Cognitive Diagnosis Of Junior Middle School Students’ Axial Symmetry Learning Based On DINA Model

Throughout the reform of mathematics basic education at home and abroad,geometry has always been the key content of primary and secondary school curriculum.As the basis of understanding graphic motion in plane geometry,axisymmetry,because of its intuitive and operable content,can promote the development of students’ spatial concepts,geometric intuition and reasoning ability,and cultivate students to see the world with intuitive imagination and mathematical logic thinking.Therefore,it has great practical significance to explore students’ learning of axisymmetric knowledge.However,at present,the evaluation of students’ mathematics learning in most schools is still based on a single score,which can not understand the internal knowledge structure of students,and can not take targeted remedial measures for students’ knowledge loopholes.Cognitive diagnosis can fully excavate the knowledge structure and cognitive process behind the test scores,and make a more accurate and detailed diagnosis of the status quo of students’ knowledge mastery.Therefore,on the theoretical basis of learning progression and cognitive diagnosis theory,based on the DINA model in the cognitive diagnosis model,this paper investigates the students’ mastery of this part of knowledge by compiling the axisymmetric cognitive diagnosis test paper of junior middle school,and proposes corresponding remedial measures to improve teaching according to the diagnosis results.This article mainly through the text analysis method,the oral report method and the test volume investigation method carries on the research,the investigation object is 463 second-year students of a provincial model middle school in Shijiazhuang.This research mainly includes two parts,the first part is the preparation of the axisymmetric cognitive diagnostic test paper: first,based on textual materials such as curriculum standards,textbooks and high school entrance examination questions,combined with the suggestions of subject experts and front-line teachers,the axisymmetric cognitive attributes and attribute hierarchical relationships are initially determined,and the oral reporting method is used to modify and verify its rationality.Then,according to Q Matrix theory compiles the test paper that meets the standard,and finally confirms the axisymmetric cognitive diagnostic test paper after the prediction result inspection.The second part is to use the DINA model for cognitive diagnosis of the test results,and encode the test results by 0-1 score.On the basis of verifying that the model parameters and item fitting are reasonable,the students’ grasp probability of each cognitive attribute of axial symmetry is obtained,and the MLE algorithm identifies which master mode students belong to.Based on the diagnosis results,the group master probability and master mode are statistically analyzed,and examples are selected to analyze the individual’s cognitive diagnosis results.Finally,analyze whether there are gender differences in the mastery of axial symmetry knowledge among junior middle school students.The following conclusions were obtained through research:(1)Axisymmetric knowledge in junior high school can be approximately abstracted as a tree-like branched attribute hierarchical model composed of 5cognitive attributes.The 5 cognitive attributes are: A1(axisymmetry),A2(axisymmetric graph),and A3(two graphs form axisymmetric),A4(line segment)and A5(angle).(2)Junior high school students have basically mastered the 5 axisymmetric cognitive attributes,with an average mastering probability of 0.79,but there are differences in the mastering probability of each cognitive attribute: students have the highest probability of grasping attribute A2(axisymmetric graph),and attribute A3(two graphs form axisymmetric),A4(line segment)and A5(angle)have relatively low mastery probability.(3)88.77% of the subjects can be classified into 11 ideal mastering modes,and the mastering modes are relatively concentrated.Among them,the number of people belonging to(11111)ideal mastering mode is the largest,reaching 44.28% of the total number.Moreover,the diagnosed mastering mode can more specifically and accurately reflect the students’ mastery of axisymmetric knowledge than a single total score.(4)There are gender differences in junior middle school students’ mastery of axisymmetry.Although there is no significant difference between male and female students in the total score of the test,the performance of female students in the two aspects of attribute mastery probability and attribute mastery mode is slightly better than that of male students.Subsequently,based on the survey results,teaching remedial measures are proposed for the three axisymmetric cognitive attributes with relatively low mastery probability.At the same time,it is recommended to focus on different student groups to adopt hierarchical teaching according to the mastery mode of the students,and emphasize that teachers should pay attention to the gender differences among students in the teaching process.