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5~6岁儿童数学问题解决认知诊断评估工具的开发及应用研究

【作者】 李莉

【导师】 周欣;

【作者基本信息】 华东师范大学, 学前教育学, 2020, 博士

【摘要】 数学问题解决是学前数学教育质量监测与评估中较为重要的内容,但相关的研究却比较薄弱。为了接轨国际儿童早期数学学习与评估的价值导向,更好地衔接小学数学课程目标,落实从数学问题解决的视角监测学前儿童的数学学习与发展,以及从微观知识结构入手真正促进儿童数学学习的发展,本研究以5~6岁儿童为研究对象,以“数与运算”领域的问题解决为研究内容,尝试应用认知诊断理论与技术开发5~6岁儿童“数与运算”问题解决的认知诊断评估工具,并使用此工具开展认知诊断评估,以及基于认知诊断评估结果开展教育干预研究。研究一:开发《5~6岁儿童“数与运算”问题解决认知诊断测验》(简称CDTMPS测验)。首先,构建5~6岁儿童“数与运算”问题解决的认知模型。该认知模型包括数学知识与技能、语义理解和数量推理3个认知成分以及下属的11个认知属性:基数概念、集合比较、10以内加减运算;合并型语义理解、结果未知型变化语义理解、变化未知型变化语义理解、一致型比较语义理解、非一致型比较语义理解;加减逆反推理、加法组合推理和一对多推理。其次,开发CDT-MPS测验。质量检验的结果表明,本研究构建的认知模型较为科学合理,CDT-MPS测验(正式版)具有良好的信度和效度,包含35道题,采用一对一口头测查及0-1计分,测试时间在30分钟左右。研究二:5~6岁儿童“数与运算”问题解决的认知诊断评估。考查5~6岁儿童“数与运算”问题解决的发展状况,了解CDT-MPS测验作为学前儿童数学教育监测评估工具的价值。第一,以上海、湖南和河南三个地区13所城乡幼儿园的680名大班儿童为被试,开展认知诊断评估的横向研究。结果表明:三个地区样本儿童的整体数学问题解决能力均处于中等水平,对数学知识与技能的掌握好于对语义理解及数量推理的掌握;虽然三个地区城市样本儿童的整体数学问题解决能力不存在显著差异,湖南和河南地区城乡和农村样本儿童以及不同性别和不同等级幼儿园儿童的整体数学问题解决能力存在显著差异,但不同地区、城乡、性别和园所等级的样本儿童对11个认知属性的掌握均存在各自的优势和不足。第二,以上海地区4所幼儿园的245名大班儿童为被试,开展认知诊断评估的跟踪研究。分别在大班上学期和下学期进行两次CDT-MPS测试,间隔为7个月。结果表明:样本儿童的整体数学问题解决能力有显著提升,但对11个认知属性的掌握进步速度各不相同;一级幼儿园和二级幼儿园样本儿童的进步不存在显著差异;男孩的进步显著大于女孩。研究三:基于认知诊断评估结果开展教育干预研究。被试来自上海市同一所幼儿园两所大班的60名儿童,分为10以内加减运算、变化语义理解、加减逆反推理、加法组合推理和一对多推理五种干预,每种干预12名被试。以小组干预和个别干预相结合的方法,每种干预每周干预1次(每次30~40分钟),共8次。结果表明:变化语义理解和加法组合推理两组的干预有显著效果;五种干预既有其各自有所需的不同核心经验,也有共同所需的基本数学技能及干预措施。综上,应用认知诊断评估开发学前数学领域的评估工具有其优势及难度,本研究为今后的应用研究提供了经验;本研究开发的CDT-MPS测验可以为学前数学教育质量监测提供丰富的信息,有助于教育行政机构从微观层面了解不同地区不同园所数学教育的优势与不足;本研究为今后开展基于认知诊断评估结果的教育干预研究提供了一定的经验和思考,但仍面临较大的挑战,需要更多的探索。

【Abstract】 Mathematics problem solving(MPS)is an important but relatively weak area in the quality monitoring and evaluation of preschool mathematical education.In order to connect with the value orientation of international early children’s mathematics learning and evaluation and the goal of primary school mathematics curriculum,and monitor and promote preschool children’s mathematical learning and development from the perspective of MPS and micro knowledge structure,this study firstly aimed to develop a cognitive diagnosis assessment tool of problem-solving in the field of “number and operation” for 5-6-year-old children.Furthermore,the second purpose of this study was to apply the tool to assess 5-6-year-old children’s MPS and intervene children’s MPS based on the assessment results.Study 1: The cognitive diagnostic test of problem-solving in the field of “number and operation” for 5-6-year-old children(CDT-MPS test for short)was developed.Firstly,the cognitive model of “number and operation” problem-solving for 5-6-yearold children was constructed.The cognitive model included three cognitive components(mathematical knowledge and skills,semantic understanding,and quantitative reasoning)with 11 cognitive attributes(cardinality concept,set comparison,addition and subtraction within the range of natural numbers to 10,combine semantic understanding,result-unknown change semantic understanding,change-unknown change semantic understanding,consistent language comparison semantic understanding,inconsistent language comparison semantic understanding,addition and subtraction inverse reasoning,addition composition reasoning,one-to-many correspondence reasoning).Secondly,the cognitive diagnostic test was developed.The results of quality test indicated that the cognitive model was reasonable.The CDT-MPS test had good reliability and validity,including 35 items.One-to-one interview and 0-1 score system were used,and the test time was about 30 minutes.Study 2: The cognitive diagnostic assessment(CDA for short)of 5-6-year-old children’s “number and operation” problem-solving ability by applying the CDT-MPS test was conducted,to test the value of using CDT-MPS test to monitor preschool children’s mathematics education.Firstly,the MPS ability of 680 children from 13 urban and rural kindergartens in Shanghai,Hunan and Henan were investigated.The results indicated that the whole sample’s overall MPS ability was at a medium level,and the mastery of mathematical knowledge and skills was better than the mastery of semantic understanding and quantitative reasoning.Althouth there was no significant difference in the overall MPS ability among the uraban children,there were significant difference in the overall MPS ability between urban-rural and rural-rural children as well as between different genders and different-level kindergartens.Furthermore,there were different strengths and weaknesses in the mastery of the 11 cognitive attributes of the children from different regions,urban and rural areas,gender and different-level kindergartens.Secondly,the development of MPS ability of 245 children from 4 kindergartens in Shanghai were investigated at two time points within seven months.The results indicated that the children’s overall MPS ability was significant improved.However,the progress speed of mastering the 11 cognitive attributes was different.There was no significant difference in the progress of the children from different-level kindergartens.The progress in MPS ability of boys was significantly greater than that of girls.Study 3: The educational intervention research was carried out based on the results of the CDA in study 2.The subjects included 60 children from two classes in the same kindergarten in Shanghai.They were five intervention groups: addition and subtraction within the range of natural numbers to 10,change semantic understanding,addition and subtraction inverse reasoning,addition composition reasoning,and one-to-many correspondence reasoning.Each kind of intervention group included 12 children and was conducted once a week(30-40 minutes each time)and lasted 8 weeks.The results indicated that the intervention of change semantic understanding and addition composition reasoning had significant effect.Each kind of intervention needed not only different core experience,but also common basic mathematical skills and intervention measures.All in all,there were some advantages and difficulties in using cognitive diagnostic theory and technique to develop and apply CDA tool in the field of preschool mathematics.This study may provide some valuable experience for future applied research.The CDT-MPS test can provide rich information for preschool mathematics education quality monitoring,and help educational administrative agencies understand the strengths and weaknesses of mathematics eudcaton in different regions and kindergartens from the micro level.This study may provide some experience and inspirations for the future research of educational intervention based on the results of CDA.However,it still faces great challenges and needs more exploration.

  • 【网络出版投稿人】 华东师范大学
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