【作者】 仲秀英；

【导师】 宋乃庆； 黄翔；

【作者基本信息】 西南大学 ， 课程与教学论， 2008， 博士

【摘要】 学生数学活动经验是学生个人经验中的重要组成部分,是学生学习数学、提高数学素养的重要基础之一。它的产生和形成过程实质上是学生经历数学活动的过程。长期以来,以“双基”教学为主要特征的我国传统数学课堂教学更多的注重了对学习结果的关注,相对忽视了对学生数学学习过程本身的重视,使得学生数学活动经验的获得常常游离于数学课堂教学的边缘,成了学生“随机而遇”、“碰巧发生”的“幸运之物”。在新课程改革背景下,国家义务教育数学课程标准(实验稿)从课程目标上对数学活动经验提出了要求。课程目标的变化,尤其是史宁中、张奠宙等数学教育专家对数学活动经验的重点关注,引起了数学教育工作者对数学活动经验相关问题的思索和探究。但是,从查阅的文献来看,目前已有的研究主要是针对数学活动经验的内涵进行个人阐释,在理论和实践方面对学生的数学活动经验相关问题的研究都十分薄弱。因此,从理论和实践层面对学生数学活动经验内涵及教学策略等问题展开研究,不仅有助于充实“数学活动经验”的基本理论,而且有助于为深化基础教育数学课程改革服务。本研究在国内外已有的数学活动经验相关研究成果基础上,采用文献分析、调查研究与案例分析等研究方法,对学生数学活动经验的内涵和具体内容的表现形式、学生获得数学活动经验的过程结构、影响因素以及教学策略等问题进行了研究,初步得到以下结论:(1)对学生数学活动经验内涵的进一步认识:学生数学活动经验有广义与狭义之分。广义的学生数学活动经验是学生在经历数学活动的过程中获得的关于数学活动目的、数学内容、数学活动行为及其方式的转换以及数学活动环境等方面的感受、理解、领悟和体验以及由此获得的数学知识、技能、智慧、情感、观念等内容组成的有机组合性经验。可以将广义的数学活动经验分为过程性数学活动经验和结果性数学活动经验两个层面的内容,也可简单地将它分为观念性层面的数学活动经验、认知性数学活动经验,情感体验性数学活动经验与动作技能性数学活动经验等层面的基本内容。狭义的学生数学活动经验,特指观念性层面的数学活动经验与情感体验性数学活动经验。(2)学生数学活动经验具体内容:学生通过写回忆、数学作文、隐喻等方式呈现的数学活动经验的具体内容主要表现为:①学生对具体的数学活动过程的回味:②学生从活动中获得的具体数学知识、技能、方法与策略;③从数学活动中获得的认识;④学生在数学活动中获得的情感经验等。通过课堂观察、访谈等手段,归纳出学生在某一堂数学课中获得的数学活动经验的具体内容主要表现为:①学生经历的具体数学活动;②学生在数学活动过程中的体验、感受和逐步形成的对数学活动的观点和看法以及对数学活动过程的一些倾向性价值判断;③在数学活动中获得的事实性知识、程序性知识;④如何进行合理的数学观察、数学发现、数学猜想以及如何验证、归纳、交流与讨论的一些方法和技巧等。(3)学生获得数学活动经验的过程结构:学生数学活动经验的获得是知、情、意、行相辅相成、相互支持的过程,是社会化情境认知的过程,是从“活动到经验,再从经验到活动”的循环往复的过程,是经验的改造与再改造的过程。从而,学生获得数学活动经验的过程至少需要经历以下几个基本阶段:原初经验阶段;再生经验阶段;再认经验阶段;概括性经验阶段;再次参与多样化的数学活动,逐渐内化为概括性经验图式阶段。相应地,按照其抽象程度的高低可将学生数学活动经验分为原初经验、再生经验、再认经验、概括性经验等四个依次从低到高的基本层次。(4)学生获得数学活动经验的影响因素:学生获得数学活动经验的影响因素主要来自于学生自身的影响、教师方面的影响、以及学生数学活动本身的影响等方面。从学生角度看,又主要表现为学生的认知风格、已有的经验、记忆、注意力、认知策略等个人自我调节的因素,学生目的、动机、情感、信念、自我效能感等个人自我意识方面的因素以及学生参与数学活动的方式三方面的因素;从教师角度看,主要表现为教师自身的教学信念、教学行为与教学风格、对学生表现的应对和反应、教师的指导与学生独立操作两者之间关系度的把握、提供的数学活动情境以及数学活动任务、教师组织的活动形式以及活动机会的公平性等方面;从数学活动情境角度看,主要表现为数学活动情境及其镶嵌的数学活动任务、数学活动情境中教室课堂文化氛围等因素。(5)促进学生获得数学活动经验的教学策略:在探究数学活动经验获得过程结构和影响因素、经验学习理论及名师授课案例对构建促进学生获得数学活动经验的教学策略启示的基础上,本研究提出了促进学生获得数学活动经验的教学应采取如下教学策略:①数学活动动机激发策略;②数学活动经验生成策略;③数学活动经验系统化实现策略;④数学活动经验层次转化策略;⑤数学活动经验拓展策略;⑥数学活动经验优化策略等。尽管国内外已有不少关于活动及经验的研究,但是关于数学活动经验的研究却不多见,尤其是对学生获得数学活动经验的影响因素和教学策略的研究更为少见,使得本研究可借鉴的资料十分匮乏,研究难度很大。本研究进一步探究了学生数学活动经验的概念内涵,并尝试性地构建了分析学生数学活动经验内容的基本框架;采取写回忆、隐喻、类比等方式,研究了学生数学活动经验的具体内容(这在国内同类研究中并不多见);初步探究了学生获得数学活动经验的过程结构及影响因素,大胆探究了促进学生获得数学活动经验的教学策略。本研究主要是从学生的角度理解数学活动经验,对于一般意义上的数学活动经验的研究,仍需进一步深入。更多还原

【Abstract】 Students’ mathematic activity experience is an important part in their personal experience, is one of the important. bases in learning mathematics and improving mathematics quality. The process of its production and formation is actually a process for students to experience mathematic activity. However, our traditional mathematic class based on Basic Knowledge and Skills show more respect to the result, and the process of leaning mathematics has been neglected, this leads to the result that students’ experiences from mathematics activity play marginal position in mathematics class, are coincident incidents. Under the contexts of new mathematics reform, Mathematics Curriculum Standards of national compulsory education put forward to requirements to mathematic activity experience based on curricular target. Changes of Curriculum target, especially, some mathematicians, such as, Shing Ningzhong, Zhang Dianzhou’s concerns about mathematic activity experience, draw mathematics educators’ consideration and exploration to mathematic activity experience. From literature review, studies are mainly personal views on connotation of mathematics activity experience, quite few of studies relating to mathematic activity experience have been done in its and theory and practice. Therefore, a complete and systematic study on mathematic activity experience from its connotation, forms and teaching strategy should be carried out, it not only helps to enrich the fundamental theory, but also promotes to provide suggestions for deepening the reforms of Basic Mathematics Education.By the analysis of documents, attending lectures, records of class teaching, interview, analysis of cases and theory, the research focuses on the connotation and forms, the process, arrangements, influencing factors and teaching strategies of mathematic activity experience. The following conclusions can be drawn:(1) Further understanding of connotation: Broad Mathematic activity experience means students obtain feeling, understanding, comprehending and experiences about the aim of teaching activity, mathematics contents, mathematics activity behaviors and transformation of forms and mathematics activity surroundings from the process of mathematics activity, and the combined experiences of mathematic knowledge, skills, wisdom, affection and ideas. Mathematics activity experience can be broadly classified into process and result mathematic activity, can also be simply divided into idea, cognitive, affective and action skills. It can be said that narrow mathematic activity means idea and affective experience.(2) Specific contents: By analyzing the students’ memory, mathematic writing, and the use of metaphor, mathematics activity experience includes:①memory of the process of mathematic activity experience;②the actual mathematics knowledge, skills, methods and strategies from activity;③the comprehension from activity;④affective experience, by observing class and interview, main contents of mathematic activity experience from one mathematics class can be induced:①Students’ specific mathematic activity,②Experience from the process, it is the experience of mathematic activity process, perception and gradually forming point of view and opinion, and some judgments of value on mathematic activity process,③acquired actual knowledge and proceeding knowledge from mathematic activity experience;④Methods and skills of how to conduct a reasonable mathematic observation, finding and guess, how to verify, how to induce, communicate and discuss.(3) Process construction: Students’ knowledge, affection, meaning and practice from mathematic activity experience is a process of supplementing and supporting each other; It is also a process of socialization situation perception; It is a cycling process "from activity to experience" and " from experience to new activity again"; It is a process of experience reformation. So, the process that students obtain mathematic activity experience should be through the following steps: preliminary experience stage; renewed experience stage; recognition experience stage; conception experience stage; participation of diversified teaching activities, conception experienced schema stage by gradual internalization. Accordingly, according to its degree of abstractness from the lowest to highest degree, students’ mathematic activity experience can be through the following stages: preliminary stage, renewed stage, recognition stage and conception stage.(4) The influencing factors of obtaining mathematic activity experience are mainly from students themselves, teachers and mathematic activity experience itself. From students’ perspective, factors can be cognitive style, students’ past experiences, memory, attention, cognitive strategy and self-adjustment factors, intention, motivation, affective, belief, efficacy, self-awareness and ways of involving in mathematic activity; From teachers’ perspective, factors include teaching belief, teaching behavior and teaching style, reply and response to students’ performance, management between teachers’ supervision and students’ independent study, providing teaching scene and teaching tasks, fairness between forms and opportunity of activity; From the perspective of teaching activity, factors contain arrangements of teaching activity scene, teaching tasks and classroom cultural atmosphere, etc..(5) The following basic teaching strategies should be carried out to cultivate teaching of mathematic activity experience:①stimulating strategies of mathematic activity experience;②generating strategies of mathematic activity experience;③systematical implementation strategies of mathematic activity experience ;④transformation strategies of mathematic activity experience;⑤extending strategies of mathematic activity experience;⑥optimizing strategies of mathematic activity experience.Many researches have been done on activities and experiences, but just few on mathematic activity, especially on the study of influencing factors and teaching strategies that students obtain mathematic activity experience, therefore data and resources are quite rare, and make the research more difficult. The paper conduct a preliminary arrangement of the connotation of meaning of mathematic activity experience, and attempts to construct the framework for analyzing contents of mathematic activity experience; By memory, metaphor and comparison, the paper studies specific contents of mathematic activity experience(These are quite rare in the study of the field). The paper makes a preliminary exploration of construction process and influencing factors, and presents teaching strategies for cultivating mathematic activity experience.更多还原