江文雄田振榮賴素貞2019-09-042003-07-012019-09-042002http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22N2002000020%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/99309本研究旨在探討「一位讓高工學生喜歡上數學的教師之教學表徵」，以一位高工數學教師為研究個案，並觀察其四班授課班級學生，為期十週，以瞭解高工學生在數學學科上的學習特質，以及探討個案教師教學表徵的來源、類別、教學特質、學生對個案教師的知覺。 本研究主要採用個案研究法，資料的蒐集包括：教室觀察、個案教師、及其輔導之實習教師、觀察班級學生的訪談、關鍵點省思扎記、研究總結性回饋表及相關文件等。訪談、觀察部分，全程均以錄音，並於研究期間前後每班各一次錄影，以便事後分析；而在學生對個案教師之知覺部分，則輔以觀察達飽和點時初步分析結果所編擬之「學生對數學老師的知覺問卷調查表」，以及開放式問卷進行施測，知覺問卷調查表並施以統計因素分析。為提高本研究之信效度，蒐集之資料均經過三角測量校正（triangulation）過程，以期真實呈現個案教師之教學原貌。 本研究結果發現： 一、高工學生在數學學科上的學習特質，包括：（一）不帶書本回家、相當被動；（二）已養成惰性及意志不堅之習性，迷於網路線上遊戲；（三）學校課業成績不做過多自我要求，及格就好；（四）喜好數學，呈現兩極化；多數學生會因數學老師教學因素而改變數學學習態度；（五）國中階段數學學習情況不良；（六）數學運算能力比較欠缺；（七）數學先備知識、概念建立不完整。 二、個案教師教學表徵的來源，來自：（一）國中階段後段班經驗；（二）高中求學階段遇到一位好老師；（三）大學階段家教、同儕之間學習、補習班工讀的歷練；（四）初為人師，實際與理想的衝突；（五）幾年來的教學經驗與觀摩學習；（六）自我個性及親人楷模學習。 三、個案教師所呈現的教學表徵具有多樣性，包括：幽默解說、類比、圖表說明、生活時事、機會教育、強化重點、概念聯結、題外話、肢體語言、目標引導、走動式表徵、對答、提問偵錯、問答引導、放下身段、敏捷反應、獎勵或懲罰、私下規勸、open book考試測驗、習題演算、上台演算、回家作業、留時間給同學抄寫、空白表徵等二十四種。而個案教師在「教學表徵」中，呈現出的最大教學特質為：（一）教師課堂上極盡所能的吸引學生注意，展現其專業及創意；（二）單向灌輸改為雙向互動學習。 四、學生對個案教師的知覺，包括：（一）讓學生感受到其跟以前接觸之數學教師教學不同，重拾其學習數學的信心和成就；（二）學生大多數是因喜歡數學老師的教學方式，進而對數學產生興趣，再進一步學習數學；（三）學生喜愛雙向式的互動式教學；（四）概念聯結、問題引導及提問偵錯等教學表徵，對學生感到可再複習以前數學學習的不足或盲點，使得數學概念和知識又重新再建立，再次尋求對數學知識的信心和成就感；（五）學生需要教師角色扮演的多重性，以能瞭解數學的好處及功用；（六）個案教師多元教學表徵有其持續性及一致性；（七）個案教師多元的教學表徵，學生受正面的學習效益作用和影響。 最後對於以上研究之結論，提出本研究可供高工數學教師、高工數學師資培育單位與未來後續研究等方面的建議。The purpose of this study was to investigate the instructional representations of a vocational high school mathematics teacher making his students like to learn mathematics. This case study is based on a vocational high school math teacher and his students from four classes for a period of ten weeks. The purpose was to explore the students’ learning characteristics, the sources and the types of the client teacher’s instructional representation, the client teacher’s characteristics, as well as the students’ perception toward the client teacher. This is a case study. The methodology of Data collection included classroom observation, interviews with the client teacher, the beginning teacher she assisted, and the students, as well as the reflective journals, conclusive feedback and referential documents. The interviews and observations were recorded. Furthermore, there was video taping of each class at the beginning and the end of the research for the purpose of analysis. A questionnaire on students’ responses to the teacher’s representations was used. In the procedure of data analysis, the methodology of triangulation was adopted to establish the validity of the research.　 The major findings of this research were as follows: I. The learning characteristics of the students in math learning included (1) going home without book bags and reluctance in learning. (2) being in the habit of laziness and indulging in internet on-line games. (3) lacking a high standard of academic results.(4) most students would adjust their learning attitudes because of the teacher’s teaching style. (5) poor learning attitudes in junior high schools. (6) lacking the ability to calculate. (7) concepts about mathematics were incomplete. II. The sources of the client’s instructional representation were derived from (1) the experience from the worst class in junior high school. (2) a competent teacher in senior high school. (3) the experience of being the tutor and part time job in the cram school. (4) the conflict of reality and idea philosophy. (5) teaching experience for several years. (6) self-personality analysis and learning from the good models of relatives. III. A wide variety of instructional representations were used by the teacher, including humorous explanation, analogy, illustration, demonstration, concept association, body language, eliciting, question and answer, discussion, rewards and punishment, advise after class, open book tests, mathematical exercise, hands-on manipulation etc. The major instructional representation of the client teacher in the study was not only (1) to activate students’ motivation during the whole class but also (2) to reverse the teacher-centered mode to a teacher-student interaction in order to exhibit professionalism and creativity. IV. The students’ perception toward the teacher included (1) students regain the confidence and achievement of math learning. (2) Students gradually became interested in math learning because of the teacher’s teaching style. (3) Students liked the teacher-student interactive way of teaching. (4) the instructional representations such as concept association and eliciting not only provide students the confidence to look for the answers but also reconstruct student’ concepts and knowledge of mathematics. (5) Students need the teacher to play the multiple and various roles to lead them to explore the function of mathematics. (6) The teacher’s multiple instructional representations are constant and unanimous. (7) The students benefited from the teacher’s multiple instructional representations. Finally, based upon the findings during the case study, some suggestions were offered for teaching math in vocational high schools and for further research.教學表徵數學知覺數學學習數學教育instructional representationperception toward mathematicsMathematics learningMathematics education