In the connection of junior high school mathematics? Steep slope effect?
It stands to reason that the first chapter of high school mathematics is a collection of related concepts. Why is this happening? I can understand the function part, but once I do it, I can't. Why? With the adjustment of junior high school textbooks several times, lose weight? . Many contents are not required to be mastered in junior high school, such as cubic difference, cubic summation formula, quadratic polynomial factorization, which is limited to the quadratic coefficient of 1, and the common problem-solving skills of inequality are basically not required. But these are still the basic requirements that high school mathematics must master, and high school teachers even think that students have mastered these knowledge, so they will not teach, but directly use it. Especially the relationship between root and coefficient is basically unnecessary in junior high school, but the final exam of college entrance examination is often necessary.
However, when we look through all the chapters in high school math textbooks, we will find a magical phenomenon, that is, we can't see it in high school textbooks at all! No wonder many freshmen are stunned by the stick as soon as they come up. The set part is bad because of quadratic inequality with parameters and complex quadratic inequality group with parameters, and the function part is bad because of quadratic function with parameters! If you are awesome and capable, you can come back to life? If it's not awesome, you can only choke on the water bit by bit, and it's a little uncertain whether you can catch your breath again. Junior high school mathematics problem-solving can be done according to a certain fixed routine mode, while senior high school is more flexible, which requires students to exercise the ability of thinking from multiple angles from now on.
That's why we have to prepare for the summer vacation, especially the math subjects! Let's take a look at many knowledge loopholes left by junior high school mathematics. You'd better master and use it skillfully during the summer vacation, and try to avoid the connection between junior high school mathematics and senior high school mathematics. Steep slope effect? . This is why we are required to attach importance to the convergence of junior high school mathematics and over-strengthen it!
Reasons and Necessity of Intermittent Teaching
Junior high school mathematics is more intuitive and application-oriented, while senior high school mathematics is more abstract and conceptual. Geometry, such as plane geometry in junior high school, is much more intuitive than solid geometry in senior high school. The angle of plane geometry is as many degrees as it looks, and the size can be judged intuitively. However, the angle in solid geometry is difficult to judge without calculation because it is a 3d perspective. Algebra, as far as our most basic function is concerned, the expression in junior high school is y=ax+b, etc. In the first lecture of senior one, I will trace back to the source, y=f(x), and explain it with a more fundamental, unified and abstract mapping. These are the deepening of abstraction and concept, and also the focus of high school mathematics thinking.
1. Due to the needs of compulsory education, junior high school mathematics textbooks have been greatly reduced; However, high school teaching does not belong to the category of compulsory education. As a close network in Luo Zhi, the syllabus of the National Education Commission Examination Center firmly sets high standards for senior high school mathematics that cannot be achieved by current textbooks, current class hours and current teaching methods.
2. As the current high school mathematics textbook, the breadth and difficulty of basic knowledge, the intensity of ability requirements and the depth of thinking methods are far from the level required by the current college entrance examination. Even so, it is still far higher than the mathematical knowledge and ability of qualified junior high school graduates, especially the quality level of mathematical thinking methods.
3. In order to minimize the difficulties that senior one students encounter in the process of completing the transition from compulsory junior high school mathematics education to senior high school mathematics, we must first make up the useful basic knowledge that junior high school mathematics owes, and pay attention to the natural transition from the actual level of junior high school mathematics to senior high school mathematics learning. Therefore, it is necessary to study the initial part of the current high school textbooks.
Because of this, the gap between the basic preparation requirements of students' knowledge in senior high school mathematics textbooks and the requirements of senior high school entrance examination is listed in detail. You can carefully compare whether you have the requirements in the list. If there is, it means that he is excellent. If not, you need to make it up quickly, otherwise it will be difficult to start school.
A little insight:
Junior high school mathematics knowledge is less, shallow and easy, with narrow knowledge, low requirements and slow progress. Junior high school teachers attach importance to intuitive image teaching, and teachers can explain exercises repeatedly. High school mathematics knowledge is extensive, which is the promotion and extension of junior high school mathematics knowledge and the perfection and sublimation of junior high school mathematics knowledge. It is demanding, fast-paced, informative and difficult, so teachers can't emphasize and rehearse repeatedly like junior high school. High school teachers emphasize mathematical thinking methods and strict reasoning. Because most high school teachers are in a small circle, most of the teachers who have just finished the first year of high school have just finished the third year of high school. The sudden change of objects makes them consciously or unconsciously demand higher standards in teaching. Therefore, the teaching methods of junior and senior high school teachers are quite different. There are higher requirements for senior high school students in learning methods, self-study ability and thinking habits. The steps are too high and there is no buffer transition. Therefore, after students enter high school, many students will soon show their inadaptability to high school mathematics learning. Therefore, the necessary transitional preparations for the connection between junior high school and senior high school mathematics teaching will play a positive role in the study of most ordinary senior high school students.
So what should we do to make a good connection between junior high school and senior high school mathematics learning? According to the above, we can preview senior high school mathematics. In the preview, we must accept knowledge from a systematic height, think about problems from a philosophical height, put the knowledge and methods of junior high school into the new senior high school system, make good use of what we have learned in junior high school, eliminate the difficulties caused by the differences between junior high school and senior high school, and enter the learning state of senior high school as soon as possible. If you find it difficult to preview, you can also consider going to a good preview class or something
There is no doubt that as long as we take precautions, make preparations early and use proper methods, we will certainly overcome the above difficulties and successfully enter the study of mathematics in senior high schools. In a word, the mathematics connection between senior high school and junior high school should be based on students' cognitive basis and requirements for students' ability. We should choose junior high school knowledge and abridged junior high school knowledge closely related to senior high school knowledge, follow the principle of gradual progress, and let students' thinking expand layer by layer and deepen gradually. Guide students' learning methods and cultivate good habits of reading comprehension, active learning and questioning. Strive to realize the role change of students from junior high school students to senior high school students as soon as possible through the guidance of our teachers.