Cognitive Diagnosis Of The "one-dimensional Quadratic Equation" In Junior High School Based On The DINA Model

Cognitive diagnosis theory is the core of a new generation of education meterage theory,is an effective combination of psychology and measurement.It breaks the limitations of the traditional measurement theory only focusing on test results,trying to analyze the psychological state of the subjects during the course of the test,to explore the relationship between the potential state of the subjects and their responses,and to diagnose the cognitive structure of the subjects.At present,the application of cognitive diagnosis theory in mathematics test is mainly focused on the primary school segment,and the research on cognitive diagnosis of middle and high mathematics is scarce.The equation is an effectivemodel to characterize the quantitative relationship in the real world,which is of great significance to cultivate students' mathematical quality such as mathematical thinking,symbolic consciousness and computing ability.One variable quadratic equation is the key learning content of junior highschool,and plays a role as a link between the preceding and the following inalgebraic learning.In addition,one variable quadratic equation is closely relatedto other disciplines such as physics,chemistry and so on.Therefore,this paperchooses the "one variable quadratic equation" knowledge as the research point,through the cognitive diagnosis theory to explore what the cognitive attributes and the hierarchical relationship of the one variable quadratic equation chapter are.Under the framework of the identified cognitive attributes,how does the students know about the content of the equation?What is the potential knowledge structure of students?Is it possible to classify students according to whether the subjects are mastering the skills or traits required for the test and provide a reference for teaching remedies?Based on the above considerations,this paper uses the DINA model to carry out the cognitive diagnosis research of one variable quadratic equation.The research contents are as follows:(1)analyze the knowledge structure of" one variable quadratic equation n in junior high school mathematics,establish the cognitive attributes,and construct the Q matrix;(2)around the knowledge of " one variable quadratic equation " section,prepare test papers with diagnostic validity;(3)the ninth-grade students in a middle school in Handan city of Hebei province were investigated;(4)based on the DINA model,the test volume of the survey and recovery is.analyzed statistically,and the measurement results are analyzed and summarized deeply;(5)according to the results of the study,the information is fed back to Teachers and students.In this paper,200 students in a municipal secondary school in Handan City,Hebei Province,were surveyed.SPSS and Excel software were used for statistical analysis of the data obtained,and based on the DINA model,the cognitive responses of the subjects were analyzed.The conclusions are as follows:(1)establish the cognitive attribute of the "one variable quadratic equation"chapter.In this study,the cognitive attributes of the "one variable quadratic equation" chapter are divided into three dimensions:content attribute,process attribute and skill attribute,and seven attributes,which are the basic concepts of the equation,the root discrimination,the relationship between the root and the coefficient,the ability to apply knowledge to scenarios,the use of algebraic rules,solving equations,and solving complex practical problems.(2)There are obvious differences in the probability of grasping the cognitive attributes of different classes.Students have a good grasp of the basic concepts of equations,and do not have a good grasp of these 3 attributes,which are the relationship between the roots and coefficients,the ability to apply knowledge to the situation,and the use of the algebraic rules.(3)Attribute mastery pattern is a response to the students' potential knowledge,which can be more comprehensive,detailed and in-depth show students learning situation."Hidden" attribute master mode and "explicit"response mode is not equivalent.Students with different attribute mastery patterns may have the same score or response,while students with the same attribute mastery pattern may also have different grades or responses.In this study,about 80%of students can be categorized into 14 master modes.