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基于高中数学课例的任务设计有效性研究

【作者】 陈行

【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】 课堂教学作为学校教育的基本形式,是学生获取知识、提高技能和形成思想观念的主要渠道。而在有限的时间里,要实现学生效益的最大化,其一条重要途径就是提高数学课堂教学的有效性。任务的设计和使用作为当前研究报告中以及数学教育研究关注的一个核心问题,无论是出于研究目的还是教学目的,数学任务的设计、分析和实证检验,都是数学教育最重要的职责之一(Sierpinska,2004)。课例研究作为校本教学研修的一种方式,以改进教学为最终目的,对教师专业发展与学校教学变革具有重要的作用。因此,本研究将数学课堂教学有效性的提升作为最终目标,聚焦数学任务,以课例研究为手段,展开对任务设计有效性的研究。研究主要探讨以下两个问题:一、影响教师任务设计有效性的因素有哪些?二、这些因素是如何影响任务设计的有效性?本研究首先根据相关研究文献和研究成果,构建初步的数学任务分析框架,并对分析框架的内容效度进行了专家论证。然后,基于修正后的分析框架,编制高中数学教师任务设计现状调查问卷,并对调查问卷的内容效度进行专家论证。接着,根据研究需要和合作学校实际情况,开发了“等比数列的前N项和”和“估计百分位数”两个课例。在研究方法方面,主要采用定量和质性相结合的混合研究途径收集和分析数据。对于研究问题一,主要采用问卷调查法。通过对上海地区107名高中数学教师任务设计现状调查问卷结果的量化分析,了解他们对任务设计意义、内涵、设计内容/方式等方面的不同理解以及在任务设计过程中存在的困难与需求。基于量化结果的深度分析,从教师角度探寻任务设计有效性的影响因素。研究问题二则从课堂教学实践的角度,探究这些因素是如何影响任务设计的有效性,主要采用量化与质性相结合的混合研究方法。首先,通过对学生前后测的量化分析,了解每个课例中两个班学生的具体表现及差异性;然后,运用文本分析法和录像分析法分别对授课教师的教案和课堂录像进行质性分析,以便探寻导致上述表现和差异性的原因。研究发现:(一)网络资源质量、任务认知需求的下降以及对“过程二:运用数学概念、事实、程序和推理”的关注度是影响教师任务设计有效性的三个重要因素。(二)教师在任务实施阶段,如果降低任务原有的认知需求,则可能导致任务设计有效性的下降。(三)教师在任务实施阶段,如果过度关注“过程二:运用数学概念、事实、程序和推理”,则可能限制学生知识远迁移的能力;反之,如果对“过程二”关注不足,同样会限制学生知识远迁移的能力,从而导致任务设计有效性的下降。上述结论带来的启示是:在教学内容方面,淡化形式,注重实质;在资源管理方面,加强网络教学资源的管控,建立数学专项任务资源库;在教师专业发展方面,丰富教研活动形式,加强教师任务设计分层教学的实践研究。

【Abstract】 As the basic form of school education,classroom teaching is the main channel for students to acquire knowledge,improve skills and form ideas.In the limited time,one of the important ways to maximize the benefit of students is to improve the effectiveness of mathematics classroom teaching.The design and use of tasks is a core issue in current research reports and research on mathematics education.The design,analysis and empirical testing of mathematical tasks is one of the most important responsibilities of mathematics education,whether for research or teaching purposes(Sierpinska,2004).As a way of research and study of school-based teaching,lesson study plays an important role in teacher professional development and school teaching reform with the ultimate goal of improving teaching.Therefore,this study takes the improvement of the effectiveness of mathematics classroom teaching as the ultimate goal,focuses on mathematical tasks,and studies the effectiveness of task design by taking the study of class examples as a means.The research mainly discusses the following two questions:1.What are the factors affecting the effectiveness of task design?2.How do these factors affect the effectiveness of task design?In this study,a preliminary mathematical task analysis framework was constructed based on relevant research literature and research results,and the content validity of the analysis framework was demonstrated by experts.Then,based on the revised analysis framework,a questionnaire on task design of high school mathematics teachers was prepared,and the content validity of the questionnaire was demonstrated by experts.Then,according to the research needs and the actual situation of the cooperative schools,two lessons of "sum of the first N items of geometric sequence" and "estimated percentile" were developed.In terms of research methods,a hybrid approach of quantitative and qualitative research is mainly adopted to collect and analyze data.For the first research question,the questionnaire survey method is mainly adopted.Through the quantitative analysis of the questionnaire results of task design of 107 senior high school mathematics teachers in Shanghai,we can understand their different understandings on the meaning,connotation,content and method of task design,as well as their difficulties and demands in the process of task design.Based on the in-depth analysis of quantitative results,the paper explores the influencing factors of the effectiveness of task design from the perspective of teachers.The second part explores how these factors affect the effectiveness of task design from the perspective of classroom teaching practice.This paper mainly adopts a hybrid research method combining quantification and quality.First of all,through the quantitative analysis of students before and after the test,to understand the specific performance and differences of the two classes of students in each lesson;Then,text analysis and video analysis are used to analyze the teachers’ teaching plans and classroom videos,so as to explore the causes of the above performance and difference.The research finds that:(1)the quality of network resources,the decline of task cognition demand and the attention to "process two: employing mathematical concepts,facts,procedures and reasoning " are three important factors that affect the effectiveness of teacher task design.(2)in the task implementation stage,if the teacher reduces the original cognitive needs of the task,the effectiveness of the task design may be reduced.(3)during the task implementation stage,if teachers pay too much attention to "process two: employing mathematical concepts,facts,procedures and reasoning ",it may restrict students’ ability of knowledge transfer;On the contrary,if insufficient attention is paid to "process 2",it will also restrict students’ ability of knowledge transfer,which will lead to the decrease of the effectiveness of task design.The enlightenment brought by the above conclusion is: in the aspect of teaching content,dilute the form,pay attention to the essence;In the aspect of resource management,we should strengthen the control of network teaching resources and establish the resource base of mathematics special tasks.In the aspect of teacher professional development,we should enrich the forms of teaching and research activities,and strengthen the practice research of hierarchical teaching in task design.

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  • 【网络出版投稿人】 华东师范大学
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