First, guide students to learn to read and cultivate their reading ability.
Liberal arts subjects need reading, and mathematics also needs to be strengthened. Only by gradual and in-depth reading can we master the subtle relationship in mathematics, develop reading ability and form self-study ability. The cultivation of self-study ability is the need of every young student's follow-up study and even lifelong self-study. Lifelong learning and lifelong education are the concepts of new curriculum standards. However, junior high school students generally can't read, especially junior one students don't have the habit of reading textbooks. So how to guide reading?
1, guide students to preview.
Students are required to read through the relevant content of each class in advance or have a general understanding of the relevant content. Therefore, teachers should prepare reading outlines in advance and send them to students, so that students can read the text with questions and outlines. Then do your own exercises in advance. The next day, the teacher checked the preview and the students listened with questions.
2. Students are required to learn comprehensive intensive reading.
Generally, when you just start learning new content, you should read the relevant content three or four times. Including knowledge points and examples, as well as questions and learning content in textbooks, are all read through. Try to make students read the text thoroughly and thickly. Intensive reading generally requires students to read concepts, definitions, theorems, laws, axioms and inferences carefully. These contents are generally concise and profound, and are the focus of mathematics, so it is required to read them carefully. Achieve the purpose of memory on the basis of understanding.
3. Ask students to do three things when reading the text: mouth, heart and hands.
Mouth-to-mouth means reading math texts fluently. Heart-to-heart refers to the understanding and profound experience of the connotation and extension of its content. A handy one is to tick off the main points while watching, or write questions next to it, or write a summary of some main points on the header.
Second, guide students to learn to participate in classroom teaching and cultivate students' exploration and innovation ability.
In the math class, whether it is the introduction of situations or the questioning in the process of learning new content, whether it is the students' mutual discussion or the teacher's correction and induction, whether it is the students' oral answers, homework exercises or summary. This series of activities embodies the teachers' ability, and then cultivates the students' learning methods and abilities. Students are participating. On the one hand, it is the accumulation and improvement of its mathematical literacy, on the other hand, it is the training of students' courage and eloquence. And the cultivation of temperament. Especially the exploration of the formation of every concept, formula, theorem, etc. , as well as the analysis and solution of each topic. It undoubtedly reflects the students' exploration process from the known to the unknown. And this process of exploring and innovating is the process of cultivating the innovative spirit and habits of every young student who will benefit for life.
Therefore, every math teacher should encourage and spur students to participate boldly. Especially those who are timid, take the initiative to ask them to answer questions or practice. And praise his good thinking and behavior, even if there are mistakes in answering questions or answering questions, as long as there are correct ones, they should be affirmed and praised. Because the process of exploring science itself is a process from failure to success, the success of any scientific research project has undoubtedly not condensed the exploration process and painstaking efforts of researchers. Therefore, math class allows students to participate in classroom teaching freely. Cultivating students' ability is our mission entrusted by history.
Third, guide students to learn various thinking methods and cultivate their ability to analyze and solve problems.
Every math teacher knows that every student who receives math education doesn't have to use what he has learned in his future work, but math is a gymnastics to exercise his thinking, leaving students with thinking methods and abilities. This is the charm of mathematics. Therefore, students should learn to learn all kinds of thinking methods of mathematics and cultivate their ability to analyze and solve problems.
1, analysis, analogy, induction
Many concepts in junior high school mathematics are descriptive definitions, and many laws are obtained through a lot of fact analysis, analogy and induction.
For example, a large number of quantitative analysis and induction with opposite meanings introduce the concept of negative numbers. The direction of travel. The rational number algorithm is analyzed and summarized. There are two quantities that change a lot in life, and then the concept of function is summarized. The nature of the score is obtained by analogy with the nature of the primary school score, and the algorithm of the score is obtained by analogy with the algorithm of the score. A large number of facts show that thinking such as analysis, analogy and induction can be seen everywhere in mathematics. Therefore, in teaching, we should not only use these thinking forms, but also point out the mystery of this thinking form to students repeatedly. Let students use this form of thinking in solving problems and understanding mathematical knowledge.
2, from special to general, from general to special.
In mathematics, from special to general, or from general to special, is also a thinking form that can be seen everywhere. For example, the distribution law of the first multiplication is a general operation law induced by concrete example operation, which is used for concrete calculation. In geometry, general axioms are summarized by drawing concrete pictures. Or demonstrate the general theorem through concrete definitions, axioms and drawing reasoning. The general axioms and theorems, which are the basis of every reasoning, undoubtedly tell us to use things repeatedly from special to general and from general to special.
3. Observe the changing law and draw a general conclusion.
In the new curriculum of junior high school, from grade one to grade three, a series of questions related to the change of natural numbers are often arranged in exercises, and these questions generally need careful observation to draw conclusions.
For example, the number of a column: "+1, -3, 5, -7, 9 ... "( 1) What is the100th number? (2) What is the sum of the first hundred numbers?
Another example is: "A line segment inserted with one point has three lines, and a line segment inserted with two points has six lines ... Q: How many lines are there when a line segment is inserted with N points?" Such topics need careful observation, analysis, summary of general laws and conclusion.
4. Classified discussion
In the whole middle school mathematics, there are many topics that lack classified discussion. This kind of topic is more difficult for students who have just entered junior high school from primary school, and it is more necessary to guide students to learn this method.
For example, A, B and C are all rational numbers.
Another example is: "It is known that it is a right angle, and the degree is calculated." And so on, such topics should be properly arranged in mathematics, so that students can practice and learn to discuss and solve problems in categories. Otherwise, you will miss the answer.
5. Seek conclusions from conditions and conditions from conclusions.
This kind of thinking is often used in deductive reasoning of geometry. Generally speaking, it is easy to draw conclusions from conditions. On the contrary, it is relatively difficult to seek conditions from the conclusion. But in geometric problems, the necessary conditions are generally found by the conclusions to be proved or calculated. Therefore, in geometric argumentation, teachers should introduce more backward methods for students to experience.
6. Read the topic carefully and find the equivalence relation.
It is difficult for junior high school students to solve application problems through column equations. In teaching, we not only introduce the routine of solving application problems with equations, but also often tell students to break through and find equivalence relations. There are two difficulties in equations: one is to find a sentence with equivalent relationship. Second, pay attention to reading the topic carefully and think about which quantities are known, which quantities are unknown, and which are implicit conditions or equivalent relationships. Regular training will break through this difficulty.
Fourth, guide students to learn to review and summarize, and cultivate their ability to understand things comprehensively and systematically.
We all know that reading through the text is to make the text thicker, and reviewing and summarizing is to make the text thinner. Review the past and learn the new. Only by systematic and comprehensive review and summary can we form a chain of knowledge, remember it deeply and understand it deeply. But junior high school students will not review and summarize. Besides introducing some methods to them, our teachers should also urge students to review and summarize after each class, unit and chapter.
First of all, before previewing each new lesson, or before doing homework, we must screen the knowledge we learned that day and remember it in time by using the memory law. Stick to the habit for a long time.
Secondly, we should tell students that we must look for a clue to review and summarize knowledge, and connect knowledge through this clue, so that knowledge points can form a string and be stored in our minds. This clue can be a knowledge structure diagram or a written statement of the adjacent relationship.
Thirdly, after each chapter, in addition to summarizing the knowledge, we should also summarize the topic types of this chapter. On the one hand, let students compile questions to summarize the types, on the other hand, the teacher writes examples for students to observe and answer, and systematically summarizes the test center area. Train the topics in the textbook in variant form, so as to draw inferences from one example to another. Form a comprehensive summary. Learn the ability to observe things comprehensively and systematically.
Five, guide students to learn mathematical language, cultivate students' mathematical language expression ability.
Chinese class has written language and spoken language. Mathematics also has a language of expression. It includes written narrative language, symbolic expression language of concepts and theorems, logical reasoning language for solving problems, graphic expression or drawing language in geometry and list narrative language. Therefore, the text narration, symbol expression and chart description in mathematics constitute a colorful mathematics kingdom and a fascinating internal thinking form. Therefore, to learn mathematics well, it is obvious to learn the expressions of these languages. You should not only know these languages, but also express them. In order to achieve this goal, we ask students to do the following:
1. Understand the connotation and extension of each concept. Understand the meaning of reading various symbols.
Mathematics is characterized by many concepts, symbols and figures, and its language is abstract, rich and special. Therefore, when strengthening the "double basics" training, on the one hand, students should be allowed to practice and consolidate from both positive and negative directions; ; On the other hand, students are required to memorize on the basis of understanding, especially to understand the preconditions of each concept and theorem.
2. Successfully passed the introductory geometry teaching.
O
B
C
A
The first thing is to have a good concept of speaking like a book. For example, there are many words in geometry, such as "only one", "congruence" and "similarity", which students must understand. The second is through the translation of language and symbols. Building a Bridge on Graphics, Language and Symbol Expression-"Translation". Such as language: a ray divides an angle into two equal angles called the bisector of the angle. The figure is as follows:
Symbolic expression:
The third is to polish your eyes through graphics. Plane geometry comes from life, higher than life, and the graphics are rich and colorful. Only by careful observation and understanding can we recognize the internal forms of graphics, such as rectangle, parallelogram, square, diamond and trapezoid. Both have their own characteristics and have the same characteristics. So you need to savor it.
At the same time, we should guide students to learn to observe the graphics in life, and organically combine the graphics in life with the graphics learned in geometry, thus forming both perceptual and intuitive life graphics and rational geometric graphics.
3. Teach students to develop a standard writing language for logical reasoning and solution in their homework. And graphic expression language.
Whether algebra or geometry, its reasoning form is very strict. Every step needs to be justified, so students are required to be justified step by step and understand every word in their homework. For example, the calculation of numbers in algebra must be based on laws and concepts. The solution of equations should be based on the properties of equations and the arithmetic of numbers, and the reasoning and solution in geometry should be based on definitions, formulas, theorems and inferences. Otherwise, it will become water without a source and a tree without a root. When drawing, you should not only be familiar with all kinds of conventional drawing sentences, but also draw with a ruler. Otherwise, "Fiona Fang cannot be achieved without rules".
To sum up, mathematics teaching under the new curriculum standard should pay attention to "double basics", and then pay attention to students' methods of learning mathematics, so as to achieve the purpose of cultivating students' ability. This work is actually a systematic project. In primary and secondary schools, especially junior high schools, it needs repeated training and tireless guidance to let students learn these methods and gradually form their abilities.