Many students have had this feeling in primary school. Whenever you know a mathematical law and solve an application problem, the joy of success is irreplaceable by anything else. It stimulates your enthusiasm and curiosity about learning. The more you learn, the more you love learning. Interest in learning and thirst for knowledge should be constantly cultivated. Besides, students have just stepped into the big garden of "the kingdom of mathematics", and many mysterious and endless mathematical problems are still waiting for you to learn, watch and study.
Second, we should form the good habit of studying hard and thinking independently.
In the past, some students thought that learning mathematics mainly depended on listening to the teacher in class, and regarded our math textbooks as "problem sets" for homework. There are two cognitive problems that must be solved. First, students should realize that our textbook records the basic knowledge that mathematicians must master and how to use this knowledge to solve problems. Therefore, in order to truly acquire knowledge, study hard and cultivate self-study ability is the fundamental way. We hope that with the guidance and help of middle school teachers, students will change from not reading in the past to loving and learning to read, and then form a good habit of reading carefully; Second, students should also realize that many math problems are not solved by teachers alone, but mainly by students themselves. Confucius said, "Learning without thinking is useless, and thinking without learning is dangerous." This sentence brilliantly expounds the dialectical relationship between learning and thinking, that is, learning and thinking, thinking and learning. The process of learning mathematics is mainly a process of continuous in-depth thinking. We hope that everyone will take math classes in the future. No matter how teachers talk about new lessons, review or comment on homework exercises, they should keep a high degree of concentration, actively think about problems while listening, capture useful information, and seize budding inspiration at any time. For problems that you don't understand, you must solve them in time and actively until you understand them.
When learning the basic knowledge of algebra, can you ask yourself the following questions by reading books? Try to solve it. For example, why use letters to represent numbers? What is algebraic expression? What is the key of column algebra? How to express a law by algebra? Wait a minute. In addition, when doing exercises, if you encounter an algebraic expression of the square of the product of the sum of two numbers and the difference between these two numbers, do you know what are the different quantities? How to use letters to express and which mathematical operation symbols to connect can reflect the hierarchical internal relationship between quantities and transform literary language into algebraic language, that is. If it is written, it is not the original meaning. In junior high school, a big difference from studying mathematics in primary school is that I have learned many mathematical concepts, especially rational numbers. Because mathematical concepts are the basis of our judgment and reasoning and solving problems, we must understand them accurately. Although mathematical concepts are often abstract, they are all abstracted from concrete cases in real life. Therefore, when learning mathematical concepts (such as positive and negative numbers, number axis, absolute value of numbers, etc.). ), we should pay attention to combine them with actual life production, and we will summarize and summarize the essence of the concept from specific cases. When reading a book, we should grasp the key words in the concept definition and think about its connotation, so as to understand the textbook. We believe that a large number of students will improve their self-study ability by cultivating the habit of studying hard; Improve your thinking ability by cultivating the habit of independent thinking.
Third, we should always grasp the important basic topic of how to "progress from arithmetic to algebra"
Generally speaking, the mathematics content of first-year algebra is mainly to solve important basic problems from arithmetic to algebra. We think it is mainly reflected in the following two aspects. On the one hand, it is "number set expansion", that is, introducing negative numbers to expand the original arithmetic number set into a rational number set; On the other hand, it is the principle and method of solving algebraic equations, that is, from expressing numbers with letters to solving application problems with "column equations" instead of "column formulas".
Every expansion of the number set is the need to solve practical problems and the contradiction of mathematics itself. The establishment of the concept of rational number, the introduction of the nature of rational number and the regulation of rational number operation rules are all necessary preparations for students to further study algebra. When studying the chapter of rational numbers, I hope everyone can consciously cultivate their logical reasoning ability, observe, compare, analyze, synthesize, abstract and generalize, and use induction and analogy to reason. In addition, we should pay special attention to improving our computing ability and have excellent basic computing ability. Therefore, we can not only operate correctly according to laws, operating rules and formulas. , but also understand the calculation principle, so that the operation can be "reasonable, simple and accurate" according to the subject conditions. In order to solve the limitation of solving application problems by arithmetic, people come up with letters to represent unknowns, and algebraic equations to represent the equality relations in problems. Because the letters representing unknowns are also numbers, we can also operate according to the generality and general method of digital operation, so as to get the appropriate value of unknowns. Students should pay full attention to this "historic" breakthrough. Therefore, it is necessary to master not only the deformation and calculation of arithmetic with numbers, but also the deformation and calculation of algebraic expressions with letters (mainly algebraic expressions at present), as well as the basic methods and steps of solving equations, all of which are carried out in order to solve application problems with column equations. Through the study of solving practical problems with equations, we can understand how to abstract practical problems into mathematical problems, deal with mathematical problems with equation ideas, form the consciousness of using mathematics, and cultivate our ability to analyze and solve problems.
Fourth, improve learning methods and grasp every link of mathematics learning.
Many students who are good at mathematics have their own learning methods that are in line with their own reality, and they can better grasp all aspects of mathematics learning. For example, make a study plan for each stage; Earnestly study and preview math textbooks before class; Concentrate on every math class with "questions" and think positively; Review what you have learned in time after class, finish your homework independently, solve difficult problems seriously and timely, and correct mistakes in your homework; At the end of each unit, make a review summary, systematically sort out the knowledge and the types and methods of solving problems, prepare carefully before the exam, and pay attention to summing up experiences and lessons after the exam; In addition, I insist on participating in extracurricular group activities and reading math tutorials. All these show that the whole process of learning activities is an interrelated and organic systematic project. Although it seems like a cliche, it is not easy to stick to it. Need to have a high degree of enterprising spirit, diligent and practical learning attitude, tenacious learning perseverance. We suggest that students should focus on overcoming a shortcoming and solving a problem at a certain stage of their study. Students help each other, learn from each other, strengthen the atmosphere of research and discussion, catch up with each other and promote each other, so that all of us can lay a solid foundation for future study in the first semester of senior one. I wish the students a great improvement in their mathematics learning level and ability under the guidance of teachers and their own efforts.