臺灣博碩士論文加值系統

摘要
本研究的目的在探討如何有效落實問題中心雙環 (PCDC) 教學模式於高職數學課室的教學。雙環教學模式強調教師要利用教學環來帶動學習環，即教師教學要把握教學環的任務、引導、環境和分析這四項要領來引導學生建構數學知識和精進自己的教學。因此，要落實PCDC教學於數學課相當於教師要做到「發展值得學習的任務」、「引導學生」、「創造有利的教學環境」及「有效分析自己的教學」這四要項。所以，本研究是本研究者以一班高職土木科一年級的學生為對象，於數學課室試行落實PCDC教學的行動研究。資料收集包含晤談、討論、錄影、問卷、日誌和文件等。資料分析主要有內容分析與交叉比對。
回顧本研究者二年多來的行動研究歷程，自然形成四個階段：照本操作、嘗試改變、漸趨熟練、調適變通。綜合這四個階段在落實PCDC四要領上，有以下的發現：
一、任務：在發展值得學習的任務時，應先考慮教學目標、學習目的、學生的舊經驗、能力和興趣等問題。在設計任務時則應注意語意表達、問題的開放度、數學概念的發展、形式化及抽象化的過程、及能否引發學生的探索、觀察、推理、歸納以形成他自己的問題，及學生是否能利用所學的數學知識來解決問題。
二、引導：在引導學生時，老師要提供各種任務及問題來挑戰學生，協助學生解決困難、鼓勵學生發表意見、教導學生上台發表的技巧、依著學生的學習情形來發展數學概念或深入探究學生的困難、對學生的說法或立論提出質疑、讓學生自行創造數學符號和語言、採用「舉手投票」和「答辯」的策略來釐清數學概念、請學生用圖形、數學式子或符號來表徵，而且老師要善用比喻及製作教具來幫助學生更具象地思考。
三、環境：在創造有利的教學環境方面，老師要調整心態，降低管理和知識上的權威，以提高教室民主氣氛。並且要對同學作適當的分組及座位安排、建立加扣分制度、在情意上鼓勵同學。此外，教師要努力營造一個學生敢於發言，不怕被譏笑且是愉快和諧的課室環境，這樣才能有利於PCDC教學的進行。
四、分析：在分析自己的教學時，要對照文獻、與指導教授接觸、和同儕團體討論分享、進行教學觀摩、與學生晤談、與觀察者討論、對課室活動進行錄影、請學生填寫問卷、觀察學生上課的情形及反應、撰寫教學日誌及自我反省等方法來分析教學。最後，本研究還發現試行PCDC教學二年，課室中教師權威角色大為降低，師生互動良好；而且學生對數學的學習興趣和理解也大為提高。

An Action Research of Practicing PCDC
in the Mathematical Classroom of Vocational High School
Shun-Liang Chien
Abstract
The main purpose of this study is to investigate the effective way to practice the Problem Centered Double Cycles (PCDC) teaching model in the mathematical classroom of vocational high school. The PCDC model emphasizes that teachers should use the teaching cycle to propel the learning cycle. That is, the teacher should have full control of the four essential factors in the learning cycle, they are: tasks, guidance, environment and analysis, in order to guide students to construct their own mathematical knowledge and refine the teacher’s teaching. Therefore, the teacher should be capable of “developing learning worthy tasks”, “guiding students”, “creating a beneficial environment for teaching and learning”, and “analyzing teaching effectively” to practice the PCDC in the mathematical classroom. This study is an action research which the researcher practiced the PCDC in the mathematical classroom of the first-grade civil engineering students of a vocational high school. The collected data includes interviews, discussions, videos, questionnaires, the researcher’s teaching journal, and related papers. The data analysis here includes content analysis and interacting analysis.
During the two-year action research, the whole process could be divided into four stages: Imitating, Trying to change, Getting masterly, and Adjusting and adapting. In the four stages of practicing the PCDC, the researcher found out:
(Ⅰ)Tasks. In developing learning worthy tasks, the teacher should first take into consideration the goal of teaching, the aim of learning, students’ former experiences, their abilities and interests. When designing tasks, the teacher should pay attention to his/her written language, the openness of the questions, developments of mathematical concept, and the process of formality and generalization. Besides, if the tasks would induce students to explore, observe, or reason and then form their own questions, and if the students would use established mathematical knowledge to solve problems should be paid attention to.
(Ⅱ)Guidance. When guiding students, the teacher should provide various kinds of tasks and problems to challenge students, help students to deal with their difficulties, encourage students to express their opinions, teach students the skills of addressing. The teacher develops mathematical concept in students and detects their difficulties according to the learning situation of the students. Also, the teacher should query students’ statements, instruct them to create mathematical symbols and languages by themselves, use the strategies of voting and debating for them to make clear mathematical concepts, and ask students to use figures, symbols, and mathematical equations to express their ideas. At the same time, the teacher should use metaphors and teaching aids to help students think more concretely.
(Ⅲ)Environment. In creating a beneficial environment for teaching and learning, the teacher should adjust his/her attitude to lessen his/her authority on administration and knowledge in order to establish an atmosphere of democracy in the classroom. The teacher should divide students into groups and arrange proper seats for them, establish the system of rewards and penalty, and give students emotional encouragement. Besides, the teacher should try his/her best to create an environment full of happiness and harmony, in which students will always feel free to talk with no fear of being laughed at. Only in this kind of environment can the PCDC be run smoothly.
(Ⅳ)Analysis. As for analyzing teaching, the teacher can contrast the literature, contact with his/her supervisor, discuss and share with his/her peer groups, observe other teacher’s classes, interview students, discuss with the observers, record classroom activities on video, ask students to answer questionnaires, observe the students’ behaviors and reactions in class, keep teaching journals, and examine his/her own teaching.
After the two-year practice of the PCDC, the researcher played his role with much less authority, the teacher and students interacted positively, and the students’ interests were aroused greatly and their comprehensions for mathematics were enhanced.

目 錄
第一章 緒論．．．．．．．．．．．．．．．．１
第一節　問題背景與研究動機．．．．．．．．．．．．．．．１
第二節　研究目的與待答問題．．．．．．．．．．．．．．．６
第三節　重要名詞釋義．．．．．．．．．．．．．．．．．．７
第四節　研究限制．．．．．．．．．．．．．．．．．．．．７
第二章 文獻探討．．．．．．．．．．．．．．８
第一節　PCDC的理論基礎與架構．．．．．．．．．．．．．８
第二節　PCDC教學模式：問題中心、內圓外方雙循環．．．１４
第三節　PCDC教學中教師的工作與角色．．．．．．．．．１５
第四節　PCDC教學的理念與傳統教學之差異．．．．．．．１８
第五節 應用PCDC模式於數學教學之實證研究．．．．．．１９
第三章 研究方法．．．．．．．．．．．．．２１
第一節　研究對象的選取．．．．．．．．．．．．．． ．２１
第二節　研究情境．．．．．．．．．．．．．．．．． ．２２
第三節　研究對象的背景．．．．．．．．．．．．．．． ２２
第四節　研究者的經歷與角色．．．．．．．．．．．．． ２２
第五節 資料蒐集的方法．．．．．．．．．．．．．．．．２４
第六節 資料分析．．．．．．．．．．．．．．．．．．．２５
第七節 研究設計與流程．．．．．．．．．．．．．．．．２５
第四章 研究結果．．．．．．．．．．．．．２８
第一節　照本操作期．．．．．．．．．．．．．．．．．．２８
第二節　嘗試改變期．．．．．．．．．．．．．．．．． ５４
　第三節　漸趨熟練期．．．．．．．．．．．．．．．．．１０２
第四節　調適變通期．．．．．．．．．．．．．．．． １４５
第五章 結論與建議．．．．．．．．．．．１７０　　
第一節 回答待答問題．．．．．．．．．．．．．．．．１７０
第二節 PCDC的回顧與評量．．．．．．．．．．．．．１７５
第三節 建議．．．．．．．．．．．．．．．．．．．．１７７
第六章 回顧與反省．．．．．．．．．．．１７８
參考文獻
一、 中文．．．．．．．．．．．．．．．．．．．． １８２
二、 英文．．．．．．．．．．．．．．．．．．．． １８４
附錄一：4-1 向量的意義(張靜嚳編著，三民書局)．．．．．１８７
附錄二：4-1 向量的意義(郭宗興等編著，廣懋出版社)．．．１９２
附錄三：2-3 任意角的三角函數．．．．．．．．．．．．．２００
附錄四：2-3任意角的三角函數(二)．．．．．．．．．．．．２０２
附錄五：2-3-3 化任意角為銳角的三角函數．．．．．．．．２０４
附錄六：2-5 複角的三角函數．．．．．．．．．．．．．．２０６
附錄七：4-1向量的意義．．．．．．．．．．．．．．．．２０８
附錄八：4-2 向量的加法．．．．．．．．．．．．．．．．２０９
附錄九：問卷（一）．．．．．．．．．．．．．．．．．．２１２
附錄十：問卷（二）．．．．．．．．．．．．．．．．．．２１３
附錄十一：問卷（三）．．．．．．．．．．．．．．．．．２１５

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