本文關鍵詞：基于DINA模型對初中“一元二次方程”內(nèi)容進行認知診斷研究　出處：《中央民族大學》2017年碩士論文　論文類型：學位論文

  更多相關文章： DINA模型 一元二次方程 項目反應模式 屬性掌握模式 認知診斷

【摘要】：認知診斷理論是新一代教育測量理論的核心,是心理學和測量學的有效結合。它打破了傳統(tǒng)測量理論只關注測驗結果的局限性,試圖分析被試在測驗作答過程中的心理狀態(tài),探索被試的潛在知識狀態(tài)與其作答結果的關系,進而對被試的認知結構進行診斷。目前,認知診斷理論在數(shù)學測驗中的應用研究主要集中在小學學段,對中高段數(shù)學的認知診斷研究比較匱乏。方程是刻畫現(xiàn)實世界數(shù)量關系的有效模型,對于培養(yǎng)學生的模型思想、符號意識、運算能力等數(shù)學素養(yǎng)有很大意義。一元二次方程是初中學段的重點學習內(nèi)容,在代數(shù)學習中具有"承上啟下"的作用。此外,一元二次方程與物理、化學等其他學科的聯(lián)系也十分緊密。所以,本文選擇以"一元二次方程"知識為研究切入點,通過認知診斷理論試圖探索"一元二次方程"章節(jié)的認知屬性及其層級關系是什么?在確定的認知屬性框架下,學生對方程內(nèi)容的知識掌握狀況如何?其潛在的知識結構是什么?能不能根據(jù)被試是否掌握測驗所需的技能或特質(zhì)對學生進行分類,為教學補救提供參考?基于以上考慮,本文運用DINA模型對"一元二次方程,"進行認知診斷研究。研究內(nèi)容有以下幾點:(1)分析初中數(shù)學"一元二次方程"章節(jié)知識結構,確立認知屬性,構建Q矩陣;(2)圍繞"一元二次方程"章節(jié)知識,編制具有診斷效度的測驗試卷;(3)以河北省邯鄲市某市直中學初三學生為研究對象,進行測驗調(diào)查;(4)基于DINA模型,對調(diào)查回收的測試卷進行認知診斷測量,并對測量結果進行深入分析與總結;(5)根據(jù)研究結果,對教師和學生進行信息反饋。本文以河北省邯鄲市某市直中學的200名學生為被試對象進行了施測調(diào)查。運用SPSS和Excel軟件對獲取的數(shù)據(jù)進行統(tǒng)計分析,并且基于DINA模型對被試的作答反應進行認知分析。研究結論如下:(1)確立了"一元二次方程"章節(jié)的認知屬性。本研究將"一元二次方程"章節(jié)的認知屬性分為了內(nèi)容屬性、過程屬性、技能屬性3個維度,以及7個屬性,分別是方程的基本概念、根的判別、根與系數(shù)的關系、把知識應用于情景中的能力、運用代數(shù)規(guī)則、方程求解、解決復雜的實際問題。(2)不同班級各認知屬性掌握概率有明顯差異。學生對方程的基本概念掌握良好,在根與系數(shù)的關系、把知識應用于情景中的能力、運用代數(shù)規(guī)則這3個屬性上的掌握比較欠缺。(3)屬性掌握模式是對學生潛在知識狀態(tài)的反應,可以更全面、細致、深入的展現(xiàn)學生的學習情況。"內(nèi)隱"的屬性掌握模式和"外顯"的作答反應模式并不等價,具有不同的屬性掌握模式的學生可能會出現(xiàn)相同的成績或作答反應,而具有相同的屬性掌握模式的學生也可能會出現(xiàn)不同的成績或作答反應。本研究中,約80%的學生可以歸類到14種掌握模式中。
[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.
【學位授予單位】：中央民族大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：G633.6

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