1, the difference between junior high school and primary school mathematics
1. 1? A leap from arithmetic to rational number
When I was in primary school, I studied natural numbers, and I was initially exposed to negative numbers, such as income and expenditure, forward and backward, and temperatures above and below zero, which laid a certain foundation for the establishment of the concept of rational numbers.
In addition to the concept, the operation of rational numbers is also very different from elementary school arithmetic. It is not only based on the operation of arithmetic numbers, but also interfered by the inherent thinking set of arithmetic numbers. For example, a similar error "-7+3=- 10" often occurs. In learning, we should first pay attention to the operation law of rational numbers, deeply understand the law, and make clear the difference and dialectical relationship between natural symbols and operation symbols. Only in this way can the interference of this mindset be ruled out. Secondly, we should also closely follow the "symbol first, then numerical value" to carry out intensive training, constantly correct the operation errors, find out the reasons for the errors, and make a smooth transition from arithmetic operation to rational number operation.
1.2 leap from simple algebra to letters
The simple equation of senior elementary school has introduced the rudiment of letter algebra, such as the length of a rectangle and the width of B, and find the area of this rectangle. Like this kind of problem, primary school students have been able to master it well, which has laid a certain foundation for sequential algebra. However, the meaning of letters has changed in the first-year algebra. Many students have some difficulties in understanding the characteristics of letter algebra, such as arbitrariness, limitation, constraint, existence, integrity and superiority, which generally takes a long time to adapt and understand. In learning, we should compare and introduce gradually and deepen our understanding step by step. For example, this question: If ab>0 determines the situation of A and B, many students' first reactions are a>0 and b>0. It is necessary to realize that when A and B are specific negative numbers, the product can also be positive. Extend it to the general case, that is, ab>0 is listed as>0 and b>0, or a < 0 and B.
1.3 Different application problems
In primary school, teachers first write down the concept of application problems and a certain type of problem-solving methods for students to remember, and then keep answering this type of problems, often students can answer them quickly. However, once the face of the application question changes slightly, many students will often be at a loss. This is mainly because the ability of reverse thinking in the use of arithmetic methods is high, and the teaching of solving practical problems is slightly lacking among primary school students, which casts a shadow on the teaching of applied problems in middle schools and produces certain psychological obstacles.
1.4 the transition from equality to inequality
In primary school, students are only exposed to equality, but in junior high school, they have to learn inequality. From equality to inequality, they often don't accept it quickly. When many students learn inequalities for the first time, they often can't understand the essence of inequalities correctly, and they will solve them wrong. In this way, there will be differentiation in learning.
? Therefore, in view of the above differences between junior high school and primary school mathematics, how to effectively prepare for junior high school mathematics?
2 junior high school mathematics teaching objectives
2. 1 Cultivate students' ability to learn to construct knowledge context.
On the one hand, it is convenient to sort out complex knowledge nodes, on the other hand, it is also conducive to deepening the impression of knowledge points.
For junior high school mathematics, mathematical concepts are very important. It is the starting point of constructing knowledge network, and it is also the focus of frequent examination in mathematics. Therefore, we should master the concepts, classifications, definitions, properties and judgments of numbers, formulas, inequalities, equations, functions, parallel lines, triangles, quadrangles and circles in algebra, and apply these concepts to solve some problems.
2.2 Cultivate students' ability to stand on textbooks at all times.
? Whether it is the review of junior high school mathematics or any other subject, it is the most basic and important link to base on textbooks and consolidate basic knowledge at any time.
Especially in the process of reviewing mathematics, we should not only lay a solid foundation, but also pay attention to the deepening of knowledge, pay attention to the internal connection and relationship between knowledge, incorporate new knowledge into the existing knowledge system in time, and gradually form and expand the knowledge structure system. In this way, when solving a problem, we can retrieve relevant information from the memory system from the information provided by the topic, choose the best combination information, find a solution to the problem and optimize the problem.
2.3 Cultivate students' habit of setting wrong problem sets.
As far as mathematics is concerned, one of the key points of learning is to comb and study the usual mistakes repeatedly and deeply, so this requires students to write down their usual mistakes and find out the reasons. In this way, while strengthening knowledge points, it can also broaden personal problem-solving ideas.
Especially on weekends or holidays, students should often come up with wrong problem sets to learn the reasons for thinking about mistakes, how to correct them and so on. Then the teacher should guide students to do a certain number of math exercises, accumulate experience in solving problems, sum up ideas for solving problems, form ideas for solving problems, give birth to inspiration for solving problems, and master learning methods.
2.4 Guide students to strengthen the memory and clever use of commonly used mathematical formulas.
In junior high school mathematics examination, nearly 70% of the questions are based on commonly used mathematical formulas, and the remaining 30% are variants of commonly used formulas.
Therefore, strengthening the use of commonly used mathematical formulas will have a multiplier effect on students' problem solving. Coupled with clever use, the effect must be much better than burying your head in a lot of practice.
2.5 Correctly and effectively guide students to do more questions.
Doing problems effectively can not only broaden students' thinking of solving problems, but also improve the speed of solving problems subtly. In practice, in addition to doing basic training questions, we can also do some comprehensive questions to develop the habit of reflection after solving problems. Reflect on your own thinking process, knowledge points and problem-solving skills, the advantages and disadvantages of various solutions, and the vertical and horizontal relations of various methods.
After completing the questions, students should be guided to summarize the mathematical thinking methods used in the questions, and the questions with similar methods should be compiled into a group, which will be refined and deepened continuously, so that students can draw inferences from one another. Then gradually learn to observe, experiment, analysis, guess, induction, analogy, association and other ways of thinking, take the initiative to find problems and ask questions.