基于DINA模型對初中“一元二次方程”內(nèi)容進(jìn)行認(rèn)知診斷研究

發(fā)布時(shí)間：2018-01-16 20:25

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

【摘要】：認(rèn)知診斷理論是新一代教育測量理論的核心,是心理學(xué)和測量學(xué)的有效結(jié)合。它打破了傳統(tǒng)測量理論只關(guān)注測驗(yàn)結(jié)果的局限性,試圖分析被試在測驗(yàn)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(jié)果的關(guān)系,進(jìn)而對被試的認(rèn)知結(jié)構(gòu)進(jìn)行診斷。目前,認(rèn)知診斷理論在數(shù)學(xué)測驗(yàn)中的應(yīng)用研究主要集中在小學(xué)學(xué)段,對中高段數(shù)學(xué)的認(rèn)知診斷研究比較匱乏。方程是刻畫現(xiàn)實(shí)世界數(shù)量關(guān)系的有效模型,對于培養(yǎng)學(xué)生的模型思想、符號意識、運(yùn)算能力等數(shù)學(xué)素養(yǎng)有很大意義。一元二次方程是初中學(xué)段的重點(diǎn)學(xué)習(xí)內(nèi)容,在代數(shù)學(xué)習(xí)中具有"承上啟下"的作用。此外,一元二次方程與物理、化學(xué)等其他學(xué)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(diǎn),通過認(rèn)知診斷理論試圖探索"一元二次方程"章節(jié)的認(rèn)知屬性及其層級關(guān)系是什么?在確定的認(rèn)知屬性框架下,學(xué)生對方程內(nèi)容的知識掌握狀況如何?其潛在的知識結(jié)構(gòu)是什么?能不能根據(jù)被試是否掌握測驗(yàn)所需的技能或特質(zhì)對學(xué)生進(jìn)行分類,為教學(xué)補(bǔ)救提供參考?基于以上考慮,本文運(yùn)用DINA模型對"一元二次方程,"進(jìn)行認(rèn)知診斷研究。研究內(nèi)容有以下幾點(diǎn):(1)分析初中數(shù)學(xué)"一元二次方程"章節(jié)知識結(jié)構(gòu),確立認(rèn)知屬性,構(gòu)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(yàn)試卷;(3)以河北省邯鄲市某市直中學(xué)初三學(xué)生為研究對象,進(jìn)行測驗(yàn)調(diào)查;(4)基于DINA模型,對調(diào)查回收的測試卷進(jìn)行認(rèn)知診斷測量,并對測量結(jié)果進(jìn)行深入分析與總結(jié);(5)根據(jù)研究結(jié)果,對教師和學(xué)生進(jìn)行信息反饋。本文以河北省邯鄲市某市直中學(xué)的200名學(xué)生為被試對象進(jìn)行了施測調(diào)查。運(yùn)用SPSS和Excel軟件對獲取的數(shù)據(jù)進(jìn)行統(tǒng)計(jì)分析,并且基于DINA模型對被試的作答反應(yīng)進(jìn)行認(rèn)知分析。研究結(jié)論如下:(1)確立了"一元二次方程"章節(jié)的認(rèn)知屬性。本研究將"一元二次方程"章節(jié)的認(rèn)知屬性分為了內(nèi)容屬性、過程屬性、技能屬性3個(gè)維度,以及7個(gè)屬性,分別是方程的基本概念、根的判別、根與系數(shù)的關(guān)系、把知識應(yīng)用于情景中的能力、運(yùn)用代數(shù)規(guī)則、方程求解、解決復(fù)雜的實(shí)際問題。(2)不同班級各認(rèn)知屬性掌握概率有明顯差異。學(xué)生對方程的基本概念掌握良好,在根與系數(shù)的關(guān)系、把知識應(yīng)用于情景中的能力、運(yùn)用代數(shù)規(guī)則這3個(gè)屬性上的掌握比較欠缺。(3)屬性掌握模式是對學(xué)生潛在知識狀態(tài)的反應(yīng),可以更全面、細(xì)致、深入的展現(xiàn)學(xué)生的學(xué)習(xí)情況。"內(nèi)隱"的屬性掌握模式和"外顯"的作答反應(yīng)模式并不等價(jià),具有不同的屬性掌握模式的學(xué)生可能會出現(xiàn)相同的成績或作答反應(yīng),而具有相同的屬性掌握模式的學(xué)生也可能會出現(xiàn)不同的成績或作答反應(yīng)。本研究中,約80%的學(xué)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(xué)位授予單位】：中央民族大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G633.6

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