Keywords: new curriculum standards, systematic principles, knowledge development order
Teaching principle is the basic requirement that teaching must follow, which is put forward according to the educational purpose, teaching process and the law of students' cognitive development. As one of the teaching principles, "systematization" pursues the integrity and continuity of knowledge structure and experience, which is a principle that should be followed in any subject teaching, especially in senior high school mathematics.
Mathematics has formed a strict system and a complete system, and knowledge is closely related. The new curriculum standard expounds the new teaching concept. Through high school mathematics learning, students can acquire the necessary mathematics literacy to adapt to modern life and future development and meet the needs of their personal development and social progress. The content of high school mathematics has also been adjusted, and the arrangement order has changed greatly compared with before. Therefore, teachers should follow the systematic principle in teaching, comprehensively and thoroughly understand the content of mathematics, grasp the coherence of knowledge, and never isolate the content of mathematics, which violates the logic and systematicness of mathematics.
First, the teaching material system and systematic lesson preparation
Mathematics curriculum standards and textbooks in ordinary senior high schools are the basis of teaching. The curriculum standard stipulates the teaching objectives, requirements and the contents of basic skills training, and expounds the arrangement system of teaching materials, teaching guiding ideology and basic teaching methods. Therefore, when preparing lessons, teachers should first seriously study and study the curriculum standards; Secondly, we should have a comprehensive view of all the teaching materials in this discipline, be familiar with the subject knowledge system, make clear the teaching objectives and requirements of each chapter and topic in this discipline, grasp the scope and depth of the teaching materials, grasp the key points and difficulties of the teaching materials, and the relationship with other disciplines, carefully design lesson preparation plans, compile semester teaching progress plans, unit teaching plans and class teaching plans, and prepare lessons for the semester before the unit; Finally, every class should be previewed to avoid watching, previewing and teaching every class, so as to enhance the planning and systematization of teaching.
Second, the systematic teaching content and teaching process
Teachers must master the teaching content system, grasp the relationship between knowledge, and reflect it well in the teaching plan, pay attention to highlighting the key points and difficulties, and ensure the systematic integrity of students' knowledge. In teaching new lessons, on the one hand, we should pay attention to reviewing and consolidating the existing knowledge and connecting with the old knowledge, on the other hand, we should prepare for the follow-up knowledge and infiltrate the later content or methods into the previous knowledge. The connection of knowledge depends on concepts, theorems and exercises. Therefore, teachers should study the teaching materials carefully, consult relevant materials, study and scrutinize carefully, understand what problems will be found in the process of mastering and applying knowledge, and what knowledge will be used, so as to clarify the status and role of concepts, theorems and exercises, master the logical relationship of these knowledge, and arrange the teaching materials in a planned way to make the contents of each part connect with each other. For example, monotonicity and parity of functions in senior algebra are both important and difficult. The textbook of Jiangsu Education Edition ranks it behind the concept and image of function, with the purpose of strengthening the understanding of specific functions and abstracting the general conclusion, that is, the dialectical thought from concrete to general. Therefore, teachers should follow this systematic principle.
This section should consciously infiltrate the ideas of monotonicity and parity into the language to lay the foundation for the next section. When talking about the properties of linear function and quadratic function, guide students to analyze the language narrative mode that "in the first quadrant, the function value increases (or decreases) with the increase of x value": first, it is reflected in the image, and in the first quadrant, the image rises (or decreases) with the increase of x value; Secondly, it is abstracted as follows: for any two independent variables x 1 and x2 in the interval (0, +∞), when X 1 >; X2, there is always f(x 1)>F(x2) or f(x 1)2). In this way, the nature of the function has actually been analyzed in the form of monotonicity definition, but the concept of monotonicity is not clear. In the next class, by reviewing this property, the definition of monotonicity is naturally introduced, which not only consolidates the old knowledge, but also enables students to understand the properties of linear function and quadratic function from a higher level, and also allows students to intuitively accept new concepts, give consideration to both before and after, and maintain the continuity of knowledge.
When analyzing the image of a function, we can consciously analyze the shape of the image of the function: we find that one kind of image is symmetrical about the Y axis; The other image is symmetrical about the origin; There is also an image that is neither symmetrical about the origin nor symmetrical about the Y axis. What properties do the image features of these three types of functions reflect? It paves the way for stimulating students' curiosity and lays the foundation for the next teaching of functional parity.
Teachers should not absolutize some procedures in the basic stage of classroom teaching, but should choose and determine the optimal lecture order according to the characteristics of teaching materials, students' understanding level and learning level, and arrange the teaching process systematically and reasonably. The overall arrangement order must be organized in a gradient pattern from shallow to deep, from easy to difficult, from near to far, from simple to complex. For example, students often use triangle knowledge when learning "Preliminary Solid Geometry", and considering the acceptance of freshmen's spatial imagination ability, Jiangsu Education Edition can explain compulsory 4 first, then compulsory 2, so as to make the development order of students' knowledge more systematic.
Third, systematic training of basic knowledge and ability.
Basic knowledge and skills are the foundation of mathematics, as well as the foundation of cultivating thinking and improving ability. The new curriculum standard emphasizes the formation and development of knowledge and ability. Therefore, teachers should first strengthen the "double basics" training, attach importance to teaching materials, and avoid putting the cart before the horse. They think that the basic concepts are simple and pass by, but they spend their time doing a lot of review questions and exercises, which violates the systematic principle. In fact, any concept and basic exercise in the textbook can play an important role in solving problems and cultivating thinking. Teachers should be able to find their own value through simple appearances and keep the basic knowledge and training ability systematic.
For example, the problem of finding the plane angle of dihedral angle in required course 2 of solid geometry published by Jiangsu Education Press is the focus and difficulty of the textbook, and it is also the basic skill that students must have. The students have always had a headache about this problem. Therefore, after defining the concept, the teacher can guide the students to systematically summarize and extend the exercises appearing in the textbook, and sum up various processing methods for finding the plane angle of dihedral angle. Textbook Required 2 Exercise 3 on page 45, "A plane is perpendicular to the edge of dihedral angle, and the angle formed by its intersection with two edges of dihedral angle is the dihedral angle", Exercise 6 on page 46, find the degree of dihedral angle, take one point of one surface of dihedral angle as the perpendicular of the other surface, and use the theorem of three perpendicular lines and the inverse theorem to make the dihedral angle. Teachers use the systematic arrangement of textbooks to guide students to learn basic knowledge, and sum up several methods to find the plane angle of dihedral angle, which can make students accept it naturally, and at the same time strengthen the cultivation of ability, and the effect is naturally much better than that of teachers without textbooks to talk about exercises. For example, after the slope of a straight line is finished, the textbook is equipped with exercises: "Judge whether A (- 1, 4), B (2, 1) and C (-2, 5) are on the same straight line." At this time, students can judge by "the slopes of straight line AB and AC are the same, so three points are on the same straight line", or by learning AB+CA=BC to judge by the distance between two points. The textbook immediately gives an exercise after the required 4 "Plane Vector Representation" section: "Knowing three points A(0, -2), B(2, 2) and C(3, 4) and verifying the straight line of A, B and C" can be proved by vectors or fixed points, indicating that the arrangement of the textbook is based on systematic principles and integrates basic knowledge. Teachers guide students to sum up and combine the knowledge of plane geometry to get a method to prove that the area of a triangle composed of three points is equal to zero. On the basis of students' practice, it is helpful to systematically summarize knowledge, so that students can master knowledge and mathematical thinking methods systematically, which is helpful to improve their ability.
Fourth, guide students to study systematically.
Teachers should systematically impart knowledge and necessary routine training, cultivate students' good habit of learning knowledge in a down-to-earth and systematic way, and learn the ability to plan learning activities reasonably. An important aspect of systematicness is the integrity of knowledge. Let the student union systematically summarize the origin, function, relationship and development of knowledge points, and form a good knowledge integrity. Considering the students' acceptance ability, some systematic mathematical thinking methods are arranged in the corresponding chapters, which penetrate into the specific contents such as theorem proof, formula and example solution. Therefore, teachers should guide students to be good at systematic summary and form a system of some fragmentary knowledge in teaching. For example, the idea of substitution is carried out in the whole mathematics, from auxiliary variables, auxiliary equations, auxiliary sequences and auxiliary functions in algebra to auxiliary lines, auxiliary circles, auxiliary surfaces, auxiliary bodies and parameters in geometry, all of which are concrete applications of substitution thought; Furthermore, through "substitution", algebraic problems can be transformed into triangular problems and solved by trigonometry, or triangular problems can be transformed into algebraic problems and solved by algebra; Similarly, the combination of numbers and shapes is also the concrete embodiment of the idea of substitution. In teaching, especially in the general review, teachers must pay attention to the systematic analysis of the mathematical thought and method system in the textbook, and cultivate and improve students' ability to systematically analyze and solve problems. Systematic arrangement is not only to be done in the review class, but also to conduct systematic and planned comprehensive summary training for each chapter, section, question and point of view.