基于DINA模型对初中“一元二次方程”内容进行认知诊断研究

发布时间：2018-01-16 20:25

本文关键词：基于DINA模型对初中“一元二次方程”内容进行认知诊断研究　出处：《中央民族大学》2017年硕士论文　论文类型：学位论文

【摘要】：认知诊断理论是新一代教育测量理论的核心,是心理学和测量学的有效结合。它打破了传统测量理论只关注测验结果的局限性,试图分析被试在测验作答过程中的心理状态,探索被试的潜在知识状态与其作答结果的关系,进而对被试的认知结构进行诊断。目前,认知诊断理论在数学测验中的应用研究主要集中在小学学段,对中高段数学的认知诊断研究比较匮乏。方程是刻画现实世界数量关系的有效模型,对于培养学生的模型思想、符号意识、运算能力等数学素养有很大意义。一元二次方程是初中学段的重点学习内容,在代数学习中具有"承上启下"的作用。此外,一元二次方程与物理、化学等其他学科的联系也十分紧密。所以,本文选择以"一元二次方程"知识为研究切入点,通过认知诊断理论试图探索"一元二次方程"章节的认知属性及其层级关系是什么?在确定的认知属性框架下,学生对方程内容的知识掌握状况如何?其潜在的知识结构是什么?能不能根据被试是否掌握测验所需的技能或特质对学生进行分类,为教学补救提供参考?基于以上考虑,本文运用DINA模型对"一元二次方程,"进行认知诊断研究。研究内容有以下几点:(1)分析初中数学"一元二次方程"章节知识结构,确立认知属性,构建Q矩阵;(2)围绕"一元二次方程"章节知识,编制具有诊断效度的测验试卷;(3)以河北省邯郸市某市直中学初三学生为研究对象,进行测验调查;(4)基于DINA模型,对调查回收的测试卷进行认知诊断测量,并对测量结果进行深入分析与总结;(5)根据研究结果,对教师和学生进行信息反馈。本文以河北省邯郸市某市直中学的200名学生为被试对象进行了施测调查。运用SPSS和Excel软件对获取的数据进行统计分析,并且基于DINA模型对被试的作答反应进行认知分析。研究结论如下:(1)确立了"一元二次方程"章节的认知属性。本研究将"一元二次方程"章节的认知属性分为了内容属性、过程属性、技能属性3个维度,以及7个属性,分别是方程的基本概念、根的判别、根与系数的关系、把知识应用于情景中的能力、运用代数规则、方程求解、解决复杂的实际问题。(2)不同班级各认知属性掌握概率有明显差异。学生对方程的基本概念掌握良好,在根与系数的关系、把知识应用于情景中的能力、运用代数规则这3个属性上的掌握比较欠缺。(3)属性掌握模式是对学生潜在知识状态的反应,可以更全面、细致、深入的展现学生的学习情况。"内隐"的属性掌握模式和"外显"的作答反应模式并不等价,具有不同的属性掌握模式的学生可能会出现相同的成绩或作答反应,而具有相同的属性掌握模式的学生也可能会出现不同的成绩或作答反应。本研究中,约80%的学生可以归类到14种掌握模式中。
[Abstract]:Cognitive diagnostic theory is the core of the new generation of educational measurement theory and an effective combination of psychology and measurement. It breaks the limitation of traditional measurement theory which only pays attention to test results. This paper attempts to analyze the psychological state of the subjects in the process of answering, to explore the relationship between the potential knowledge state of the subjects and their answer results, and then to diagnose the cognitive structure of the subjects. The research on the application of cognitive diagnostic theory in mathematics test is mainly focused on primary school, but the research on cognitive diagnosis of middle and high level mathematics is scarce. The equation is an effective model to describe the quantitative relationship in the real world. It is of great significance to cultivate students' mathematical literacy, such as model thought, symbol consciousness, operation ability and so on. In algebra learning has the role of "connecting between the past and the next." in addition, the quadratic equation of the United States and physics, chemistry and other disciplines are also very close. In this paper, we choose the knowledge of "quadratic equation" as the starting point, and try to explore the cognitive properties and hierarchical relationship of the chapter of "quadratic equation of one variable" through the theory of cognitive diagnosis. What is the status of students' knowledge of the content of equation under the frame of definite cognitive attributes? What is its potential knowledge structure? Can the students be classified according to whether they have mastered the skills or characteristics required for the test, so as to provide reference for teaching remedies? Based on the above considerations, this paper uses the DINA model to study the cognitive diagnosis of "quadratic equation of one variable," which includes the following points: 1) analyzing the knowledge structure of the chapter of "quadratic equation of one variable" in junior high school mathematics. Establishing cognitive attribute and constructing Q matrix; (2) compiling the test papers with diagnostic validity around the knowledge of "quadratic equation of one variable"; (3) taking the junior high school students of Handan City, Hebei Province as the research object, to carry on the test investigation; (4) based on the DINA model, the cognitive diagnostic measurement of the test papers collected from the investigation was carried out, and the results were analyzed and summarized deeply. According to the results of the study. In this paper, 200 students from a middle school in Handan City, Hebei Province, were investigated. SPSS and Excel software were used to analyze the data obtained. Counting analysis. And based on the DINA model, the cognitive analysis of the subjects' responses was carried out. The conclusions are as follows: 1). The cognitive attribute of the chapter of "quadratic equation of one variable" is established, and the cognitive attribute of the chapter of "quadratic equation of one variable" is divided into content attribute. The three dimensions of process attribute, skill attribute and seven attributes are the basic concept of equation, the discrimination of root, the relationship between root and coefficient, the ability to apply knowledge to the situation, the application of algebraic rules, and the solution of equation. To solve the complex practical problem. (2) there are significant differences in the probability of grasping cognitive attributes in different classes. The students have a good grasp of the basic concepts of equations, the relationship between the root and the coefficient, and the ability to apply knowledge to the situation. The application of algebraic rules to the mastery of these three attributes is relatively deficient. The mode of attribute mastery is a response to the students' potential knowledge status and can be more comprehensive and meticulous. Show the students' learning situation in depth. The attribute mastering mode of "implicit" and the "explicit" response mode are not equivalent. Students with different attribute mastery models may have the same scores or answer responses, while students with the same attribute mastery model may also have different scores or responses. About 80% students can be categorized into 14 mastery models.
【学位授予单位】：中央民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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