Study On Cognitive Diagnosis Of Acute Angle Trigonometric Function Of Ninth Grade Students Based On DINA Model

This paper studies the cognitive diagnosis results of grade nine students on trigonometric function of acute angle based on the DINA model.It also studies which cognitive properties of trigonometric function of acute angle have not been mastered by grade nine students and what are the reasons for the difficulties in the cognition of grade nine students.The research adopts questionnaire method,oral report method,questionnaire test method,interview method.Combined with the modern cognitive diagnosis theory,divides the cognitive attributes of the content of acute angle trigonometric function into six attributes,establishes the hierarchical relationship between attributes.The rationality of the hierarchy relation of cognitive attributes was verified by questionnaire and oral report.According to Q-matrix theory,a cognitive diagnostic test tool of acute trigonometric function was developed.Then 179 subjects from three schools were tested for cognitive diagnosis.Through interviews with students,this paper analyzes the typical mistakes of students' acute angle trigonometry and analyzes the reasons why students in grade nine have difficulty in recognizing acute angle trigonometry.The study shows that the cognitive diagnosis results of grade nine students about acute angle trigonometry are as follows:(1)More than half of the subjects mastered all the cognitive attributes of trigonometric function of acute angle,and had better cognitive structure of it.The other 41.9% of the subjects had more or less difficulty in recognizing trigonometric function of acute angle.(2)On the whole,the subjects' mastery of six cognitive attributes were uneven,with some strong and some weak.The concept of trigonometric function of acute angle is best grasped by students.The better cognitive attributes are A1(the concept of acute angle trigonometric function),A4(calculate the acute angle trigonometric functions using the calculator)and A6(practical application of acute angle trigonometric functions);the poorer cognitive attribute is A5(solving right triangle).(3)There are 12 kinds of cognitive attributes mastery models,and more than half of the subjects belong to the ideal mastery model.(4)The subjects with the same scores in the cognitive test of acute angle trigonometric function may not have the same cognitive attributes mastery mode.The subjects with the same mastery pattern did not necessarily score the same.(5)The average,median,mode and other data of the three schools showed no significant difference,but the average probability of mastering cognitive attribute A4(calculate the acute angle trigonometric functions using the calculator)and A5(solving right triangle)in school C was significantly lower than in the other two schools.The objective reasons for the students' cognitive difficulties in trigonometric function of acute angle are as follows:(1)difficulties brought by the particularity of trigonometric function of acute angle to students' cognition;(2)the arrangement of content and the design of teaching materials;(3)the teachers' subject knowledge and teaching methods.The subjective reasons are as follows:(1)students' own foundation is weak,and the degree of knowledge organization is poor;(2)students' learning methods are not appropriate,and they do not pay attention to thinking and reflection;(3)students' weak operational ability;(4)students' lack confidence in solving math problems.The teaching suggestions on the acute angle trigonometry are as follows:(1)strengthen the cognition of the concept of trigonometric function of acute angle;(2)pay attention to the context introduction,pay attention to enlighten and guide;(3)help students understand acute angle trigonometry from the prospective of history;(4)Integrate information technology,promote students' deep understanding.