【作者】 陈顺；

【导师】 韩继伟；

【作者基本信息】 东北师范大学 ， 数学教育， 2021， 硕士

【摘要】 学习进阶是描述学生在一定时间跨度内学习和探究某一主题时依次进阶、逐级深化的纵向思维发展过程。近年来,学习进阶逐步渗入到数学等众多学科的教育研究领域中,但我国的相关研究仍处于初步探索阶段。《义务教育数学课程标准(2011年版)》指出,学生对小数的理解过程是教师培养学生建立“数感”的重要途径之一。且诸多研究成果显示,学生无法透彻理解小数相关知识,而小数知识与其他知识(如分数)密切相关。因此,探寻学生对小数的认知发展过程尤为重要。本研究围绕基于Rasch理论对学生的小数学习进阶框架进行构建和检验这一核心问题,主要采用文本分析法、专家咨询法及调查法三种研究方法展开研究。首先对学习进阶以及小数迷思概念的相关研究进行综述。其次,依据《义务教育数学课程标准(2011年版)》,北师大版、人教版、苏教版三版数学教科书及学生小数学习认知发展的相关研究构建小数假设性学习进阶,并结合专家的建议修订学习进阶。再参照小数认知水平相关研究的测试题、TIMSS测试题及教科书中的例习题自主编制小数测试题,并结合专家意见与预测试结果修正试题,以获取正式测试的测量工具。进而,在三、四、五年级中选取六个不同层次的班级进行正式测试,并对其结果进行统计分析,验证正式测量工具的质量。最后,通过对各进阶水平及对应认知任务的平均难度值的分析,适当调整学习进阶,得到最终的小数学习进阶,并用Rasch模型理论验证此学习进阶是否符合学生小数学习的发展轨迹,进而获悉小学生小数学习进阶的实际水平。本研究发现:1.小数学习进阶包含5个进阶水平,由低水平到高水平的进阶顺序依次是小数识别——小数表征——小数(与分数之间)关系——小数运算——小数应用;2.小数学习进阶的测量工具单维性、信效度、拟合度、项目功能差异等各项指标良好,具有较好的质量;3.Rasch模型验证了小数的学习进阶,具体表现为小数学习进阶各进阶水平所对应题目的平均难度,随着进阶水平的升高而依次增加;4.学生对小数知识的掌握整体情况良好,但在“小数(与分数之间)关系”“小数运算”的理解水平上表现较差,进阶水平仍需加强。针对研究结论提出三点建议:完善小学数学教科书有关小数的知识结构及编排顺序;加强小数与分数的联系教学;在小数教学中着重培养学生的运算能力。更多还原

【Abstract】 Learning progression is used to describe the vertical thinking development process of students who are learning and exploring a topic over a certain period of time.In recent years,learning progression has gradually penetrated into the educational research fields of many subjects such as mathematics,but related research in our country is still in the initial stage of exploration.The “Compulsory Education Mathematics Curriculum Standard(2011 edition)”points out that The process of students’ understanding of decimals is one of the important ways for teachers to cultivate students’ “number sense”.And many research results show that students cannot fully understand the knowledge of decimals,and the knowledge of decimals is closely related to other knowledge(such as fractions).so it is particularly important to explore the process of students’ cognitive development of decimals.This research focuses on the core problem of constructing and testing the progression’s framework of students’ decimal learning based on Rasch theory,which mainly uses three research methods: text analysis method,expert consultation method and survey method.First of all,summarizing the study of learning progression and the development of the concept of decimals.Secondly,according to the “Compulsory Education Mathematics Curriculum Standard(2011 edition)”,Beijing Normal University,People’s Education Edition,Jiangsu Education Edition three editions of mathematics textbooks and related research on the cognitive development of students’ decimal learning establishes hypothetical learning progression,and then combines them Expert’s suggestion to revise the learning progression.Thirdly,refer to the test questions related to the cognitive level of decimals,the TIMSS test questions and the sample exercises in the textbooks to independently prepare the decimal test questions,and combine the experts’ opinions and the results of pre-test to modify the test questions to obtain the measurement tools for the formal test.And then,in the third,fourth,and fifth grades,six classes of different levels are selected for formal testing,and perform statistical analysis on the results to verify the quality of the formal measurement tools.Finally,through the analysis of each progression’s level and the average difficulty value of the corresponding cognitive task,after appropriately adjusting the learning progression,the final decimal learning progression is obtained,And use the Rasch model theory to verify whether this learning progression conforms to the development trajectory of students’ decimal learning,and then learn the actual level of elementary school students’ learning progression of decimals.The findings of this study are as follows:1.The learning progression of decimals contains5 progression’s levels.And the progression’s order from low level to high level is decimal recognition-decimal representation-relationship between decimals(and fractions)-decimal operations-decimal applications;2.The advanced measurement tools for decimal learning progression have good indicators such as unidimensionality,reliability and validity,fitness,and differential item functioning;3.The Rasch model validates the learning progression of decimals,which is specifically expressed as the average difficulty of the corresponding questions for each learning progression’s level of decimals,which increases in turn with the increase of the progression’s level;4.Students have a good overall grasp of the knowledge of decimals,but they have poor performance in the understanding of the “relationship between decimals(and fractions)” and “decimal operations”,and the progression’s level still needs to be strengthened.According to the research conclusions,three suggestions are put forward:improve the knowledge structure and arrangement order of decimals in the primary school mathematics textbook;strengthen the teaching of the connection between decimals and fractions;focus on training students’ arithmetic ability in decimal teaching.更多还原