Cognitive Diagnosis Of Fractional Addition And Subtraction In Junior High School Students

Fractional addition and subtraction is the difficulty of the four operations of fractions.And it is also one of the emphases of the "number and algebra" in junior high school.It is more comprehensive.It is not only closely connected with integral expression operation and factorization,but also closely related to fractional arithmetic and rational number operation,which poses a challenge to the development of students’arithmetic capability.In order to promote the improvement of junior high school students’ arithmetic ability,it is necessary to have a detailed understanding of their mastery of fractional addition and subtraction.The development of cognitive diagnosis theory makes it possible to measure students’ internal knowledge structure.Compared with traditional examination evaluation which only provides a total score or ability value,the cognitive diagnosis assessment can provide the diagnostic information of students’ knowledge.And it provides guidance for remedial learning.Based on the theory of cognitive diagnosis,this study carried out a cognitive diagnosis study on the content of fractional addition and subtraction in junior high school students.Firstly,this study adopted literature analysis,expert evaluation and verbal report to establish a reasonable cognitive model of fractional addition and subtraction.Secondly,according to the Q matrix theory,the cognitive diagnostic test was compiled.And then we made cognitive diagnostic assessment for 308 subjects from 6 classes by the linear logistic model.Thirdly,the feedback of diagnosis results and the design of remedial teaching plan were carried out.Finally,we put forward the teaching suggestions of fractional addition and subtraction.The results show that:First,the cognitive model of fractional addition and subtraction for junior high school students consists of 8 attributes.And there was a certain logical relationship between the attributes.The validity of this cognitive model was verified by the method of oral report and the hierarchy consistency index(HCI).Second,by modifying the problems whose difficulty and degree of differentiation were unreasonable in small-scale test,the test paper of fractional addition and subtraction was finally obtained.The difficult degree of the questions was reasonable.The discrimination degree was basically qualified.And the test had relatively good reliability and validity.Third,we analyzed the response data of the subjects by flexCDMs and reached the following conclusions:(1)There were differences in the mastery of the eight cognitive attributes of the students in this school.The probability of eight cognitive attributes was as follows:A7(multi-step operation),A8(sign problem),A6(the simplest fraction),A4(reduction of a fraction),A5(add and subtract the fractions in the different denominator),A3(reduction to common denominator),A1(the basic knowledge)and A2(add and subtract the fractions in the same denominator)from low to high.Especially,the probability of A6,A7,A8 were less than 60%,which were the focus of remedy.(2)65.22%of the subjects were distributed in 6 ideal mastery modes,which indicated that the students’ knowledge state was relatively concentrated.(3)78.13%of the subjects were distributed in the ideal mastery mode with 5 or more attributes.This showed that most of the students were in the middle and high level in the design remedial teaching plans with the help of the learning path characterization for classes and individuals,which were conducive to the teachers and students to identify the direction of improvement.Fifth,we divided 8 cognitive attributes into four quadrants according to certain standards,and put forward four teaching suggestions.(1)Deepen understanding and strengthen the teaching of algorithms and algorithms fractional addition and subtraction algorithm and calculation theory.(2)Expand training and pay attention to train students’ operational thinking and symbol sense.(3)Focus on details and cultivate students’ good habit of adding and subtracting fractions.(4)Integrate knowledge and improve the cognitive structure of students’ symbolic operation.