Research On Cognitive Diagnosis Of Letter Representation Of Pupils Based On DINA Model

In the " Compulsory Education Mathematics Curriculum Standard(2011 Edition)",the term "symbolic consciousness" is clearly put forward as one of the ten core mathematical concepts.The "symbolic consciousness" mainly refers to the use of letters to represent numbers and the use of letters to represent equivalent relations in primary school.The abstract thinking of the fourth grade students is in the period of rapid development,letter representation plays an important role in promoting the development of mathematical abstraction.This study is based on the cognitive diagnosis theory and using DINA model to study the "letter representation" ability of fourth-grade primary school students.This study consists of 5 parts:(1)Analyze and determine the cognitive attributes and attribute hierarchy contained in the content of "letter representation",establish a test Q matrix according to the attribute hierarchy of "letter representation",and work out a high quality cognitive diagnostic test of elementary school students'letter representation through the test Q matrix;(2)Using the convenient sampling method,139 students in grade 5 of a primary school in Beijing were selected as the actual test objects to represent the students' academic level at the end of grade 4;(3)Using flexCDMs to analyze the collected test data,cognitive diagnosis of fourth-grade primary school students' letter representation ability,and exploration of students' knowledge state and cognitive structure;(4)Using the method of oral report,analyze the process of students' thinking in letter representation,and explore their mathematical abstraction ability;(5)According to the results of cognitive diagnosis and oral report analysis,specific improvement suggestions are provided for the teaching of "letter representation".The main conclusions of this study include the following four aspects:(1)The cognitive attribute contained in the content of "letter representation" is established,which are A1 letter representation quantity,A2 letters represent numbers,A3 letters represent a single relationship,A4 letters represent combinatorial relationships.Attribute hierarchy is linear and progressive.(2)The fourth grade students had a good grasp of the cognitive attributes of "letter representation",among which the subjects had a relatively good grasp of the cognitive attribute of the quantity of letter representations(A1),and a relatively poor grasp of the two cognitive attributes of letter representation numbers(A2)and letter representation combination(A4).(3)139 students participated in the"letter representation" test,among which 121 students were classified into four ideal master patterns.The classification rate of ideal master pattern was 87.05%,and the proportion of master pattern was(1111)reached 74.1%,it showed that 74.1%of the students mastered all the cognitive attributes.(4)For the real situation of the problem,if there is no letter,the students' mathematical abstraction ability is not high,the active use of letter symbol consciousness is weak.According to the results of cognitive diagnosis and oral report analysis,this study proposes the following four suggestions for teaching improvement:(1)Pay attention to the analysis of quantitative relationship in teaching.(2)To establish a realistic situation and guide students to understand that number is the abstraction of quantity,and then to understand the abstract meaning of letter representation numbers.(3)Permeate the idea of letter representation in the teaching of lower grades.(4)The teaching method of simple equation a±x=b in primary schools should be flexible.