本文選題：空間與圖形　切入點(diǎn)：認(rèn)知診斷　出處：《浙江師范大學(xué)》2014年碩士論文

【摘要】：數(shù)學(xué)問題解決能力是學(xué)生數(shù)學(xué)素養(yǎng)的重要標(biāo)志,培養(yǎng)學(xué)生數(shù)學(xué)問題解決能力是小學(xué)數(shù)學(xué)教育的一個(gè)重要目標(biāo),空間與圖形是小學(xué)生數(shù)學(xué)學(xué)習(xí)的一個(gè)主要部分。國(guó)內(nèi)目前使用的傳統(tǒng)的學(xué)業(yè)測(cè)評(píng)方式和測(cè)驗(yàn)理論不能揭示學(xué)生問題解決的內(nèi)在心理過程,而作為新一代測(cè)驗(yàn)理論的核心發(fā)展起來的認(rèn)知診斷則很好地解決了這一問題。但國(guó)內(nèi)對(duì)認(rèn)知診斷的研究多集中在理論研究上,實(shí)踐研究較少,國(guó)內(nèi)尚未有人對(duì)空間與圖形問題解決進(jìn)行系統(tǒng)的研究,其相關(guān)研究主要集中在圖形推理部分。針對(duì)以往研究的不足,本研究使用規(guī)則空間方法從模擬和實(shí)證兩個(gè)方面對(duì)小學(xué)數(shù)學(xué)空間與圖形問題解決進(jìn)行了認(rèn)知診斷研究。 模擬研究部分采用Leighton,Gierl和Hunka(2004)提出的無結(jié)構(gòu)型、線型、收斂型和發(fā)散型四種基本屬性層級(jí)關(guān)系,比較了0-1計(jì)分與多級(jí)計(jì)分下四種層級(jí)結(jié)構(gòu)規(guī)則空間方法分類的屬性診斷判準(zhǔn)率(MMR)和模式判準(zhǔn)率(PMR)。 實(shí)證研究部分以浙江金華和溫州地區(qū)5所小學(xué)六年級(jí)學(xué)生為研究對(duì)象,采用自編的小學(xué)數(shù)學(xué)空間與圖形認(rèn)知診斷測(cè)驗(yàn)為測(cè)驗(yàn)工具,共收集1106名學(xué)生有效數(shù)據(jù)。針對(duì)以往研究的不足,本研究采用0-1計(jì)分和多級(jí)計(jì)分的規(guī)則空間方法對(duì)學(xué)生的空間與圖形問題解決能力進(jìn)行了診斷,并對(duì)0-1計(jì)分和多級(jí)計(jì)分的規(guī)則空間方法的診斷結(jié)果進(jìn)行了比較。 模擬研究的主要結(jié)論如下： (1)不同計(jì)分方式和不同的層級(jí)結(jié)構(gòu)以及兩者間的交互效應(yīng)均會(huì)影響PMR準(zhǔn)確性。在0-1計(jì)分下,無結(jié)構(gòu)型的PMR顯著低于結(jié)構(gòu)型,但結(jié)構(gòu)型之間無顯著差異；在多級(jí)計(jì)分下,無結(jié)構(gòu)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(jí)結(jié)構(gòu)下,多級(jí)計(jì)分的PMR均顯著高于0-1計(jì)分。 (2)不同計(jì)分方式和不同的層級(jí)結(jié)構(gòu)以及兩者間的交互效應(yīng)均會(huì)影響MMR準(zhǔn)確性。在0-1計(jì)分下,無結(jié)構(gòu)型的MMR顯著低于結(jié)構(gòu)型,但結(jié)構(gòu)型之間無顯著差異；在多級(jí)計(jì)分下,各層級(jí)結(jié)構(gòu)的MMR均較高；而且無論是在哪種層級(jí)結(jié)構(gòu)下,多級(jí)計(jì)分的MMR均顯著高于0-1計(jì)分。 實(shí)證研究的主要結(jié)論如下： (1)基于認(rèn)知診斷理論所編制的空間與圖形測(cè)驗(yàn)具有良好的心理計(jì)量學(xué)屬性,測(cè)驗(yàn)信效度良好。采用項(xiàng)目反應(yīng)理論與分層回歸統(tǒng)計(jì)方法相結(jié)合的方法進(jìn)行研究,發(fā)現(xiàn)認(rèn)知內(nèi)容屬性和認(rèn)知技能屬性是影響項(xiàng)目難度的兩個(gè)主要的認(rèn)知特征,是影響小學(xué)數(shù)學(xué)空間與圖形問題解決的兩個(gè)主要認(rèn)知因素。 (2)基本算術(shù)運(yùn)算和基本空間與圖形知識(shí)是小學(xué)六年級(jí)學(xué)生掌握較為鞏固的屬性,而在轉(zhuǎn)置、圖式表征和識(shí)別隱含條件這種認(rèn)知技能屬性方面的能力較為薄弱,是教師應(yīng)當(dāng)注意補(bǔ)救教學(xué)以及學(xué)生學(xué)習(xí)的重點(diǎn)。 (3)0-1計(jì)分和多級(jí)計(jì)分的規(guī)則空間方法對(duì)學(xué)生的知識(shí)狀態(tài)以及屬性掌握概率的診斷存在較大的差別,0-1計(jì)分對(duì)學(xué)生的學(xué)習(xí)診斷信息不如多級(jí)計(jì)分的細(xì)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(xué)位授予單位】：浙江師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：B842

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 丁樹良;楊淑群;汪文義;;可達(dá)矩陣在認(rèn)知診斷測(cè)驗(yàn)編制中的重要作用[J];江西師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2010年05期

2 封平華,谷艷華;新課程標(biāo)準(zhǔn)下《空間與圖形》的教育理念[J];河南教育學(xué)院學(xué)報(bào)(自然科學(xué)版);2003年02期

3 余娜;辛濤;;認(rèn)知診斷理論的新進(jìn)展[J];考試研究;2009年03期

4 郭民;;中美兩國(guó)義務(wù)教育階段幾何課程的比較研究及其啟示[J];外國(guó)中小學(xué)教育;2009年10期

5 李峰;余娜;辛濤;;小學(xué)四、五年級(jí)數(shù)學(xué)診斷性測(cè)驗(yàn)的編制——基于規(guī)則空間模型的方法[J];心理發(fā)展與教育;2009年03期

6 紀(jì)桂萍，焦書蘭，，何海東;小學(xué)生數(shù)學(xué)問題解決與心理表征[J];心理發(fā)展與教育;1996年01期

7 張慶林,管鵬;小學(xué)生表征應(yīng)用題的元認(rèn)知分析[J];心理發(fā)展與教育;1997年03期

8 陳曉云;10一14歲兒童幾何圖形推理能力的研究[J];心理科學(xué);1999年03期

9 曾盼盼,俞國(guó)良;小學(xué)生視覺—空間表征類型和數(shù)學(xué)問題解決的研究[J];心理科學(xué);2003年02期

10 涂冬波;戴海琦;蔡艷;丁樹良;;小學(xué)兒童數(shù)學(xué)問題解決認(rèn)知診斷[J];心理科學(xué);2010年06期

相關(guān)博士學(xué)位論文 前1條

1 涂冬波;項(xiàng)目自動(dòng)生成的小學(xué)兒童數(shù)學(xué)問題解決認(rèn)知診斷CAT編制[D];江西師范大學(xué);2009年

本文編號(hào)：1710457