The Cognitive Diagnosis On Trigonometric Functions Of High School Based On The DINA Model

Trigonometric functions not only serve as a bridge between geometry and algebra,but also provide a pathway linking elementary mathematics to advanced mathematics.With the development of cognitive diagnostic theory,the use of the DINA model for cognitive diagnosis has attracted the attention of researchers due to its high accuracy in diagnostic rates.The author of this study conducts a cognitive diagnosis of high school students’ learning status in trigonometric functions based on the DINA model.The first step was to extract four attributes from the knowledge points of trigonometric functions: arbitrary angle and radian measure,trigonometric function concepts,graphs and properties,and formulas.Next,a Q matrix was designed based on the hierarchical relationship of the four attributes,and a cognitive diagnostic test was developed accordingly.Then,the quality of the test paper was evaluated based on the results of the pre-test,indicating high reliability and validity for formal testing.Finally,a total of 148 students from three classes(A,B,and C)in the third grade participated in the formal test,and data analysis was conducted using the DINA model with the help of the cognitive diagnostic analysis platform(flex CDMs).The following conclusions were drawn:1.56.76% of the students were able to master all four attributes;with the probabilities of mastery for each attribute being 0.968,0.847,0.740,and 0.746,respectively.2.The cognitive diagnostic results for trigonometric functions in the three classes are as follows: Class A has 6 mastery patterns for the attributes,while Classes B and C have 8 patterns,with some students only mastering the arbitrary angle and radian measure attribute.The ideal mastery pattern rates for the three classes are 95.91%,92%,and 91.83%,respectively.After analyzing the diagnostic results,it was found that 43.24% of the students were facing cognitive difficulties in trigonometric functions.The author of this paper investigates the possible reasons behind this and provides teaching recommendations based on the research findings.