Research On Isosceles Triangle Teaching Based On APOS Theory

Isosceles triangle is one of the basic graphics in the "graphics and geometry" section,which provides students with ideas and methods for studying other graphics in the future.The isosceles triangle has many related properties and complex knowledge points,and it is often examined in combination with other knowledge such as triangle,axisymmetric,congruent triangle and so on that has been learned before.It is highly comprehensive.Students pay little attention to it in the learning process,and it is easy to get confused about this part of content.How to make students master this part of content efficiently and accurately is a topic of concern for many scholars.APOS theory is a theory established for the subject of mathematics,with strong operability and certain feasibility.It is of practical significance to apply this theory to the teaching of isosceles triangle,and it can also provide some suggestions for the teaching of isosceles triangle.The study is divided into five parts.In the first part,the author combs the related literature of APOS theory and isosceles triangle teaching at home and abroad,constructs the theoretical foundation of this thesis,and puts forward the main research questions: how to carry out isosceles triangle teaching based on APOS theory? The second part investigates the problems and causes of the current isosceles triangle teaching in junior high school through student questionnaires and teacher interviews,and finds the following problems in the current isosceles triangle teaching in junior high school: junior high school students are interested in the learning of isosceles triangle,but do not attach importance to the learning of isosceles triangle in thought and action;Junior high school students have a good understanding of the definition of isosceles triangle,most of them are at the stage of activity,process and object,and some are at the stage of schema;Most of the students’ understanding of the nature and judgment of isosceles triangle is in the active stage,some are in the process and object stage,and a few students can reach the schema stage;The ability of students to comprehensively apply isosceles triangle knowledge to solve problems is relatively weak.In view of the problems found above,the third part proposes the isosceles triangle teaching principles and strategies under the guidance of APOS theory.The fourth part carries out isosceles triangle teaching based on APOS theory,selects two classes of a middle school in Hefei as the research object,the experimental class carries out teaching under the guidance of APOS theory,and the control class adopts the conventional teaching mode.After the experiment,the isosceles triangle test is carried out on the two classes.Through the analysis of the test data of the two classes,the following conclusions are drawn:(1)The teaching based on APOS theory can effectively improve students’ isosceles triangle learning performance,deepen students’ understanding of isosceles triangle knowledge;(2)There is no significant difference between male and female students in understanding and mastering isosceles triangle knowledge.Finally,based on the above conclusions,the following teaching suggestions are proposed: to conduct a good analysis of the learning situation and achieve hierarchical teaching in each stage;The activity stage--connecting with the reality of life to attract students to learn active learning knowledge;Process stage-creating exploration opportunities and experiencing the process of knowledge formation;Object stage-consolidation exercises to deepen students’ understanding of knowledge;Schema stage-guide students to reflect and summarize in a timely manner,and actively construct a knowledge "schema".