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    Title: 數學建模教學在國中二年級的行動研究
    Other Titles: An action research on mathematical modeling teaching in the eighth grade
    Authors: 潘靜慧;Pan, Ching-Hui
    Contributors: 淡江大學教育科技學系碩士在職專班
    高熏芳;Kao, Hsun-Fung Kitty
    Keywords: 數學建模;建模教學;行動研究;mathematical modeling;modeling teaching;Action Research
    Date: 2012
    Issue Date: 2013-04-13 10:42:25 (UTC+8)
    Abstract: 本研究是以行動研究的方式,針對國中二年級學生進行「數列與級數」單元的數學建模教學,探究國中教師實施數學建模教學與學生數學建模學習的歷程。本研究中的數學建模教學指的是「引模」、「探模」、「修模」、「討論」及「延伸」等五個教學活動;而學生數學建模歷程指的「分析簡化」、「模型假設與建立」、「計算及求解」、「驗證答案」及「模型應用」等五個步驟。在三階段的行動循環中,研究者根據教師數學建模教學與學生數學建模歷程之對應表,透過教學錄影、教學省思札記、同儕教師回饋、學生學習單及學生學習紀錄表等方式收集並分析資料,以了解課程如何設計、教學如何實施、學生建模的歷程與學生困難與獲得為何。
    一、本研究的結果發現如下:
    (一)數學建模教學的課程設計
    1.應從學生個人生活經驗與舊知識的連結著手。
    2.從基測題中尋找合乎建模的題目。
    3.應符合建模活動設計的六個原則,即「模型建構」、「真實」、「自我評估」、「模型外顯化」、「模型可分享與可再用性」、「簡單原型」原則。
    (二)在數學建模教學的實施方面
    1.引模活動可請學生先討論再發問。
    2.觀察學生探模活動時的反應,做為教師引模階段成敗的依據。
    3.確實讓學生發表並注意學生的專心度。
    4.進行數學建模教學活動應結合分組討論與個別指導。
    (三)學生數學建模的困難方面
    1.學生簡化分析生活化的問題不易。
    2.學生不熟稔於討論活動。
    (四)學生數學建模學習的獲得
    1.對於數學會嘗試解題。
    2.覺得數學是有用的。
    3.藉由分組活動,學習他人解題經驗。
    4.發現數學是可以討論的。
    二、本研究對未來運用數學建模教學的建議如下:
    (一)教師應精進熟練建模教學經驗。
    (二)教師須清楚學生解題的盲點再給與引導的成效較佳。
    (三)教師注意生活中的數學並運用,以提升設計學習單的能力。
    關鍵字:數學建模、建模教學、行動研究
    This study is an action research which aims to investigate the processes of teaching and students’ learning in mathematical modeling of “Arithmetic Progression” in the eighth grade. Mathematical modeling in this study includes five teaching activities which are “Model-Eliciting,” “Model-Exploration ,” “Model-Adaptation ,” “Presentations & Discussions,” and “follow-up activities.” Mathematical modeling processes of students include five steps which are “analysis and simplicity,” “modeling hypotheses and build,” “calculation and solutions,” “verifying the answers,” and “modeling application.” During the circles of the three stages, we understand how to design the lessons, how to teach, how students’ processes of modeling work, and what difficulties and gains students may have.
    The main findings of the study are as follows:
    I. The designs of mathematical modeling in lessons
    1. Teachers should start from the connection of students’ personal experience and existent knowledge.
    2. Teachers can find proper subjects from “The Basic Competence Test for Junior High School Students.”
    3. The lessons should follow the six rules which are “Model Construction principle,” “The Reality Principle,” “Self-assessment principle,” “Construct Documentation Principle,” “Construct Shareability and Reusability Principle,” and “Effective Prototype Principle.”
    II. The practice of mathematical modeling
    1. Teachers can make students discuss before they ask questions during the model-eliciting activity.
    2. Teachers should observe students’ reaction in model-eliciting activities and judge the success or failure in model-eliciting stage.
    3. Teachers should make students speak more and take notice of students’ attention.
    4. The model-eliciting activities include group discussion and teaching individually.
    III. The difficulties of students’ mathematical modeling
    1. It’s hard for students to simplify real-life questions.
    2. Students aren’t familiar with discussions.
    IV. The gains of students’ mathematical modeling
    1. Students would try to solve math questions.
    2. Students start to understand that math is useful.
    3. Students would try to learn from others by group discussion.
    4. Students find that math is discussible.
    The suggestions to the researchers on mathematical modeling are as follows:
    I. Teachers should improve the experience of teachers’ teaching in modeling.
    II. Teachers should guide students after clarifying their blind spots of calculation.
    III. Teachers should notice math in real life and apply it to improve the abilities of designing worksheets.
    Appears in Collections:[教育科技學系暨研究所] 學位論文

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