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指向小学生统计推理能力培养的教学模式建构 ——以S校六年级学生为例

【作者】 高翔

【导师】 徐斌艳;

【作者基本信息】 华东师范大学, 课程与教学论, 2020, 博士

【副题名】以S校六年级学生为例

【摘要】 随着“大数据”时代、“互联网+教育”时代的来临,“数据”这一概念逐步渗透到各行各业,并对生产产生了深远的影响。对数据的深度挖掘与分析,并在数据驱动下做出决策成为未来公民必备的技能之一。无论是2018年联合国教科文组织颁布的学生数字化素养,还是2019年国际经济合作与发展组织颁布的PISA 2021数学框架都倡导学生应当具备信息与数据的相关能力与素养。统计推理能力(Statistical Reasoning)是学生在统计问题解决过程中逐步发展的,能运用统计的相关概念进行推理、理解统计信息是如何得出的、根据已有的数据信息作出解释、进行统计推断的能力,具体表现为学生能描述数据的呈现、整理与简化数据、表征数据、分析和解释数据的能力。统计推理能力很好地契合了“大数据”时代对未来公民的“时代诉求”。然而,传统的统计教学存在将统计与数学的教学混为一谈、重视培养学生统计技能过程和运算的培养忽视对学生进行“统计地”思考和推理的培养、学生对统计内容容易失去兴趣等诸多问题。国际上许多研究者已经开始探索进行统计教学改革的尝试,取得了一定的效果,并指出希望在学校数学教育的较早阶段实施。本研究旨在改变我国统计教学的现状,探索培养小学生统计推理能力的教学模式,以期为我国小学阶段的统计教学提供理论支持与实践建议。本研究立足我国小学统计教学存在的三方面问题:(1)教师将“统计教学与现实生活的紧密联系割裂”,导致“统计问题解决活动沦为低水平的、以记忆为主的简单模仿活动”;(2)教师没有意识到“统计活动是一个完整的问题解决过程”、“忽视学生在统计活动中的主动参与”、“无法高效使用合作学习的方式”,从而降低学生对统计学习的兴趣;(3)教师因为“小学阶段统计内容少、考试比重低”等客观原因以及主观上不够重视统计的教学导致的“照本宣科”、“一带而过”现象,忽视学生在统计问题解决过程中的推理与表达等问题,以情境认知理论、情境学习理论、社会文化理论、社会建构理论为理论基础,将设计研究作为方法论的指导,通过借鉴设计研究的研究范式“形成性的研究”,经历了教学模式原型的构建、三轮教学实施的迭代与修正,最终得到了有效培养小学生统计推理能力的教学模式(简称“FC-SR教学模式”)。本研究紧紧围绕三个研究问题:(1)基于相关文献和教学理论,结合我国的统计教学实际,培养小学生统计推理能力的教学模式原型是什么?(2)如何在具体的教学实践中修正、精致教学模式的原型?(3)教学模式产生了怎样的效果?展开了三个方面具体的工作:第一,基于文献综述中统计推理能力的内涵、我国小学阶段统计教学存在的问题、小学阶段统计内容教学的相关建议与策略、已有“问题解决”类教学模式的梳理和统计推理能力学习环境构建原则的文献,梳理出培养小学生统计推理能力教学模式的三个核心要素:真实的数据问题情境、学生为中心的问题解决活动、重视学生统计推理能力的话语,并且在这三个核心要素的基础之上,结合小学阶段统计教学的特点和现状,提出“培养小学生统计推理能力的教学模式”原型。第二,笔者进入华东地区的S校,在相关教师的协助下,将教学模式的原型进行了具身化,展开三轮的教学迭代,结合学生在课上的具体表现、课后反馈问卷、课后访谈以及对作为观察者全程参与的C老师进行的课后访谈,确定教学模式修正的依据,并在三轮教学中不断修正和精致教学模式的原型。第三,通过运用统计推理能力的测试题和学生对统计的态度量表对学生进行测试和调查,同时结合学生在三轮教学中的课堂表现、课后访谈等“形成性”数据来确定该教学模式产生的效果。本研究最终的成果是建构了培养小学生统计推理能力的教学模式(FC-SR教学模式),包含6个环节的具体操作流程:(1)创设真实数据问题情境;(2)合作问题解决初探;(3)小组展示、自评;(4)回归真实情境再探;(5)讲解相关统计内容;(6)总结反思,并给出详细的依据与操作建议。通过运用统计推理能力的测试题和学生对统计的态度量表对学生进行测试和调查,结合学生在三轮教学中的课堂表现、课后访谈等“形成性”数据来确定FC-SR教学模式产生的两个教学效果:(1)FC-SR教学模式能提升学生的统计推理能力(主要表现在统计推理能力的整理与简化数据(O)和分析与解释数据(A)子能力的显著提高);(2)FC-SR教学模式对学生的统计态度产生了积极的影响(表现在学生对待统计态度的情感维度、认知能力维度、难度维度和兴趣维度有了积极提升),同时FC-SR教学模式对学生认识统计与数学的差异、感悟统计的“不确定性”和领略统计的魅力方面也产生了一定的影响。

【Abstract】 With the advent of the "big data" era and "Internet + Education" era,the concept of "data" has gradually penetrated into all walks of life and has had a profound impact on production.In-depth data mining and analysis,and data-driven decision-making have become one of the necessary skills for future citizens.Whether it is the digital literacy of students issued by UNESCO in 2018 or the PISA 2021 mathematical framework issued by the International Organization for Economic Cooperation and Development in 2019,it is advocated that students should have relevant capabilities and literacy of information and data.Statistical Reasoning is developed gradually by students in the process of solving statistical problems.They can use statistical concepts to make inferences,understand how statistical information is derived,explain based on existing data and make statistical inferences.meanwhile,the ability of describing data displays(D),organizing and reducing data(O),representing data(R),analyzing and interpreting data(A)are also the requirement of statistical reasoning.The statistical reasoning ability fits well with the "age demands" of future citizens in the "big data" era.However,traditional statistics teaching has many problems such as confusing statistics with mathematics teaching,attaching importance to the training of students’ statistical skills and operations,neglecting the training of students’ "statistical" thinking and reasoning,and students’ easy loss of interest in statistics.Many researchers in the world have begun to explore the attempt of statistical teaching reform,and have achieved certain results,and have pointed out that they hope to implement it at an early stage of school mathematics education.This research aims to change the current status of statistical teaching and explore the teaching mode of elementary school students focusing on statistical reasoning,with a view to providing theoretical support and practical suggestions for statistical teaching in primary school.This research is based on three aspects of problems of statistical teaching in primary schools in China:(1)Teachers have "separated the close connection between statistical teaching and real life",leading to "statistical problem-solving activities reduced to low-level,simple memory-based imitation activities;(2)Teachers do not realize that "statistical activities are a complete problem-solving process","ignore students’ active participation in statistical activities","cannot efficiently use cooperative learning methods",thereby reducing students’ interests on statistical learning;(3)Teachers ignore the reasoning and expression of students in the process of solving statistical problems due to objective reasons such as “few statistics content in primary school and low proportion of statistics in examinations” and subjective reasons such as “lectures,speeches are rigidly followed by textbooks without carefully designing and vivid explaining”,“simply introducing without expansion” which leads to teachers do not pay enough attention to statistics.So,this research is based on situational cognition theory,situational learning theory,social culture theory,and social construction theory.It takes design research as a guide to methodology,and borrows the research paradigm of design research,"formative research," and has gone through the prototype of teaching mode.The construction,iteration and modification of the three rounds of teaching implementation,finally got an effective teaching mode focusing on the cultivation of statistical reasoning ability of elementary school students(referred to as "FC-SR teaching mode").This research focuses on three research questions:(1)What is the prototype of teaching mode focusing on statistical reasoning ability for elementary school students based on relevant literature and teaching theory,combined with China’s statistical teaching practice?(2)How to modify and refine the prototype of the teaching mode in specific teaching practice?(3)What effect has the teaching mode produced? Carried out three specific work:First,based on the content of statistical reasoning in the literature review,relevant suggestions and strategies for teaching statistical content in elementary school,combing the existing "problem-solving" teaching mode and the principles of statistical reasoning learning environment construction,sort out three core elements of the teaching mode: real data problem situations,student-centered problem-solving activities,discourses that emphasize statistical reasoning ability,and on the basis of these three core elements,combined with statistical teaching in the primary stage,the characteristics and current situation of the teaching mode of "focusing on the cultivation of statistical reasoning ability" prototype are proposed.Second,the author entered the S school in East China,with the assistance of relevant teachers,embodied the prototype of the teaching mode,carried out three rounds of teaching iterations,combined with the students’ specific performance in class,after-class feedback questionnaires,after-class interviews and observer Teacher C’s suggestions to determine the reasons for the revision of the teaching mode,and in the three rounds of teaching,the prototype of the teaching mode is continuously revised and refined.Thirdly,testing and surveying students through the use of statistical reasoning test questions and students’ attitudes towards statistics,meanwhile,combining the “formative” data of students’ classroom performance and after-class interviews in the three rounds of teaching to determine the effort of this teaching mode.The final conclusion of this research is the construction of a teaching mode focusing on the cultivation of statistical reasoning ability of elementary school students(FC-SR teaching mode),which includes six operational procedures:(1)The creation of real data problem situations;(2)A preliminary exploration of cooperative problem solving;(3)Group display and self-evaluation;(4)Re-examination of returning to the real situation;(5)Explaining relevant statistical content;(6)Summarizing and reflections,and giving detailed basis and operational suggestions.The two teaching effects of FC-SR teaching mode is determined using test questions of statistical reasoning and students’ attitdes towards statistics to test and investigate students and combined with “formative” data such as classroom performance and after-class interviews during the three rounds of teaching.FC-SR teaching mode can:(1)improve students’ statistical reasoning ability(mainly manifested in the significant improvement of sub-statistical reasoning ability,such as organizing and reducing data(O)and analyzing and interpreting data(A);(2)has a positive impact on students’ attitudes towards statistics,expressed in the positive improvement of affect dimensions,cognitive competence dimensions,difficulty dimensions and interest dimensions.At the same time,the FC-SR teaching mode also has a certain impact on students’ understanding of the differences between statistics and mathematics,the "uncertainty" of statistics,and the charm of statistics.

  • 【网络出版投稿人】 华东师范大学
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