Next, I will talk about the general review strategy of junior high school mathematics teaching in recent years.
The first round of review: systematic review to lay a solid foundation (March to mid-April)
1. Form of the first round of review
The purpose of the first round of review is to "pass three levels":
(1) passing memory passing. We must remember all the formulas, theorems, etc.
(2) Through basic methods. Such as the undetermined coefficient method.
(3) basic skills. If you are given a question, you can find its correct answer.
The teaching at this stage is to organize the contents of the book, chunk them and form a knowledge system. I summarized all the contents of junior high school into nine units: number and formula, equation and inequality, function, parallel line and triangle, quadrilateral, right triangle, circle, figure and transformation, statistics and probability. Supporting exercises are mainly based on "successful entrance examination". After reviewing each unit, conduct a unit test, and pay attention to filling the gaps.
2. Several problems that should be paid attention to in the first round of review.
(1) Be sure to lay a solid foundation. The first activity of our teaching and research group this semester is to study the new curriculum standard and learn the important basic knowledge, basic skills and basic thinking methods of mathematics stipulated in the curriculum standard. By analyzing the examination questions in recent three years, it can be found that the examination questions strengthen the examination of the basic knowledge of mathematics, and the proposition form is novel, avoiding tedious calculation proofs and simple rote memorization. Therefore, through review, every student should meet the requirements of "understanding" and "mastering" junior high school mathematics knowledge, and use basic knowledge skillfully, correctly and quickly.
(2) Return to teaching materials. Some basic questions in the senior high school entrance examination are original or transformed questions in textbooks, and prototypes can be found in books. So we must dig deep into the teaching materials and never leave them behind.
(3) Don't engage in sea tactics, but concentrate on perfection. "A lot of practice" is relative. It is not blind practice, nor blind practice, but targeted, typical and hierarchical intensive practice. Therefore, teachers also need to prepare lessons before reviewing lessons, focus on preparing exercises, and choose representative exercises that are easy to make mistakes to practice.
(4) Teaching students in accordance with their aptitude, that is, carrying out teaching work at different levels to improve the review efficiency in an all-round way. Classroom review teaching adopts the method of "low starting point, multi-induction and fast feedback". At the same time, we should pay attention to the cultivation of top students at this stage. Arrange an inquiry question properly every day, cultivate problem-solving skills, improve flexibility and make it "sharp"
(5) Different chapters adopt different review modes. For example, for numbers and algebra, equations and inequalities, triangles, quadrilaterals and other chapters. Students generally think that knowledge is relatively simple and proud, so I adopt the method of reviewing after taking the exam to expose students' problems, find out their own problems and review them in a targeted way. For these difficult chapters, because the last new lesson ended in a hurry, students' knowledge is not very solid, so I took the steps of reviewing the basic knowledge first, explaining typical examples, consolidating exercises, then discovering and discovering problems in time, and then checking for leaks and filling gaps in a targeted manner.
The second round of review: review of hot topics (from late April to mid-May)
1. Form of the second round of review
If the first stage is the basis of general review, focusing on double-base training, then the second stage should focus on cultivating students' mathematical ability. The second round of review time is relatively concentrated. On the basis of the first round of review, we should improve our level and increase the difficulty appropriately. The second round of review focuses on hot spots, difficulties and key contents, especially the key points; Paying attention to the formation of mathematical thoughts and the mastery of mathematical methods requires giving full play to the leading role of teachers. We can review special topics, such as Equation-based Synthesis Problem, Application Function Problem, Inequality Application Problem, Statistical Application Problem, Geometry Synthesis Problem, Exploratory Application Problem, Reading Comprehension Problem, Scheme Design, and Hands-on Operation, so that students can be familiar with and adapt to this kind of questions.
2. Some problems that should be paid attention to in the second round of review
(1) Choose the topic accurately and arrange the time reasonably. The choice of topics mainly depends on the study of curriculum standards and test questions for senior high school entrance examination. The topic should be representative, not comprehensive; The topic should be targeted, focusing on hot spots, difficulties and key points, especially the content that must be tested in the senior high school entrance examination; Arrange time according to the characteristics of the topic, work hard at important points, and be willing to invest energy at the expense of "wasting" time.
(2) The focus of special review is to reveal the thinking process. We can't increase students' practice, let alone push them into the sea of questions. It is more difficult to review special topics. Without certain difficulty, it is difficult to improve students' ability. Improving students' ability is the task of the second round of review.
(3) Pay attention to the reflection after solving the problem. After solving a problem, students must review the mathematical knowledge used in the problem, the mathematical ideas and methods embodied, the starting point of solving the problem, what basic graphics are constructed and how the methods are thought of.
Third, the third round of review: comprehensive simulation to improve adaptability (from late May to senior high school entrance examination)
1. Form of the third round of review
The form of the third round of review is to simulate the comprehensive training of the senior high school entrance examination, train the answering skills, the mentality of the examination room and develop the ability on the spot.
2. Several problems that should be paid attention to in the third round of review
(1) The key to simulation training is to select the simulation test questions, and combine the structural characteristics and proposition trends of the senior high school entrance examination mathematics papers to select the real simulation test questions. The arrangement of time, the number of questions, the proportion of low, medium and high grade questions, and the control of overall difficulty must meet the requirements of the senior high school entrance examination.
(2) After the mock exam, you should look at the paper in time, comment on it in time, and check for leaks in time. In addition, you should often talk with students, analyze the gains and losses in the exam, whether gifted students or students with learning difficulties, let them feel your concern for them, especially poor students, analyze where he can get points on the basis, and constantly encourage him.
(3) Give students some time to correct their mistakes and digest.
(4) Properly "liberate" students, especially in terms of time arrangement. After a period of exams, almost all students will feel physically and mentally exhausted. If you bring this tired state into the examination room of the senior high school entrance examination, it will definitely be a poor result. However, it should be noted that liberation is not complete relaxation, and a moderately tense mental state must be guaranteed. Maintaining moderate tension is the best state of normal or extraordinary play.
Four, the finale problem solving method guidance
After the senior high school entrance examination every year, the most talked about by teachers and students is the difficulty of geometry. In a sense, how well you do in the geometry of the senior high school entrance examination directly determines whether you can get high marks and widen the gap. Mathematics students in the senior high school entrance examination often get stuck in the questions, which are divided into multiple-choice questions-function questions and geometric calculation questions; Fill in the blanks-function questions, graphics questions, geometric calculation questions, and finding rules questions; Solve problems-geometric problems, function problems, application problems, geometric function combination problems, and innovative problems related to these knowledge. Through the above analysis, we will find that the knowledge of jam in senior high school entrance examination focuses on function and geometry. In fact, the geometric information in function graphics is difficult for students, and students will not convert geometric information into algebraic information. This is why students find it more difficult to calculate geometric problems (area calculation, side length calculation, angle calculation), and finally the finale problem is more difficult to chew.
After careful analysis, it is found that the finale questions are not so mysterious, but we need to understand the starting point of these finale questions. I think the starting point is as follows:
Cut-in point 1: the basic graph needed to construct the theorem.
In the process of solving problems, it is sometimes necessary to add auxiliary lines. Mathematics in the senior high school entrance examination does not require students to add lines. Adding auxiliary lines almost always follows the principle of constructing the graphs required by the theorem or constructing some common basic graphs. We will ask the students to find out what the basic figures are in the finale questions that students usually practice after the analysis of the whole class, so that students can easily find the "feeling" after accumulating more.
Breakthrough point 2: No congruence, no similarity, similarity and similarity.
The finale involves many knowledge points and it is difficult to transform knowledge. Students often don't know how to start. At this time, they should look for congruence or similar triangles according to the meaning of the question.
Breakthrough point 3: stick to the invariants and be good at using the methods or conclusions adopted in the previous questions.
When the movement of the figure changes, the position, size and direction of the figure may change, but in this process, there are often some two line segments, or some two angles, or some two triangles corresponding to the position or quantitative relationship does not change. The setting of geometry questions is gradual, so I often instill in students the idea of "changing the questions and changing the methods". I should be good at transferring the ideas and methods of solving the previous question to the next question and making appropriate modifications, and I should also be good at applying the conclusions already drawn from the previous question.
Point 4: Find the information of multiple solutions in the topic.
There are more than one situation in which a graph may meet the conditions in motion, that is, two solutions or multiple solutions. How to avoid missing answers is also a headache for candidates. In fact, we can find more information in the topic, which requires us to dig deep into the stem of the topic, in fact, it is repeated and serious examination.
In short, the starting point of the question is many, so you don't have to look for so many in the exam. You often only need to find one or two. The key is to dare to do it after finding it. Some students often give up when they think they can't do it. In fact, most problems can be basically solved as long as you think of the above-mentioned breakthrough point and work hard.
Pay attention to every student when they need it most-when students answer confidently in the exam, and when the good news is frequently spread after the exam, we can really hear the sound of flowers!