Study On Cognitive Measurement And Diagnosis Of“Addition And Subtraction Of Integral Expression” In Seventh Grade Students

“Addition and subtraction of integral expression”is the basis for middle school students to learn algebra,and mastering this part of knowledge plays an important role in cultivating the core accomplishment of mathematics of middle school students.However,there are various problems in students' cognition of “addition and subtraction of integral expression”in practical teaching.For the reason mentioned above,we select the students in Grade 7 in a middle school in Anshan as the research object in this paper,and a set of test papers has been compiled.The Rasch model and the rule space model are used to conduct cognitive measurement and diagnostic research on the “ addition and subtraction of integral expression”.First of all,according to the curriculum standards and examination syllabus,we compile a set of prediction test papers of “addition and subtraction of integral expression”.Secondly,the Rasch model is used as a cognitive measurement tool to study the cognitive measurement of “addition and subtraction of integral expression”,including the following two aspects:(1)we analyse the test questions of the prediction test papers,and then modify the test questions that do not meet the requirements to form the final formal test paper;(2)we analyze the cognitive measurement results of “addition and subtraction of integral expression”for the students' overall and individual,respectively.Next,the rule space model is used to conduct cognitive diagnosis research on“addition and subtraction of integral expression”,including the following two aspects:(1)we analyze the students' overall cognitive diagnosis results of “ addition and subtraction of integral expression ” according to the estimation of parameters and pattern discrimination;(2)we analyze the students' individual cognitive diagnosis results of “addition and subtraction of integral expression”according to the division of the students' attribute patterns.Finally,it is concluded that most of the students have mastered "using letters to represent numbers","columns to represent quantitative relations","monomials","polynomials" and "similar terms",while a few students have not mastered "combining similar terms","eliminating parentheses" and "whole substitution thinking",and the following four teaching suggestions are put forward for teachers:(1)helping students to clarify basic concepts and grasping the essence of concepts;(2)paying attention to students ' hands-on practice and strengthen basic operations;(3)paying attention to the guidance of problems and improving students' thinking ability;(4)focusing on individual differences and improving the cognitive structure.