Investigation And Researgh On The Status Of High School Students' Definite Integral Learning

As one of the core concepts of calculus,definite integral is introduced into senior high school textbooks,which not only establishes the relationship between derivative and definite integral,but also helps to cultivate the core mathematical literacy of students.The study of definite integral provides basic ideas and methods for students to solve simple mathematical and physical problems,which can well reflect the practical application value of mathematics.Compared with other mathematical knowledge,definite integral is more abstract.Although students have a preliminary understanding of the idea of "replacing curves with straight lines" when learning the area of circles,this idea is still immature,which leads to obstacles in understanding and application of students.Therefore,under the concept of core literacy,it is necessary to investigate the learning situation of definite integral of students,what obstacles exist in the process of learning definite integral,the reasons for the obstacles and put forward reasonable suggestions.Through questionnaires and test papers,this paper investigates the current situation of students' definite score learning from both subjective and objective perspectives,including three aspects:1.Using IBM SPSS Statistics 22,the author collated and analyzed the data of the questionnaire survey,and understood the basic situation of students' learning definite score from four aspects:learning emotion,habits,knowledge and ability,and meta-cognition.2.Using APOS theory and SOLO classification and evaluation theory,the author analyzed and evaluated the answers of the test paper.3.Combining the interviews with teachers and students,as well as the survey results of test papers and questionnaires,the author summarized the learning status and learning obstacles of high school students'definite score,and put forward reasonable suggestions according to students' cognitive rules and knowledge structure.Through the research on the results of questionnaire and test papers and interviews between teachers and students,the author found that most senior high school students'understanding of definite integral concept was at the middle and inferior level.The results are mainly shown in the following aspects:1.In the activity stage and the process stage,students do not grasp the essence of definite integral concept in place,nor can they grasp the basic ideas contained therein.2.Influenced by the stage of activity and process,students perform poorly in the stage of schema.Only a few students can use definite integral to solve the problem of geometric volume.3.Most students can only use fixed mode to solve problems,but can not use it flexibly.4.According to the results of the test paper,students' core qualities of mathematics such as mathematical ion,mathematical modeling and logical reasoning need to be improved.Finally,the author put forward feasible suggestions for students to learn definite integrals better,aiming at the students'learning status and learning obstacles.