First, the understanding of concept teaching
1. Focus on concept exploration and formation.
The formation of each concept has different experiences. Revealing the formation process of mathematical concepts in teaching can stimulate students' interest in learning, guide students to explore the whole process of concept generation, and enable students to form a good concept consciousness and understand mathematical concepts through the construction of mathematical knowledge on the premise of perceptual cognition.
2. Pay attention to the abstract expression of concepts
Mathematics concept can not only cultivate students' core literacy, but also improve students' mathematical thinking. It is an important element in the mathematical knowledge system, which can be found in every module of high school mathematics and can be said to be the foundation of foundation. However, students have to go through the process from concrete to abstract and from special to general when they understand concepts. Therefore, in teaching, students should experience the formation process of concepts and attach importance to the qualitative grasp of concepts.
Second, based on high school mathematics concept teaching to cultivate students' core literacy
(A) the problem situation of cultivating students' core literacy
Einstein once said that it is more important to ask questions than to solve them. A person can ask questions, which proves that he is thinking seriously. Therefore, under the current students' learning level, appropriately creating problem situations can better promote teaching activities and stimulate students' thinking, thus realizing the construction of mathematics and achieving teaching objectives. Problems are the source of thinking and the carrier of inquiry. Solving problems is one of the sources of thinking. In the process of designing problems, grasp the relationship between knowledge, and finally focus on the formation of concepts, so that students can understand mathematical knowledge from concrete to abstract from the transformation of graphic language, written language and symbolic language, and develop their own intuitive image and core literacy of mathematical thinking.
For example, when teachers teach students the concept of trigonometric function, they should first teach trigonometric function, so that students can create rich scenes according to their actual life experience and understand the model of trigonometric function clearly. The essence of trigonometric function is to describe the periodic model. Teachers can ask students questions to make them think about which of the most common objects in life are similar to the periodic model of trigonometric functions. In the introduction of teacher's question situation, students think about objects similar to trigonometric functions in life. At first, students can think of few things, most of which have little to do with trigonometric functions. Teachers can continue to guide students and show them all the graphs of trigonometric functions through dynamic pictures. At this time, some students answered that the ferris wheel in life is closest to trigonometric function. Then, on this basis, the teacher asks questions and teaches students to think about what tourists in the park care most about when watching the operation of the Ferris wheel. The purpose of the teacher's setting this question is to let students perceive the change of people's position through observation, and through intuitive imagination, combined with abstract mathematical knowledge, take the Ferris wheel as the origin and take the artificial abstract point on the Ferris wheel as? | point movement, which point people turn to, is transformed into the position change of the moving point P on the circumference. Teachers can use this method to cultivate students' intuitive imagination and mathematical abstraction ability.
(B) autonomous learning teaching method to cultivate students' core literacy
Under the guidance of the new curriculum standards, teachers are required to guide students in classroom teaching, so that students can continuously improve their core literacy through various forms of independent learning and independent inquiry, so that students can collect relevant information through their own efforts, understand the history of mathematics development and strengthen their overall understanding of mathematics. It is necessary for students to form good study habits and independent thinking ability in the process of independent inquiry. In the teaching process, teachers should straighten their positions, guide students appropriately, do not interfere with students' autonomous learning too much, and give students enough time and space.
Teachers should promote cooperative learning among students, so that students can exercise their cooperative ability and spirit while learning good theoretical knowledge, and better improve their core literacy. In cooperative learning, teachers should actively guide students, so that students can take fewer detours in the process of cooperative learning, thus improving learning efficiency.
The introduction of inquiry teaching method by teachers can stimulate students' active learning, cultivate students' independent inquiry ability, help students develop good study habits, make students understand concepts more thoroughly, and cultivate students' good mathematical literacy of independent thinking. For example, when explaining the concept of the distance between a straight line and a plane parallel to it, we can understand that any point on a straight line can reach the plane distance parallel to it. The teacher encourages students to think, is the word "any point" used in the concept too positive? Teachers mainly stimulate students' independent inquiry ability by asking questions, so that students can experience the process from affirmation to negation, confirming negative views and deepening knowledge connotation, and finally let students form logical mathematical thinking in repeated inquiry.
In short, through the introduction of autonomous learning, students can effectively carry out concept teaching, at the same time, fully exercise their inquiry spirit and inquiry ability, form a good habit of cooperative learning, and improve students' mathematical core literacy.
Concluding remarks
From the perspective of concept, we can know that concept understanding is a process from concrete to abstract, and then from abstract to concrete. From abstract to concrete, let students establish a good understanding of mathematical concepts, let students understand the reasoning and operation process in the application of concepts, let students use mathematical concepts to solve various mathematical problems, and then cultivate students' abstract thinking ability. In the process of concept learning, only by returning the specific content of learning to practical application can students consolidate the concepts they have learned, and then improve their ability to use concepts, develop their logical reasoning ability and cultivate their core literacy in mathematics.