Research On The Hyperbolic Cognition Level Of High School Students Under SOLO Theory

The hyperbola is a common conic section and one of the key and difficult points in the annual college entrance examination.Researching on the learning situation of students in hyperbola,reasonably evaluating their cognitive level,and timely identifying problems in their learning process are of great significance of teaching.This thesis uses literature analysis,questionnaire survey and interview methods to investigate the cognitive level of high school students in hyperbola.Firstly,based on the SOLO classification theory and the requirements of the "National Curriculum Standards for High School Mathematics," it develops an evaluation framework for the cognitive level of hyperbola which includes four dimensions: definition,standard equation,geometric properties,and comprehensive applications.Then,based on the examination requirements of hyperbola in the "New Curriculum Standard," this thesis provides a hierarchical test paper to test the cognitive level of high school students in hyperbola and the statistical analysis of students’ cognitive level by SPSS.Finally,we interview some representative students.And we get the following conclusions :In terms of the definition and geometric properties of hyperbola,most students are at the multi-point structure level.In terms of the standard equation of hyperbola,most students are at the multi-point structure level and the correlational structure level.The cognitive level of students in the comprehensive application of hyperbola is relatively poor.There are not significant difference in the number of students in each cognitive level.There are not significant difference in the number of students in each cognitive level and the cognitive levels of hyperbola between male and female students,but there are significant differences between students in the second and third grades of high school.Overall,the level of knowledge and understanding of hyperbolic geometry among third-year students is moderately advanced,with some degree of improvement compared to students in their second year.In addition,the four dimensions of hyperbola are significant positive correlation and mutually influential and promoted each other.This thesis divides the five cognitive levels of the SOLO classification evaluation theory into three stages of student thinking development and determines the factors that affect student cognitive development through the analysis of test and interview results.Students in the lowlevel thinking stage are mainly of low learning interest and weak basic knowledge.Students in the medium-level thinking stage are mainly lack of knowledge system and have insufficient calculation ability and unfamiliar thinking methods.Students in the high-level thinking stage are mainly lack of reflective spirit problems with rigid thinking in problem-solving.Based on the different thinking levels of students,this thesis puts forward corresponding teaching suggestions:For students in the low-level thinking stage,attentions should be paid to cultivating the learning confidence and mastering the basic knowledge.For students in the medium-level thinking stage,the knowledge network should be constructed,the calculation ability should be improved and the mathematical thinking methods should be deepened.For students in the high-level thinking stage,attentions should be paid to training the variation,cultivating the reflective spirit and optimizing the problem-solving strategies.