As the old saying goes: "A good beginning is half the battle." However, after entering middle school, some students who were originally good at mathematics in primary school plummeted. This phenomenon has troubled me for a long time. This time I taught a class of sixth-grade students studying in junior high school. Through careful comparison and thinking, I found that the reason for these phenomena was that the students did not make a good transition between primary school mathematics and junior high school mathematics. How to help first-grade students adapt to middle school mathematics learning more quickly. I think we should pay attention to the connection between primary and secondary school mathematics and the cultivation of students' good mathematics methods. Grades 1, 6 and 7 seem to be the same grade separation, but they are actually a leap from elementary school to junior high school. The "Mathematics" textbook for the first grade of junior high school involves preliminary knowledge of numbers, formulas, equations and geometry. These contents are related to arithmetic numbers, simple equations, arithmetic problems and simple graphics in primary school mathematics. However, the content of mathematics for the first grade of junior high school is more detailed than that of elementary school. To be rich, abstract, and complex. Therefore, we must pay attention to the connection between primary and secondary school mathematics in the learning process. 1. From "arithmetic numbers" to "rational numbers" From "arithmetic numbers" to "rational numbers". This seems simple to us now, but it is a big problem for students who have just entered middle school. Problems such as sign changes, absolute values, opposite numbers, and number lines in the calculation of negative numbers cannot be solved when encountering some difficult problems. Therefore, the transition from arithmetic numbers to rational numbers is a major turning point. To this end, the following points must be grasped: (1) Clarifying the quantities with opposite meanings is the key to introducing negative numbers. We can understand the necessity of introducing negative numbers and the significance of negative numbers by giving more familiar practical examples. For example, how to distinguish between above-zero temperature and below-zero temperature, two quantities with opposite meanings? You can give more examples in your study to understand that in order to distinguish between quantities with opposite meanings, a new number must be introduced - negative numbers. (2) Gradually deepen the understanding of rational numbers. First, clearly understand the fundamental difference between rational numbers and arithmetic numbers. Rational numbers are composed of two parts: the symbolic part and the numerical part (ie, arithmetic numbers). In this way, it is much easier to understand the concept of rational numbers and master operations. Secondly, it is clear that the classification of rational numbers is only more negative integers and negative fractions than the arithmetic numbers in primary school. (3) The operations of rational numbers are actually composed of two parts: the operations learned in primary school plus the "symbol" determination learned in middle school. , as long as special attention is paid to the determination of the symbols, then the operation of rational numbers will not become difficult. (4) Understand the concepts carefully and do more exercises. This can be said to be the basis of junior high school mathematics. If you don’t understand the basics well, you will be completely confused when you learn the later content, and you will have to look back later. 2. From "numbers" to "formulas" In six years, primary school students mainly learn specific numbers and operations between specific numbers. In the first grade of junior high school, they are exposed to the use of letters to represent numbers and establish the concept of algebra. In our mind, "algebra" means using letters to represent a number, but in fact it is anything but that. Algebra is divided into elementary algebra and advanced algebra. The real meaning of elementary algebra we are learning now is very complicated, so I won’t go into details here. In the first grade of junior high school mathematics, we first talked about "using letters to represent numbers", and then started to delve into "equations". From this, we learned the concept of "formulas containing letters", and then started learning about "functions". In fact, careful people will find that the content learned in junior high school is mostly an expansion of the content in primary school. This is especially noticeable in the changes in "number" and "formula".
It can be said that from the special and concrete numbers of primary school mathematics to the general and abstract algebraic expressions of middle school, this is a leap in mathematical thinking. Therefore, when learning, students must gradually be guided to pass this level. (1) The necessity of using letters to represent numbers. Take the examples of using letters to represent numbers that we learned in elementary school, such as: the commutative law of multiplication ab=ba and some formulas such as the speed formula v=s/t. The formulas for the perimeter and area of ??a square, l=4a, s=a2, etc., illustrate that numbers represented by letters can express the relationship between quantities concisely and concisely. It is easier to research and solve problems. (2) Deepen our understanding of the letter a. Because we do not fully understand the meaning of the number represented by the letter a, we often mistakenly believe that -a must be a negative number. Therefore, we must understand the meaning of a in learning and know that a may be a negative number, and -a is not necessarily a negative number, etc. First of all, we need to understand the three functions of the symbol "-". ①Arithmetic symbols, such as 27-6 means 26 minus 6; ②Property symbols, such as -9 means negative 9, 27+(-6) means 27 plus negative 6; ③Add "-" sign in front of a number, Represents the opposite number of the number, such as -9 indicates the opposite number of 9, -(-9) indicates the opposite number of -9, -a indicates the opposite number of a. Then explain that a represents a rational number, which can be a positive number, a negative number, or zero. That is, including symbols and numbers, so that students can truly understand the meaning of a, -a. (3) Strengthen the training of mathematical language and sequence algebraic expressions. For example: if a is a positive number, it is expressed as a>0, if a is a negative number, it is expressed as a<0, 8 times a certain number a is expressed as 8a, etc. Therefore, students can find out the "number" and "formula" under the guidance of the teacher. "The internal connections and differences between them build a bridge of connection between knowledge and lay a solid foundation for the following content. Only in this way can we remain calm in the face of numerous exams and be able to handle them with ease. 3. "Arithmetic solution" to "equation" In elementary school, arithmetic solution is used to solve word problems. The so-called "arithmetic method" refers to an equation composed entirely of numbers and symbols. Because of the simplicity of calculation, it has become the method for students to solve problems in the past six years of elementary school. The "main course", even if you learn equations in elementary school, can only be regarded as a "side dish". But it was different after entering junior high school: after learning linear equations in detail in the first semester of junior high school, gradually, the first reaction to any word problem was to set up equations of unknown sequences, and I had no impression of the original "arithmetic method". This is because using arithmetic to solve word problems mostly requires reverse thinking, while middle school requires formulating equations. The arithmetic solution is to put the unknown quantity in a special position and try to find the unknown quantity through the known quantity; and the equation is to put the required quantity and the known quantity in an equal position to find the equivalent relationship between the quantities. , establish an equation to find the unknown quantity. In addition, the arithmetic solution method emphasizes the set of types, while the equation series emphasizes the flexible use of knowledge and the ability to analyze and solve problems. This is a major turning point in the way of thinking. However, students are often accustomed to using arithmetic solutions at first, and are not comfortable with algebraic solutions, and do not know how to find the equality relationship. Therefore, it is necessary to make a good connection in this aspect during study. It is necessary to understand that it is not convenient to use arithmetic solutions to some problems. It is better to use algebraic solutions. As long as the equality relationship is found, the equations are expressed by equations, and then the equations are listed. By solving equations, you can find the value of the unknown. 2. Good learning methods can not only ensure the improvement of students' knowledge level, but also enable students to fully develop their abilities. The cultivation of good mathematics learning methods is one of the teaching tasks of mathematics teachers. After the first year of junior high school, many good learning methods in primary schools should be continued. I think they should also be cultivated in the following four aspects: 1. Listening guidance. Primary school textbooks have simple content and long class hours. Xuesheng's learning is mostly based on simple imitation, and students lack thinking when learning. Therefore, in the first grade of junior high school, students must be trained to think, ask questions in a timely manner and take class notes when listening to classes. 2. Calligraphy guidance: The writing format of junior high schools is strictly different from that of primary schools. For example, when solving a problem in middle school, the first step must be to write "solution" or "proof". Good writing habits can make students' thinking more logical. 3. "Notation" guidance. Since junior middle school students are in the primary stage of logical thinking, when memorizing knowledge, there are more components of mechanical memory and less components of understanding memory. This cannot adapt to the new requirements of junior middle school students. Therefore, attention should be paid to students. Providing notation guidance is an inevitable requirement for junior high school mathematics.
In teaching, we must first abandon "filling the classroom" to avoid students' "indigestion". Secondly, we must be good at combining mathematical reality and teaching students corresponding methods. Through analogies between knowledge, students can learn to associate and memorize. It becomes a jingle so that students can learn to use formulas to memorize. By drawing intuitive diagrams, students can learn to memorize numbers and shapes while using shapes to help students learn. By exploring and summarizing the knowledge learned, students can learn to accept the knowledge structure and memorize it systematically. Acquire knowledge through revelation. The thinking process enables students to learn step by step. 4. "Thinking" guides learning inseparable from thinking. If you are good at thinking, you will learn quickly and with high efficiency; if you are not good at thinking, you will learn poorly and have poor results. When providing guidance on thinking, we should focus on the following points; (1) Start from the "proximal development zone" of students' thinking to carry out heuristic teaching, cultivate students to think proactively, and enable students to think more and think more; ( 2) Carry out exploratory teaching by creating problem situations, cultivate students' learning habits of thinking, and enable students to learn to think deeply; (3) Carry out variant training by exploring "problem chains" to cultivate students' observation, comparison, analysis, and reduction, The ability of reasoning and generalization enables students to learn to think well; (4) Evaluation is carried out by reviewing problem-solving strategies and methods to train students to analyze and enable students to learn to reflect. In addition, we should also be good at exposing ourselves during the teaching process. The thinking process leaves a certain amount of thinking time and space, allowing students to "think about the turning points of knowledge, the difficulties of problems, the resolution of contradictions, and the fourth is the exploration of the truth", and achieve enlightenment and understanding. Integrate everything. The first year of junior high school is a critical transition period. How to make students pass smoothly is an important task during this period.