Research On The Cognitive Diagnosis Of The Ninth Grade Students’ Quadratic Function Learning Based On DINA Model

Based on the classic test theory(CTT)and item response theory(IRT),cognitive diagnosis theory combines psychology and measurement,and has occupied a core position in the new generation of educational measurement theory.Its effectiveness lies in that it is based on the research results of cognitive science,overcomes the shortcoming of traditional measurement theory that only looks at the score results,and focuses on the psychological path of the participants in the test in the process of answering,So as to further diagnose the cognitive level of the subjects within the scope of the test paper.This new generation of educational measurement method,which measures the cognitive structure of subjects,has been favored by researchers and gradually began to be applied in many different fields on a large scale.Up to now,the application research of cognitive diagnosis theory in mathematics mainly focuses on the primary school stage,while the corresponding research in middle school stage is less.The traditional test theory evaluates the individual’s ability level with a single score result,which pays too much attention to screening and selection,but ignores diagnosis and improvement.The cognitive diagnosis theory is based on the method of modern psychometrics.It diagnoses the unique internal knowledge structure of different subjects.Its significance lies in breaking through the limitations of the traditional measurement theory of score only,and diagnosing the advantages and disadvantages of the subjects in cognitive aspects at a deeper level,so as to evaluate their internal knowledge state,cognitive structure and processing skills,This also provides an empirical basis for teachers to carry out remedial teaching and individualized teaching for different individuals.In order to study the cognitive structure of ninth grade students in learning quadratic functions,this study used literature research,questionnaire testing,and statistical analysis methods to develop a set of cognitive diagnostic tests for quadratic functions with good diagnostic validity.The preparation of the test paper is mainly based on the 2022 compulsory education curriculum standards,the middle school entrance examination questions,textbooks,and other text materials.Through discussions with experts and front-line teachers,the cognitive properties and hierarchical relationships of the quadratic function are determined,and on this basis,the test item Q matrix is established.This study first analyzes the quality of small-scale test results,eliminating or improving test questions that are not within the reasonable parameter range.Then,during the formal test,298 ninth grade students from W Middle School are selected,and differences in the scores of different classes are analyzed using SPSS26.0 and EXCEL software.Based on the DINA model,the cognitive attribute mastery probability and mastery mode of the subjects are diagnosed on the flex CDMS cognitive diagnostic platform,Select representative subjects for individual case selection analysis and case selection analysis of the answers to question 15.Finally,through parameter estimation and fitting tests,it is verified that the test items meet the requirements of the DINA model,and the diagnostic results have good reliability and validity.Through statistical analysis of the results of the responses,the main conclusions are as follows:(1)The diagnostic validity of the test paper is good;(2)The subjects scored higher on questions 1 and 3,but lower on questions 12 and 15;(3)Class 5 and Class 6 had the best overall cognitive level;(4)Subjects have a relatively centralized pattern of grasping the cognitive attributes of quadratic functions;(5)The results of cognitive diagnosis can more objectively reflect the cognitive level of subjects than traditional scores;(6)Subjects have different probabilities of mastering the six cognitive attributes of quadratic functions.Finally,based on the conclusions obtained,the following suggestions are made:(1)Guide students to clarify their thinking and reduce the guessing coefficient;(2)Based on cognitive diagnostic models,evaluation promotes learning and evaluation promotes teaching;(3)Adjusting the teaching focus through attribute mastery probability;(4)Carrying out hierarchical remedial teaching based on differences in attribute mastery modes.