本研究以「個案研究法」探討14位國中職前數學教師與現職數學教師在數學教學覺察力，並討論兩組教師在「行為者、覺察主題、分析立場以及再次觀看影片」上數學教學覺察力之表現，研究程序為先撥放一段教學影片給受訪者觀看，觀看後再詢問受訪者在這段影片中你印象深刻的事件，研究者再從這些回答分析受訪者的覺察力。

本研究主要發現如下：

一、 國中職前教師與現職教師在「行為者」向度的覺察表現，職前教師組所關注對象多以單人為主，單一覺察教師或學生，現職教師組較能同時關注兩者。
二、 國中職前教師與現職教師在「覺察主題」向度的覺察表現，現職教師組比職前教師組更注重如何聯貫發展數學知識，以及現職教師組對於各面向的覺察主題具有較為平均的觀察，而職前教師組關注到較多課堂的表面特徵。
三、 國中職前教師與現職教師在「分析立場」向度的覺察表現，現職前教師組大多還是聚焦在表層的現象，而職教師組對於聚焦在數學內容以及教學策略上都能進行較好的說明以及猜想。
四、 國中職前教師與現職教師在"第一次"與"再次"觀看影片兩階段覺察力表現，不論是職前教師組或現職教師組都可以有顯著提高覺察事件的表現。

This study applied a “case study” to investigate fourteen pre-service and in-service junior high school mathematics teachers on their Noticing methods. Discuss the performances of two groups of teachers on their Teaching Noticing Method on agent, topic stance and videos replaying. The procedures of this study were to play a part of the teaching videos for the interviewees, and then asked them about the events that they were impressed with. The researcher then analyzed the interviewees’ Teaching Noticing Methods by these responses.
The major findings showed:
1. The Noticing performances of pre-service teachers on “agent” dimension mainly focused on a single person, with merely asking the perspective of teachers or students, and the in-service teachers could be better focused on both at the same time.
2. The Noticing performances of in-service teachers on “topic” dimension pay more attention on how to develop mathematics knowledge coherently than pre-service teachers. In addition, in-service teachers possess observations that are more balanced, and the pre-service teachers pay more attention on the external characteristics instead.
3. The Noticing performances of pre-service teachers on “stance” dimension mostly focus on the external features. However, in-service could provide better descriptions and presumptions on mathematics content and teaching strategies.
4. The Noticing performances of pre-service and in-service teachers on attending to play the videos once or replay again could both significantly improve the performances of Teaching Noticing events.

摘要
目錄
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與待答問題 4
第三節 名詞釋義 5
第四節 研究範圍與限制 7
第二章 文獻探討 11
第一節 教師覺察力之定義與重要性 11
第二節 職前與現職教師覺察力 17
第三節 覺察力實徵性研究 19
第四節 畢氏定理與平方根 27
第三章 研究方法 31
第一節 研究設計 31
第二節 研究對象 32
第三節 研究流程 36
第四節 研究工具與實施 39
第五節 資料收集與分析架構 44
第六節 研究檢核 51
第四章 研究結果 55
第一節 職前與現職教師在「行為者」向度的覺察表現 55
第二節 職前與現職教師在「覺察主題」向度的覺察表現 62
第三節 職前與現職教師在「分析立場」向度的覺察表現 76
第四節 職前與現職教師在"第一次"與"再次"觀看影片兩階段覺察力表現 85
第五章 研究發現與建議 93
第一節 研究發現 93
第二節 研究建議 95
參考文獻 98

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