation brick by brick, we must first test the firmness of the foundation and whether it can withstand hundreds of floors. Only after that can you decorate your building as you please. It can be seen that learning mathematics should be both "innovative" and "conservative" in "innovation". That is to pursue new development in the simplest knowledge and not deviate from the basic principles in new fields. The most important thing here is the connection of knowledge. If you learn to draw inferences from others, you will make progress in your study, otherwise you can only stand still. Innovation is the fundamental driving force to trigger the historical revolution, which is likely to trigger a new mathematical revolution and eventually push the whole society forward. Therefore, we should have the spirit of innovation, and at the same time have the belief of asking questions boldly, studying problems seriously, imagining problems reasonably and solving problems skillfully.
Related to mathematics
We have been studying mathematics since primary school, so what have we been studying for so long?
I think, first of all, mathematics gives us a clear mind, so that we can see the connection between things clearly; Secondly, mathematics has deepened our ability to judge things; Third, mathematics develops our logical thinking.
Over the past few years, I have constantly realized that mathematics has provided us with many available resources in all aspects of study and life. Not everyone understands this. After all, mathematics is a very abstract subject, which is completely different from physical chemistry in essence. Although applied disciplines have brought great economic benefits, without mathematics as the foundation, all disciplines will become castles in the air. If a person wants to be a scientist, he must first become a mathematician. Mathematics has produced a magic power to control our thinking. Once the brain loses its mathematical function, it is as illusory as the body loses its gravity. The magic of mathematics not only makes people's brains have strict logic, but also greatly improves people's work efficiency, which is obvious to all.
Learning mathematics requires two prerequisites: one is savvy, and the other is the ability to calculate, both of which are indispensable. The improvement of understanding lies in thinking more and asking more questions. Take myself as an example, I often process some discrete information to get other continuous or more valuable information (for example, we can see the law of formula change by deducing a special formula back to the general formula) to increase the known quantity to solve the problems I have to face.
Mathematics is a computational science, and learning mathematics well requires a certain amount of computational ability. People who are not good at mathematics usually have two reasons: one is confusion of logical thinking, and the other is poor analytical and computational ability. As long as you find your weaknesses and work hard, you will succeed in the end. There is no end to learning mathematics. Success is only one stop in a long journey, and failure is more in the journey. Success in mathematics comes from strength, not luck. Strength is honed bit by bit through unremitting struggle.
Mathematics is an abstraction of the relationship between quantity and space in the objective world. It can be said that there is mathematics everywhere in life. "Curriculum Standard" points out: "Mathematics teaching is a kind of mathematics activity, and teachers should closely contact with students' living environment and create vivid mathematics situations according to students' experience and existing knowledge ..." Interest in mathematics and confidence in learning mathematics are very important issues for students. Teachers should combine students' life with mathematics learning, make students familiar with and close to real-life mathematics, enter the mathematics classroom, make mathematics textbooks concrete, vivid and intuitive, let students feel and discover the role and significance of mathematics, learn to observe the objective world around them with mathematical eyes, and enhance the sense of function of mathematics. Therefore, teachers should always guide students to provide their familiar experience, make full use of students' existing knowledge and experience and what they are familiar with to organize teaching, so that students can better perceive and understand what they have learned.
First, the teaching content strives for life.
In the process of mathematicization, teachers should make full use of students' cognitive rules, existing life experience and mathematical reality, change the old concept of "teaching materials as the main", deal with teaching materials flexibly and optimize the combination of raw materials according to actual needs. Especially in the primary school stage, it is a direct experience for children to personally experience and feel what they have gained. This kind of direct experience not only belongs to the category of cognition and rationality, but also extends to the fields of emotion, physiology and personality. It is the child's own cleverness. In mathematics teaching, we should "seek" mathematics materials from various aspects, so that students can "discover" mathematics and "think" mathematics in their lives and truly feel that mathematics is everywhere in their lives. "For example, when teaching' percentage application problems', you can make full use of the relationship between the number of boys and girls in this class and the number of groups to design exercises. There are 60 students in Class Three (3), including 33 boys and 27 girls. What percentage of boys are in this class? What percentage of girls are in the class? Students are also free to give questions. The student union will make up the topic that there are more boys than girls and fewer girls than boys. In this way, students feel that there is mathematics everywhere in their lives and realize the usefulness of mathematics in their lives.
Second, teaching methods and means should be as life-oriented as possible.
From the perspective of teaching methods, we should adhere to the heuristic method, create problem scenarios, stimulate students' positive thinking, and guide students to discover and master relevant laws themselves. Teachers should be good at asking questions and guiding students to think. The questions raised, whether practical or theoretical, should be closely combined with the teaching content and compiled into scientific inquiry procedures, so that students can form clear ideas. In order to explore students' creativity, students should be encouraged to guess boldly, dare to question and consciously train their thinking of seeking differences. In addition, we should pay special attention to the guidance of learning methods so that students can learn to learn and develop themselves. From the perspective of teaching methods, we should attach importance to observation and experimental teaching, strive to improve students' observation ability, experimental ability and hands-on operation ability, and cultivate their serious and realistic scientific attitude and habits. We should also try our best to use advanced teaching methods to increase the modern flavor of teaching and let them feel the promotion of modern scientific and technological achievements to teaching. It is difficult for students to distinguish geometric figures. When we teach the understanding of rectangle, square, triangle and circle, we can first show the table, book, red scarf, ball and other physical objects we usually see with slides, and then take them away, leaving geometric shapes such as corners, rectangles, squares, triangles and circles, so that students can find that these graphics are around us, which invisibly generates learning motivation.
Third, the application of life.
Students' learning mathematics is "a necessary tool in daily life to solve some simple practical problems by using the mathematical knowledge and methods they have learned." Guiding students to apply what they have learned can promote the formation of students' awareness of exploration and innovation and cultivate their preliminary practical ability. Every time you teach a knowledge point, you can make up some practical questions for students to practice and cultivate their ability to solve practical problems by using what they have learned. For example, after teaching "step measurement and visual inspection", students can consciously go to the playground to measure and experience step measurement and visual inspection. Doing so strengthens students' understanding of mathematics knowledge and realizes the fun of solving problems. Mathematics is widely used in life. For example, after teaching the stability of triangles, students can explain: Why is the roof of the house where we live framed into triangles? Why did the carpenter fix the desk for his classmates and nail a diagonal strip at the foot of the desk? Another example is teaching the characteristics of parallelogram. Ask the students to explain: Why should the gate be made into a parallelogram grid instead of a triangle? Through the explanation of some life phenomena, students can feel the close connection between mathematics and real life more deeply. In addition, students should use mathematical knowledge to solve practical problems. For example, in the teaching of preliminary understanding of statistics, students collect their own water consumption for several months, and through the process of collecting, describing and analyzing data (population, the elderly, children, etc. ), they got a judgment on whether their water consumption is reasonable or not, and made a decision on the future water consumption. It not only permeates environmental education, but also makes students feel the application of mathematical knowledge.
Mathematics teaching is closely related to life. In the process of imparting mathematical knowledge and cultivating mathematical ability, teachers naturally inject life content; In the process of caring for students' lives, teachers guide students to learn to use what they have learned to serve their own lives. This design is not only close to students' living standards, but also meets their psychological needs. At the same time, it also leaves some defects and expectations for students, so that they can connect their mathematics knowledge with real life more closely. Let mathematics teaching be full of life flavor and times color, really stimulate students' enthusiasm for learning mathematics, and cultivate students' independent innovation ability and problem-solving ability.