At present, the new characteristics of adapting to the new curriculum mainly include:
(1) In the field of numbers and algebra, law consciousness will become the mainstream. "Law Consciousness Test" helps to guide students to explore consciously in the usual learning process, so that students can better understand the significance and role of algebra in the process of independent exploration and cultivate students' inquiry ability. In recent years, the law consciousness test questions have been reflected in the mathematics test questions of the senior high school entrance examination in various places.
(2) In the field of geometric proof, the difficulty of test questions is reduced, and it will shift from previous argumentation to discovery, speculation and inquiry. Let students ask questions from common geometric figures, and discover mathematical laws by exploring questions. In algebra, with the increasing popularity of computer application, the requirement for computing power has decreased, especially some complicated and difficult calculation problems have not appeared, and the calculation amount of mathematics problems in the senior high school entrance examination is very small, which is also a trend of the proposition of the senior high school entrance examination.
(3) The test questions to examine the innovative consciousness and practical ability will become the direction of the proposition. Open and inquiry questions help to examine students' thinking ability and innovative consciousness, increase innovative questions and highlight the openness and inquiry of questions, which has become one of the hot issues.
(4) Pay attention to real life and attach importance to subject learning. In recent years, many test questions are not limited to the examination of knowledge itself, but focus on creating novel situations and examining students' ability to use knowledge flexibly to solve problems in specific situations.
Review is mainly based on textbooks.
Some suggestions:
1. Pay attention to the consolidation and improvement of basic knowledge and methods.
Although there have been many new questions in the senior high school entrance examination mathematics in recent years, the traditional basic questions still account for a large proportion of the scores. In the first stage of preparing for the senior high school entrance examination, we should take textbooks as the blueprint. In particular, the review of basic questions should be achieved through the review of typical examples and exercises.
2, pay attention to the use of knowledge and skills to analyze and solve problems.
Actively participate in observation and experimental activities, and complete the conjecture and proof of knowledge through comparison, analysis, induction, analogy and abstraction. This can not only deepen the understanding of knowledge, but also learn creative strategies and methods.
3. Strengthen simulation exercises, and strengthen the mastery of knowledge and the accumulation of training in answering questions in terms of speed, rhythm and experience. , and training test ability. Some students usually get good grades, but they don't do well in the exam. This problem can be solved by strengthening training. Use the test paper with the same structure as the senior high school entrance examination paper for simulation training. When reviewing, we should pay attention to standardized training, answer questions in strict accordance with the requirements of the senior high school entrance examination, answer questions in a standard format, and correct bad habits in the process of answering questions.
4. Correctly treat the content deleted from the new outline.
On the one hand, the revised outline omits the use of chord tangent angle theorem, intersecting chord theorem and line cutting theorem in relevant proofs; Accordingly, the plane geometry test questions turn to examine students' understanding and reasonable reasoning ability of geometric facts, which obviously reduces the difficulty of geometry test questions. On the other hand, it weakens the special investigation of quadratic equation knowledge in algebra, and only needs to solve simple quadratic equation with numerical coefficients. However, knowledge points can be reduced, thinking methods have not been reduced, and students should treat them correctly.
Math: The total number of questions is reduced, but the numbers and words are combined. You should learn to "discard the false and retain the true"
Examine the information processing ability in real life.
Compared with the original compulsory education syllabus, the new curriculum standard of mathematics pays more attention to cultivating students' independent inquiry ability and strengthening mathematics application consciousness. This year's senior high school entrance examination will inevitably strengthen these aspects, which need our attention.
First, from the perspective of the types of questions, the total number of questions decreases, mainly because the number of multiple-choice questions for objective questions decreases, but the number of subjective questions increases, so as to better examine the process of students' mathematical thinking and the level of solving mathematical problems by using mathematical language;
Secondly, from the perspective of the proportion of each knowledge sector, statistics and probability, practice and comprehensive application are listed as separate knowledge fields, which obviously increases the weight of these two contents, from which we can see that practicality and comprehensiveness will be the direction of this year's proposition;
It is very important to change the wrong idea of ignoring statistical content in the review process, strengthen the training of information screening and sorting from pictures, tables and words accurately, and improve the information processing ability.
Thirdly, from the examination goal, in the knowledge field of space and graphics, the requirements of geometric proof are reduced, and the contents that need to be operated by hands, such as ruler drawing, view and projection, graphics and transformation, are added to examine students' comprehensive application ability of knowledge.
You should have ideas to solve problems.
Let's give an example to illustrate the idea.
Through experimental research, experts found that the number of attention indicators of the audience at a venue changed with the change of the speaker's speech time. At the beginning of the speech, the audience's interest surged. For a while, the audience's interest remained stable and then began to disperse. The function image of the audience's attention index number y changing with time x (minutes) is shown in the following figure (the greater the Y, the more attentive the audience is). When 0≤x≤ 10, the image is a part of a parabola; When 10≤x≤20 and 20≤x≤40, the image is a line segment.
(1) When 0≤x≤ 10, find the functional relationship between the number of concerned indicators y and time x;
(2) Wang Biao needs to give a 24-minute speech when running for the post of student union cadre. Ask him if he can make proper arrangements so that when listening to his speech, he will pay attention to no less than 36 indicators. If yes, please write down the time period he arranged; If not, please explain why.
Analysis: This is a function reading problem combined with the actual situation. Connecting with the reality of life and strengthening the consciousness of mathematics application is the biggest reform of the new curriculum standard, and it is also the focus of the senior high school entrance examination. Moreover, this kind of test questions not only combine with practice, but also can examine students' reading comprehension ability, observation and analysis ability, abstract generalization ability and so on, so it has become a hot spot in the senior high school entrance examination in recent years.
This topic requires students to analyze and calculate data according to the image of the function. The main mathematical knowledge examined is the related knowledge of functions, such as finding the resolution function by undetermined coefficient method, and the meaning of abscissa and ordinate of each point on the image.
Although the knowledge points are very basic, the score of this question is not high. On the one hand, students can't clearly understand the meaning of the question, the meaning of "24 minutes" and "the number of indicators to pay attention to is not less than 36" in the conditions, and they can't be correctly applied to piecewise functions; On the other hand, in question (2), "the number of concerned indicators is not less than 36" is written as "y≥36", and the calculation is also difficult. Many students can't solve the corresponding inequality. In fact, if we can combine graphics and convert y≥36 into a function image when the ordinate of a point is not less than 36, the problem will be solved.
When solving this kind of problems, we should first carefully read and sort out the context of materials, then find the relationship between quantities and establish appropriate mathematical models (such as equations, inequalities and functions). In the review, we must change the emphasis on formal questions and proof questions, ignore the actual situation, and strengthen appropriate training to solve practical problems.
In addition, open questions, inquiry questions, etc. Must master, because of the limitation of space, not much to talk about. As long as we are in the sprint stage before the middle school entrance examination, strictly follow the examination implementation rules, rely on textbooks, review and practice in a targeted manner, lay a solid foundation and attach importance to our own abilities, every candidate will certainly achieve excellent results in this year's middle school entrance examination mathematics.
The review time of senior high school entrance examination is tight and the task is heavy. How to improve the efficiency and quality of review in a short time is a concern of every junior high school student. To this end, in view of the general review of mathematics in the senior high school entrance examination, I will talk about some of my own ideas for your reference.
Prevention of Deviation (1) Research on the Detailed Rules of Proposition Mathematics for the Senior High School Entrance Examination in 2006 will continue the propositional thinking of these years, attach importance to grasping mathematics as a whole, use mathematics flexibly, emphasize application, ability and innovation, and realize seamless "soft docking" with the new curriculum standards. In the whole general review process, we should reflect on our review contents from time to time according to the detailed rules and sample papers to prevent deviations and adjust the review direction at any time.
Leave no hidden dangers (2) Clarify concepts, lay a solid foundation and form a framework.
In the general review of the senior high school entrance examination, we must summarize and sort out the knowledge points of the teaching materials and form a knowledge network. Never neglect the memory and analysis of the most basic concepts, axioms, theorems and formulas when doing math problems. In particular, multiple-choice questions need a clear concept to distinguish right from wrong. If the concept is unclear, you will feel ambiguous and eventually lead to the wrong choice. Therefore, it is necessary to sort out the concepts in the teaching materials, and thoroughly understand the concepts that are easily confused, leaving no hidden dangers. Some students just didn't notice this and paid a heavy price.
(C) Pay attention to the induction of mathematical thinking methods
Mathematical thinking method is the essence of mathematics. Although there is no special chapter in the textbook, it permeates the whole process of mathematics in junior middle school for three years, and it is a higher level mathematics with mathematical knowledge as the carrier. In recent years, Hangzhou senior high school entrance examination questions attach great importance to the examination of mathematical thinking methods, including the combination of numbers and shapes, functional equations, transformation, analogy, association, analogy and induction, classified discussion, statistical thought and method of substitution, collocation method, undetermined coefficient method, elimination method, reduction method, parameter method and construction method.
Ignoring the review and arrangement of mathematical thinking methods is one of the fundamental reasons why many students always fail to get results in review. In the general review, students should master the essence of each thinking method and the types of questions it applies, including the steps of solving problems.
Connecting with practice (4) comprehensively applying knowledge to improve one's abilities.
On the level of junior middle school mathematics ability, it mainly investigates: sense of number and symbol, concept of space, concept of statistics, ability of preliminary reasoning, ability of analyzing and solving practical problems, etc.
In 2006, the senior high school entrance examination in Hangzhou will pay more attention to the relationship between mathematics and reality, the ability to obtain mathematical information, the ability to communicate with mathematics and the consciousness of "using mathematics" and "doing mathematics". There may be more new problems such as openness, application, information acquisition, practical operation and law exploration, which require higher ability. When doing problems at ordinary times, we should deeply understand the nature of knowledge, strengthen the exercise of the ability to examine questions, and practice hot questions appropriately, so that we can be unhurried and handy after changing the expression form of the proposition.
In the review process, we should pay special attention to reflection and summary, such as the experience and lessons of review and the experience of solving problems. Compiling a set of wrong questions for deep error correction is an effective review method proved by many students. Carefully analyze your previous exams, especially the important exams and mock exams starting from the next semester of Grade Three, find out the reasons and correct the mistakes. You can cut and paste the test paper again, classify and compare it, and find out the * * * problems in your review.