Research On Learning Trajectory Of Congruent Triangle

The congruent triangle plays an important role in the study of students' geometric reasoning.It is the first knowledge to explore the relationship between figures.Students can accumulate their experience of activities,develop their learning ability and improve their geometric literacy through the teaching activities of congruent triangles.The optimization of congruent triangle learning trajectory makes the teaching sequence in the learning trajectory more in line with the law of the development of students' geometric thinking,which is conducive to better grasp the essence of knowledge and improve the level of geometric thinking.In this study,questionnaire,literature research and interview are used to pre investigate the learning situation of students' congruent triangle,determine the research direction,research content and theoretical basis of this paper;then,van hile's geometric thinking level is used to investigate and select the research object;then,action research method is used to investigate the version of Beijing Normal University,the version of People's Education and the hypothetical learning trajectory.This paper analyzes and tests the selected objects,arranges the test data,draws conclusions,gives suggestions,further improves the learning trajectory of congruent triangle,and summarizes the optimization model of the learning trajectory.Some phenomena and results of tests are analyzed and some valuable conclusions are obtained in this paper:(1)The results show that there is a significant difference in the level of geometric thinking between grade eight and grade seven students,and the level of geometric thinking between grade eight and grade seven students is significantly higher than that of grade seven students.There is no significant difference in the level of geometric thinking between grade seven and grade seven students.(2)In the process of learning trajectory optimization and post test data analysis,it is found that:(1)there is no significant difference in the learning trajectory teaching effect between Beijing Normal University version and People's Education version.(2)The optimized assumed learning trajectory can promote the students' understanding of the judgment theorem of congruent triangle.(3)The learning trajectory is continuously optimized,and the optimization model of learning trajectory is concluded.According to the conclusion,the following suggestions are put forward from three aspects: students,teachers and textbook compilation:(1)The learning suggestions of congruent triangle for students are as follows:(1)cultivate good habits of preparation before class;(2)pay attention to the connection between knowledge and the construction of knowledge system;(3)summarize in time and pay attention to reflection.(2)The teaching suggestions of congruent triangle for teachers are as follows:(1)create a reasonable teaching scenario and focous on the development of teenagers' logical thinking;(2)use the strategy of "multiple connection representation" to strengthen the teaching of students' mathematical theorem;(3)use the principles of students' existing knowledge system to pay attention to the development order of students' thinking;(4)pay attention to the "thinking process" of geometric reasoning and proof to give full play to the classroom.The aim of teaching is to cultivate the ability of logical thinking.(3)The textbook compilation suggestions of congruent triangles are as follows:(1)the arrangement of textbook should be carried out in the way of "main line——theme——core content";(2)the compilation of textbook should pay attention to the representation of students;(3)the design of teaching activities in textbook should be adapted to the development of students' geometric thinking.