透過教室言談展現數學課堂中資優生的探究思考歷程

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2005

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摘 要 這是一個關於資優生思考的研究。為了理解資優班課堂上學生思考改變的動態歷程,我進入資優班數學課堂中進行參與觀察,並以能夠展現思考的語言表徵即教室情境中的教室言談為主要的視角,輔以訪談及文件資料,理解數學課堂中資優生參與學習與數學探究的情形,且進一步歸納出資優生的思考型態,也詮釋出思考在此情境中的意義。 教師企圖在這個數學課堂營造一個由數學符號與規則所構成的意義世界,而在這個世界中是以語言溝通為主要的習得、創造與傳遞意義的媒介。研究中所觀察的兩個學習單元以數學遊戲的形式進行,目標在尋求數學關係與規律,在此任務空間下,資優兒童言談探究的目的在表達與澄清、假設與檢驗、歸納與演繹。 若將分析的焦點放在兒童的思考,可以發現,兒童的思考是內在需求與外在情境的交互作用,一方面為求掌握局面,於是在複雜的情境訊息中找尋方向、範圍和原則,力求精簡;另一方面為了求精確,一直關注情境中的訊息,並讓自己保持敏覺的狀態,於是能迅速的反應、彈性的調整。 透過與情境的交互作用,資優兒童會因應情境展現不同的思考風貌:在情境任務引導下的思考,兒童不斷思考以感知外在情境,並進行協調的歷程,以尋求一致與客觀;在兒童對話情境脈絡下的思考,兒童同樣關心著課堂內容與任務,同樣會努力感知外在情境中同儕話語的意義,透過不同觀點的互相激盪、交疊,累積出更深更廣的思考。我看到資優兒童的思考是一種內在的需求促發後,主動與環境互動下的遭遇。 將兒童的思考放置在單純的尋求關係與規律、強調語言溝通也允許自由探究的數學情境中進行詮釋,顯現出四種的思考特質,包括:抽象的形式思考能力、複雜渾沌的思考特質、跳躍且理性的思考歷程及優秀的後設認知。
Abstract This is a study on the thinking process of gifted students. In order to understand the dynamic process regarding the changes of gifted students’ thinking, the participant observation is taken in the Mathematic classroom. The main frame adopted is classroom discourse, in which, thinking can be displayed in language representation; interviews and document are used as supplements to understand the way of learning and math inquiry of the gifted students. The research further inducted the thinking types of gifted students, and interpreted the significance of the thinking pattern under these circumstances. The teachers attempted to create a meaningful world composed of mathematic symbols and rules. In this world, language communication is the major medium of learning acquisitions, creations, and meaning delivery. The two learning units observed in this research are carried out by the form of mathematic games. The goal is to establish math relations and rules. Under such a task, the goal of discourse inquiry of gifted students is to express and clarify, make hypothesis, and conduct experiment, induction, and deduction. If the analytical focus is placed on the thinking process of children, I discovered that children’s thinking is an interaction between need and context. On the one hand, to control the situation, they searched direction, range and principles, and tried to simplify; on the other hand, in order to be precise, they constantly concerned about the information in the context, and kept sensitive perceptions, therefore, they could respond quickly and accommodate flexibly. Through the interactions with the context, gifted children demonstrated different thinking patterns: the thinking which took place under the guide of the context, children constantly engaged themselves in thinking to gain perception of the circumstance, and went through a process of adjustment in search of congruence and objectivity. As for the thinking took place in the context of children’s discourse, children cared about the contents of the class and the task the same way, and tried very hard to perceive the significance of their peer discourses of the circumstances. Through stimulation and accumulation, deeper and broader thinking can be obtained. My observation shows that the thinking pattern of gifted children is a kind of triggered need, which is an actively interacted encounter with the environment. Placing the thinking pattern of children under the mathematical environment which encouraged establishing of relationships and rules, emphasized communication, and allowed interpretation through inquiring freely, demonstrated four traits of children’s thinking: abstract formal operation, chaotic thinking pattern, lateral and rational thinking process, and excellent metacognition.

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資優生, 思考, 數學探究, 教室言談, gifted student, thinking, math inquiry, classroom discourse

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