Advanced Study Of Congruent Triangle

The concept of learning progression originated in the field of science education,which can describe the trajectory of students’ thinking development and achieve consistency in curriculum,teaching and evaluation.In learning congruent triangles,due to lack of reasoning experience and uneven thinking development,students have many cognitive impairments in the process of proposition proof.However,congruent triangles are not only an important foundation for subsequent learning of graphics and geometry,but also a key carrier for cultivating students’ mathematical abstraction,spatial imagination and reasoning ability.Therefore,this paper applies the learning progression theory to the thinking development of congruent triangles,reveals the advanced path of students learning congruent triangles,and helps students break through cognitive barriers and enhance reasoning ability.The research is divided into three stages:at the first stage,the construction of a hypothetical model of congruent triangle learning progression.Firstly,by combing the "Mathematics Curriculum Standards for Compulsory Education " and three versions of Mathematics textbooks,the framework of learning progression model was built.Then,according to the existing thinking disorder research,the framework of the learning progression model is supplemented and refined.Finally,the model is revised through teacher interviews and expert consultation,and a hypothesis model for congruent triangle learning is proposed.In the second stage,test tools for congruent triangle learning progression models are compiled.Based on the hypothetical model,22 test projects are designed,and the test paper is revised through pre-test and interview,and the formal test paper is obtained.In the third stage,the learning progression model is tested and revised,and 316 second-year students are selected as the research objects to carry out empirical research,and the learning progression model is tested and revised again by analyzing the data results,and finally the learning progression model of congruent triangle is obtained.It is found that:(1)the learning progression model of congruent triangle which involves 8 core concepts such as the determination theorem of triangles and parallel lines,divides students’ thinking development into 7 achievement levels;(2)The learning progression test tools compiled in this study are of good quality,and the difficulty of the test paper is well adapted to the ability level of the second year of junior high school students;(3)Nearly 70%of junior high school students are at or below the level 4,and only a very small number of students can reach the level 6.The main obstacles for students to learn congruent triangles:insufficient understanding of congruence connotation,insufficient flexibility in mastering the five judgment methods,lack of rigor in reasoning and proof ideas,and easy thinking patterns in standard graphics.Finally,based on the research results,suggestions are made from three aspects:textbook development,teaching and student evaluation.