An Application Of The Fusion Model For Cognitive Diagnosis In Junior Algebra

With the further development of quality education, assessment for mathematics learning is also a higher demanded that no longer just provides a result but is as a teaching tool to enhance learning quality. In the field of mathematics education, it is important to study how to apply various cognitive diagnosis models to assess students'learning.This article will go depth study into the fusion model and try to provide a better assessment, through the cognitive analysis at the fusion model in junior algebra, for improving mathematics methodology and students'cognitive development. The main issues studied in the article are:How to apply it in cognitive diagnosis? How do student grasp hypothetical cognitive attributes? Where are the students'strengths? Where are the weaknesses? What are the students'Potential states of knowledge? How should we help the students with individualized remedial teaching?This article compiles and summarizes some relevant literatures about cognitive diagnosis and its models to have a better understanding of cognitive diagnosis and decide on our cognitive diagnostic model. Based on previous empirical researches about cognitive diagnosis, we create our framework of cognitive attributes and prepare the test questionnaire.540 junior students from two average middle school in Zhejiang Province attend the test. We use the software Arpeggio for fusion model to cognitively analyse the questionnaire, so as to explore students'mastery level in hypothetical cognitive attributes, classification of the potential state of knowledge and approaches to remedial teaching. According to this study, the author brings forward some suggestions on inproving teaching in order to help the students with algebra learning.The basic conclusions of this study are as follows:1,The cognitive attributes of the content are needed to diagnose cognition with the fusion model. The study assumed seven cognitive attributes:the basic concepts of algebra expression, the basic operations of algebra expression, the basic concepts of equations,the application of knowledge in problem situation,logical reasoning, using algebraic rules and solving complex problems.2,Students perform differently on the mastery of each cognitive attribute and have various potential states of knowledge. They perform the best in the basic operations of algebra expression among the seven cognitive attributes, and also do well in the basic concepts of equations, the application of knowledge in problem situation and logical reasoning; However students do the poorest in using algebraic rules, and meanwhile they don't do well in the basic concepts of algebra expression and solving complex problems.3,According to the performance of students in tests, the author use fusion model method to generate 46 different possible states of knowledge and draw the tree graph to find possible approaches to remedial teaching.This article mainly includes five parts:In the first part, based on some literatures about cognitive diagnoses,the author obtained the concept of cognitive diagnoses and selected the cognitive diagnostic model for the study--Fusion Model, studying the method and logistica of its parameter estimation,as well as the steps of cognitive diagnosis.In the second part, the author elaborates the general design of the study, and the process of implementation.The third part discusses the design of questionnaire. The questionnaire for cognitive diagnosis should be specially designed so that the possible states of knowledge can be diagnosed according to different responses. It is divided into two steps:Firstly, to determine cognitive skills and form the hypothesis of cognitive attributes. Secondly,to associate the cognitive attributes with the questionnaire and thus creating correlational matrix Q. The questionnaire is key to fusion model for cognitive diagnosis, and should be pre-prepared tested.The fourth part is the results and analyses of the questionnaire, which is the core part of this study. The author carefully analyzes the questionnaire, and discusses the steps of fusion model for cognitive diagnosis, relationship between test subject and cognitive attributes, mastery in every cognitive attribute and possible potential state of konwledge.In the fifth part, according to the analyses on test results of the study, the author summarizes main conclusion of the study and brings forward suggestions on approaches to remedial teaching. At the same time, the author points out some deficiencies of the study.