Teaching Research On Primary School Mathematics“Triangle”learning Progression

The concept of "learning progression" originated in the field of science education in the United States,and is used to describe the cognitive development process of students towards a certain learning concept or topic over a period of time.In recent years,learning progression has started to enter the research field of mathematics in China,and triangles belong to the content of "geometry and graphics" in primary school mathematics.Triangles are a relatively complex and critical part of learning in primary school mathematics plane geometry,and the research on the learning progression of triangles is based on the perspective of students’ geometric thinking,which is beneficial for helping primary school students overcome difficulties in learning triangles and promoting the development of their geometric intuition and ability.This study focused on the core topic of "triangles" in primary school,using literature analysis,testing,and interviews to investigate the following three questions: first,how to construct a hypothetical learning progression model for primary school mathematics triangles? Second,how to understand the learning progression of primary school students in triangles? Third,how to use the revised learning progression framework for primary school mathematics triangles to guide teaching?Based on textbook and curriculum analysis,teaching design and practice,testing and interview results,the following conclusions were drawn:(1)The learning progression model of primary school mathematics triangles.The learning progression of primary school mathematics triangles is divided into four levels: Level 1: Mastery of recognition,stability,and derivation of the area formula and simple applications of triangles;Level 2: Ability to recognize triangles through mathematical properties and characteristics,to verify and apply simple theorems,and to classify triangles and grasp their containment relationships;Level 3:Ability to apply more complex theorems of triangles;Level 4: Ability to further explore the intrinsic properties and containment relationships of triangles.(2)Learning progression of primary school students in triangles.In the student sample tested,more than 80% of students were distributed in levels 3 and 4,9.1% in level 2,and only 0.7% in level 1.With regards to grade differences,except for level1,there were extremely significant differences in levels 2,3,and 4 between fourth and fifth-grade students.There was no significant difference in performance on each level between male and female students.(3)Three teaching cases were developed based on the learning progression of triangles.Based on the analysis of primary school students’ learning progression in triangles,three lessons on "Characteristics of Triangles","Classification of Triangles",and "Sum of Interior Angles of Triangles" were selected.Through the application of the learning progression model of triangles to teaching design and practice,it was found that teaching based on the learning progression of triangles was more conducive to students’ learning than conventional teaching.Based on teaching practice and research conclusions,the following recommendations were made:(1)Develop teaching goals based on the content progression of triangles;(2)Write teaching designs based on the learning progression levels of triangles;(3)Use testing tools based on the learning progression of triangles to evaluate students.