First of all, pay attention to the creation of teaching situation and realize the naturalization of concept introduction.
Most mathematics textbooks give concepts directly. Teachers should strengthen the introduction of concepts and guide students to experience the process of abstracting mathematical concepts from concrete examples according to the requirements of the new curriculum standards for senior high school mathematics. Setting the situation reasonably can make students actively participate in teaching, understand the background and process of knowledge development, make students feel the fun of learning, and also deepen their memory and understanding of concepts.
1. Introducing concepts with mathematical historical stories
In teaching, properly introducing stories related to mathematical concepts and skillfully handling them can not only stimulate learning interest, but also achieve the purpose of education. For example, when teaching curve equations, we talk about Descartes and Fermat; The story of mathematician Gauss when giving lectures on series; Introduce Yang Hui and others to students when talking about binomial theorem. Encourage students to explore bravely while introducing stories, and cultivate students' scientific spirit of loving science, learning science and applying science.
2. Introduce concepts with practical problems
Mathematical concepts come from practice and serve practice. Introducing concepts from practical problems makes abstract mathematical concepts close to life and easy for students to accept. It can also make students understand the practical significance of mathematical concepts and enhance their awareness of mathematical application. For example, the concept of "two planes are perpendicular to each other" can be introduced from the practical problem that the wall of a teaching room intersects the ground and the dihedral angle is right angle.
3. Use students to explore and realize the natural introduction of concepts.
Concept-based and process-oriented are the basic concepts of concept teaching. It is the best embodiment of the new curriculum concept to let students find problems in their study and solve them in a certain way. In the process of concept teaching, teachers should provide students with appropriate examples on the basis of students' existing knowledge background, ability level and psychological characteristics, guide students to observe and compare examples, make assumptions and verify concepts, and thus obtain correct concepts. For example, in the teaching of the concept of "straight line distance in different planes", students may wish to review the concepts of distance they have learned, such as the distance between two points, the distance between a point and a straight line, and the distance between two parallel lines, so as to guide students to find that the same characteristics of these distances are shortest and vertical. Then inspire students to think about whether there are such two points on two straight lines with different planes, and the distance between them is the shortest. If it exists, what are its characteristics? Through exploration, it is found that if the line segment connecting these two points is perpendicular to two straight lines in different planes, its length is the shortest, and the existence of such a line segment is confirmed by physical model demonstration. On this basis, the concept of "straight line distance in different planes" is naturally obtained. In the process of introduction, the enthusiasm of students is mobilized and the spirit of daring to discover and explore is cultivated.
Second, be good at dissecting concepts and deepen concept teaching.
Mathematical concept is to solve mathematical problems. If you don't understand the concept clearly, you will make mistakes in solving problems. If you don't understand the concept thoroughly, you will often encounter problems and be helpless. It is not easy to understand the concept correctly and profoundly, and the mathematical concept is strict and scientific. Therefore, concept teaching should enable students to accurately grasp the connotation and extension of concepts, and teachers should start from all aspects according to students' knowledge structure and ability characteristics, correctly guide students to analyze concepts and grasp the essence of concepts. In teaching, we can dissect concepts from the following aspects:
1. Emphasize the key words in the concept
For example, both "arbitrary" and "unique" in the concept of function should be emphasized. Then, for example, the former can be called the function of, and the latter can't be called the function of. Because for any one, it is not unique. In this way, we can emphasize the key words in the concept through positive and negative examples and deepen our understanding of the concept.
2. Pay attention to the translation of mathematical language
Mathematical languages include written language, symbolic language and graphic language. Symbolic language is universal and can better reflect the essence of concepts. For example, arithmetic progression's concept can be summarized by the symbol ""(constant). When a sequence is defined and proved to be arithmetic progression, it is the symbolic language of applying concepts. Graphic language can reflect the content of concepts more vividly. For example, when talking about the concept of "intersection", it is easy to understand the concept by using venn diagram to represent "A B".
3. Pay attention to the comparative analysis of similar concepts
It can only be identified by comparison. Finding out the similarities and differences of confusing concepts by comparison is helpful for students to distinguish concepts and gain accurate and clear understanding. For example, concepts such as classified counting principle, step-by-step counting principle, permutation and combination can be deepened through concept comparison and examples.
Third, carefully design exercises to realize the continuity of concept teaching.
The main purpose of mathematics concept teaching is to make students use knowledge to solve mathematics problems, improve mathematics ability and improve students' quality in an all-round way on the basis of understanding concepts. Therefore, practice design must be accurate and targeted to improve students' ability.
1. Strengthen the analysis of the causes of application concept errors.
Many concepts themselves are problem-solving methods. For example, the concept of "inverse function" has already embodied the solution of the inverse function: the inverse solution-will and-indicate the domain of the inverse function (determined by the value domain of the original function) are interchanged. In solving the inverse function, students often make the mistake that the domain of the inverse function is determined by the analytical formula of the inverse function itself. If we pay attention to the concept and origin of inverse function in solving problems, we can avoid such mistakes.
2. Strengthen the reversal and variation of concepts and get solutions from them.