Investigation And Research On Conceptual Understanding Level Of Quadratic Function Based On APOS Theory

Quadratic function is the important content of middle school mathematics study which is also the basis for students to further study other functions.It plays a pivotal role in the senior high school entrance examination.Meanwhile,it is a learning difficult point for students.Because different students will have different levels of understanding of the concept of quadratic function,it will generate various problems.And this point is worthy of attention.This study is aimed at ninth grade students from three schools in Jianchang County,Huludao City.In this study,a textbook based on human education is used as an example and the test papers are designed based on the four stages of APOS theory which is a research tool to research the ninth grade students' understanding of the concept of quadratic functions.This research is divided into five parts.The first part is the introduction,which discusses the theoretical and practical significance of the research questions.The second part is the literature review,including the related research on APOS theory.The third part is the design and process of the research,including the selection of research objects,determination of test papers,and research methods.The fourth part is the statistics and analysis of the data,including the participants' analysis of the learning of the quadratic function concept,the analysis of the learning of the quadratic function concept at different stages of the APOS theory,and the analysis of the differences between different schools and students of different genders.The fifth part is conclusions and recommendations.The conclusion of this study is that the level of understanding of the concept of quadratic function in the ninth grade students can reach the active stage and the process stage,some students can reach the object stage,and only a few students can reach the schema stage;There are significant differences among the three schools.The ninth grade students in rural boarding schools have a poor grasp of the concept of quadratic functions,and most students can reach the active stage and process stage,while few students reach the object stage and schema stage;There are significant differences between boys and girls only in the active stage,and there are no significant differences in later learning.At the same time,this article draws several teaching suggestions: pay attention to the formation of concepts and effectively carry out hierarchical teaching;use multiple representations to understand mathematical ideas;pay attention to classroom communication and improve students' expression ability;strengthen the internal relationship between lessons to form a complete knowledge context.