An Empirical Study On Students' Cmperehension Level Of Quadratic Function In Grade Nine

Comprehension is the key to solving mathematical problems as well as one of the targets of Mathematics Curriculum Standards of Compulsory Education.Comprehension level is the manifestation of comprehension ability.The research of comprehension level of mathematics have a lot of achievements.Researchers have put forward some different opinions from the perspective of pedagogy and psychology and some scholars even hold the opinion that “Teaching is oriented toward comprehension ”.During the teaching process,teachers always stress the importance of comprehension,but there exists discrepancy among each student' comprehension of the same question.As a crucial component of mathematics in junior high school,quadratic function serves as a connecting link between what comes before and what goes after it.It is not only used in daily life but also a frequently examined part in Secondary School Entrance Examination.According to statistics,quadratic function accounts for 15%—20% of mathematics in Secondary School Entrance Examination in each province and each city.Therefore,this paper employs literature analysis,method of testing,questionnaire survey and interview to explore comprehension level of quadratic function of students in grade nine and the factors affecting comprehension level with students in nine grade from one junior high school in Fuyang City as the research subjects.Based on analysis of previous research,textbooks and questions in Secondary School Entrance Examination,examination paper of quadratic function and questionnaires of students and teachers are designed to examine and survey 200 students in nine grade and more than 20 teachers.Based on both quantitative and qualitative analysis of the data,several conclusions can be drawn:Firstly,as for students' comprehension level of quadratic function,several conclusions can be drawn base on three dimensions of analysis including visual interpretation,abstract interpretation and formal interpretation and synthetic correlation of three stages:(1)comprehension level of quadratic function of students in grade nine is quite high;(2)students' difficulty in comprehending quadraticfunction lies in that they cannot distinguish quadratic function and other kinds of functions;(3)students in grade nine cannot make a flexible switch between functional image and the characteristic of quadratic function,which makes it hard for students in grade nine learn quadratic function;(4)students' formal comprehension level of quadratic function is the lowest among the three dimensions;(5)students' comprehension of quadratic function image and characteristic and its application is not based on their comprehension of the concept of quadratic function,but on their proficient grasp of quadratic function image and characteristic.Secondly,based on the research,there are three factors which exert influence on students' comprehension level of quadratic function:(1)teachers' influence;(2)students themselves;(3)the difficulty coefficient of the textbook.Based on the research conclusions and the problems found during data analysis,the author has provided some specific suggestions for students,textbook compilers and teachers and then has reflected on the problems in this research.