小学数学空间与图形问题解决的认知诊断研究：0-1计分与多级计分的比较

发布时间：2018-04-04 15:00

本文选题：空间与图形　切入点：认知诊断　出处：《浙江师范大学》2014年硕士论文

【摘要】：数学问题解决能力是学生数学素养的重要标志,培养学生数学问题解决能力是小学数学教育的一个重要目标,空间与图形是小学生数学学习的一个主要部分。国内目前使用的传统的学业测评方式和测验理论不能揭示学生问题解决的内在心理过程,而作为新一代测验理论的核心发展起来的认知诊断则很好地解决了这一问题。但国内对认知诊断的研究多集中在理论研究上,实践研究较少,国内尚未有人对空间与图形问题解决进行系统的研究,其相关研究主要集中在图形推理部分。针对以往研究的不足,本研究使用规则空间方法从模拟和实证两个方面对小学数学空间与图形问题解决进行了认知诊断研究。模拟研究部分采用Leighton,Gierl和Hunka(2004)提出的无结构型、线型、收敛型和发散型四种基本属性层级关系,比较了0-1计分与多级计分下四种层级结构规则空间方法分类的属性诊断判准率(MMR)和模式判准率(PMR)。实证研究部分以浙江金华和温州地区5所小学六年级学生为研究对象,采用自编的小学数学空间与图形认知诊断测验为测验工具,共收集1106名学生有效数据。针对以往研究的不足,本研究采用0-1计分和多级计分的规则空间方法对学生的空间与图形问题解决能力进行了诊断,并对0-1计分和多级计分的规则空间方法的诊断结果进行了比较。模拟研究的主要结论如下： (1)不同计分方式和不同的层级结构以及两者间的交互效应均会影响PMR准确性。在0-1计分下,无结构型的PMR显著低于结构型,但结构型之间无显著差异；在多级计分下,无结构型、发散型和收敛型显著低于线型；而且无论是在哪种层级结构下,多级计分的PMR均显著高于0-1计分。 (2)不同计分方式和不同的层级结构以及两者间的交互效应均会影响MMR准确性。在0-1计分下,无结构型的MMR显著低于结构型,但结构型之间无显著差异；在多级计分下,各层级结构的MMR均较高；而且无论是在哪种层级结构下,多级计分的MMR均显著高于0-1计分。实证研究的主要结论如下： (1)基于认知诊断理论所编制的空间与图形测验具有良好的心理计量学属性,测验信效度良好。采用项目反应理论与分层回归统计方法相结合的方法进行研究,发现认知内容属性和认知技能属性是影响项目难度的两个主要的认知特征,是影响小学数学空间与图形问题解决的两个主要认知因素。 (2)基本算术运算和基本空间与图形知识是小学六年级学生掌握较为巩固的属性,而在转置、图式表征和识别隐含条件这种认知技能属性方面的能力较为薄弱,是教师应当注意补救教学以及学生学习的重点。 (3)0-1计分和多级计分的规则空间方法对学生的知识状态以及属性掌握概率的诊断存在较大的差别,0-1计分对学生的学习诊断信息不如多级计分的细致。
[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.
【学位授予单位】：浙江师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：B842

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