本文選題：空間與圖形　切入點：認知診斷　出處：《浙江師范大學》2014年碩士論文

【摘要】：數學問題解決能力是學生數學素養(yǎng)的重要標志,培養(yǎng)學生數學問題解決能力是小學數學教育的一個重要目標,空間與圖形是小學生數學學習的一個主要部分。國內目前使用的傳統(tǒng)的學業(yè)測評方式和測驗理論不能揭示學生問題解決的內在心理過程,而作為新一代測驗理論的核心發(fā)展起來的認知診斷則很好地解決了這一問題。但國內對認知診斷的研究多集中在理論研究上,實踐研究較少,國內尚未有人對空間與圖形問題解決進行系統(tǒng)的研究,其相關研究主要集中在圖形推理部分。針對以往研究的不足,本研究使用規(guī)則空間方法從模擬和實證兩個方面對小學數學空間與圖形問題解決進行了認知診斷研究。 模擬研究部分采用Leighton,Gierl和Hunka(2004)提出的無結構型、線型、收斂型和發(fā)散型四種基本屬性層級關系,比較了0-1計分與多級計分下四種層級結構規(guī)則空間方法分類的屬性診斷判準率(MMR)和模式判準率(PMR)。 實證研究部分以浙江金華和溫州地區(qū)5所小學六年級學生為研究對象,采用自編的小學數學空間與圖形認知診斷測驗為測驗工具,共收集1106名學生有效數據。針對以往研究的不足,本研究采用0-1計分和多級計分的規(guī)則空間方法對學生的空間與圖形問題解決能力進行了診斷,并對0-1計分和多級計分的規(guī)則空間方法的診斷結果進行了比較。 模擬研究的主要結論如下： (1)不同計分方式和不同的層級結構以及兩者間的交互效應均會影響PMR準確性。在0-1計分下,無結構型的PMR顯著低于結構型,但結構型之間無顯著差異；在多級計分下,無結構型、發(fā)散型和收斂型顯著低于線型；而且無論是在哪種層級結構下,多級計分的PMR均顯著高于0-1計分。 (2)不同計分方式和不同的層級結構以及兩者間的交互效應均會影響MMR準確性。在0-1計分下,無結構型的MMR顯著低于結構型,但結構型之間無顯著差異；在多級計分下,各層級結構的MMR均較高；而且無論是在哪種層級結構下,多級計分的MMR均顯著高于0-1計分。 實證研究的主要結論如下： (1)基于認知診斷理論所編制的空間與圖形測驗具有良好的心理計量學屬性,測驗信效度良好。采用項目反應理論與分層回歸統(tǒng)計方法相結合的方法進行研究,發(fā)現認知內容屬性和認知技能屬性是影響項目難度的兩個主要的認知特征,是影響小學數學空間與圖形問題解決的兩個主要認知因素。 (2)基本算術運算和基本空間與圖形知識是小學六年級學生掌握較為鞏固的屬性,而在轉置、圖式表征和識別隱含條件這種認知技能屬性方面的能力較為薄弱,是教師應當注意補救教學以及學生學習的重點。 (3)0-1計分和多級計分的規(guī)則空間方法對學生的知識狀態(tài)以及屬性掌握概率的診斷存在較大的差別,0-1計分對學生的學習診斷信息不如多級計分的細致。
[Abstract]:Mathematical problem-solving ability is an important symbol of students' mathematical literacy. Cultivating students' mathematical problem-solving ability is an important goal of primary school mathematics education. Space and graphics are one of the main parts of primary school students' mathematics learning.The traditional academic evaluation methods and test theories currently used in China can not reveal the inner psychological process of students' problem-solving, but the cognitive diagnosis, which is the core of the new generation of test theory, has solved this problem very well.In view of the shortcomings of previous studies, this study uses the rule space method to study the cognitive diagnosis of mathematical space and figure problem solving in primary school from the aspects of simulation and demonstration.In the simulation part, four basic attribute hierarchies, which are non-structural, linear, convergent and divergent, are proposed by Leighton Gierl and Hunkaer (2004).The attribute diagnostic accuracy (MMRs) and the pattern estimation rate (PMRs) of four hierarchical structure rule space methods under 0-1 score and multilevel score are compared.In view of the shortcomings of previous studies, this study uses the rule space method of 0-1 score and multilevel scoring to diagnose the students' ability to solve spatial and graphic problems.The diagnostic results of 0-1 score and multi-level scoring rule space method are compared.The main conclusions of the simulation study are as follows:1) the accuracy of PMR is affected by different scoring methods, different hierarchies and the interaction between them.Under the 0-1 score, the PMR of the unstructured type was significantly lower than that of the structural type, but there was no significant difference between the structural type and the structural type; the non-structural, divergent and convergent type was significantly lower than that of the linear type under the multi-level score; and no matter under any hierarchical structure,The PMR of multilevel score was significantly higher than that of 0-1 score.2) the accuracy of MMR is affected by different scoring methods, different hierarchies and the interaction between them.Under the 0-1 score, the MMR of the unstructured type was significantly lower than that of the structural type, but there was no significant difference between the structural types; under the multi-level score, the MMR of each hierarchy was higher; and no matter what the hierarchical structure,The MMR of multilevel score was significantly higher than that of 0-1 score.The main conclusions of the empirical study are as follows:1) the spatial and graphic tests based on cognitive diagnostic theory have good psychometric properties and good reliability and validity.Using the method of item response theory and hierarchical regression statistics, it is found that cognitive content attribute and cognitive skill attribute are the two main cognitive characteristics that affect the difficulty of the project.It is the two main cognitive factors that affect the problem solving of mathematics space and graph in primary school.(2) basic arithmetic operations and basic knowledge of space and graphics are relatively strong attributes of primary school students in sixth grade, but their ability in transposition, schema representation and recognition of implicit conditions is relatively weak.Teachers should pay attention to remedial teaching and students' study.There is a great difference between the rule space method of 0-1 score and multilevel score in the diagnosis of students' knowledge state and attribute mastery probability. The 0-1 score is not as detailed as the multilevel score in the diagnosis of students' learning information.
【學位授予單位】：浙江師范大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：B842

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