"Discipline core accomplishment" is a word that has been talked about a lot nowadays. How to cultivate students' core literacy in classroom teaching is a problem that we need to pay attention to. A teacher with certain attainments has formed his own unique teaching style, and his classroom teaching has a natural "artistry", which can make all teachers and students who have listened to his class deeply shocked and influenced by his personality charm and teaching art. After careful analysis, there are many reasons. Just from the perspective of "core literacy", it is the cultivation and implementation of students' "core literacy". Specifically, it has two meanings: one is to help students transform declarative knowledge into procedural knowledge, that is, to let students master the thinking method of analyzing and solving problems, and to cultivate students' transferable independent learning ability; Second, in the process of teacher-student activities, students can fully experience the joy of learning, which effectively exercises the will quality of students to make progress despite difficulties. In fact, the key is the question of "how to teach". This is an extremely realistic problem and has been discussed too much. There seems to be no fixed answer and no fixed classroom teaching mode to follow. As Mr. Wei Shusheng said, if you are good at speaking, give full play to the advantages of speaking. If you are good at inspiring students to learn by themselves, guide them to learn by themselves. In short, seek efficient methods that you are good at. In this paper, I start with the conventional ecological classroom teaching, mainly from three aspects: hierarchical design, classroom operation and process evaluation for your reference. I. Hierarchical Design The Book of Rites puts forward that "learning should not be too fast", which has two meanings: one is that different students have different knowledge levels and levels, and the other is that students of the same level (level) need to apply different teaching contents and different teaching methods at different growth stages. Therefore, we need to fully understand the level of different students and the same student at different stages, and then carry out targeted hierarchical design. The practice of the eleventh school is as follows: first, the pre-entrance test results are used to guide stratification, the course selection instruction manual is issued, the course selection suggestions are put forward, and the "small class" teaching is implemented; Second, in the initial grade, teachers should be equipped to provide targeted individual guidance-find the tree, that is, pay attention to the individual and publicize the personality. The three basic functions of a tutor are academic guidance, psychological consultation and life guidance. Second, the classroom operation should demonstrate the self-study method of each class to students; All subjects should design activities that allow teachers and students to gain and grow together. For example, in math class, we can build a basic routine for students to learn math objects, that is, by designing a series of math activities, students can experience the complete process of "fact-concept-nature (relationship)-structure (connection)-application" (as the bright line of teaching content) and complete "fact-method-methodology-math discipline". From the point of view of the core literacy of mathematics, if we want to integrate "mathematical abstraction" from facts into concepts, we can create problem situations to make students enter the state as soon as possible and stimulate students' desire to explore; From understanding concepts to understanding nature, this process should make students get the basic training of "mathematical reasoning", including discovering nature through inductive reasoning and proving nature through (logical) deductive reasoning; From understanding the essence to forming the structure is mainly "mathematical reasoning", because it is the process of establishing the connection of related knowledge and forming a mathematical cognitive structure with good structural function and strong migration ability; In this process, teachers should always pay attention to guiding students to solve problems other than mathematics with mathematical knowledge, so that students can get effective training in "mathematical modeling". At the key points of the above steps, we should pay attention to timely guidance and strengthen the guiding role of "general concepts", such as "how to think", "how to find" and "from what angle to observe"; We can observe the structural characteristics from two angles (number and shape). From a dynamic point of view, we can change the form of the current problem, and then let the students observe it after the equivalent transformation and make the necessary pattern recognition. Students often make new discoveries, and then they can be trained in "intuitive imagination" and "data analysis". I take the heterogeneous course type of the topic "Calculation of Spatial Angle" as an example to explain in detail. Teacher A directly defines the angle, line angle and dihedral angle formed by straight lines on different planes, and introduces the space vector method after a little explanation. Then the teacher spent two-thirds of the class hours explaining examples and practicing exercise groups, focusing on training students' ability to solve three spatial angles with vector method. Students don't find it difficult, and their acceptance is good. Teachers generally respond that the classroom effect is good. Teacher B 1. First, create a situation (fact), project it, and give four pictures for students to observe: criss-crossing expressways (the angle formed by straight lines on different planes), the moment when two wires are short-circuited and discharged (the distance of straight lines on different planes), the measurement of the inclination of the leaning tower of Pisa (the angle between lines and planes), and the process of butterflies flapping their wings back and forth (the size of dihedral angle). 2. Introduce the concept (mathematical abstraction) to demonstrate the changing process from plane to space, thus abstracting the essential attributes of the concept. For example, a non-planar straight line can be regarded as two intersecting straight lines (using local materials instead of two pieces of chalk), one of which does not move and the other moves up (or down) in parallel in space; It can also be regarded as two parallel straight lines, one of which does not move and the other rotates around its point in space. This kind of demonstration can effectively inspire students to discover two elements that represent straight lines in different planes: the angle and distance formed by straight lines in different planes, and also provide an intuitive image carrier for students to further abstract the definition of straight lines in different planes. 3. Research on the solution (that is, exploring the nature and structure) The graphs are all spatial graphs, so it is difficult to measure them directly. The solution should consider the transformation and simplification of a plane and express it with a plane angle, that is, to find a typical section. As mentioned above, regression can lead to the idea of using plane angles to characterize the angles formed by lines on different planes. This not only analyzes the relationship between straight lines and planes in space, but also gives a basic method to find the angles formed by straight lines in different planes, that is, passing a fixed point (it is best to choose a fixed point on these two straight lines) as one of the parallel lines, effectively transforming the relevant conditions of the topic into triangles to solve triangles. Similarly, the line-plane angle is converted into the included angle between the oblique line and its projection on the plane, and the dihedral angle is expressed by the included angle between two rays cut by the plane perpendicular to the edge. But it is not practical in solving specific problems. We can find dihedral angles by imitating the method of finding line and plane angles, that is, first draw a vertical line to another half plane through point P (not on the edge) on one half plane, then draw a vertical line to the edge through vertical foot H, and connect PA with vertical foot A, then angle PAH is the plane angle of dihedral angle, or the intersection point P draws a vertical line to the edge and the other half plane respectively. The vertical feet are Re-inspiration: Is there a better way to find these angles? Introduce space vector and vector method. Guide students: For space graphics with obvious right-angle structure, vector coordinate method can be used to establish a coordinate system and solve it, while for those with less obvious right-angle structure, a group of bases can be selected and solved by vector geometry method as appropriate, or inclined to straight lines, and space right-angle coordinate system can be established and solved by vector coordinate method.