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统计活动视角下的高中生统计学习研究

【作者】 贺睿杰

【导师】 鲍建生;

【作者基本信息】 华东师范大学, 课程与教学论, 2020, 博士

【摘要】 面对社会的需求和变化,从20世纪80年代开始,各国的教育研究者、政策制定者和统计学家逐渐重视学校统计的教学。我国在历次数学课程改革中也逐渐提升了统计内容在数学课程中的地位和重要性。但尽管如此,学校的统计教学似乎并不能满足现代社会对统计学习的需求,学习者在学习统计概念、知识后,不能运用其解决实际问题的现象时有发生。通过统计活动的方式进行统计教学是增强统计教学效果的重要手段之一。传统的统计学习评价方式仅仅能够评测学生的知识和概念的掌握,不能从活动的角度的对学生学习进行评价。所以构建一个符合统计学科特点的评价框架是十分必要的。基于上述考虑,本文的一个研究目标就是构建一个能够从统计活动的角度反映学生统计学习水平的评价框架,并且在这个基础上,解决以下两个问题:(1)学习高中统计前,学生的统计活动具有怎样的表现特征和水平?各个阶段中学生的统计活动具有怎样的表现特征和水平?不同类型班级学生之间的表现水平是否存在差异?如果存在差异,那么与差异相关的因素是什么?(2)高中统计学习后,学生的统计活动具有怎样的表现特征与水平?课堂教学期间学生统计活动水平如何?高中统计内容学习后学生在统计活动各个阶段具有怎样的表现特征和水平,相比于学习前是否有变化?不同类型班级学生之间的水平表现是否存在差异,差异是否有所改变?为了完成评价框架的构建,研究者以美国LOCUS统计水平测试的理论框架为基础,通过对相关资料和研究的梳理,对其进行补充和修订,得到统计活动水平测试框架。该框架将统计活动划分为计划和形成问题、收集数据、处理和分析数据、推断和说明结论四个阶段,每个阶段有不同的要求,每个水平学生会有不同的活动表现。在研究框架的基础上,本研究编制了相应的测试卷,通过对约170名高中生统计内容学习前后的活动水平变化分析,回答本研究的问题。此外,为了研究课堂教学过程中的活动,本研究同时构建了一个课堂统计观察框架,通过课堂录像分析的方式从数据、情境、变异三个维度评价课堂统计活动的构建。在研究过程中同时对师生进行了访谈,以发现他们对统计活动的看法。经过量化和质性的分析,研究得到如下的主要结论:1.学生在高中统计学习前后统计活动表现特征和水平没有实质性的提高;2.学生四个阶段整体水平处于知晓术语、概念和过程的水平,学生当并不能灵活运用统计知识和技能解决实际问题;3.除形成和提出问题阶段外,文科班级学生表现优于理科班级学生。同时笔者在研究过程中发现,统计变异性和学生统计活动具有较强的相关关系。基于这个发现,笔者对统计教学的改革提出具体的教学改革建议:进一步改革考试题目关注点;增加统计教学课时;加强跨学科联动;加强信息技术使用;提高数学教师的统计活动水平;对教师进行现代信息技术的培训。最后,笔者对说明了本研究的局限指出,并对后期可能做出的改进和后续研究提出了展望。

【Abstract】 Facing the needs and changes of the modern society,education researchers,policy makers,and statisticians in various countries have gradually realized the importance of the teaching and learning of statistics in school curriculum since the1980 s.China’s curriculum reforms have also gradually increased the status and importance of statistical content in the mathematics curriculum.However,statistical teaching in basic education stage does not seem to meet the needs of modern society for statistics.After learning statistics,learners often fail to use it to solve practical problems in real context.Teaching statistics through practices is a way to enhance the effectiveness of statistical education.Traditional assessments method for statistics can only assess students’ knowledge and concept,and cannot assess their practical abilities.Therefore,it is very necessary to construct an assessment framework in line with the characteristics of the statistics.Based on the above considerations,one of the goals of this research is to build an assessment framework that can reflect students’ statistical learning level from the perspective of statistical activities,and on this basis,solve the following two questions:A.Before students learn statistics of high school mathematics,what are the performance characteristics and level of their statistical activities?What are the performances of statistical activities of students in each stage? Is there are differences in performance levels between liberal arts classes and science classes? If there are differences,what are the factors related to the differences?B.After students learn statistics of high school mathematics,what are the performance characteristics and level of their statistical activities?What is the performance level of students’ statistical activities during instruction?What are the performances of students in each stage after they learn high school statistics? Is there any change of students’ performances? Is there any difference between different class types of students,and has the difference changed?In order to complete the construction of the assessment framework,the author adapted the Level of Conceptual Understanding of Statistics based on the relevant researches and get an assessment framework.The framework divides statistical activities into four stages: planning and posing questions,collecting data,processing and analyzing data,inferring and interpreting conclusions.Each stage has different requirements.Based on the framework,this research has built test papers to analyzed about 170 high school students’ changes before and after learning high school statistics.In order to study statistical activities in the classroom,this research also constructs an observation framework to evaluates classroom activities from three dimensions: data,context,and variability.During the research,teachers and students were interviewed to discover their thoughts on statistical activities.Through quantitative and qualitative analysis,the main conclusions as follow:1.These is no significance improvement of students’ performance level of statistical activities after studying high school statistics compared to before studying;2.The level of students’ statistical activities in four stages are at level one,that is,students know concepts and processes but cannot flexibly solve practical questions;3.Except for the planning and posing question,the performance of students from liberal art classes is better than the students from science class.The author also found there is a strong correlation between statistical variability and students’ practice.Based on the findings,some suggestions are posed: further reform of examination questions;increase the hours of statistics;strengthen interdisciplinary link;strengthen the using of ICT;improve mathematics teachers’ ability.In the end,the author points out the limitations of this research,and puts forward the future improvements and possible future research.

  • 【网络出版投稿人】 华东师范大学
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