Understanding Of Conic Sections Among High School Students

The topic of Conic sections is the fundamental content in plane analytical geometry at school level. After the new curriculum reform, its teaching periods has decreased from 40 periods to 20 periods, and its teaching content has increased (e.g., its applications with ICT is added). The requirements, key points and difficulty of conic sections in the new curriculum have changed. The author, from her own teaching experiences, found that students thought the learning of conic sections is very difficult for them. Under this background, this study intends to carry out a thorough investigation on high school students' understanding of conic sections and hopes that its finding could benefit the classroom teaching of conic sections.The four research questions of this study are listed in the following:1. What is high school students' understanding of the concept of conic sections?2. What is high school students' understanding of the uniform properties of conic sections?3. What is high school students' ability to solve real world problems about conic sections?4. Is there any difference in high school students' understanding of conic sections?Based on the requirement of conic sections from the curriculum and the exam syllabus, this study constructed levels of understanding of conic sections, and designed five tests to measure high school students' understanding of conic sections. 426 students from a key high school in Anhui province took the tests. The main findings of the study are listed below.1. The high school students' understanding of the concept of conic sections: their performance in "using" the concept is better than "saying" the concept; they should improve their ability to flexibly use the concept to solve problems; the decreasing sequence of their performance in the equations of conic sections is parabola, ellipse, and hyperbola. These students tended to mix the meaning of "a,b,c,p" and the equations when they come across more than two types of conic sections; these students could use the geometric properties of conic sections to solve easy questions, but have difficulties in sophisticated problems.2. These students' understanding of the uniform properties of conic sections relies on the context of the given problem. They tended to ignore the given conditions of the uniform properties. Some of the students even did not know the uniform properties of conic sections.3. These students' ability to solve real world problems on conic sections is weak.4. The difference on the understanding of concept of conic sections between Grade 11 and Grade 12 is big, but their difference in the uniform properties and the application ability is not so much.