I. Content cohesion 1. Arithmetic number and rational number
Primary school mathematics studies the problem of arithmetic numbers, and middle school mathematics has rational numbers from the beginning. Therefore, the transition from arithmetic number to rational number is a major turning point. To this end, we must grasp the following points: (1) It is the key to introduce negative numbers to clarify quantities with opposite meanings.
For example, the elevation of Mount Everest and the elevation of Turpan Basin are quantities with opposite meanings. In teaching, we can give more examples to let students know that in order to distinguish quantities with opposite meanings, a new number-negative number must be introduced. (2) Gradually deepen the understanding of rational numbers.
First, let students clearly understand the fundamental difference between rational numbers and arithmetic numbers. Rational number consists of two parts: symbol part and number part (namely arithmetic number). In this way, it is much easier to understand the concept of rational numbers and master operations.
Secondly, let students know that there are only negative integers and negative scores in the classification of rational numbers compared with the arithmetic numbers in primary schools. (3) The operation of rational numbers actually consists of two parts: the operation in primary school and the symbol judgment in secondary school. As long as special attention is paid to the determination of symbols, the operation of rational numbers is not difficult. For example, (-2)+(-4) first determines that the symbol is "-"
That is, (-2)+(-4) =-(2+4) =-6 2. Numbers and algebra
It is a leap in mathematical thinking from the special concrete mathematics number in primary school to the general abstract algebra number in middle school. Therefore, students should be gradually guided through this barrier in teaching. (1) It is necessary to express numbers in letters.
Take the numbers that students have learned in primary school as an example, such as: additive commutative law A+B = B+A; Multiplicative commutative law ab=ba and some formulas such as velocity formula V = S/T and square perimeter formula l=4a,
S=a2, etc. It shows that the number expressed by letters can concisely express the relationship between quantity and quantity, and it can be more convenient to study and solve problems. (2) Deepening the understanding of the letter A Many students often mistakenly think that -A must be negative because they don't understand the meaning of the number represented by the letter A. Therefore, they must help students understand the meaning of A in teaching and know that A may be negative, but -A is not necessarily negative.
First, let the students understand the three functions of the symbol "-". (1) operation symbols, such as 5-3 for 5 minus 3, 2-4 for 2 minus 4; ② Natural symbols, such as-1 means negative 1,
5+(-3) means 5 plus or minus 3; (3) Adding a "-"before a number indicates the reciprocal of the number, such as -3 indicating the reciprocal of 3, -3 indicating the reciprocal of -3, and -A indicating the reciprocal of A, and then indicating that A indicates a rational number, which can be positive, negative or zero. That is to say, it includes symbols and numbers, so that students can really understand A.
(3) Strengthen the training of mathematical language and column algebra, such as: A is positive, which means a>0, A > 0, and A is negative, which means A < 0.
Two times a certain number a is expressed as 2a, etc. 3. Arithmetic solution and algebraic solution
Elementary schools use arithmetic to solve application problems, while middle schools need algebraic methods (column equations). Arithmetic is to put the unknown quantity in a special position and try to find the unknown quantity through the known quantity. Algebraic solution is to put the required quantity and the known quantity in an equal position, find out the equivalence relationship between each quantity, establish the equation and find out the unknown quantity. In addition, the arithmetic solution emphasizes the type of set, while the algebraic solution emphasizes the flexible use of knowledge and the cultivation of the ability to analyze and solve problems, which is a major turning point in the way of thinking. However, students are often used to arithmetic solutions at first, but they are not suitable for algebraic solutions, and they don't know how to find equivalence relations. Therefore, in teaching, we should do a good job in this area, so that students can understand that some problems can not be solved by arithmetic, and it is best to solve them by algebra. As long as we find the equation relationship, express it with the equation, list the equation, and then we can get the unknown value by solving the equation.
Second, the convergence of teaching methods
The way of thinking of first-year students still retains the characteristics of intuitive and image thinking of primary school students. Therefore, we should pay attention to the study of primary school mathematics teaching methods, absorb its advantages, and improve teaching methods according to the characteristics of first-year students. Check for leaks, build ladders, and pay attention to the connection between old and new knowledge. 58660.68866868666
The first chapter of algebra in senior one is based on algebra knowledge in primary school mathematics. It occupies a considerable proportion in the mathematics class of grade one in primary school, and it is a systematic summary and review of algebra knowledge in primary school mathematics. But the content of this chapter is based on the objective needs of junior high school algebra learning, rather than the simple repetition of primary school knowledge. Therefore, we should pay attention to the role of this chapter in teaching. Do a good job of connecting old and new knowledge. 2. From concrete to abstract, from special to general, teaching students in accordance with their aptitude and improving teaching methods. (1) Step by Step Students need to gradually develop their abstract thinking ability after entering middle school. Freshmen are used to detailed, meticulous and vivid explanations in primary school. If they encounter a "sharp turn" as soon as they enter middle school, they will often feel uncomfortable. Therefore, in the teaching process, we should not talk too much, too fast, too abstract and too general at once, but try to use some physical teaching AIDS to make students see clearly and clearly, and gradually transition to the intuition of graphics, language and words, and finally to abstract thinking.
For example, we can teach the concept of reciprocal in the following order. ② Observe the characteristics of these groups of numbers: only the symbols are different. ③ Guide students to draw the concept of reciprocal by themselves. (2) Contrast before and after In the teaching process of algebra in senior one, proper use of contrast can enable students to quickly understand and master new knowledge.
For example, when learning linear inequality and linear inequality group, because the arrangement of knowledge system of inequality in grade one is basically the same as that of equation, in teaching, we can compare the meaning and nature of inequality and equation, the solution set of inequality and the solution of equation, the solution of linear inequality and the solution of linear equation, which not only shows their similarities, but also points out their differences and reveals their particularity. It is helpful for students to master the knowledge about inequalities as soon as possible and avoid confusion with the knowledge about equations. (3) Open up new ideas. First-year students have simple thinking and are not good at comprehensive and in-depth thinking. They often pay attention to this side of a problem and ignore the other side, only seeing the phenomenon but not the essence. The immaturity of this kind of thinking has brought difficulties to junior high school teaching, which has doubled the subjects and deepened the knowledge content obviously. Therefore, in teaching, we should give students more opportunities to express their opinions, carefully understand their thinking methods, analyze the reasons for their mistakes, and inspire students to seriously analyze problems and not to draw conclusions easily.
For example, students often mistakenly think that 2A > A.
The reason is simple: two A's are obviously greater than 1 A's.
Ignore the meaning of a, a stands for rational number, which can be positive, negative or zero, resulting in an error.
3. The relationship between study habits and study methods 1. Continue to maintain good study methods and habits.
From primary school to senior one, many good learning methods and habits should be maintained in primary school, such as sitting correctly in class, answering questions enthusiastically, raising your hand and speaking actively, and so on. 2. Guide scientific learning methods and cultivate good study habits.
Based on the study habits and methods of primary school, the first-grade students think that learning mathematics means doing homework and doing more exercises, and the textbook has become a "problem set". Therefore, in the teaching process, we should gradually cultivate students' self-study ability, guide them to preview, review and summarize, appropriately select extracurricular reading materials, cultivate interest and broaden their horizons.