1, the requirements of the new curriculum standard for mathematics concept teaching
The new curriculum standard of high school mathematics clearly points out: let students acquire the necessary basic knowledge and skills of mathematics and understand the basic concepts and essence of mathematics. In high school mathematics teaching, it is necessary to strengthen the understanding and mastery of basic concepts and ideas, understand their background, application and role in subsequent learning, and put some core concepts and basic ideas into high school mathematics teaching to help students gradually deepen their understanding and appreciate their mathematical ideas and methods. Because mathematics is highly abstract, we should pay attention to the context of basic concepts, explore the connotation and extension of key and core concepts, guide students to experience the process of abstracting mathematical concepts from concrete examples, and gradually understand the essence of concepts in preliminary application.
2. The requirements of mathematics concept teaching for teachers under the new curriculum standards.
Mathematical concept is the cornerstone of mathematical building, and mathematics is a theoretical system composed of many interrelated concepts through logical reasoning. As an important part of mathematics teaching, concept teaching should also conform to the trend of educational reform and innovate constantly.
Under the new curriculum standards, teachers should update their teaching concepts and attach importance to conceptual teaching. In the specific teaching process, students should be made aware of the universality of concepts and the mathematical ideas infiltrated in concepts, stimulate their interest in learning mathematics, and improve their ability to think, summarize and apply concepts to solve problems. The teaching of mathematical concepts does not lie in how thoroughly the teacher explains the concepts, nor does it lie in imposing the concepts on students. Instead, it inspires, guides and encourages students to actively explore problems according to the background of the concept itself and the knowledge that students have mastered, so as to learn and construct mathematical concepts in the exploration activities. Therefore, the teaching of mathematical concepts under the new curriculum requires teachers to position themselves reasonably and realize the renewal and upgrading of their roles.
In the traditional teaching of mathematical concepts, teachers often only pay attention to the teaching of concepts, ignoring the background introduction of concepts and the analysis of students' cognitive structure, which can't make students understand concepts from many sides and angles and correctly analyze the essential and non-essential attributes of mathematical concepts. This kind of teaching will only make students form some isolated knowledge blocks in their minds, which is not conducive to students' comprehensive use of knowledge to analyze and solve problems, and violates the learning theory of constructivism. If the teaching of mathematical concept course is regarded as a kind of film cultural activity, then the teacher is not only the investment promoter of the concept script, but also plays the role of screenwriter, director and film critic before and after the concept is formed.
3. Thinking about concept classroom teaching based on classroom process design.
The process of concept class returning to the classroom is nothing more than three stages: concept introduction stage, concept exploration stage and concept application stage. How to improve the effectiveness of mathematical concept course? The author thinks according to the three stages of the classroom process.
(1) Concept introduction stage: the question should be put forward with practical significance, which can arouse students' great interest, touch students' observation nerves and get close to the theme. Through the intuitive feeling of contradiction, real life or graphics, give students appropriate perceptual knowledge, pave the way for breaking through difficulties, and then naturally introduce concepts.
There are two ways to introduce new concepts in middle school mathematics teaching: first, introduce them with practical examples or objects and models, so that students can understand the research object from perceptual to rational, gradually understand its essential attributes and establish new concepts. Especially in the teaching of analytic geometry and solid geometry concepts, such as teaching the concept of "cylinder, cone and platform", let students observe related objects, figures and models first, and then introduce concepts on the basis of full perceptual knowledge. Secondly, it is also an effective method to introduce concepts from the internal development needs of mathematics. For example, the introduction of concepts such as "imaginary number" and "dihedral angle". Third, the extension or deformation of the old concept leads to the emergence of new concepts. Such as "the modulus of vector", "the distance formula between two points" and "the inclination angle of a straight line".
(2) Concept exploration stage: Explore concepts, go deep step by step, mobilize students, discuss in groups and think positively. Enlighten and guide students in the inspection, keep abreast of students' trends, help students remember and understand, and form concepts.
The teaching of new mathematical concepts must seriously explore concepts, clarify the connotation and extension of mathematical concepts, and communicate the internal relations of knowledge. What are the terms and conditions in the concept? Is there anything confusing compared with other concepts? How do they relate to what they have learned in the past? What exactly do these terms and conditions mean? How should we understand these differences? Can these concepts be extended and deformed? This is what teachers should focus on.
Teachers should use various means in time to help students deepen their understanding of concepts. For example, students can retell concepts, give some relevant examples to help students grasp the connotation and extension of concepts, and compare them with some related concepts to find out their connections and differences. Such as permutation and combination, exponent and logarithm, trigonometric function and inverse trigonometric function, can all get good results through comparison. You can also use some idioms such as three-character formula and four-character formula to help you remember, such as the inductive formula of trigonometric function, "odd even, sign according to quadrant" and so on.
(3) Concept application stage: After the students know and form the concept, it is an essential link to consolidate the concept. By selecting examples, designing clever questions and strengthening exercises, we can consolidate and apply concepts, so that students can finally master mathematical thinking methods through mastering and applying concepts.
The main means of consolidation is to practice more and use more. Only in this way can we communicate the memory relationship among concepts, theorems, laws, properties and formulas. For example, after learning the concept of "the first definition and the second definition of ellipse", you can practice with examples and consolidate the original concept by solving problems. These exercises can be divided into two steps: first, start with basic exercises to help students get familiar with and master new concepts and knowledge. After mastering the basic content, design some small turning points, small changes and small comprehensive topics according to the actual situation of the class students, so that students can use their knowledge flexibly to solve problems.