Research On Elliptic Understanding Level Of Sophomores In High School Based On The SOLO Taxonomy Theory

Conic section is an important part of high school mathematics curriculum.Ellipse is one of the most common conic sections.The study of ellipse has an original development function for students' subsequent hyperbola and parabola learning.The study about students' comprehension level of the ellipse is of great significance.This study uses literature analysis and testing methods to study the ellipse comprehension level of high school students and the problems in their learning.Taking SOLO taxonomy theory as the theoretical basis,the author compiled the elliptical comprehension test paper for high school students on the basis of analyzing the"Curriculum Standards",summarizing the college entrance examination questions of various provinces and cities in the past five years,collecting documents,consulting teaching materials and teachers.The test paper includes the definition of the ellipse,the standard equation of the ellipse,the geometric properties of the ellipse,and the application of the ellipse in 4 dimensions.Accoding to the answer of the students,the students' comprehension level of the ellipse in each dimension and the students'problems of the ellipse are analyzed.Corresponding teaching suggestions in response to the problems are put forward.The main conclusions of the research are:1.The level of ellipse comprehension of sophomores are:(1)The largest number of students' comprehension level of the definition of ellipse,the standard equation of ellipse,the geometric properties of ellipse and the application of ellipse are all level 2,and the proportion is about 40%,indicating that two-fifths of the students have a low level of understanding of the ellipse,and have not yet reached the mastery level required by the "Curriculum Standards".Analyzing the number of students whose understanding level of each dimension of the ellipse is not lower than level 3,it can be found that students have the highest level of understanding about the standard equation of the ellipse and the proportion is 41.9%.(2)From the perspective of different genders,there is a significant difference between boys and girls in the comprehension level of the definition of ellipse,the geometric properties of ellipse and the application of ellipse,boys have a significantly higher level of understanding in these three dimensions than girls.There is no significant difference between boys and girls in the understanding level of the elliptic standard equation.(3)From the perspective of relevance,there is a significant low-degree positive correlation between students'understanding of the definition of ellipse and students' understanding of ellipse standard equation,ellipse geometric properties and ellipse application.2.The main problems in students' ellipse learning are:(1)There are problems in understanding the definition of ellipse,it is easy to ignore keywords such as "in-plane","2a>|F1F2|",and "trajectory" in the definition;confusing the concepts of "trajectory"and "trajectory equation".(2)It is easy to ignore the standard equation of ellipse with focus on the y-axis.(3)Insufficient mastery of mathematical thinking methods in combination of number and shape and category discussion.3.In view of the above problems,teaching suggestions are put forward as follows:(1)Pay attention to the students' existing cognitive foundation and value the teaching of the ellipse concepts.(2)Pay attention to the cultivation of mathematical thinking methods.(3)Improve learning evaluation methods and enhance students' confidence in learning.