A Cognitive Diagnosis Research Of Studying "Quadratic Function" Of Junior High School Student Based On DINA Model

Cognitive diagnosis is a new generation of educational measurement methods based on the classic test theory(CTT)and item response theory(IRT),in order to break the shortcomings of traditional tests that only know the test results.Cognitive diagnosis is based on the results of cognitive scientific research and modern psychometric methods,and is a diagnostic evaluation of the knowledge structure,processing skills or cognitive processes(collectively referred to as attributes)possessed by an individual.At present,cognitive diagnosis has been applied in many fields,but in middle school mathematics,there aren’t many applications.The quadratic function is one of the important contents in the "number and algebra"section of junior high school mathematics.In the current junior high school mathematics textbooks,it is arranged in the first volume of the ninth grade for learning.It is a link between the "number and algebra" section.In the senior high school entrance examination,the quadratic function is also an important test point in all provinces and cities across the country.The quadratic function is also closely related to the related knowledge of other subjects.This article takes "quadratic function" as the main line of research,based on cognitive diagnosis theory and related research methods,and aims to solve the following questions-how to divide the cognitive attributes and relationships of the "quadratic function" chapter?How to obtain the knowledge of students through cognitive diagnostic tests based on the divided cognitive attributes and their relationships,and to infer the knowledge structure in their minds based on this?How to classify students’ knowledge mastery based on the results of the cognitive diagnostic test,and provide reasonable suggestions for the corresponding teachers in teaching?In order to solve the above problems,this article uses the "quadratic function" as the knowledge carrier to compile a better quality cognitive diagnostic test paper,and learns the knowledge of "quadratic function" among 108 students in 4 classes of A middle school in a certain city.Based on the theory of cognitive diagnosis and using the DINA model,a cognitive diagnosis study of the "quadratic function" is carried out.The research content includes:(1)Based on the "Mathematics Curriculum Standards for Compulsory Education" and the teaching material of "Mathematics Ninth Grade Volume One" published by the People’s Education Edition,analyze the knowledge structure of the "quadratic function",determine the cognitive attributes and their relationships,and determine the Q matrix.(2)Compile cognitive diagnostic test papers with good reliability,validity,and discrimination,and moderate difficulty around the relevant knowledge of the "quadratic function".(3)Taking two students from ordinary classes randomly selected by A middle school in a certain city as the research object,conduct pre-test.According to the results of the pre-test,evaluate the four descriptive statistics of reliability,validity,discrimination,and difficulty of the test paper,and make appropriate modifications to the test paper based on them.(4)Taking 108 students from 4 classes of A middle school in a certain city as the research objects,a formal survey and test were conducted.(5)Based on the DINA model,conduct routine quantitative analysis of survey data and cognitive diagnostic measurement on the retrieved valid test papers,and analyze the measurement results.(6)Based on the results of data analysis,give reasonable teaching suggestions.The main research conclusions are as follows:(1)Seven cognitive attributes of the "quadratic function" chapter are given,including(Al)the definition of the quadratic function,(A2)the image of the quadratic function,(A3)the properties of the quadratic function,(A4)find the analytic formula of the quadratic function,(A5)several forms of the analytic formula of the quadratic function and their mutual transformation,(A6)quadratic function and image transformation and(A7)the integrated application of the quadratic function,with the attribute hierarchical relationship between them.(2)The reliability of the test paper is in a reasonable range,the validity is slightly low,and the discrimination is high.After deleting some more difficult test questions,the difficulty is moderate,which makes the overall quality of the test paper higher.The conclusion based on the test paper is reliable.(3)There are certain differences in the probabilities of the subjects in each class in mastering each cognitive attribute.Most of the subjects had a poor grasp of the cognitive properties of(A4)the analytical expression of the quadratic function and(A5)the several forms of the analytical expression of the quadratic function and their mutual transformation.(4)The attribute mastering mode is to combine the answering response of the subjects and the Q matrix to determine the mastery of each cognitive attribute of each subject.In terms of attribute mastery mode,about 75%of the subjects’ attribute mastery mode belongs to the ideal mastery mode.