Learning Progression Of Content Of "Axial Symmetry" In Math In Meddle School

Learning progression is the process by which students' thinking and understanding of a learning topic deepens over time over a span of time,allowing for the integration of curriculum,instruction,and assessment so that all three are aligned.Through literature combing,we found that "Axial Symmetry",as the core concept of Graphical Transformations,has been studied throughout the three school years of elementary,middle and high school,and the knowledge is spiraling upward.However,when students learn "Axial Symmetry",they do not have a clear understanding of the content of "Axial Symmetry",so it is important to explore the path of students' thinking development about "Axial Symmetry".This study focused on the core question of "What is the progression of secondary school students' learning in the content of 'Axial Symmetry'",using four research methods: literature analysis,expert consultation,survey,and interview.This study has gone through the following process.First,a review of studies related to learning progression and "Axial Symmetry" in recent years was conducted.Then,based on the curriculum standards,different versions of the textbook "Axial Symmetry" content,literature on the development of students' understanding of "Axial Symmetry" content,text analysis,expert advice and interviews with some students in the second,third and senior years,a theoretical model of "Axial Symmetry" learning progression was constructed.Finally,a set of "Axial Symmetry" measurement and evaluation tools were developed based on the "Axial Symmetry" learning progression model with reference to typical examples and exercises in textbooks.The quality of the test papers was examined using the Rasch model.Based on the empirical data,the original "Axial Symmetry" learning progression model was tested and revised to obtain the "Axial Symmetry" learning progression model,and based on the model,the actual learning progression of "Axial Symmetry" content for secondary school students was examined.Based on the model,we analyze the actual learning progression level of secondary school students in "axis symmetry" and make suggestions for the curriculum,teaching,and evaluation of "axis symmetry".The study found that: 1.Secondary school students' progression levels of learning about "Axial Symmetry" were roughly divided into 8 levels,described from low to high as follows.Level 0: Experience the phenomenon of axial symmetry based on the perspective of geometric intuition.Level 1: Recognize the concept of axial symmetry based on the perspective of geometric intuition.Level 2: Recognize two diagrams forming axial symmetry based on the perspective of geometric intuition.Level 3: Understanding the nature of axial symmetry based on geometric intuitive perspective.Level 4: Recognize the axisymmetric properties of simple axisymmetric figures(isosceles triangles,line segments,angles)based on a geometric intuitive perspective.Level 5: Solve integrated application problems of "axial symmetry" based on the perspective of geometric intuition.Level 6: Understanding axisymmetric transformation of coordinates based on the perspective of analytic geometry.Level 7: Understanding the axisymmetry of functions based on the perspective of analytic geometry.2.There were significant differences in students' understanding of the content of "axial symmetry" among the three grades,and they had difficulties in the learning process from Level 4 to Level 5.Based on the conclusions,the following suggestions are made: the textbook should be organized in such a way as to add integrated application problems using Axial Symmetry properties;the results of the "Axial Symmetry" learning progression research can be used to design teaching and academic assessment to promote students' understanding of "Axial Symmetry" and the development of mathematical thinking.