A Probe Into The Understanding Of Mathematics Concepts Of High School Students Of Grade One Based On APOS Theory

Mathematical concepts play a very important role in the high school mathematics knowledge system.It is the foundation for students to learn mathematics.Understanding mathematics concepts is the starting point for students to conduct mathematical activities.In actual teaching,most front-line teachers tend to explain mathematical concepts as knowledge points,so that students have very low participation in the construction of mathematical concepts.They pay too much attention to the teaching of mathematical knowledge and ignore students' autonomy in mathematical concepts.Cognitive process,and the division of the four stages of APOS theory is very consistent with the process of students' conceptual cognition,and has important guiding significance in the teaching of mathematical concepts.This research uses the concept of logarithmic function in the Compulsory 1 of Mathematics textbook for senior high school published by Beijing Normal University as an entry point,combined with the APOS theory,to study the following questions:(1)understand the status of the level of understanding of logarithmic function concepts of high school students;(2)analyze the concept of logarithmic function of high school students Understand the common mistakes in the four stages;(3)initially formulate the corresponding logarithmic function concept teaching design and put forward corresponding teaching suggestions.This study uses three research methods: literature analysis,interviews and questionnaire surveys to investigate a total of 251 students in two liberal arts classes and two science classes in the first grade of a key middle school in Jiangxi Province,and explore the logarithm of the first grade students The current state of learning function concepts.Firstly,the literature analysis method is used to sort out mathematical concepts and related literature to provide a theoretical basis for subsequent research.Then,through the test survey,understand the current level of understanding of the logarithmic function concept of the first year students,and analyze the common errors in the four stages of students' understanding of the logarithmic function concept based on the specific answer of the test paper,and understand the logarithm of the first year students through the questionnaire Interest in learning functional concepts.Finally,on the basis of understanding the status quo of students' learning of the concept of logarithmic function,a preliminary design of the concept of logarithmic function guided by APOS theory is designed,and some teaching suggestions for applying the theory to classroom teaching are put forward.Using Excel and SPSS 21.0 education statistics software to carry out quantitative and qualitative analysis of the collected data and information,the following conclusions are obtained:(1)The level of understanding of logarithmic function concepts of high school students is quite different in the four stages,among which the understanding in the operation stage The level of understanding is the best.As the stage rises,the level of understanding becomes lower;(2)there is a gender difference in understanding between boys and girls.The difference in the first three stages is not obvious.In the illustrated stage,boys' realization is significantly better than girls';(3)The level of understanding of the concept of logarithmic function of science students is better than that of liberal arts students.Finally,based on the research results,the following teaching suggestions are put forward:(1)Teachers should use textbooks reasonably and carefully arrange teaching content;(2)Teachers should moderately adjust the pace of teaching to cultivate students' ability to apply mathematics;(3)Focus on enhancing students' drawing,The ability to recognize and use pictures;(4)Appropriate use of multimedia information technology,infiltrating the mathematical thinking of the combination of number and shape.