A Study On The Cognitive Diagnosis Of Probability And Statistical Learning For Senior High School Students And Their Data Analysis Literacy Level

Since the 1990s,elementary and middle school students in various countries have been exposed to courses related to probability and statistics.Improving national statistical literacy is the purpose of universal probability and statistical education in various countries.In 2011,"Compulsory Education Mathematics Curriculum Standards"proposed that mathematics literacy is the basic literacy that every citizen of modern society should have.The concept of data analysis is one of the mathematical qualities that citizens should possess."General High School Mathematics Curriculum Standards(Experimental)",on the basis of achieving compulsory education curriculum goals,further pointed out that to improve students' basic abilities such as data processing,this is a necessary mathematical literacy as a future citizen."General High School Mathematics Curriculum Standards(2017 Edition)" officially proposed the core qualities of the six major mathematics disciplines,which embodies the objectives of the mathematics curriculum and its educational value.One of the core literacy of the six university subjects is data analysis literacy,which is the key ability students should possess through learning.The transition from "data processing capability" to "data analysis literacy"reflects the process of people's understanding of probability and statistical education value.Taking probability and statistical knowledge as the carrier to develop students' data analysis capabilities and generate data analysis literacy is the educational path of high school probability and statistics courses in China.Mathematics knowledge is the basic tool for students to solve practical problems,so it is the most basic and important.Testing is a method commonly used in teaching to check up and monitor the situation of students'basic tools mastering,but routine testing could not give students,teachers,and parents an accurate diagnosis.Cognitive diagnosis theory as a new generation of test theory can effectively make up for the shortcomings of traditional tests.It can help teachers grasp the cognitive structure of students from a micro perspective,provide detailed and effective diagnostic information for the analysis of students'academic conditions,and provide teachers with teaching plans The formulation provides a realistic basis."General High School Mathematics Curriculum Standards(2017 Edition)" also discusses the main performance and level of data analysis literacy in the cultivation of students' core literacy in mathematics disciplines.It can help teachers grasp the achievement of students' data analysis literacy at a macro level.Both the detection of the students' microscopic cognitive structure and the macroscopic ability level are for the students to form a monitoring method for data analysis literacy.Data analysis is the core of statistics.Statistics is a science about data collection,collation,description and analysis.It often contains the meaning of probability when giving statistical inferences.In the past ten years,under the influence of the development of computer technology,the frequency definition of probability has risen rapidly,and there is a close relationship between probability and statistics.In order to evaluate the quality of students' data analysis and literacy in a more detailed manner,this article takes high school probability and statistical content as the knowledge carrier,based on cognitive diagnosis theory,develop probabilistic and statistical cognitive model testing tools to investigate the grasp of probabilistic and statistical knowledge and the level of data analysis literacy of senior third grade students.This article uses literature research method,expert determination method,verbal report method,test paper survey method and other research methods to carry out research.The research is mainly divided into three parts.The first part is the construction of probability and statistical cognitive models and the preparation of test tools.The veracity of the cognitive model is verified by the verbal report and the attribute hierarchy consistency test.The second part is to carry out probabilistic and statistical cognitive diagnostic analysis.The student's answer data is encoded by 0-1,and the DINA model is selected as a cognitive diagnosis model to obtain the student's knowledge of probability and statistical content.The third part is the evaluation of the literacy level of data analysis for students.Using SPSS software for data analysis,we can obtain the probability and statistical knowledge of each student and their data analysis literacy level.The following results were obtained through the above research:(1)The probability and statistical cognition model established in Study 1 is reasonable;(2)The results of Study 2 indicate that students have greater difficulty in extracting information from the data and explaining specific problems.(3)Research III divides the data analysis literacy level into four levels.From the empirical research results,46%of the students are at level zero,39%of the students have reached level one,and 15%of the students have reached level two.No student has reached the level of data analysis literacy.(4)Students' usual performance has nothing to do with their data analysis literacy level.Students who usually have better grades do not necessarily have a higher level of data analysis literacy.(5)The student's cognitive attribute mastering mode has nothing to do with its data analysis literacy level.Students whose data analysis literacy level is at the same level may not have the same cognitive attribute control mode.(6)The student's cognitive attribute control mode has nothing to do with his usual grades.It is impossible to judge students' grasping mode of cognitive attributes based on their usual grades.Finally,based on the research results,I put forward my personal teaching suggestions on probability and statistics.