Analysis Of "Congruent Triangle" Critical Learning Path Based On Knowledge Space Theory And Concept Map

Geometry teaching is an important branch of mathematics teaching,and the chapter of "congruent triangle" as the initial chapter of geometric reasoning proof teaching in junior high school is an important chapter of students’ geometry learning,which has an important impact on cultivating students’ geometric inquiry ability and logical reasoning ability.However,there are certain "blind spots" in evaluating students’ knowledge mastery and ability level through the scores of traditional tests,and they can no longer meet the needs of current social development.Therefore,this paper combines Knowledge space theory and Concept map to analyze and discuss the critical learning paths of students’ "congruent triangle",so as to study the specific cognitive processes of students.On this basis,we first review the relevant literature around the research topic,sort out the existing research results,and decide to select 234 eighth-grade students from a middle school in Suzhou as the research object,in order to explore the key learning path of students’ "congruent triangle",compile the "congruent triangle" test paper based on knowledge space theory,and cooperate to develop a KST statistical program in python language to process data,describe students’ knowledge space and knowledge state,and obtain key learning paths as quantitative research.In qualitative research,the concept map test paper was selected as the research tool,the limited concept map test paper was prepared according to the preset concept map,and a representative part of the answer sheet was selected to use the text analysis method for research.Finally,combined with the results of quantitative and qualitative research,the actual key learning paths of students are discussed,and scientific suggestions are provided for subsequent teachers to teach "remediate" and "preventive" aspects in this chapter.The conclusions of this study include the following four aspects:(a)on the whole,all participants performed well in the test,and there were differences in the performance of various knowledge points,among which the basic concepts and properties application questions performed well,the topics involving geometric proofs and ruler drawings performed moderately,and the topics that distinguished mathematical principles and practical applications performed poorly;(b)From the knowledge space map constructed in each subsection,in the two subsections of "Congruent Graphs" and "Congruent Triangles",students’ cognitive differences are small,and the distribution of ability states is relatively concentrated,and in the two subsections of "Exploring the Conditions of Triangle Congruence" and "Application of SSS Theorem-Ruler Drawing",students’cognitive differences are large,and the distribution of ability states is relatively scattered.(c)The measured critical learning paths of the four subsections in the "Congruent Triangle" chapter are relatively close to the expert prediction learning path,and there are certain differences,and the subsections with large differences in path order are"Congruent Graphs" and "Application of SSS Theorem-Ruler Drawing";(d)The generation process of the measured critical learning path is basically consistent with the concept map distribution of each knowledge state,and the concept map constructed by the tested students in different knowledge states is basically consistent,that is,the measured students in the same knowledge state have the same or similar cognitive errors.In view of the teaching status of the above "congruent triangle" chapter and the common cognitive misunderstanding of students,this paper gives suggestions from two aspects:students’ learning and teachers’ teaching.