| Plane vector has profound mathematical connotation,rich physical background,has the double attribute of "number and form",is a good combination carrier of number and form,is an effective tool to solve problems.However,in actual teaching,the content of the plane vector is too abstract,which makes it difficult for students to understand its essential attributes,so the learning effect is not ideal.Therefore,it is very necessary to explore the appropriate teaching mode to improve students’ learning status.APOS theory is a mathematical learning theory proposed by Dubinsky.Its basic assumption is that mathematical knowledge is acquired by students in the process of solving perceived mathematical problems.Students learn mathematical concepts through the three processes of "activity","process" and "object",and finally form a cognitive "schema".In this process,students not only learn the definition of knowledge itself,but also experience the formation process of knowledge and understand the nature of mathematical knowledge.Therefore,it is of theoretical significance to apply APOS theory in plane vector teaching.The research methods adopted in this paper include literature research,questionnaire survey,interview and case analysis.Firstly,the literature related to APOS theory and plane vector teaching is summarized to form a scientific understanding of this research.Then,the source,connotation and characteristics of APOS theory are analyzed,and the content of plane vector is analyzed in teaching materials and the Interpretation of Curriculum Standards,so as to provide a theoretical basis for demonstrating the feasibility and necessity of APOS theory in plane-oriented teaching.Next,the author explores the current situation of plane vector teaching from the perspectives of students and teachers by means of test papers and interviews,and makes attribution analysis for the problems found,which provides empirical basis for the formulation of teaching strategies and the design of teaching cases in the following articles.The results show that the students’ understanding degree of plane vector knowledge can reach the level of operation and process,but rarely reach the level of object and schema.The learning effect of students in the previous stage will have an impact on the learning of the next stage;Students have a better understanding of the symbolic representation of plane vector,followed by the coordinate representation and the geometric representation.At the same time,from the perspective of the students’ answers to the test papers,the students’ grasp of the basic concepts,laws,properties,theorems and other basic knowledge of plane vectors is not enough,the comprehensive application of knowledge ability is insufficient,and there are bad learning habits such as carelessness and sloppiness.However,teachers generally recognize the educational value of plane vectors and pay special attention to the teaching of "vector operation",but they do not pay enough attention to the teaching materials and the "Curriculum Standards",the teaching methods are single,and the recognition of mathematical learning theory is not high.Finally,through the analysis of two high school mathematics teaching cases guided by APOS theory,the plane vector teaching strategy based on APOS theory is obtained:the teaching in the operation stage should design appropriate teaching activities to enrich students’ perceptual experience,and pay attention to the application of "analogy" thought;In the process stage,students’ thinking development should be promoted by the problem-driven way.Example training and variant training should be introduced in the object stage to help students master the nature of mathematical objects.Schema stage should pay attention to students’ construction of knowledge schema.Based on the above teaching strategies,specific teaching design cases are given for the reference of front-line mathematics teachers. |
