Conic curve is a very important content in high school mathematics, but the concept of conic curve itself is not easy to understand, and it also contains many complex levels and many related lower-level concepts, so conic curve has become one of the most difficult concepts to teach and learn in high school mathematics. Based on American educator Dobinsky's APOS theory on mathematical concept learning, this paper investigates and analyzes students' understanding of the concept of conic curve, and probes into the teaching of the concept of conic curve.

First of all, we should establish a correct teaching concept and carefully design learning activities in teaching.

APOS theory emphasizes that the first mathematical problem to be dealt with in learning mathematical concepts should have a social and realistic background, and requires students to carry out various mathematical activities. On the basis of existing knowledge and experience, students synthesize the intuitive background and formal definition of concepts through thinking operation and reflection abstraction in activities, so as to achieve the purpose of constructing mathematical concepts. This requires teachers to attach importance to students' learning activities and let students experience and construct mathematical concepts.

Case 1: Problem Situation Design of Elliptic Concept Teaching

(1) Take the flight of Shenzhou VII as an example, demonstrate the orbit video of the spacecraft flying around the earth with multimedia (design intent: to stimulate students' patriotism, arouse students' curiosity and interest in learning this lesson through video recording, and make students have a perceptual understanding of the ellipse).

(2) Ask students to give examples of ellipses in daily life (design intent: to make students play their imagination, fully stimulate students' interest in learning ellipses, further deepen students' understanding of ellipses, and clarify two different geometric figures of ellipses and ellipsoids in students' examples. If some students think that eggs are oval, they are actually ellipsoid.

(3) Example demonstration: The section obtained by vertically cutting watermelon is round; The cross section obtained by changing the angle is an ellipse (design intention: to make the ellipse closer to daily life, improve students' perceptual knowledge of the ellipse and activate the classroom atmosphere).

Before learning the concepts of hyperbola and parabola, we can also design some related life situations. Through this activity (or operation), students can initially understand the meaning of the concept of conic curve and fully stimulate their interest in learning.

However, concept teaching can't just stay at the activity (operation) level, spending a lot of energy and time in the activity stage and ending hastily in other stages, which also doesn't conform to the theory or even gives up the foundation.

Second, reflect the formation process of concepts in teaching and grasp the essence of concepts.

From the perspective of learning psychology, the analysis of the four learning levels of APOS theory reflects students' real thinking process in the process of learning mathematical concepts, and the value of process stages in concept establishment is very significant. Dobinsky and others believe that students cannot cross the stage of "process" when establishing concepts. We can have three understandings of "process": it takes a process to abstract mathematical concepts from real life; The result of thinking is presented in the form of "process", which is helpful for students to analyze and solve problems; The biggest innovation of APOS theory is to regard mathematical concepts as a process from one example to another. This process can make students have a new understanding of mathematical concepts, thus changing their views on the whole mathematics. Teachers induce students to understand the process in the process stage, which is also conducive to the formation of values in the process of students' growth.