Research On Cognitive Diagnosis And Remedial Teaching Of Logarithmic Function

Logarithmic function has a wide range of applications and is an important part of high school mathematics.Since the logarithmic function is a new elementary function for high school students,and its symbols and forms are relatively abstract,it is difficult for students to understand and apply the logarithmic function.Therefore,teachers often need to carry out remedial teaching to promote students with mathematics learning difficulties to achieve teaching goals.Cognitive diagnosis theory can not only provide individual macro-level ability evaluation,but also reveal individual micro-level cognitive structure,which can help teachers target remedial teaching to promote students’ development and improve the efficiency of remedial teaching.which is helpful for teachers to carry out remedial teaching in a targeted manner,promote the development of students,and improve the efficiency of remedial teaching.Therefore,based on the cognitive diagnosis theory,this study adopts the DINA cognitive diagnosis model to analyze the cognitive structure of the logarithmic function of the first grade students,and carry out research on the remedial teaching of the logarithmic function.The content of this research mainly includes the following three parts:First,a cognitive diagnostic test paper for logarithmic function was developed.First of all,after combing and analyzing relevant literature and consulting with front-line teachers,7 cognitive attributes and their hierarchical relationships of the content of logarithmic function are determined.The 7 cognitive attributes are the concept of logarithm(A1),the operation of logarithm(A2),the concept of logarithmic function(A3),the graph of logarithmic function(A4),the properties of logarithmic function(A5),the growth characteristics of logarithmic function(A6)and the comprehensive application of logarithmic function(A7).Then,the Q-matrix theory was used as a guide to develop a cognitive diagnostic test paper on logarithmic functions.Finally,a small-scale pretest was conducted to test the rationality of the attribute hierarchy relationship and analyze the quality of the test paper,and the results showed that the overall quality of the test paper was good.Second,the DINA model was used to make a cognitive diagnosis of the content of the logarithmic function in high schools.First of all,the scores of 466 students in the first grade of three middle schools in Fujian Province are statistically analyzed by using Excel software and SPSS software.Then,the DINA model was used to calculate the attribute mastering probability of each student,and the attribute mastery probability of students was statistically analyzed.The results showed that(1)all students had the lowest mastery probability of attribute A7;(2)W middle school had significantly better mastery of attribute A3 than that of L,and H middle school had significantly better mastery of attributes A4～A6 than that of L;(3)There was no significant difference in the gender of each attribute mastery probability.Finally,the maximum likelihood estimation(MLE)was used to identify students’ attribute mastery mode,classify the students’ ideal mastery mode and calculate the inclusion rate.Third,based on the results of cognitive diagnosis,the corresponding remedial teaching principles and strategies were put forward,and the concept of logarithmic function(A3),the properties of logarithmic function(A5)and the comprehensive application of logarithmic function(A7)were selected to carry out the remedial teaching design,which can provide a reference for the front-line teachers to carry out the remedial teaching of logarithmic function.