An Advanced Study Of Eighth-grade Congruent Triangles Based On APOS Theory

Learning progression refers to the process in which learners continuously understand a core concept from shallow to deep within a period of time.The phase of junior middle school is a critical period for the development of students’ mathematical abstract logical thinking,and geometry learning can cultivate students’ mathematical thinking ability.This research is a case study of "congruent triangle" and it studies the learning progression model of congruent triangle in middle school based on APOS theory.Firstly,on the basis of literature research,the content of congruent triangle in curriculum standards and textbooks of different editions is analyzed,and the hypothetical learning progression model of congruent triangle is constructed to demonstrate the scientific nature and applicability of the hypothetical learning progression model.Then,based on the learning progression hypothesis model,the congruent triangle learning progression test is developed,and the reliability and validity of the test questions are tested through expert consultation and testing.Secondly,a total of 694 eighth-grade students from Jiangsu province,Guizhou Province and Chongqing city were selected for data collection and analysis,and the learning progression model of congruent triangle was revised and improved.Thirdly,carry out the practice research on the learning progression of congruent triangle based on APOS theory.It is found that the learning progression model of congruent triangle concept includes five stages and nine levels,which are preparatory stage,operation stage,process stage,object stage and schema stage respectively.The quality of the test questions for learning the concept of congruent triangle is good,the students have a good grasp of the preparatory stage of congruent triangle,but a weak grasp of the knowledge of the congruent triangle diagram stage,which needs to be strengthened.The teaching of learning progression based on APOS theory has stronger advantages compared with traditional teaching and can make students better grasp the concept.Learning progression is the link and bridge that combines "curriculum standard","textbook" and "students".Mathematics teachers should pay attention to learning progression and pay attention to students’ foundation in teaching.Focus on the key points of the course to clarify the relationship between concepts;Active thinking of students,promote the advancement of thinking.