Research On Senior High School Mathematics Concept Learning Errors From The Perspective Of APOS Theory

The learning of mathematical concepts is the foundation of all mathematical knowledge learning.The learning of mathematical concepts has stages,and students may make mistakes in each stage,which will affect the learning quality of subsequent related mathematical knowledge.This paper draws lessons from the APOS theory to divide the stages of mathematical concept learning,and makes an investigation on the concept learning in the first chapter “ Set and Common Logical Terms ” of Mathematics Compulsory Book 1(People's Education A Edition)of ordinary high school textbooks.Then,based on the theory of APOS and the survey results,the error types of students in each stage of learning the concepts related to sets and common logical terms are summarized and analyzed.in the operation(activity)stage,errors due to the influence of the number of intuitive background materials;Errors due to the typical influence of intuitive background materials,which is reflected in the inability to form conceptual images.In the process stage,errors due to insufficient generalization and abstraction capabilities;Errors due to the influence of the concept of daily life;There are errors due to the influence of conceptual prototype.In the object stage,the connotation and extension of the concept are confused,and the error of expanding or shrinking the connotation appears;Errors in the understanding and application of concepts and related symbols;Errors due to the lack of conceptual language conversion ability.In the generalized(schema)stage,errors due to the influence of adjacent concepts;Errors due to improper concept connection or omission of some concepts;There is an error in the reverse use of concepts;Flexible use of concepts:Problems can't be linked with concepts,resulting in errors.According to the types of errors in each stage,combining constructivism theory and APOS theory,the following teaching strategies are put forward.in the operation(activity)stage:based on students' cognitive structure,pay attention to the quantity and typicality of background materials;Pay attention to students' psychological construction.in the process stage,pay attention to the existing concepts of daily life and accumulate correct experience;Cultivate students' abstract generalization ability;Pay attention to the application of counterexamples.in the object stage:reveal the concept connotation and clarify the concept extension;Strengthen discrimination,analyze the concept and the meaning of symbols;Strengthen the transformation training of mathematical concept language.In the stage of generalization(schema):strengthen concept discrimination and clarify the differences between adjacent concepts;Strengthen the combing of concepts and establish the connection between concepts;Attach importance to the consolidation of concepts and strengthen the application of concepts.Finally,taking the concept teaching process of union and intersection as an example,the corresponding teaching process is designed,put into practice and analyzed.